text stringlengths 6 976k | token_count float64 677 677 | cluster_id int64 1 1 |
|---|---|---|
MTH303: Algebra II (Comprehensive)
Course Overview
This course builds upon algebraic concepts covered in Algebra I and prepares students for advanced-level coursesCompared to MTH302, this course has a more rigorous pace as well as more challenging assignments and assessments. This course requires the use of a graphing calculator equivalent to a TI-84 and includes tutorials and activities for using a handheld graphing calculator. MTH303 also covers additional topics such as linear programming, advanced factoring techniques, even and odd functions, graphing radical functions, quadratic inequalities, the binomial theorem, weighted averages, advanced operations with matrices, and putting conic sections into graphing form. | 677.169 | 1 |
College Algebra for STEM
Description This book is designed specifically as a College
Algebra course for prospective STEM students. Topics covered includes: Review of Beginning/Intermediate
Algebra, Functions and Related Topics, Polynomial Functions, Rational Functions,
Exponential and Logarithmic Functions. | 677.169 | 1 |
...
Show More Martin-Gay's algebra series continues her focus on students and what they need to be successful. Martin-Gay also strives to provide the highest level of instructor and adjunct support. Review of Real Numbers; Equations, Inequalities, and Problem Solving; Graphing; Solving Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Roots and Radicals; Quadratic Equations For all readers interested in algebra, and for all readers interested in learning or revisiting essential skills in beginning algebra through the use of lively and up-to-date applications | 677.169 | 1 |
Math Workbook 4th Edition
This fourth edition of the Math Workbook for Middle School and High School Entrance Exams has been overhauled from the third edition to reflect the most up-to-date knowledge of the private school admissions exams, as well as to incorporate new insights gleaned by our experts as they used the second edition to prepare students for these exams. Here are some new features you will find in the fourth edition:
A more logical progression and classification of concepts, exercises, and question
Over 20 new practice sets throughout the book
Inclusion of more high value material that is likely to show up on the exams
A more Lower Level-friendly interface, including "8th Grade Only" notations in the table of contents and new basic practice sets to introduce 5th grade students to complex concepts such as percentages, exponents, and geometry
New advanced concepts exclusively for upper level students
Cumulative review benchmark skills tests throughout the book to help students judge their level of mastery in each concept
Stylistic upgrades that increase the navigational functionality of the book
A consolidated reference section at the beginning of the book, featuring a new unit conversion chart.
While private school entrance exam preparation is the primary purpose of this book, we recognize that it may serve other purposes as well. This book would be useful for anyone looking for a workbook that encompasses all fundamental math concepts up through an 8th grade math program. For further information about the book and our test prep offerings, check out our book's Amazon link, here, where you can find reviews and many additional details. | 677.169 | 1 |
Mathematics is often part of many school common entrance selection exams or Elevenplus exams. A good grasp and knowledge of all aspects of Mathematics are essential for these demanding tests. This product contains hundreds of maths questions each based on the requirements of the National Curriculum and the 11+exam and 12+ exam. It covers various aspects of Maths such as Algebra, measures, shape and space and data handling. Knowledge of all these areas will help prepare your child for the demands of any school selection exam. This is a very comprehensive online product making use of a variety of question types. No time limit is set and this allows children to work through the tests at their own pace. The level of mathematical language used is appropriate for the Eleven plus exams and other grammar school selection tests. There is the option to try the free sample questions. A glossary of the main mathematical terms is provided. (This product is suitable for the Northern Ireland AQE transfer Test and the GL transfer Test.)
This Mathematics course forms part of the complete 11+ and 12+ preparation course.
The complete 11+/12+ course for all four subject areas that you have purchased will appear in this "My courses " list. This Mathematics 11+ and 12+ Course provides unlimited practice in these areas of Mathematics. There is also the option to take unlimited and timed tests. | 677.169 | 1 |
Torrent Files List
college_algebra.zip (Size: 3.11 MB) (Files: 1)
college_algebra.zip
3.11 MB
Announce URL:
Torrent description
If you're looking for help in college algebra, you've come to the right place. College Algebra Solved!™ solves your most difficult college algebra problems, providing the answers you want with all of the step-by-step work and explanations you need. With additional powerful features including infinite example problems, practice tests, progress tracking, and a math document designer, College Algebra Solved!™ is the complete all-in-one college algebra solution you've been looking for. | 677.169 | 1 |
For the most part, standardized tests like the SAT and ACT are good indicators of math aptitude and college readiness. Since the tests are timed, you have about a minute to answer each problem. Success on these tests means having your fundamental math rules memorized and being fluent with their use.
However, there are some problems types that are really good for students to learn, and that take more than a minute to solve, even for the most fluent student. And these are not found on the SAT, PSAT or ACT. So, if a teacher and/or a math course is designed to "teach to the test," it may be lacking some key concepts that are fantastic at building good problem-solving skills. More importantly, these concepts are (or should be) vital for teaching math as the "language of science," which is what makes math real and useful and connects students to their world and their Creator.
The following is a list of 4 key concepts, all of which are present in Shormann Mathematics, but are normally missing from the SAT and ACT. Shormann Math teaches these concepts in more basic forms starting in Algebra 1, progressing to more complex forms later. Much of the text below was pulled directly from our Shormann Math lessons.
Measurement/Unit analysis
"To measure is to know" is a quote by William Thompson, Lord Kelvin(1824–1907), a Christian and scientist. What Kelvin meant was that if we can measure something, we then know something about it. As Christians, we must be careful about faulty reasoning that says by building our knowledge of nature, we gain enough evidence to conclude God's existence. We should never think we need to "conclude" God from the evidence. On the contrary, God designed us to know He exists (Romans 1:20), so we start with God, who is the beginning of knowledge (Proverbs 1:7).
When we measure things, we often have to convert the measurement from one unit to another. Measuring and converting units are essential skills in everything from cooking to engineering. Measuring accurately, and honestly, is also important to God (Proverbs 20:10 and elsewhere).
Proofs
To understand any subject well, not just math, one must start with rules and definitions. As the famous math teacher John Saxon said, fundamentals like these form the "basis of creativity," and this is true. Likewise, to understand God, you have to start with some foundational rules. And while Scripture is much more than a "rulebook", it contains Truth that helps us know who He is, how to build a relationship with Him, and how to do the things He has called us to do. It is self-evident that to learn anything, we must do so using the deductive process of applying rules.
While postulates are statements assumed to be true without proof, theorems (propositions) are true statements requiring proof. One mark of a maturing Christian is that they are able to use Scripture to "give a reason" for the hope that is in them (I Peter 3:15). In the same way, a mature math student should be able to give a reason for the steps they use to complete a problem. In mathematics, proof and the techniques used to write proofs require us to be prepared to have an answer we can back up. It forces us to slow down and think things through a little more before we answer.
Infinite Series
Leonhard Euler (1707-1783) said that infinite series are a subject that should be studied with "the greatest attention." Unfortunately, in most modern math courses, infinite series are studied little, if any, until calculus, where they tend to create a lot of confusion because students have a poor foundation. But Euler put them in his algebra book, Elements of Algebra, a book that most modern Algebra 1 and 2 courses are based off. If you start Shormann Math in Algebra 1, you will learn a lot about Euler and other famous mathematicians, and you will probably know more about series and infinite series than the average student your age.
But why did Euler think infinite series were so important, especially in regards to fractions? Well, what is calculus? It's the study of speed, right? Or even more generally, it's the study of rates of change. It's a study of how this changes as that changes, and when we compare this to that, we are studying fractions! Not only that, when we break a fraction into an infinite series of discrete pieces, we are doing computations that computer programs must do. Building fluency with infinite series can really go far in connecting students to fundamental aspects of computers.
Vectors
If you understand that traveling North at 60 mph is different than traveling South at 60 mph, then you have a basic understanding of vectors. Vectors allow us to consider two things at the same time, such as an object's speed and it direction of travel. And something called the Parallelogram Law provides a simple way for understanding how to add vectors. In fact, the famous mathematician Alfred North Whitehead (1861-1947) believed that the Parallelogram Law "is the chief bridge over which the results of pure mathematics pass in order to obtain application to the facts of nature." In other words, vectors are a really important tool for studying God's creation!
Concepts like these are not usually learned overnight. Like learning a language or a new instrument, sport, etc., it take patient practice over several years. That's why Shormann Math introduces these concepts in more basic forms starting in Algebra 1, giving students time to gradually build skills through practice and repetition. Click here to learn more about Shormann Math, and how Shormann Algebra 1 and 2 also help prepare students for the SAT, ACT and CLEP exams. Thanks for reading this post!
Comments:Comments Off on 4 Key Math Concepts You Won't Find on Standardized Tests
We just completed the beta-test of Shormann Algebra 2, our second course in the Shormann Math series. We learned a lot about what does and doesn't work last year in the Shormann Algebra 1 course, so in building Shormann Algebra 2, we applied the good and cast the bad into the lake of fire.
A key part of Shormann Math is TruePractice™, the result of our efforts to design the most efficient system for building fluency in mathematics. If you want to be good at something, whether it's baseball, piano, math, etc., there is simply no substitute for the need to practice. A lot. If, however, you think you can be good at something by receiving magical superhero powers while sitting on your couch, then you either watch way too many movies, or you're weird. Or both! But there are more and less efficient systems for practice, and we are finding that our TruePractice™ system that includes 100 lessons with 20 problems per lesson is achieving good results, compared to John Saxon-authored math courses which average 120 lessons and 30 problems per lesson.
With Shormann Math, students build fluency through 1) Practice Sets that are designed with the understanding that "practice time" is different than "game time," 2) Weekly Quizzes that are like a "practice game," and 3) Quarterly Exams that equate with "game day," "piano recital," etc.
Regarding Quarterly Exams, take a look at the graph of average student score vs. study effort. On the week of a quarterly exam, we provide detailed instructions on what we believe are the best methods for studying for an exam. The key, as you probably know, is to practice a lot. Because our eLearning campus provides data on some, but not all aspects of student study effort, we can group students into those who followed our study guidelines (blue line) and those who did not (red line).
The results are not surprising at all and show that we have a good system in place for helping students build fluency in math. Follow the system and make an A. Don't follow the system and make a B or worse. Our study guidelines are based on years of teaching experience, combined with years more of learning from good college math, science and engineering professors at top universities.
Are you a parent who wants a good and God-glorifying math curriculum for your child? Or, even better, are you a student who wants to know God better by using math as a tool for studying His creation, and you've been looking for a curriculum that will help you do this? If yes, take a look at Shormann Math today.
Comments:Comments Off on Building Good Study Habits with Shormann Math
Common Core Cancer
A brave Texas 7th-grader alleges that during an assignment about Common Core's fake version of critical thinking, the teacher directed students to label God as a myth. This type of "anchor chart" assignment forces students to wrongfully classify all statements as either fact, opinion, or commonplace assertion. Here's how these categories are defined in a typical Common Core-diseased classroom:
fact: Something that is true about a subject and can be tested or proven.
opinion: What someone thinks, feels or believes
commonplace assertion: Stating something is true without supporting it with facts or proof.
Notice how only facts are considered "true", while opinions and commonplaces assertions are categorized as things that are either false or just "true for me but not necessarily true for you."
This type of assignment is at the heart of Common Core educational standards (standards that supposedly aren't taught in Texas. Surprise!). In his excellent March 2015 New York Times article about this fundamental problem with Common Core , philosopher Justin McBrayer described how students are required to fit things into one, and only one of these categories. In other words, you can't believe in a fact, and only facts can be true. So, God can't be believed in AND also be a fact! But neither can you believe that 2+2 = 4, the sky is blue, or grass is green. Those are just facts, not things you also believe, you silly non-Common Core indoctrinated person!
I hope you agree with me that it is absolutely absurd to force students to categorize all statements into only one of three "anchor chart" categories, and then call it a "critical thinking" assignment. It is sad that so many millions of students are being taught "how to think" using such irrational methods. And it doesn't just start in 7th grade; McBrayer spotted the same type of anchor chart assignment in his child's 2nd grade classroom!
The Katy ISD 7th-grade teacher directed the class to categorize the statement "There is a God" as opinion by labeling God as a myth. This is a fine tactic for someone who hates God to employ, because when most people, not just Common Core indoctrinated schoolchildren, hear the word myth, they think "legend," or "fake story about the past."
C.S. Lewis to the Rescue
But, could a great story about the past also be true? Why does myth have to always make us think "fake Greek sky gods?" Here's where C.S. Lewis rescues us from oversimplifying our world in a way that gives us a false view of reality:
Now the story of Christ is simply a true myth: a myth working on us the same way as the others, but with this tremendous difference that it really happened: and one must be content to accept it in the same way, remembering that it is God's myth where the others are men's myths: i.e., the Pagan stories are God expressing Himself through the minds of poets, using such images as He found there, while Christianity is God expressing Himself through what we call 'real things'.
In one long, beautiful, eloquent, God-glorifying sentence, C.S. Lewis destroys the Common Core's ridiculous "anchor chart." Lewis words reassure us that legends can also be true! Or in Common Core language, opinions can also be facts, facts can be assertions, etc.
Tools to Use in Your Thinking
You see, school-aged children don't need to be trained "what to think," nor do they need to be trained "how to think." As math-teaching legend John Saxon once said,
God gives students the ability to think. Society does not give children that ability.
God designed us with the ability to think critically. The 7th grade Katy ISD student is a perfect example of that, as she was able to spot the flaw in her teachers' fake "critical thinking" assignment, an assignment that will no longer be taught in Katy ISD thanks to her efforts.
What students need are tools to use in their thinking. And one of the best tools is mathematics. Some math curriculum to consider include any John Saxon-authored courses, as well as my company's new curriculum, Shormann Math, a curriculum built on a solid foundation of mathematics' legends, with Jesus Christ as the common core. Logic is another course worth considering. At a minimum, study this logical fallacy poster. Another resource is Introductory Logic by Roman Roads Media. Books by Nancy Pearcey are also excellent resources for understanding the negative impact of oversimplifying the 'real things' C.S. Lewis was describing. Total Truth, Saving Leonard0, and Finding Truth are all excellent. And of course, any books or essays by C.S. Lewis! And last but not least, the Bible, without which we would not know that we are supposed to reason together (Isaiah 1:18).
Comments:Comments Off on C.S. Lewis Destroys Common Core in One Sentence
With Shormann Math, using 21st Century technology to create a math course allows us to obtain valuable information revealing that, regardless of skill level, students who want to learn math, can, and Shormann Math has the tools for them to do so.
For example, during quarterly exam week, students are provided with two full-length practice exams. Practice exams allow students to prove to themselves that they really do (or don't) know the material covered that quarter. Besides the practice exams, they are given other guidelines on how to prepare for the exams. The guidelines are based on years of teaching experience, as well as observing university professors. Between my bachelor's in aerospace engineering, and a PhD in aquatic science, I had a lot of professors and exams! And the best professors, the ones who really wanted you to learn the material, did two things: 1) they kept a file of previous exams in the library that students could check out and study, and 2) they had office hours so students could ask questions. Shormann Math provides both, with 1) practice exams that reward students for a good study effort and 2) free email Q&A any time.
But are the practice exams helpful? Well, see for yourself. The following graph displays the recent results of Quarterly Exam 1 scores for Shormann Algebra 1 and 2(beta) students.* The bottom line is that students with "Good" study habits made A's on the exam. The graph is a display of the obvious fact that good study habits build fluency, resulting in good scores on the actual exam. Being fluent in math means you know how to use the rules to solve new problems. And the purpose of the Practice Exams in Shormann Math is to provide new problems so the student can prove to themselves whether they are fluent, and if not, what they need to review.
At some point in your life, you will be tested on a large amount of information. Whether it's for a job you really want, a driver's license, an SAT, ACT, MCAT, etc., sooner or later, test day is coming. And if you really want that license, or that job, etc., you are going to put the personal effort into it to study. Shormann Math is designed to help students build effective study habits in a less important setting where the stakes aren't as high. But, as the results above reveal, the best curriculum in the world won't make a bit of difference if the student doesn't put that personal effort into following directions and studying effectively.
*Graph details: Scores are from Quarterly Exam 1 taken by students in Dr. Shormann's live online Algebra 1 and 2 classes, October 2015. The three categories are based on student performance on the 2 practice exams take prior to the actual exam. The students are allowed to take the practice exam, review mistakes using the solutions manual provided, and then take it again. Students who put the effort into retaking each practice exam were rewarded for their effort with a higher grade. Students are also encouraged to show work on their paper, solving each problem by hand. For the actual exam, they are required to submit handwritten work on each problem. The practice exams were counted as one of their homework grades, providing further encouragement to complete them. The three categories were broken down as follows: "Good" students averaged 95% or better on the practice exams, all of which took at least one of the exams more than once in order to get a higher score, which means they took the time to correct their mistakes and study the problems they missed. "Mediocre" students took each exam once, but averaged below 95%, and showed little to no effort to try the exam again, missing a valuable opportunity to review and build fluency. "Poor" students did not attempt either practice exam. Of special note is the fact that the trend was consistent, regardless of which course students were doing (Algebra 1 or 2). Also, because the students had the opportunity to retake each practice exam until they received a 100, study effort, and not skill level, was the main factor influencing performance on the actual exam. Not all students are equally gifted in math (or any subject), but students who are less-skilled at math can do better by studying harder. These results provide good evidence that, with Shormann Math, students who want to learn math, can, regardless of skill level!
A Great Question
We recently received a great question about our new Shormann Algebra 1 course:
Are your courses best for mathy children, or can average students also complete them?
While "mathy" really isn't a word, anyone with any teaching experience knows what this parent was talking about. Some students just "get" math quicker than others. They're able to go farther and faster in math than most children their age. So, is Shormann Math mainly for these students, or is it more for students who are gifted in other, "non-mathy" areas?
An Illustration
The best answer is that Shormann Math is for everyone! To help me explain how, first take a look at this photo I shot a few months ago of a Hawaiian green sea turtle. The photo appears at the top of Shormann Algebra 2, Lesson 25. You'll see what this has to do with answering the parent's question shortly:
Everyone loves sea turtles, right? I mean, do you know anyone who hates sea turtles? I don't. There are some things in this photo that everyone can relate to, like beauty, design, color, and function, to name a few. There are also things that individuals gifted in certain areas would appreciate that others won't. Photographers, for example, may be curious about what type of camera was used, resolution, lighting, etc. Everyone might notice how the magnified view of the eye is blurred, and composed of rows and columns of tiny squares. But only someone with a good knowledge of computers and/or digital photography could explain the "why" behind the tiny squares (called pixels).
Connecting Students to Their World and Their Creator
But what if your child is a future computer scientist, engineer, etc., and they just don't know it yet? What if they, or you, haven't already drawn the line between "mathy" and "non-mathy?" Well, Shormann Math is for you, too! Because everyone is created in God's image (Genesis 1:26-28), everyone is designed to be creative like Him, too. But while God can just create by speaking (John 1:1-5), we humans need tools. And mathematics is like a giant treasure chest of tools, waiting to be discovered and put to use.
But the primary focus of Shormann Math is not about math. It's about relationship. It's about using math to help a child discover more about God's Word and His creation, and build their relationship with Christ.
If you study the greatest mathematicians in history, like we do in Shormann Math, you find that all their new mathematical discoveries were connected to their study of Creation. While not all of them acknowledged God, a lot of them did, and in doing so it allowed them to see farther and discover more than any of their predecessors. The rich Christian heritage of modern mathematics is not something to hide in the back of a dark closet, but, like a favorite painting, it should be placed in the right frame, with the right lighting, and set in a prominent place.
In a nutshell, here's what Shormann Math is about:
Shormann Math is designed to connect students to their world and their Creator by using an incremental approach with continual review to teach 10 major math concepts from a Christian foundation.
But Does it Work?
But does this "incremental approach with continual review" work? Well, the results of our Shormann Algebra 1 beta-test say "yes!" Pioneered by the late John Saxon (1923-1996), his "incremental approach with continual review" has achieved astounding results. The results of Saxon Math in a traditionally low-performing Dallas public school were highlighted in this 1990 interview on 60 Minutes.
If the 60 Minutes interview doesn't convince you of the merits of John Saxon's approach, then maybe this historic quote by President Ronald Reagan will:
I'm sure you've probably heard about that new math textbook. It's by a fellow named John Saxon, that has average I.Q. students scoring above high I.Q. students and has Algebra I students who use this textbook doing better on tests than Algebra II students who use the traditional text…
(Remarks at a White House Reception for the National Association of Elementary School Principals and the National Association of Secondary School Principals, July 29, 1983)
Even a former U.S. President saw the merits of a teaching method that could help the average student go farther in mathematics than they ever dreamed.
Scholars describe mathematics as "the language of science." And what is a good way to learn a new language (or a sport, or an instrument)? Well, you learn some of the basics, practice for a while, and then learn some more. You use an "incremental approach with continual review!" And like a language, sport, or instrument, mathematics is not a passive, textbook-only activity. It's an active, pencil and paper pursuit. The method is instrumental in making Shormann Math for everyone!
Click here if you want to learn more about Shormann Math, including pricing, sample lectures and homework, a detailed teacher's guide, and more.
Why do results matter?
Shormann Math builds on a solid foundation of time-tested teaching methods, including the incremental development + continual review format pioneered by John Saxon(1923-1996). And not just Saxon's teaching methods, but his teaching thoughts as well, including his thought that
Results, not methodology, should be the basis of curriculum decisions.
One of the primary reasons John Saxon developed his math curriculum in the 1980s was because new ways of teaching math were not working. Math "educrats" at the time were promoting their untested "visions" of math teaching. But with 3 engineering degrees, John was a math user before he became a math teacher. Not only that, he was a test pilot. If anyone knew the extreme value and importance of testing a new product, it was John!
Results matter because they reveal whether or not a new product really works. And while statistics certainly don't reveal everything about a new product, they can certainly reveal many things. Most math curricula don't provide this level of detail on student performance. But with Shormann Math, each new course is beta-tested in a live, online setting first before releasing it to the general public. The following are statistics from the beta-test of Shormann Algebra 1. The results show that the majority of students made an A! The following statistics, plus other detailed information about the course, can also be found in our Shormann Algebra 1 teacher's guide. To purchase Shormann Math, click here.
Overall Performance
Discussion: The average student in our beta test made an A in the class! Because each new Shormann Math course is beta-tested in a live online class setting, Dr. Shormann gets to know the students on more than just a "numbers only" basis. And we all know that God doesn't make clones, so the fact that not every student performed the same should not be a surprise. Natural talent definitely matters, but so do things like attitude and maturity. Dr. Shormann spends time during the video lectures encouraging students to develop fruits like patience and self-control (Galatians 5:22-23), as well as persevering with joy (James 1:2-3), and gratefulness (I Thessalonians 5:18).
Practice Sets
Discussion: You've probably never seen statistics on student performance in a math class before, which is why it is important to discuss the data! The decreasing trend over time is exactly what we expected. Two big factors are responsible for the trend: 1) There's more review of previously-learned concepts at the beginning, so it's easier and 2) student effort tends to decrease the closer you get to the end of the year!
What we had hoped for was a Practice Set average above 85%, and that was achieved in all 4 quarters! 85% is a good cutoff for determining whether students are understanding, and retaining most of the concepts learned.
Note also the high first quarter average. Because Shormann Math is built on John Saxon's method of integrating geometry and algebra, students using Saxon Math 8/7 or Saxon Algebra ½ will be most comfortable starting Shormann Math. However, not all beta-test students used Saxon previously, so the high first quarter average is a good indication that students who successfully completed any pre-algebra course should do just fine in Shormann Math.
Weekly Quizzes
Discussion: Weekly Quizzes show a similar trend to the Practice Sets, challenging the students more as the year progressed. A score of 8 out of 10 or higher is a good indication of whether students understood the lessons covered that week. We are pleased that scores were well above this in all four quarters!
Quarterly Exams
Discussion: Notice the Quarterly Exams do not follow the same trend as Practice Sets or Weekly Quizzes, with Quarter 1 having the lowest average. And this is where beta-testing a new product is so valuable. We realized that we were asking a lot for 9th-grade level students, most of which had never taken a cumulative exam like this. The solution? Practice exams! Just like when learning a sport, a musical instrument, etc., good practice results in good performance. The beta-test students clearly performed best on first quarter Practice Sets and Quizzes. Most likely, if they were given practice exams prior to their quarterly exam 1, this would have been their highest exam average. Now, all quarterly exams have two practice exams that students use to study for their actual exam.
85%+ is an indicator of good retention and understanding of concepts covered in a quarter. For all 4 quarters, student averages were at, or well above 85%. Because of Shormann Math's format of continual review, we are basically asking students to be responsible for "all their math, all the time." These results show that on average, students are responding very well!
Euclid's Proposition 1 overlaying a pod of spinner dolphins swimming in a near-perfect equilateral triangle formation! The concept of proof applies to everything from building a rocket to the simple beauty of a pod of dolphins. Photo Credit clarklittlephotography.com
What is proof?
Proof is really nothing more than providing a reason for statements made or steps taken. In the standard American government school 3-year "layer cake" approach to high school math, the concept of proof is normally limited to some sections in the geometry layer. But proof is not a concept that is the exclusive domain of geometry. Shormann Math teaches proof in 3 main ways, by 1) studying Euclid's foundational work on proof, 2) showing that proof is for all of math, not just a few weeks in geometry class, and 3) showing how proof applies in the real world.
Euclid and proof
Around 300 B.C., Euclid (330 – 275 B.C.) organized the previous 3 centuries of Greek mathematical work into a 13-volume thesis known today as The Elements or Euclid's Elements. Scholars believe that only the Holy Bible has been more universally distributed, studied and translated. Starting with a foundation of 5 postulates, 5 axioms, and 23 definitions, Euclid proved 465 theorems, or propositions.While postulates are basically rules that are assumed to be true without proof, theorems are true statements requiring proof. Postulates are also referred to as self-evident truths.
Surprisingly, even though Euclid is considered the "Father of proof," most American high school geometry textbooks mention little to nothing about Euclid. In Shormann Math though, students will learn who Euclid was, and the importance of his contribution to Western Civilization. Shormann Algebra 1 and 2 students will become very familiar with Euclid's first 5 propositions, giving them a good understanding of proof technique. They will gain an appreciation for the deductive nature of geometry and geometric constructions, seeing how one proposition often requires the previous one. And they will also see the simple beauty and elegance of Euclid's propositions.
Proof and mathematics
Perhaps one of the greatest flaws in the "layer cake" approach to high school math is that the concept of proof is almost always limited to a few weeks during the geometry year. In Shormann Math, we'll do the standard triangle proofs and circle proofs, but we will also apply proof technique in other topics like algebra, trigonometry and calculus.
But how can proof be for more than just geometry? Well, proof is based on a type of reasoning called deductive reasoning (applying rules). Every single math concept begins with rules. And every single math problem can be solved by applying those rules. All of mathematics is deductive in nature, which means at any time, a student should be able to explain the rules (provide reasons for) they used to solve a problem.
Because Shormann Math is integrated, we're able to help students make connections between the major concepts like algebra and geometry. This results in students getting a better feel for what mathematics is about, which will make it easier to learn. Instead of thinking that they are always learning something new and different, they will see how one lesson builds on previous ones, which makes it less intimidating.
Proof and the the real world
Sure, proof is important to mathematicians, but it's also important in the real world. As we explain in Lesson 68 of Shormann Algebra 1,
"Supporting statements with reasons is a technique used by, and expected of, people that society refers to with words like professional, leader, wise, helpful, and trustworthy. People like Abraham Lincoln, the 16th President of the United States of America, known for his study of Euclid's Elements and his application of the idea of proof to solving societal problems."
We also helps students see the application of proof technique in the real world, as this table from Shormann Algebra 2 explains:
Most importantly, proof is profoundly important in sharing the Gospel with unbelievers. God wants us to be ready to give reasons for the hope of salvation (I Peter 3:15). Our reasons should primarily be Scriptures we have memorized, or at least remember where to find them.
Conclusion
As you can see, proof is about a lot more than geometry! Shormann Math gives students a basic understanding of proof technique and it's application to the real world. It's a great tool to help them in their thinking, planning, designing and serving. If you think you would like your child to learn math in a more natural way that connects them to their world and their Creator, click here to learn more! | 677.169 | 1 |
Keywords:
Background Tutorials
Matrices can help solve all sorts of problems! This tutorial explains what a matrix is and how to find the dimensions of a matrix.
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Add, subtract, and multiply matrices of appropriate dimensions.
Adding matrices is easier than you might think! Just find the corresponding positions in each matrix and add the elements in them! This tutorial can show you the entire process step-by-step.
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | 677.169 | 1 |
NEW - FREE SHIPPING
This title is In Stock in the Booktopia Distribution Centre. We will send you a confirmation email with a Tracking Code to follow the progress of your parcel when it ships.
Pearson Mathematics 9 Essentials Edition Author: David Coffey
ISBN: 9781442529618 Format: Paperback Number Of Pages: 484 Published: 29 June 2012 Country of Publication: AU Description: Pearson Mathematics 9 Essentials Edition Student Book is a streamlined edition of the Pearson Mathematics 9 Student Book, providing the same strong pedagogy and up-to-date research to comprehensively cover the Australian Curriculum requirements. Avoiding additional content and concentrating on essential theory, you and your students can focus on the national curriculum's outcomes. This student book is an uncluttered, clean and concise making it manageable for students, plus it is more economical, lighter and thinner than other Pearson Mathematics books. This text is compatible with Pearson Mathematics' bridging workbooks, homework programs and teacher companions | 677.169 | 1 |
Need to keep your rental past your due date? At any time before your due date you can extend or purchase your rental through your account.
Sorry, this item is currently unavailable.
Summary
For courses in Algebra-based Physics. Walker's suite of pedagogical tools fosters understanding of physical principles and active involvement in the learning process. Because one-size-fits-all examples do not sufficiently address the needs of students, Walker employs a variety of pedagogical elements, each used where it can contribute most to developing conceptual insight and problem-solving skills. | 677.169 | 1 |
You may also like
About this product
Description
Description
This is an unusual math book: it is meant to be read aloud by a tutor and a student. It consists primarily of explanations, in words, of important math concepts. Reading comprehension questions rather than math problems check whether the reader is understanding. The learner who uses it practices reading comprehension in the subject area of math. This book starts with very basic ideas such as place value, sets, and addition, and moves through concepts of algebra. The format of small sections with a comprehension probe after each is custom made for tutoring, but also suited for the individual reader. | 677.169 | 1 |
DependingThis calculator performs all matrix, vector operations. You can add, subtract, find length, find dot and cross product, check if vectors are dependant. For every operation, calculator will generate a detailed explanationComplex Numbers is a calculator for mathmatical problems involving the field of complex numbers. It's designed to help students and engineers find reliable answers quickly and point them in the right direction, if they wish to dive deeper into the math behind the calculations | 677.169 | 1 |
Share this Page
Videos Will Help Students "Ace" Math
02/01/97
Ace-Math, an award-winning video tutorial series, is suited for students trying to grasp fundamental mathematical concepts, parents who want to help their child with their homework, or people who need to brush up on math skills for a specialized license or test.
There are nine separate series, each with many individual videos: Basic Mathematical Skills, Pre-Algebra, Algebra I, Algebra II, Advanced Algebra, Trigonometry, Calculus, Geometry, and Probability and Statistics. Each series except Algebra I consists of 30-minute videotapes explaining various concepts. Algebra I has 16 hour-long videos.
For only $29.95, Ace-Math purchasers get a 30-minute tape with the right to make two back-up copies. This lets educators keep the tape in the learning center and let students check out a copy to take home -- with the added security of another back-up copy!
These innovative tapes have been purchased by institutions such as NASA, the U.S. Coast Guard and IBM, and are in use at institutions such as the Los Angeles Public Library and New York Public Library.Video Resources Software, Miami, FL, (888) ACE-MATH,
This article originally appeared in the 02 | 677.169 | 1 |
This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees the reader quickly becomes acquainted with this equally 'real' analysis and appreciates its relevance. The reader's understanding is enhanced and deepened by the large number of exercises included throughout; these both test the reader's grasp and extend the text in interesting directions. As a consequence, this book will become a standard reference for professionals (especially in p-adic analysis, number theory and algebraic geometry) and will be welcomed as a textbook for advanced students of mathematics familiar with algebra and analysis. | 677.169 | 1 |
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
GMAT Math Preparation Class
Master All Concepts in GMAT Maths Section to Achieve A High Score In GMAT!
4.6
(146WhoWhat are the requirements?
Determination To Get A High Score the GMAT Exam
What am I going to get from this course?
Know what to expect and what topics to prepare for GMAT Math section.
Get an overview of all the topics covered in the GMAT Math section.
Have a firm grasp of the kind of questions that will be asked in the GMAT Math Exam.
Maximize the score of your Quant section : 100% is the goal
WhatData Sufficiency(DS) questions are unique to the GMAT, so they may seem strange to you at first. In this lecture, you will learn the basic format of GMAT data sufficiency questions, and you will learn systematic techniques for solving them.
GMAT Data Sufficiency
10:31
Memory versus Memorizing
04:45
You won't be able to solve a complex overlapping probability question if you don't understand overlapping sets. Good fundamentals make the extraordinary feats possible. That's why the best athletes practice the fundamentals of their sport everyday, and it's also why you should practice and master the math fundamentals that underlying many of the GMAT's math questions.
These GMAT math formulas are the basis for countless questions on the exam; expect to have to employ them while solving both easy and difficulty questions.
Top 5 Formulas
07:09
Number Theory is concerned with the properties of numbers in general, and in particular integers. As this is a huge issue we decided to divide it into smaller topics.
GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.
Integers are defined as: all negative natural numbers , zero , and positive natural numbers . Note that integers do not include decimals or fractions - just whole numbers.
An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.
An even number is an integer of the form , where is an integer. An odd number is an integer that is not evenly divisible by 2. An odd number is an integer of the form , where is an integer. Zero is an even number. Addition / Subtraction: even +/- even = even; even +/- odd = odd; odd +/- odd = even. Multiplication: even * even = even; even * odd = even; odd * odd = odd. Division of two integers can result into an even/odd integer or a fraction.
Number Theory
16:45
Fractions
10:20
Base - the number that is multiplied by itself a certain quantity of times.
For example, in the expression 23, the number 2 is the base.
Exponent - the number of times a quantity is multiplied by itself.
For example, in the expression 23, the number 3 is the exponent.
Radical - the sign used to denote the square or nth root of a number.
For example, the value of "radical 4" is 2 and the value of "radical 9" is 3.
Exponential Expression - an expression or term with a power or exponent that is not one.
For example, x2 is an exponential expression while x is not an exponential expression. Similarly, x1/2 (called the square root of x) is an exponential expression while 2x is not an exponential expression.
Exponential Equation - an equation with a term that has an exponent greater than one.
For example, x3/2 + 2x + 1 is an exponential expression while 2x + 3 is not an exponential expression. Similarly, x3 = 27 is an exponential equation while x + 2 = 29 is not an exponential equation.
Exponents signify repeated self-multiplication. E.g.,: 23= 2*2*2
Exponents are a shorthand way of representing repeated multiplication. Consider the following examples, which are all exponential equations because a term is multiplied by itself multiple times
Exponents
04:51
While most questions in this Products, Powers and Roots rely on a few basic rules, many test-takers don't know those rules, and the harder questions make it difficult to recognize how to apply them
Products, Powers and Roots
05:27
A percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is oftendenoted using the percent sign, "%", or the abbreviation "pct". Since a percent is an amount per 100, percent canbe represented as fractions with a denominator of 100. For example, 25% means 25 per 100, 25/100 and 350%means 350 per 100, 350/100.
A percent can be represented as a decimal. The following relationship characterizes how percent and decimals interact. Percent Form / 100 = Decimal Form
For example: What is 2% represented as a decimal? Percent Form / 100 = Decimal Form: 2%/100=0.02
Percentages
05:02
The absolute value (or modulus) of a real number x is x's numerical value without regard to its sign.
Absolute Value
08:52
Manipulation of various algebraic expressions
Equations in 1 & more variables
Dealing with non-linear equations
Algebraic identities
Algebra
14:17
If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y= divisor*quotient+remainder = xq+r and 0<=r<x .
For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since 15 = 6*2+3. Notice that 0<=r<=x means that remainder is a non-negative integer and always less than divisor. This formula can also be written as y/x = q+r/x.
Remainders
05:43
1) Read the entire question carefully and get a feel for what is happening. Identify what kind of word problem you're up against. 2) Make a note of exactly what is being asked. 3) Simplify the problem - this is what is usually meant by 'translating the English to Math'. Draw a figure or table. Sometimes a simple illustration makes the problem much easier to approach. 4) It is not always necessary to start from the first line. Invariably, you will find it easier to define what you have been asked for and then work backwards to get the information that is needed to obtain the answer. 5) Use variables (a, b, x, y, etc.) or numbers (100 in case of percentages, any common multiple in case of fractions, etc.) depending on the situation. 6) Use SMART values. Think for a moment and choose the best possible value that would help you reach the solution in the quickest possible time. DO NOT choose values that would serve only to confuse you. Also, remember to make note of what the value you selected stands for. 7) Once you have the equations written down it's time to do the math! This is usually quite simple. Be very careful so as not to make any silly mistakes in calculations. 8) Lastly, after solving, cross check to see that the answer you have obtained corresponds to what was asked. The makers of these GMAT questions love to trick students who don't pay careful attention to what is being asked. For example, if the question asks you to find 'what fraction of the remaining...' you can be pretty sure one of the answer choices will have a value corresponding to 'what fraction of the total…'
Word Problems
09:33
What is a 'D/S/T' Word Problem? Distance, Speed, Time Usually involve something/someone moving at a constant or average speed. Out of the three quantities (speed/distance/time), we are required to find one. Information regarding the other two will be provided in the question stem. The 'D/S/T' Formula: Distance = Speed x Time
Distance
04:10
What is a 'Work' Word Problem?
It involves a number of people or machines working together to complete a task. We are usually given individual rates of completion. We are asked to find out how long it would take if they work together. Sounds simple enough doesn't it? Well it is! There is just one simple concept you need to understand in order to solve any 'work' related word problem.
Work Word Problems
04:49
Some 700+ GMAT quantitative questions will require you to know and understand the formulas for set theory,presenting three sets and asking various questions about them. There are two main formulas to solve questions involving three overlapping sets.
Total = A+B+C - (sum of 2-group overlaps) + (all three) + Neither
Let's see how this formula is derived.
When we add three groups A, B, and C some sections are counted more than once. For instance: sections d, e, and f are counted twice and section g thrice. Hence we need to subtract sections d, e, and f ONCE (to count section g only once) and subtract section g TWICE (again to count section g only once)
Advanced Overlapping Sets
10:13
Triangle is a closed figure consisting of three line segments linked end-to-end. A 3-sided polygon.
The vertex (plural: vertices) is a corner of the triangle. Every triangle has three vertices.
The base of a triangle can be any one of the three sides, usually the one drawn at the bottom.
The altitude of a triangle is the perpendicular from the base to the opposite vertex. (The base may need to be extended).
The median of a triangle is a line from a vertex to the midpoint of the opposite side.
Area: The number of square units it takes to exactly fill the interior of a triangle.
Triangles
16:47
Types of Polygon
Regular A polygon with all sides and interior angles the same. Regular polygons are always convex. Convex All interior angles less than 180°, and all vertices 'point outwards' away from the interior. The opposite of concave. Regular polygons are always convex.
Polygons
11:06
A line forming a closed loop, every point on which is a fixed distance from a center point. Circle could also be defined as the set of all points equidistant from the center.
Circles
09:51
Coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.
In coordinate geometry, points are placed on the "coordinate plane" as shown below. The coordinate plane is a two-dimensional surface on which we can plot points, lines and curves. It has two scales, called the x-axis and yaxis,at right angles to each other. The plural of axis is 'axes' .
Coordinate Geometry
13:42
Standard Deviation (SD, or STD or sigma ) - a measure of the dispersion or variation in a distribution, equal to the square root of variance or the arithmetic mean (average) of squares of deviations from the arithmetic mean.
In simple terms, it shows how much variation there is from the "average" (mean). It may be thought of as the average difference from the mean of distribution, how far data points are away from the mean. A low standard deviation indicates that data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values
Standard Deviation
05:51
A number expressing the probability (p) that a specific event will occur, expressed as the ratio of the number of actual occurrences (n) to the number of possible occurrences (N).
p=n/N A number expressing the probability (q) that a specific event will not occur:
q=(N-n)/N=1-p
Probability
11:49
Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their properties.
Enumeration is a method of counting all possible ways to arrange elements. Although it is the simplest method, it is often the fastest method to solve hard GMAT problems and is a pivotal principle for any other combinatorial method. In fact, combination and permutation is shortcuts for enumeration. The main idea of enumeration is writing down all possible ways and then count them.
Combinations and Permutations
05:41
Sequence: It is an ordered list of objects. It can be finite or infinite. The elements may repeat themselves more than once in the sequence, and their ordering is important unlike a set.
Sequences and Progressions
06:29
The GMAT often tests on the knowledge of the geometries of 3-D objects such cylinders, cones, cubes & spheres. The purpose of this lecture is to summarize some of the important ideas and formulae and act as a useful cheat sheet for such questions
Sri has 5 years of teaching experience where she helped several students to get rid of their fear and in developing an interest for the subject.
Her aim is to provide students a good learning experience and help them to reach their goals in different subjects. She wants all her students to be highly successful in whatever dream they pursue and strives to work towards making this possible. | 677.169 | 1 |
If you read a proof but cannot repeat it afterwards, did you learn much?
If you read a proof of a theorem (e.g. a long and/or difficult one), and you fully understood every step perfectly while reading it, but cannot repeat it afterwards, would you say that your math ability has really improved much through reading it? Should you read proofs of theorems only if you know that you can repeat it afterwards, otherwise you are simply wasting your time and are better off doing exercises using the theorems? What are your opinions?
In my opinion the most important ability is what is implied in Rudin's format. You are asked to read 10-20-30-40 pages or material, then solve problems at the end of the chapter based on that material - and the fact of the matter is that there may be one or more theorems in the book that you won't really need (or need much).
Once you solve problems, write them down in a place where you can reference it 1 month/year/ or decade later. Note that the theorems in question are already written down in the book... (Personally speaking, I prefer doing this on a computer - and backing up the data - but I use html-math ( along with inserting tex images ([url] [Broken]) manually into a web page).
If the book author did a good job in choosing problems, then you will most definitely be needing to look carefully at certain proofs to find a various trick that was used, and reapply it to the problem -- because it's in the very nature of advanced math books that the problems are not going to be rote one line applications of a theorem (unless it's a clever use of such..).
I don't particularly like Spivak's Calculus on Manifolds format, where there is a really short material section followed by very tough problem sets (however I must admit that when I read through chapters 1-4 I was indeed very impressed at how much information you could convey in such a small space, so it's still a very good book).
Actually there is a lot to say about the open ended question of "memorization of proofs" in Math, but I think the simplest answer is that there are some proofs that you would really want to know because they are particularly easy: such as a continuous image of a compact set is compact, a compact subset of a Hausdorff space is closed, etc..
But it's probably not economically optimal to try to memorize them once and for all the first time you encounter them (especially if you don't continue in math). But instead as you continue in math, and you run into those "facts" in more advanced problems, go ahead and take the time to try to resolve(reprove) them.. After you do that enough times you tend to remember them.
But the other point is that a really juicy source of learning "how to do math" is that when you find that you need an answer to a problem you solved 6 months ago, and you look at your old solution, and you really find it was poorly written... It teaches you to write down solutions clearly the first time and do not abuse the terms such as "obviously...", "it then follows that..." especially when you are rereading your own work and finding that what you said was obvious is not even obvious to yourself anymore!I'm not a math major myself, but there was a number of times when I sought the help of some maths graduate students for some particular problems. When I asked for a proof of some of the theorems they used, they would think for a while, then say "Well I can't give you one now, but in general for maths proofs, there are theorems out there where you just read and understand it just once in the course of your studies, then basically it can be forgotten as long as you understand its implications and applications".
It kind of made me wonder for a math major at least, to what extent is being able to reproduce a proof without reference to a text or even a sketch of a strategy of how to execute it actually important when learning mathematics on its own? (ie. not because one needs it for physics, computing courses etc.)
Is this mindset typical of maths majors or are these people just lazy to explain to me how to prove them?
From the point of view of a professional, "memorizing" proofs is not terribly important (although it can save time looking them up!) but knowing the general concepts of the proof is- since that may suggest techniques for a new problem. On the other hand, studying a proof carefully (not necessarily "memorizing") because you can learn methods that will apply to other proofs.
And, of course, there is the classic (probably apocryphal) story about the oral exam: A professor asks the student to prove a well-known theorem. The student answers that he hasn't memorized the proof but " I know where to look it up if I need it". To which the professors reply is "You need it it now!"
I think that the content of a proof is as important as its result. Proofs constitute a great resource for learning new notions, techniques or bringing to your attention things you never quite noticed, even within concepts you were long familiar with. If you cannot repeat the proof but have absorbed new ideas from it, you definitely have learned something.
It's usually not best to venture out trying to memorize the proof, but rather the key techniques or devices used in that proof. It saves a lot of brain memory, you can remember it better, and if you've actually learned something, you can go through the whole proof with just those few devices.
For example, when using Riemann sums to derive the formula for the integral of a function x^n, n being a positive integer, you can either try to remember every step in the 2 or 3 page derivation, or just remember the key step; subintervals of [tex](b/a)^{1/n}[/tex].This is not what I was suggesting... I was actually saying you don't even need to look at the proofs (or the chapter content) if 1) you can solve the problems and 2) you aren't interested in them. But I was saying you should write down the problems because in general they aren't written in the book so if you need to reference them later, it really sucks if you solved it once, then look at it again, and not know the answer..
But ultimately to 1) solve the problems in a good book you end up needing to read most or all the proofs carefully -- or at least a part of them.
I will give an example from personal experience, as a case in point, in L'Hospital's rule.
I still haven't memorized the proof, and I won't even look it up on wiki for the sake of this thread. But what I do remember about it is that I didn't like the proof in baby Rudin, and I prefer to prove L'Hospital using sequences. (I.e. to show f -> L as x -> c you can take an arbtrary sequence p_n (!= c) that converges to c).
The other point is that you need to apply some sort of multiplication/division trick to change the infty/infty and 0/0 terms using the mean value theorem into f'/g'..
It's actually a poor memory, and in fact in the future eventually I am going to try to be able to remember more.. But still I know the statement, that if f/g gives inf/inf, then you can take the limit as f'/g'.
if you learn to ride a bike and cannot ride one afterwards, have you learned a lot?
I don't think this is an appropriate analogy. After all, the skill of riding a bike is due to procedural memory, while reading and understanding is declarative memory. Hence someone who is extremely forgetful may be able to learn to ride a bike but probably cannot remember enough to follow through a long and difficult proof:
I believe that understanding a proof is much more important than remembering a proof. And if you continously flip back some pages to take a look at the proof for a theorem as you are using it you will become familiar with the proof, and perhaps enough to know the proof step by step. The worst thing you can do is to skip the proof of a theorem you are going to use.
some of you obviously have never understood a proof well enough to have it in your molecules. you cant ride a bike by memorizing the rules either.
In the example of L'Hospital's rule, it's actually a pretty hard theorem in comparison to other differential calculus theorems. So I think it partially depends on a particular theorem whether or not a graduate student should be condemned for not "having it in his/her molecules". In my original post I was being very extreme in theory but not in practice about "not needing to read" etc.., but ultimately I still think the best approach is to "write it down". As for L'Hospital, this is the second time I have written (part of) it down. After finding my old solution, I didn't really like it that much (I hate when that happens!), and in retrospect I wish to banish the idea of using sequences. Yet still, I found it easier to read my solution than the one in baby Rudin.. so it helped me reprove L'Hospitals more quickly than if I hadn't written it..
So here goes (only one case addressed).... One of the things that makes L'Hospital tricky is that it addresses multiple cases.. So let's look at a single case, and try to be content with a (smaller) theorem that f,g -> [itex]\infty[/itex], and f'(x)/g'(x) -> L implies f/g -> L. (We assume f,g are differentiable and nonzero in a region for the theorem to make sense):
The trick is to use the equality
f(x)/g(x) = f(y)/g(x) + (1-g(y)/g(x))*(f(x)-f(y))/(g(x)-g(y)).
Fix e > 0. Let x_n be a sequence in (a,infinity) such that x_n -> infinity. Fix N0 large enough so that f'(x_n)/g'(x_n) is in (L-e,L+e)Fix M > 0. Let x_n be a sequence in (a,infinity) such that x_n -> infinity. Fix N0 large enough so that f'(x_n)/g'(x_n) > MActually, I wrote the above reply kind of without concern of how it sounded.. because I doubt wonk was aiming his comment at me (though some of my remarks were kind of weak when taken to the extreme..)..
Since I'm not good at number theory (as of yet) I woud have also have trouble proving 937*234 = 219258 (on the spot, If it was a homework assignment, I could make some arguments).. In fact I am not expecting that in my future grad studies that I will ever be able to prove such arbitrary statements on the spot.. But I don't expect that was what the point was..
But to add to wonk's comments... There was a point in time (after I had already got the epsilon-delta experience) where I was considering switching from math into to engineering.. Ultimately I decided to pursue the math Phd.
After learning how to make simple epsilon-delta arguments, I would have been MUCH better at the math in engineering than without it, despite whether or not engineering(or physics?) students probably sense that you just need to remember a handful of formulas..
if you learn to ride a bike and cannot ride one afterwards, have you learned a lot?
It will give you the confidence to be able to try it again. And fail, and then learn again. I never really did understand this memorize this and that hype that surrounds the math community.
-- DISCLAIMER: IAM NOT A MATHEMATICIAN AND NEVER WILL BE --
However, I do find the question a bit off. Say you read a calculus proof, and its carried out with algebra. Just because you understand the algebraic operations it doesn't mean you know the analytic part - the important part. However, if you understand both and then just "forget" it, no harm done, you probably know it and will be able to use it without rabbling the theorem all over again. (who cares about people having to rabble theorems to be able to state a valid point anyways?)
I think just reading proofs has value. As long as you understand each step and don't desire to be an expert in that subject matter. If all you want to do is use the formula, then reading and understanding the proofs once is a good exercise so that you KNOW that the derivations are valid. An engineer doesn't need to understand in detail (or even can understand) every mathematical tool he uses, BUT he has to have gone through and understood the proofs some time in his career. | 677.169 | 1 |
Student's Solutions Manual for Elementary Algebra for College Students
Today's students are visual learners, and this text offers a visual presentation to help them succeed in math. Visual examples and diagrams are used to explain concepts and procedures. Short, clear sentences reinforce the presentation of each topic and help students overcome language barriers to learn math.
"synopsis" may belong to another edition of this title.
Product Description:
This manual contains completely worked-out solutions for all the odd-numbered exercises in the text. | 677.169 | 1 |
Functions and Inequalities Notes
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.77 MB | 83 pages
PRODUCT DESCRIPTION
~~These guided notes allow teacher and student to work together and also allows students time to work independently.
~~ Notes start with ICANS listed clearly so students know what they are expected to learn
~~ Students self reflect throughout the notes to make sure students and teacher know where each student feels they are
~~ Answer Key is included | 677.169 | 1 |
Helpful resources
Who will help me with my college algebra homework?
Mathematics is important in all technical fields and for general use living. Algebra is considered the entry to this wide of beautiful world of formulas and equations, and it is important to do well in the fundamentals so you can succeed in later courses. Even if you do not plan to go further in algebra in your academy career, it is still the base level of math you need to be able to understand information from other friends and deal with other aspects in day-to-day career applications. In addition, the path to mastery of math is practice, and most practice is done in the form of homework. However, sometimes homework is complicated, and there is little to be done except to seek help. Thankfully, there are many avenues to success when looking for help.
The first thing to look for is to use the resources available to you. Many colleges understand that you will need help with college algebra homework, so they have various ways for you to get the assistance you need. Most colleges offer some type of tutor program- simply sign up for an available slot. There are professors with office hours that are paid to make sure that you do well. There are libraries, resource centers, and so forth. These should all be your go to resources.
If time is a factor, or for any other reason traditional paths are closed to you, consider asking your fellow students. You should be prepared for this- within the first few classes get contact information for other students and be sure to keep in contact with them for when you need help. If you cannot figure it out, several minds are better than one. Do not be afraid to ask, especially with you grade on the line. Just be sure not to overuse this, because students do not appreciate doing someone else's homework for them, even if they are glad to explain things.
If none of this work out, then consider turning to the internet. If you really care about learning, try tutoring websites, even if you might have to pay a little bit, it is worth it if you understand the material. Various maths related forums would be glad to help you with homework, and often there are archive threads relevant for the information that you are looking for. Online there are also various powerful mathematical tools you can download to help you see the relationships between different functions and variables | 677.169 | 1 |
MATH1049 Linear Algebra II
Module Overview
Building on the intuitive understanding and calculation techniques from Linear Algebra I, this module introduces the concepts of vector spaces and linear maps in an abstract, axiomatic way. In particular, matrices are revisited as the representation of a linear map in a specific basis. We furthermore introduce the concept of bases of vector spaces and study diagonalisation of linear maps.
We apply the abstract theory both in the context of Rn (as seen in Linear Algebra I) and in the context of function spaces; these are particularly important in the study of linear differential equations and hence for instance in physical sciences; for example we look at the derivative operator on the space of polynomial functions.
Module Details
Semester:
Semester 2
CATS points:
15
ECTS points:
7.5
Level:
Level 4
Module Lead:
Jan Spakula
Aims and Objectives
Module Aims
This module aims to introduce the student to an abstract viewpoint on the concepts of linear algebra.
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
Explain the axiomatic structures of abstract linear algebra and apply them in simple proofs
Apply concepts and theorems from linear algebra to vector spaces other than Rn, in particular
function spaces
Find matrix representation of linear transformations on vectors spaces other than Rn.
Determine whether a linear transformation given by a matrix is diagonalisable.
Resources & Reading list
Robert Valenza (1993). Linear Algebra: An Introduction to Abstract Mathematics.
Any other book on Linear Algebra covering vector spaces other than R n can be used..
Assessment
Summative
Method
Percentage contribution
Class Test
10%
Coursework
20%
Exam
70%
Referral
Method
Percentage contribution
Exam
100%
Repeat Information
Repeat type: Internal & External
Linked modules
Prerequisites: MATH1048 and (MATH1AAA or MATH1006 or MATH1008)Course texts are provided by the library and there are no additional compulsory costs associated with
the module.
Please also ensure you read the section on additional costs in the University's Fees, Charges and Expenses Regulations in the University Calendar available at | 677.169 | 1 |
Each section begins with key vocabulary words that are important for students to understand. There are guided questions and steps that break each problem down. The presentation is color coded for students who need more of a visual in order to really understand | 677.169 | 1 |
An Introduction to Simplifying Trigonometric Expressions (and perhaps a preview of Trig Identities)
Note: This is a guest post written by one of my friends/colleagues Brendan Kinnell.
For a recent job-interview demo lesson, I was tasked with introducing simplifying trigonometric expressions and/or trig identities…my choice! And, geesh, that seemed like a LOT to tackle in less than an hour with students I've never met. Sooo, with some serious help from my colleague and an awesome activity from Shireen Dadmehr, I was able to cobble together a fairly solid introduction to simplifying trigonometric expressions with nod towards trig identities.
First, we opened with a nifty warm-up. I had four different problems on half sheets of paper to give out (one easyish algebra problem, one easyish trig equation, one tough polynomial equation, and one tough trig equation). Each student received one problem, and I didn't announce they were different. I tried to be sure that no two students near each other received the same problem. I told them they had 2 minutes to solve these. "Do the best you can on the Warm-up — this is just to see what you remember. There are a few problems on the back in case you finish early." (I didn't really care about the problems on the back, but just in case some students breezed through them, I wanted them to have more to do.) [Intro to Trig Identities Warm-up file]
A few kids with the easier ones solved them pretty quickly, but most other students with the tougher ones were writing frantically. After two minutes (I may have given three minutes in the end), I stopped everyone abruptly and revealed how not all the problems were the same. I made a *BIG* deal about how unfair it was that some people got really "much easier" problems to solve. Specifically, we focused on the polynomial equations. I had one student share a solution to the "easier" equation, and then I walked them through how you can solve the "more difficult" polynomial equation by recognizing a binomial expansion. In the end, the two equations are the same. The same? Yes. The same! "So, if you had to choose which problem you would solve, which one would you pick?" Hopefully, they all agree that the non-expanded form is preferable. But I didn't want to kick the expanded form to the curb — perhaps some students like the expanded version, and that's okay. But in the end, they are algebraically identical.
With a bubbling energy in the room, I didn't even bother to review the other trig-based warm-up questions. We went right to the next part of the lesson. Direct Instruction! Seriously.
I gave them all a little handout with same basic reciprocal trig identities and the basic pythagorean identity.
I had prepared about 10 different sheets of paper that had a new expression that was just a slightly altered form of the previous expression. I taped the first one to the board and then I wrote an equals sign next to it. I grabbed the next sheet and taped it alongside it. And then I wrote another equals sign. I had a third sheet ready to go with a bit more simplification. I taped it to the board, and wrote another equals sign. I briefly explained each step, but more often emphasized how at any point, I could use the expression on ANY of the cards to replace the original. It was my choice. Choice!
And finally…
Every now and then I would untape on of the later sheet and hold it up next to the original expression. "See? These are equal. They don't look anything alike, but they are fundamentally identical." Or move any two sheets next to each other. Doesn't matter. All equal.
Eventually, the original expression gets you to something really simple. I think here you can really play up the fact that it's surprising that this weird trig expression is essentially just sec x (I think).
So in the end, the kids had this sort of "train" of equivalent expressions, each implementing a slightly different sort of simplification technique. And then, the engaging part.
Finally, I used this brilliant matching activity ( where each group of students (groups of 3 worked really well) gets a bunch of these cards cut out and all jumbled up. (Although I think they are already jumbled if you want kids to cut them out for you!) Ask them to find two cards that "match". A match being any two cards that are equal by an obvious simplification technique. Students might start slow, but matches will emerge. Give them time.
And what is really cool about this activity is that students will start to recognize that not only are there pairs, but there are trios of matches…and sets of four(!). Students were super pumped to find more than just pairs. "We found a triple!" "We got a four!" They were finding three and four cards that formed a "train" of simplification like the giant one that was currently taped to the board.
In the end I ran out of time to finish the activity, so I didn't get to see it through. But I believe that Shireen has designed this so that there are four different "trains" of various lengths (up to six or eight cards in length for some of them, I believe. I suggest that you give students time to justify the order of each part of these "trains." And in the end, I would hope that they could appreciate that every step along the way reveals a new way to denote any other expression in that "train", and each of these new expressions is available for them to choose. | 677.169 | 1 |
Review lesson applies to the Common Core Standard:
High School: Algebra » Reasoning with Equations & Inequalities A.REI.3, A.REI.11
Solve equations and inequalities in one variable.
3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Represent and solve equations and inequalities graphically.
11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
High School: Algebra » Seeing Structure in Expressions A.SSE.1a, A.SSE.1b
Interpret the structure of expressions.
1. Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
High School: Functions » Building Functions F.BF.2, F.BF.3
Build a function that models a relationship between two quantities.
2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Build new functions from existing functions.
3. IdentAnalyze functions using different representations.
7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
High School: Functions » Linear, Quadratic, & Exponential Models F.LE.1a, F.LE.2
Construct and compare linear, quadratic, and exponential models and solve problems.
1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
High School: Number and Quantity » The Real Number System N.RN.1, N.RN.2
Extend the properties of exponents to rational exponents.
1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Curriculum Bundle? Coming Soon!For this item, the cost for one user (you) is $32.00.
If you plan to share this product with other teachers in your school, please add the number of additional users licenses that you need to purchase.
Each additional license costs only $16.00. | 677.169 | 1 |
Illustrations, a manual of geometry and postscript
by Bill CasselThis is a wonderful read...This book is highly recommended for a variety of readers. Authors of mathematics (and various related fields) might learn about how to build better illustrations. Students of mathematics might use the text to explore a variety of mathematical problems including the convex hull, triangulation, three-dimensional projections and more (indeed the author notes that the book has been used as a text in an undergraduate geometry class). Programming students might use it as a springboard to learn an underused (and perhaps underappreciated) programming language, as well as some basics of geometry. Even casual readers might learn more than a bit of programming, geometry and how to use illustrations to illuminate...This book will take a permanent place on my bookshelf and I will surely recommend it highly to anyone interested in geometry, mathematics, and illustrations as well as those who appreciate a good mathematical read." Computing Reviews
"The geometry that best illustrates vector-graphic drawing methods is the subject of Casselman's book... I recommend it to all who are professionally or even casually interested in mathematical illustration... To read this text profitably requires, in addition to paper and pencil, a computer running a PostScript interpreter... Still, for lazy or computerphobic readers there remains close to a third of the book that is superb geometry. These passages can be enjoyed without even a glance at PostScript... Today most images end up in PostScript on the way to the printer, regardless of their origins. Sometimes it becomes necessary to open the arcane code in a text editor and modify PostScript by hand. Even if you will never need to go this far, Casselman's book teaches you to appreciate the marvels of PostScript and of the geometry ideas relevant to this curious computer language." American Scientist
"...this manual is a rich and educational guide to applying geometry and getting the most out of PostScript." MAA Reviews
"Casselman is a mathematician interested in graphics and the book will appeal as much to mathematicians as it will appeal to programmers. Casselman's book certainly does its best to address the two topics of geometry and PostScript, and in this respect it is excellent." Notices of the AMS
Book Description Code for many of the illustrations is included, and can be downloaded from the book's web site: scientists, engineers, and even graphic designers seeking help in creating technical illustrations need look no further.
About the Author
Bill Casselman holds a doctorate from Princeton University for his work on automorphic forms. He is currently Professor of Mathematics at the University of British Columbia. Additionally, he is the technical editor of the online collected works of Robert Langlands and the Graphics Editor of NOTICES of the American Mathematical Society.
Comments
iwant to commend your effort so far on the books particularly some of your books that i saw on the internet when i'm on network which has really helped me through. please continue.
Peter, Ibadan, Oye State Nigeria., 2008-02-25 19:18:10 | 677.169 | 1 |
Description:
The University of Akron has created these excellent algebra tutorials that review some of the main topics in the discipline. There are ten lessons, which focus on topics like radicals and exponents, basic algebra, expansion, polynomials, functions, and trig curves. Each lesson has a table of contents and interactive resources like quizzes, in-line examples, and exercises. Words that appear in green or brown are hyperlinks; click on them to learn more about that topic. Tutorials are viewed as a PDF file, and users must have Acrobat Reader 3.0 or greater to access them. This is a perfect resource for anyone who needs to refresh their knowledge of basic algebra concepts, and is also great for those who are just learning about the subject. | 677.169 | 1 |
10th grade accounting tutorials,
Cost accounting- free guide,
help on enrichment and answers for test of genius,
Free worksheet on teaching year six maths.,
polynomials cubed,
how to count numbers divisible by 3 in java using for loop,
factoring two-variable.
How do we learn and understand algebra?,
mcdougal math having fun with the coordinate plane,
linear programing using a caculator,
rational expressions(addition)example,
c: fraction to decimal,
free integer worksheets.
Teach me college algebra 1,
summer practice worksheets for 6th graders,
trivias of algebra,
order and factoring a four-term polynomial,
practices on algebraic expressions using long division and synthetic division.
Mathematical solutions in algebra/multiple choice,
how to use TI 30X IIS calculator for order of operations,
how to show trig graphs on t1-83,
practices on special products (algebra),
boolean algebra help,
formulas fractions,
nth term online calculator.
Root method to solve polynomials,
softmath,
solving systems polynomial equations,
how to solve first order linear differential equations with the ti 89,
if your subtracting decimals, are two negatives a positive?,
college algebra poems.
Algebrator 4.0 instructions,
using graphing calculate find slope,
Find the sum of integers divisible by 3,
download free a handbook of cost accounting by indian authors,
explanation of simultaneous equations on the ti-89 calculator,
How to find a equation on T1-83,
solve simultaneous quadratic equations MATLAB.
Nonlinear differential substitution,
trivia about math mathematics algebra,
abstract algebra problems to solve,
how to program a graphing calculator to solve three equations with three variables,
software to solve logarithms.
Can the radical 30 be simplified in algebra,
large number maths multiply without computer,
Sample Prep High School Entrance Exams,
HELP WITH EVALUATING STANDARD FORM OF LINEAR EQUATIONS,
printable math activities for 3rd grade algebra,
compound interest factors ti 89,
use free online algebra calculator.
Best apptitude book,
How to teach addition and subtraction of algebraic expressions to high school students,
ti 83 quadratic ecuation.
Examples of math poem mathematics,
aptitude questions with solutions,
free books on accountancy,
newton method to find the root of a polynomial in c++,
I need a free online Algebra solver that will show me step by step how to slove an equation.
Add radicals calculator,
pretest for pre algebra,
Aptitude questions for GMAT,
solving polynomials using a TI84,
solutions of excel assignments for solving algebraic equations,
how to find the value of x in a graphing calculator.
Solving trinomials without common terms,
group terms when factoring a four term polynomial,
"application of logarithmic function,
simple steps to calculate percentage problems,
algebra answer machines,
boolean simplifier.
First in math cheats,
least common denominator calculator,
formula for solving cubed,
algebrator helper,
applications of trigonometry in daily life,
worksheets on real life application of sequences and series.
Games on factoring quadratic equations,
sample lesson plan of LCM for elementary,
download free ebook Advanced Financial analysis and Valuation,
how to write an equation if you have the zeros of the function?.
How to factor cubed polynomials,
literature connections to algebra,
trace on graphing calculator,
calculare radical,
in math how do you add a negative fraction and a positive fraction together,
7th grade math adding and subtracting fractions free.
Math worksheets combining terms,
subtracting mixed numbers w/different denominators,
What are some examples from real life in which you might use polynomial division?,
paid algebra homework answers,
i factor ode matlab.
Formula for +foiling a cube,
ti 84 vocab games,
2nd order differential equation into system of first order initial conditions,
gcse bitesize compound interest,
+simultaneous equations on the ti-89 calculator,
solving an equation with multiple variables.
Least Common Denominator calculator,
math worksheets for 5th graders that is about decimals and is printable and free,
variable in the exponent,
Quiz yourself in algebra,
Equations Linear – simultaneous linear equations up to three variables, quadratic and cubic equations in one.
Two terms with exactly the same variables and exponents,
equalities algebra excercises,
radicals in linears equations,
"analysis with an introduction to proof"/ solution,
general aptitude questions,
convert number to radical,
calculator simplify indefinate integral.
Adding, subtracting, multiplying and divding fractions and negative numbers,
how to solve fractional exponents on a TI-83,
rules for adding and subtracting even and odd integers,
quadratic equation solver find the constant term,
calulator for rational,
source code how to print sum of 10 numbers in java.
Multiply two graphs in matlab,
conversion of ellipse to standard form using vb download,
first grade equation solving.
Free rounding decimals calculator,
free factor tree worksheets,
solving domain of an expression,
how to find intersection on TI-83 calculator,
where can we use factorization in our real life?,
free manual solutions for prentice-hall.
Activities to teach algebraic variables,
can quadratic equations have irrational numbers,
Answers to the Prentice Hall Intermediate Algebra Third Edition Chapter 2 Review,
can we divide a variable with a number?,
Solve The System Of Equationsusing The Addition Method If The,
lesson plans Add and subtraction integers,
how to solve nonhomogeneous linear differential equations.
Math rearranging formulae past paper,
Algebra 2 solution,
what is the importance of algebra?,
eighth grade algebra practice problem,
english work sheet for nine year olds,
HOW TO DO SEVENTH GRADE ALGEBRA.
Square roots without calculator by common factors,
best pre algebra software,
Grade 7 Power Worksheet Mathematics free,
how to solve simultaneous equations polynomials,
finding the lowest common denominator.
Algebra homework calculator for single linear equations,
college algebra use a graph to solve each inequality.,
ti 84 programs for equalities,
solve the formula for the specified variable helper,
partials differences method method 5th grade,
how to do fraction sums.
Permutations gmat formula,
math word problems about age with solutions,
How do I do a partial sum method equation?,
how to solve algebraic fractions,
quadratic equation examples w/ answers,
college algebra for dummy's online,
algeba solver.
How to use scientific notation on ti 83 plus,
negative numbers worksheets,
age problem in college algebra,
free worksheet primary school,
instructions on how to solve multi-step equations in 9th grade algebra.
Free study material and solved test paper on fourier series introduction in pdf,
test equtions first degree,
quadratic equation in real life.
9online graphing calc,
greatest common of 10,
elementry algerba,
Adding And Subtracting Integers Worksheet,
how to convert a mix fraction to a decimal,
scale factor of porportions,
program to solve second order polynomial equation simultaneously.
Square of the integer, the cube of the integer, the inverse x1, and the square root of the integer+simplified java code,
pizzazz worksheet,
percentage equations,
how to solve equations with variables and fractions,
permutation and combination programming,
saxon algebra video tutorials.
Search Engine users found us today by entering these math terms:
T1-83 plus user guide
matlab solving simultaneous equations
ti-83 plus finding domain
past sixth form exam worksheets
objectives, linear algebra, lay
grammer worksheets
Algebra cubes
code in java to determine whether an integer is prime or not
vb6 calculating permutations
inequalities union and intersection definitions
chapter 6 the chemistry of life worksheet answers
math trivia for grade 4
mixed fraction to decimal
"geometry book" an investor approach
absolute value second degree
Graph parabola calculator
practice test Ks2 online math
factoring using a calculator
solving third polynomial equations
How to solve radicles without a calculater
example of a rational expressions equivalent
maple + solve fraction exponent
gelosia multiplication demo
online free calculator for adding and subtracting integers
ti-83 plus graphing calculator-method of least squares
square maths worksheets
how to solve tricky problem on excel manually
solving nonlinear simultaneous equations in matlab
"artin" + "algebra" + "answers"
algebra with pizzazz answers worksheets
free ebooks about Advanced accounting in Pdf format
example of how algebra is used today
use free online graphing calculator ti 83
5th grade Worksheets on interpreting graphs
how to work equations into percentages
free leson online algebra 1 book tool for a changing world
rudin solutions manual
example activities trigonometry word problems
Free Online Math Problem Solvers
solve simultaneous equation 3 unknowns
solving multi variable integrals
equations using the substitution method
free 4th grade probability worksheets
fastest way to find common denominator on a calculator
quadratic factoring calculator
absolute value piecewise function
printable free sixth grade math worksheets
algebric calculator online
DECIMAL LEAST TO GREATEST
In a word sentence how to solve for QUADRATIC FUNCTIONS
ALGEBRATOR free
subtracting integers game
factorising algebra online answers
fraction powers
algebra math games ks2
Free Grade 12 Math Questions
free statistics worksheet
solving quadratics ti89
converting square roots into fractions
scale of graphs and elementary math and printable
rational expressions
samples of math investigatory projects
10 grade algebra test
When solving a rational equation, why is it necessary to perform a check
subtracting complex rational expressions
factionmath
math investigatory
how to find an exponent variable
combination and permutation gre practice problems
equations for fifth grader
simplifying absolute value fractions
USING TI-84
"algebra 2 resource book"+mcdougal
simplify square roots x
download Graphical Approach to College Algebra, A (4th Edition) (Hornsby/Lial/Rockswold | 677.169 | 1 |
Tag Archives: teaching function
Most Grade 10 syllabus do not yet include the concept and calculation of derivative. At this level, the study of function which started in Year 7 and Year 8 on linear function is simply extended to investigating other function classes such as polynomial function to which linear and quadratics belong, the exponential function and its… Read More »
In solving generalization problems that involve figures and diagrams, I have always found working with the figures—constructing and deconstructing them—to generate the formula more interesting than working with the sequence of numbers directly that is, making a table of values and apply some technique to find the formula. Here's a sample problem involving counting hexagons.… Read More »… Read More »
One of the most difficult items for the Philippine sample in the Trends and Issues in Science and Mathematics Education Study (TIMSS) for Advanced Mathematics and Science students conducted in 2008, is about comparing the slopes of the tangent at a point on a curve. The question is constructed so that it assesses not only… Read More » | 677.169 | 1 |
Course Notes:
This course is for students who need a transferable math course or a course to prepare for Calculus. Please see me or a counselor for more information about the prerequisites for Calculus and how Math 175 helps to meet those requirements.
Course Notes:
Welcome to Learning Mathematics!
I love teaching math and helping students see the value in achieving a strong foundation in mathematical knowledge and skills. By improving your math abilities, you become more hirable, less likely to be swindled, and better able to navigate the challenges in our society. I believe that everyone can learn math, and I'm here to help you.
My Background
BA, Mathematics, San Diego State University MA, Applied Mathematics, UC San Diego | 677.169 | 1 |
Browse by
From the Publisher
This eBook introduces the subject of algebra to the student encompassing, inverse operators, equations, the order of precedence, algebraic conventions, BODMAS, expressions, formulae, factorising, rearranging and solving linear, quadratic and simultaneous equations as well as inequalities.
This eBook is part of our range of Key Stage 3 (KS3) maths eBooks that are fully aligned with the UK Governments national curriculum.
Our maths eBooks are produced such as that as well as a Publications Guide, and three principle publications corresponding to the principle sections (Number and Algebra, Geometry and Measures and Handling Data) there are individual modules produced within each principle section which are published as eBooks.
Algebra is a module within the Number and Algebra principle section our Key Stage 3 (KS3) publications. It is one module out of a total of seven modules in that principle section, the others being: •Factors, Prime Numbers and Directed Numbers •Fractions, Percentages and Ratio •Decimal •Indices and Standard Index Form •Number Patterns and Sequences •Graphs | 677.169 | 1 |
View a Recorded Webinar
Maple Training for Engineers, Researchers and Scientists
Maple Training for Engineers, Researchers and Scientists
This webinar offers a quick and easy way to learn some of the fundamental concepts for using Maple. Learn the basic steps on how to compose, plot and solve various types of mathematical problems. This webinar also demonstrates how to create professional looking documents using Maple, as well as the basic steps for using Maple packages.
During the session we'll explore some of the new tools and resources available in Maple 2016. Maple 2016 contains new features that support all aspects of your work, including tools for the thermophysical properties of fluids, a data structure for heterogeneous data, and a file container format for Maple-based analysis projects. | 677.169 | 1 |
Math Power is a site created by Professor Freedman, a highly acclaimed teacher of basic mathematics. She has several resources to help students of all ages learn pre-algebra and elementary algebra skills. Many sample...
A paper motivated by Polya's book How to Solve It, which presents material mindful of students who may believe they have "Math Anxiety." The unit reviews the solutions of word problems starting with the concept of a...
Brought to you by Elizabeth Stapel and purplemath.com, this collection of learning modules contains over 100 mathematics modules designed to teach beginning, intermediate, and advanced algebra concepts. Some algebra...
Understanding Algebra is a textbook written by James Brennan of Boise State University. The entire contents of the textbook are located on this site, and a PDF version is also available through the author's Website....
A problem (with solution) sent by Prof. W. McWorter's: Byzantine Basketball is like regular basketball except that foul shots are worth a points instead of two points and field shots are worth b points instead of three... | 677.169 | 1 |
For homework assignments for Chapter L, see: 1-9,
11-12, 15-19, 29-37, 46-52; please also look at 53-60, since we'll talk
about them in class.Also do the four
problems on Knights and Knaves at the end of Chapter L.
On the Homework Page, the
problems of 5.3, except for problem 1 are of interest—they are on Knights
and Knaves—and the problems of 5.6, except for problem 5, are good logic
problems.The problems of 4.8 give you
some work on Euler circuits, and some of 5.4 and 5.5 can be of help in logic,
although some of the terminology is different.
All email correspondence must include your full
name and student number as well as professor's name and/or section number. Any email which does not include all of this
information will NOT be answered.
Textbook: For All
Practical Purposes by COMAP—FAU custom edition of the Seventh
Edition, published by Freeman Custom Publishing Online study tools for the textbook: `
Course Outline
Mathematics for Liberal Arts I is the first of two
courses offered at FAU aimed at the liberal arts major. Students passing both
courses of Mathematics for Liberal Arts will have satisfied the mathematics part
of the Gordon rule, which requires students to complete successfully, with
grades of "C" or higher, 6 credits hours of mathematics ... in
courses at or above the level of College Algebra.We do not assume mathematical
sophistication or calculational facility on the part
of the students. We do assume that students will attend ALL lectures,
read the text, complete the homework assignments and quizzes, and study for the
exams. While some students may find the pace of the course rather leisurely, it
is dangerous to allow oneself to fall behind. Homework
assignments and quizzes using Blackboard as well as some supplementary material
will be available online. Students will be required to spend several hours per
week on a computer with internet access either at home or in campus computer
labs. A general rule of thumb is that a student should spend at least two hours studying for a
course outside of class for every hour in class. The amount of time must be
increased when you miss class.
This course is NOT a remedial mathematics course. This is a serious course
in college-level mathematics at approximately the same difficulty level as
College Algebra, but with an emphasis on topics involving logical and
mathematical reasoning rather than manipulation of algebraic formulas. Students
who do not have prerequisite mathematics at the level of Intermediate Algebra
may be at a serious disadvantage in this course and are advised to take such a
prerequisite course before taking MGF 1106 and/or MGF 1107.
Homework and Quizzes
There will be homework assignments for each section covered. These homework
assignments and some solutions are posted on theHomework Page.
There will be at least one quiz per week (sometimes two in a week)
administered online using a web-based program called Blackboard.These quizzes do not count toward the final
grade, but students have found them valuable drill.
Exams
There will be four exams, counting equally toward the final grade. The
scheduled exam dates are in bold face in the above table.
Also during the final exam period, students will have the option of taking
an additional exam over material in Chapters P, 5-11, 18-20 which will
replace the lowest grade from Exams 1-3.
A PHOTO ID WILL BE REQUIRED TO TAKE AN EXAM
Make-up or early exams will be given only under
very exceptional circumstances, and written, verifiable reasons must be
provided.
No make-up will be given under any circumstances
if the professor is not contacted by phone or email within no more than 24
hours from the starting time of the exam.
Grading Scale
A: 90% - 100%
B: 80% - 82%
C: 65% - 72%
A-: 87% - 89%
B-: 77% - 79%
D: 60% - 64%
B+: 83% - 86%
C+: 73% - 76%
D-: 55% - 59%
The grade of I (incomplete) will only be given
under the conditions specified in the FAU Undergraduate Catalog.
Classroom Etiquette
Due to the size of the class, it is necessary that all students remain
quiet during lectures.
TURN OFF ALL CELL PHONES AND PAGERS WHILE IN
CLASS.
This is a university policy; violations are
punishable by removal from the class.
THANK YOU.
DEMERITS for Disrupting Class
A student who leaves class before the end
of instruction without permission or disrupts class while arriving late will be
given a demerit.
Students accumulating 4 demerits will have
their grades lowered by one letter grade. | 677.169 | 1 |
History of Mathematics Burton covers the history behind the topics typically covered in an undergraduate maths curriculum or in elementary or high schools. He illuminates the people, stories, and social context behind mathematics' greatest historical advances, whileMore...
David Burton covers the history behind the topics typically covered in an undergraduate maths curriculum or in elementary or high schools. He illuminates the people, stories, and social context behind mathematics' greatest historical advances, while maintaining appropriate focus on the mathematical concepts themselves | 677.169 | 1 |
This is a lesson to teach magnitude in the topic of vectors. It is the first of a three part series to teach vectors and is available as a bundle at a reduced rate.The lesson comes with a starter, lesson objectives, key words, teaching slides, questions with answers and plenary.NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thanks.
This is a lesson to teach using vectors in more complex geometric problems. It includes the use of midpoints and in particular the use of ratio in vectors. It is the LAST of a three part series to teach vectors and is available as a bundle at a reduced rate.The lesson comes with a starter, lesson objectives, key words, teaching slides, exam questions with answers and basic plenary.NOTE: Feel free to browse my shop for more excellent free and premium resources and if you do purchase then please rate and feedback as it is really helpful, thanks.
This is a lesson to teach the basic of vectors in geometry. It is the second of a three part series to teach vectors and is available as a bundle at a reduced rate.The lesson comes with a starter, lesson objectives, key words, teaching slides, a worksheet with answers and a plenary.NOTE: Feel free to browse my shop for more excellent free and premium resources and if you do purchase then please rate and feedback as it is really helpful, thanks.
This resource is suitable for 'A,' level students and provides a comprehensive explantion of the topic of 'Vector Cross Product.' In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance)
This is a valuable resource for 'A,' level students. The lesson outlines, 'in three-dimensional space, the dot product contrasts with the cross product of two vectors, which produces a pseudovector as the result.' The dot product is directly related to the cosine of the angle between two vectors in Euclidean space of any number of dimensions
Here is my power point trying to structure questions for M1 from past papers. I have split the paper into 6 sections and tried to group questions together. For use by giving to pupils and leaving them to it, or working through topics as a class. Every question from 2006-present. Also works extremely well on iPads.
The lesson is intended for 'A,' level students and is intended to assist the students with the understanding of the vector cross product. In mathematics and vector calculus, the cross product or vector product It has many applications in mathematics.
Power Point presentation, 10 slides, Explaining how to use the scalar product to determine whether two vectors are perpendicular, parallel or neither, and find the angle between two vectors, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser:
Power Point presentation, 7 slides, Explaining how to identify position vectors, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser:
Power Point presentation, 8 slides, Explaining how to add and subtract vectors, represent graphically the addition and subtraction of vectors, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser:
Power Point presentation, 7 slides, Explaining how to find the vector equation of a line passing through two points, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser:
Power Point presentation, 7 slides, Explaining how to use vector addition, subtraction and scalar multiples to deduce some geometrical results, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser:
Power Point presentation, 4 slides, Explaining how to calculate the distance between two points in the space, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser:
Power Point presentation, 14 slides, Explaining how to use the correct notation of vectors, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser:
Power Point presentation, 6 slides, Explaining how to identify unit vectors, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser:
Designed for senior physics this presentation outlines the difference between vectors and scalars. The addition, subtraction and multiplication of vectors. Additionally the use of geometry to resolve components of vectors is also included with examples employed to test understanding.
Linked to the defining vectors activity, using the vectors defined in the image to prove standard results like ratios of line segments, whether points lie on straight lines, etc. For extra challenge take out the image with the pre-defined vectors and add the image from my vector definition activity so that pupils have to define the vectors before using them. Answers can be found on the prezi at link
Adapted from an image in Back to Back activities, 2 vectors are defined as a and b and the activity asks how many further vectors can be defined in terms of a and b. The image gives all of the other lines defined as vectors in terms of a and b.
A powerpoint-activity to learn and revise about vectors.There's been a robbery! Can you help Inspector Vector solve the crime by collecting clues? This is a fun activity for groups that includes:- adding and subtracting 2D and 3D vectors- finding the magnitude of 2D and 3D vectors- adding and subtracting vectors like a and b- some practice with surds for magnitude of vectors- visualizing vectors in 3D- using some logic to solve the crimeSolutions to each clue included in the Power Point notes.Takes a very good class about 1 hour 30 minutes. | 677.169 | 1 |
Similar presentations
2A Production Problem Weekly supply of raw materials: Products: 8 Small Bricks6 Large BricksProducts:Slides 2.32–2.47 are based upon a lecture introducing the basic concepts of linear programming and the Solver to first-year MBA students at the University of Washington (as taught by one of the authors).The lecture is largely based upon a production problem using lego building blocks. This example is based upon an example introduced in an OR/MS Today article.To start the example, students are given a set of legos (8 small bricks and 6 large bricks)—one set per two students works pretty well. These are their "raw materials". They are then to produce tables and chairs out of these legos (see the diagram on the slide). These are their "products". Each table generates $20 profit and each chair generates $15 profit. Their goal is to use their limited resources (the bricks) to make products (tables and chairs) so as to make as much profit as possible.After some experimentation, the students discover the optimal solution. This then leads into discussing and illustrating how formulating a mathematical model (or, more specifically, a linear programming model) can enable finding this optimal solution.TableProfit = $20 / TableChairProfit = $15 / Chair
3Linear ProgrammingLinear programming uses a mathematical model to find the best allocation of scarce resources to various activities so as to maximize profit or minimize cost.Let T = Number of tables to produce C = Number of chairs to produce Maximize Profit = ($20)T + ($15)C subject to 2T + C ≤ 6 large bricks 2T + 2C ≤ 8 small bricks and T ≥ 0, C ≥ 0.In the class at UW, the model is not shown to the students. Instead, it is built interactively (e.g., using an overhead or the blackboard), step by step. Then, the complete model is shown.
4Figure 2.1 The initial spreadsheet for the Wyndor problem after transferring the data into data cells.
567 ≤ Quantity B, put these three items (Quantity A, ≤, Quantity B) in consecutive cells.Note the use of relative and absolute addressing to make it easy to copy formulas in column E.
8Defining the Target Cell Choose the "Solver" from the Tools menu.Select the cell you wish to optimize in the "Set Target Cell" window.Choose "Max" or "Min" depending on whether you want to maximize or minimize the target cell.
9Identifying the Changing Cells Enter all the changing cells in the "By Changing Cells" window.You may either drag the cursor across the cells or type the addresses.If there are multiple sets of changing cells, separate them by typing a comma.
10Adding ConstraintsTo begin entering constraints, click the "Add" button to the right of the constraints window.Fill in the entries in the resulting Add Constraint dialogue box.
11
12The SolutionAfter clicking "Solve", you will receive one of four messages:"Solver found a solution. All constraints and optimality conditions are satisfied.""Set cell values did not converge.""Solver could not find a feasible solution.""Conditions for Assume Linear Model are not satisfied."
14Wyndor Glass Co. Product Mix Problem Wyndor has developed the following new products:An 8-foot glass door with aluminum framing.A 4-foot by 6-foot double-hung, wood-framed window.The company has three plantsPlant 1 produces aluminum frames and hardware.Plant 2 produces wood frames.Plant 3 produces glass and assembles the windows and doors.Questions:Should they go ahead with launching these two new products?If so, what should be the product mix?
16
171819 <= Quantity B, put these three items (Quantity A, <=, Quantity B) in consecutive cells.Figure 2.2 The complete spreadsheet for the Wyndor problem with an initial trial solution (both production rates equal to 1) entered into the changing cells (C12 and D12).
20A Trial SolutionFigure 2.4 The spreadsheet for the Wyndor problem with a new trial solution entered into the changing cells Units Produced (C12:D12).The spreadsheet for the Wyndor problem with a trial solution (4 doors and 3 windows) entered into the changing cells.
21Identifying the Target Cell and Changing Cells Choose the "Solver" from the Tools menu.Select the cell you wish to optimize in the "Set Target Cell" window.Choose "Max" or "Min" depending on whether you want to maximize or minimize the target cell.Enter all the changing cells in the "By Changing Cells" window.Figure 2.8 The Solver dialogue box after specifying which cells in the spreadsheet are the target cell and the changing cells, plus indicating that the target cell is to be maximized.
22Adding ConstraintsTo begin entering constraints, click the "Add" button to the right of the constraints window.Fill in the entries in the resulting Add Constraint dialogue box.Figure 2.9 The Add Constraint dialogue box after specifying that cells E7, E8, and E9 (HoursUsed) in the spreadsheet are required to be less than or equal to cells G7, G8, and G9 (HoursAvailable), respectively.
23The Complete Solver Dialogue Box Figure The Solver dialogue box after specifying the entire model in terms of the spreadsheet.
24Figure The Solver Options dialogue box after checking the Assume Linear Model and Assume Non-Negative options to indicate that we wish to solve a linear programming model that has nonnegativity constraints.
27Summary of the Graphical Method Draw the constraint boundary line for each constraint. Use the origin (or any point not on the line) to determine which side of the line is permitted by the constraint.Find the feasible region by determining where all constraints are satisfied simultaneously.Determine the slope of one objective function line. All other objective function lines will have the same slope.Move a straight edge with this slope through the feasible region in the direction of improving values of the objective function. Stop at the last instant that the straight edge still passes through a point in the feasible region. This line given by the straight edge is the optimal objective function line.A feasible point on the optimal objective function line is an optimal solution.
28Graph Showing Constraints: D ≥ 0 and W ≥ 0 Graph showing that the constraints D ≥ 0 and W ≥ 0 rule out solutions for the Wyndor Glass Co. product-mix problem that are to the left of the vertical axis or under the horizontal axis.
29Nonnegative Solutions Permitted by D ≤ 4 Graph showing that the nonnegative solutions permitted by the constraint D ≤ 4 lie between the vertical axis and the line where D = 4.
30Nonnegative Solutions Permitted by 2W ≤ 12 Graph showing that the nonnegative solutions permitted by the constraint 2W ≤ 12 must lie between the horizontal axis and the constraint boundary line whose equation is 2W = 12.
31Boundary Line for Constraint 3D + 2W ≤ 18 Graph showing that the boundary line for the constraint 3D + 2W ≤ 18 intercepts the horizontal axis at D = 6 and intercepts the vertical axis at W = 9.
34Graph of Feasible Region Figure 2.6 Graph showing how the feasible region is formed by the constraint boundary lines, where the arrows indicate which side of each line is permitted by the corresponding constraint.
35Objective Function (P = 1,500) Graph showing the line containing all the points (D, W) that give a value P = 1,500 for the objective function.
36Finding the Optimal Solution Figure 2.7 Graph showing three objective function lines for the Wyndor Glass Co. product-mix problem, where the top one passes through the optimal solution.
37The Profit & Gambit Co.Management has decided to undertake a major advertising campaign that will focus on the following three key products:A spray prewash stain remover.A liquid laundry detergent.A powder laundry detergent.The campaign will use both television and print mediaThe general goal is to increase sales of these products.Management has set the following goals for the campaign:Sales of the stain remover should increase by at least 3%.Sales of the liquid detergent should increase by at least 18%.Sales of the powder detergent should increase by at least 4%.Question: how much should they advertise in each medium to meet the sales goals at a minimum total cost?
40Applying the Graphical Method Graph showing the feasible region for the Profit & Gambit Co. advertising-mix problem, where the ≥ functional constraints have moved this region up and away from the origin.
41The Optimal SolutionGraph showing two objective function lines for the Profit & Gambit Co. advertising-mix problem, where the bottom one passes through the optimal solution.
42Components of a Linear Program Data CellsChanging Cells ("Decision Variables")Target Cell ("Objective Function")ConstraintsData CellsParameters of the problem (e.g. profit/unit)Changing Cells ("Decision Variables")The decisions to be made (level of an activity)Ex: $ to spend, # to produce, # of peopleA separate cell should be assigned for each number neededTarget Cell ("Objective Function")Usually maximize profit or minimize costMust be an equation in a single cell(If there are multiple objectives, can use goal programming)ConstraintsLimited resources (Ex: $, raw materials, time, people)Requirements to be met (Ex: staffing needs)Lay out in 3 consecutive cells: LHS (≤, =, ≥) RHSLHS is typically an equation (e.g., resource used)RHS is typically a number (e.g., amount of resource)
43Four Assumptions of Linear Programming LinearityDivisibilityCertaintyNonnegativityLinearityAll equations must be linear (e.g., 1x + 2y + 3z, or SUM, or SUMPRODUCT)Implications: no economies of scale, each unit contributes equally to profitIf not: nonlinear programmingDivisibilityFractions must be okay (optimal solution may be fractional)Okay if production rate, or if rounding reasonableIf not: integer programmingCertaintyAll parameters known and certainSolution is only optimal with respect to model givenIf not: use expected value, sensitivity analysis, decision analysis, simulationNonnegativityAll variables nonnegative
44Why Use Linear Programming? Linear programs are easy (efficient) to solveThe best (optimal) solution is guaranteed to be found (if it exists)Useful sensitivity analysis information is generatedMany problems are essentially linearWith all of the restrictions, why bother with LP?Linear programs are easy (efficient) to solveSimplex method developed by George Dantzig (1947)Problems with thousands of variables or constraints routinely solvedNonlinear and integer programs much more limitedThe best (optimal) solution is guaranteed to be found (if it exists)NLP might get stuck at a local optima (at this point, an example can be shown on an overhead or the blackboard)Useful sensitivity analysis information is generatedWhat if we could get more large bricks? How much would that be worth?What if the profit/table is lower/higher?This information is only available with linear programmingMany problems are essentially linearCan approximate and iterate if necessary
45Properties of Linear Programming Solutions An optimal solution must lie on the boundary of the feasible region.There are exactly four possible outcomes of linear programming:A unique optimal solution is found.An infinite number of optimal solutions exist.No feasible solutions exist.The objective function is unbounded (there is no optimal solution).If an LP model has one optimal solution, it must be at a corner point.If an LP model has many optimal solutions, at least two of these optimal solutions are at corner points.Examples #1-#3 were examples with one unique optimal solution.Example #4 will look a case where an infinite number of solutions exist.Example #5 will look at a case where no feasible solutions exist.Example #6 will look at a case with an unbounded objective function.The last two bullet points are the key to the simplex method. Because of these two points, the simplex method need only consider the corner points of the feasible region. | 677.169 | 1 |
MATH 24: Linear Algebra & Differential Eqs - Discussion Section 8
Spring 2016
Vector spaces
1. Write down the definition of a vector space.
2. Prove that the following are vector spaces. (Note: You do not need to prove results known
from basic algebra but
Math 24 Final Exam: 123pm, May 12, 2006
Instructor: Boaz Ilan
READ ALL THE INSTRUCTIONS!
1. Write your name on the front of your bluebook as well as in the space below.
YOUR NAME:
2. This exam is closed-book and no calculators are allowed. You are allowed
COMPLEX NUMBERS
Introduction:
A real number a can be graphically displayed as a point on a real number line
-1
0
1
a
Imaginary axis
Similarly, we can display a complex number a + i b as a point in a complex plane
a+ib
b
r
a
Real axis
Instead of using Cart
MATH 24: Linear Algebra & Differential Eqns - Discussion Section 1
Spring 2016
Differentiation & Integration Review
(1) Calculate the first nonzero term in a Taylor Series expansion for x3 about x = 0. What can you
say about other nonzero terms in the exp
Math 24,
Midterm Exam 2 Solutions,
March 29, 2016
ON THE FRONT OF YOUR GREEN/BLUEBOOK WRITE: YOUR NAME AND A FOUR-PROBLEM
GRADING GRID. Show ALL of your work and box in your final answers. Unless otherwise mentioned, an answer without the relevant work wi
MATH 24: Linear Algebra & Differential Eqns - Discussion Section 6
Spring 2016
Nonlinear Models
1. Draw the phase line (not the full graph) for the following equation, and use it to determine
the behavior of the system:
dy
= y + y2
dt
2. For the following
MATH 24: Linear Algebra & Differential Eqns - Discussion Section 7
Spring 2016
Conceptual review questions
1. What is a solution of a first-order differential equation? How do you verify such a solution?
2. What is a solution of a first-order initial valu
J.G. Pieters, G.G.J. Neukermans, M.B.A. Colanbeen, Farm-scale Membrane Filtration
of Sow Slurry, Journal of Agricultural Engineering, No. 73, 403-409, 1999.
One way to assess the uses of membrane filtration is to test it against the most complex and
chall
Writing 116: Writing in the Natural Sciences
Habecker/ Spring 2017
Technical Explanation for a Lay Audience (TELA)
Topic:
Select a relatively current scientific topic that interests you; topics can be found in original research
articles, in the news, in p
MATH 24: Linear Algebra & Differential Eqns - Discussion Section 5
Spring 2016
Growth & Decay
1. A 25 year old individual gets a job and begins earning $50,000 per year but has expenses of
$40,000 a year. She puts all her remaining money after expenses in | 677.169 | 1 |
Category Archives: Math
Overview: What Are Random Numbers? In a set of random numbers, the numbers do not follow any pattern. Each number has an equal probability of occurring, and each number event is independent of any others . Most of the time, numbers that are close to random are generated by computer programs or calculator programs designed […]
Overview: What Are Measures of Central Tendency? Measures of central tendency represent the most typical score or value in a group of scores on some measure in either a population or a sample of that population. Along with measures of variability, they convey much information about a distribution. The three most common measurements are the […]
Overview: What Is Solid Geometry? Solid geometry was developed after plane geometry as a way to describe the three-dimensional world and the objects in it. In the ideal three-dimensional world, objects exist with faces and angles, depth and volume. Objects are regular, or consist of a combination of regular objects, just as two-dimensional figures can […]
Overview: What Are Functions? Functions in mathematics describe two different types of relationships between numbers. The simplest definitions are that a function can be either the set of ordered pairs in which the first element is paired with a second element or the relationship between two sets of elements in which every element in Set […]
Overview Mathematical combinations occur in problems that involve the number of ways that sets can be combined, where order does not matter. Permutations are similar arrangements, but order does matter. They are related through principles of multiplication and arrangements involving factorials. How Many Choices Are There? If the problem is merely a combination of a […] | 677.169 | 1 |
NCERT Solutions For Class 8 Civics […]
NCERT Solutions For Class 8 History and […]
NCERT Solutions For Class 11 solutions for class 8 science […]
NCERT Solutions For Class 11 Economics is an exclusive guide fulfil with the latest update. It has been approved by experts. It covers every chapter of Class 11 Economics NCERT Solutions. The answers are advanced and easy to understand. Every student can understand it without any instructions. You don't need to take coaching because it is recommended by teachers. At the […]
The material in the NCERT Solutions For Class 8 Geography has been further updated. The subject has been discussed in such a simple way that the students will find no difficulty to understand it.the proofs of various theorems and NCERT Solution have been given with minute details. Each chapter of this Geography NCERT Solutions Class 8 contains complete […]
NCERT Solutions For Class 7 Geography is a comprehensive guide to NCERT solutions written by experts. It covers every aspect of each chapter as well as covers examination including how to prepare, what to prepare. It covers detailed concept of Chemical Reactions and Equations, Carbon and its Compound, How do Organisms Reproduce etc. The material in the […]
The material in the NCERT Solutions For Class 6 maths has been further updated. The subject has been discussed in such a simple way that the students will find no difficulty to understand it.the proofs of various theorems and NCERT Solution have been given with minute details. Each chapter of this Maths NCERT Solutions Class 6 contains complete […]
NCERT Solutions For Class 6 Science 7 History | 677.169 | 1 |
Description
Year 12 and Year 13 students are invited to join a series of maths problem-solving sessions which offer students the opportunity to develop their problem-solving skills by trying out challenging problems that require deep mathematical thinking, and so help them meet the challenges they may face in taking a maths-rich university degree or career. The problems students will tackle are fun and rewarding. Attending the sessions will enrich students' mathematical experience. Students will look at problems from a range of sources including Sixth Term Examination Papers used by Cambridge and Warwick and the Mathematics Admissions Test used by Oxford and Imperial. | 677.169 | 1 |
worksheet answers pdf ebooks because this workshop books about graphing simple 4 pdf ebooks because this workshop books about ebooks because this workshop books about general knowledge quizzes questions answer key pdf ebooks because this workshop books about genetic a answers pdf ebooks because this workshop books about geometry lesson 10 4 practice a answers You could answers pdf ebooks because this workshop books about gitman soccer referee test answers pdf ebooks because this workshop books about grade 8 2013 mhhe pdf ebooks because this workshop books about frog dissection pre lab answer key mhhe You could find and download any of books you like and save it into your disk without any problem at all. We also provide a lot of books, user manual, or guidebook that related.
Best paper document online ebooks because this workshop books about grade 9 answers crosswords pdf ebooks because this workshop books about food web ebooks because this workshop books about financial acct 2nd ed math and science answers pdf ebooks because this workshop books about fiesta texas math and science answers You could find and download any of books you like and save it into your disk without any problem at all. We also provide a lot of books, user manual, or guidebook that related.
Best paper document online to eBook graphing rational functions word problems with answers pdf ebooks because this workshop books about graphing rational functions solutions manual pdf ebooks because this workshop books about pdf ebooks because this workshop books about questions pdf ebooks because this workshop books about ge 32 bit pdf ebooks because this workshop books about hp solution centre pdf ebooks because this workshop books about glencoe biology answer precourse self assessment answers 2013 pdf ebooks because this workshop books about free sear inclined plane sliding objects pdf ebooks because this workshop books about gizmo answers for inclined plane sliding objects lab notebook answers pdf ebooks because this workshop books about foss populations and ecosystems with answer key pdf ebooks because this workshop books about grade 8 science module books computer studies waec 2014 pdf ebooks because this workshop books about free questions and answers for computer studies find biology questions and answers pdf ebooks because this workshop books about find 1 answers key pdf ebooks because this workshop books about gokkusagi turkce calisma kitabica pdf ebooks because this workshop books about group discussion topics with euilibrium answers pdf ebooks because this workshop books about flinn chemtopic labs euilibrium 9 pdf ebooks because this workshop books about gateway b1 students sans frontieres answers pdf ebooks because this workshop books about grade 9 sans frontieres answer key pdf ebooks because this workshop books about glencoe language arts grade 11 answer pdf ebooks because this workshop books about glencoe advanced mathematical concepts answer ar test answers pdf ebooks because this workshop books about frankenstein semester 1 exam answers pdf ebooks because this workshop books about flvs 1 answer key pdf ebooks because this workshop books about genetics pedigree document analysis john gardner answers pdf ebooks because this workshop books about grendel analysis pdf ebooks because this workshop books about oxidation number pdf ebooks because this workshop books about gpb chemistry answer key oxidation number visual basic pdf ebooks because this workshop books about final exam answers visual basic answers unit 1 pdf ebooks because this workshop books about gateway b1 manual pdf ebooks because this workshop books about halliday resnick walker integrated science chapter 10 answer key pdf ebooks because this workshop books about glencoe integrated science ebooks because this workshop books about gene pools foundation for geometry test form a answers pdf ebooks because this workshop books about foundation for froensic psychology basic question and answer pdf ebooks because this workshop books about froensic psychology basic question and answer You could find and download any of books you like and save it into your disk without any problem at all. We also provide a lot of books, user manual, or guidebook that related.
Best paper document online to eBook financial literacy quiz answers eruralfamilies org pdf ebooks because this workshop books about financial literacy quiz answers eruralfamilies org gorgeous grammar answers pdf ebooks because this workshop books about gorgeous grammar and answers pdf ebooks because this workshop books about great gatsby ebooks because this workshop books about geometry 5 pdf ebooks because this workshop books about gateway b1 student star questions pdf ebooks because this workshop books about how to answer star questions groups chemistry 2009 answers pdf ebooks because this workshop books about gauss contest grade 7 2009 answer guys questions pdf ebooks because this workshop books about girls answer guys questions answers pdf ebooks because this workshop books about geography may june 2014 answers pdf ebooks because this workshop books about geography may goblet fire ar test answers pdf ebooks because this workshop books about harry potter goblet ebooks because this workshop books about guess the answers pdf ebooks because this workshop books about fahrenheit 451 answers pdf ebooks because this workshop books about general organic and heat transfer 10th edition solutions pdf ebooks because this workshop books about holman heat transfer review answers pdf ebooks because this workshop books about geometry word search 1 answerkey pdf ebooks because this workshop books about frank tapson word search 7 2 practice answers pdf ebooks because this workshop books about geometry ebooks because this workshop books about packet answer key pdf ebooks because this workshop books about fish anatomy geography final problems and answers pdf ebooks because this workshop books about ged ebooks because this workshop books about glencoe geometry 2012 pdf ebooks because this workshop books about gujarati linkage dragon civics pdf ebooks because this workshop books about flvs answer key 2013 grade 8 answer sheet pdf ebooks because this workshop books about gauss 2013 answers sine pdf ebooks because this workshop books about faceing math lesson 17 answers s government nonprofit accounting chapter 1 solutions pdf ebooks because this workshop books about government nonprofit movie discussion question answers pdf ebooks because this workshop books about freedom writers pdf ebooks because this workshop books about fcat explorer answers gear pulley answers pdf ebooks because this workshop books about gear university of chicago review answers pdf ebooks because this workshop books about geometry university of chicago answers pdf ebooks because this workshop books about financial geometry 10 6 practice answers pdf ebooks because this workshop books about geometry with two traits answers enrich pdf ebooks because this workshop books about genetic crosses with two traits answers enrich chapter by answer key pdf ebooks because this workshop books about government 7 answers pdf ebooks because this workshop books about foss mid summative guess picture celebrity app answers pdf ebooks because this workshop books about guess picture reteaching activity answer pdf ebooks because this workshop books about french revolution and napoleon questions and answers pdf ebooks because this workshop books about gcse ict document answers pdf ebooks because this workshop books about genetics pedigree with answers pdf ebooks because this workshop books about grade 2 35 answers pdf ebooks because this workshop books about grade 6 daily geography answer key pdf ebooks because this workshop books about george washington socks calorimetry lab answers pdf ebooks because this workshop books about flinn scientific 3 pdf ebooks because this workshop books about fetal pig dissection lab us government answer sheet pdf ebooks because this workshop books about final exam review us and work text ii answers pdf ebooks because this workshop books about grammar and composition work text ii map with answers pdf ebooks because this workshop books about geography challenge hand 2012 answers pdf ebooks because this workshop books about global history guidebook that related.
Best paper document online to eBook gpb chemistry 605 answers pdf ebooks because this workshop books about gpb chemistry unit 5 week 3 pdf ebooks because this workshop books about fresh reads answers unit 5 week 3 pdf ebooks because this workshop books about frog first aid multiple choice questions and answers pdf ebooks because this workshop books about first aid nz pdf ebooks because this workshop books about firearm safety test answers nz ch 33 restructuring the postwar world answers pdf ebooks because this workshop books about form a ch 33 ebooks school curriculum answers pdf ebooks because this workshop books aboutb test answers pdf ebooks because this workshop books about fema ics final physics review answers pdf ebooks because this workshop books about final subway university test answers pdf ebooks because this workshop books about free subway the crucible answers pdf ebooks because this workshop books about holt mcdougal american key for water polo pdf ebooks because this workshop books about gym packets answers key for water pol answers genetics vocabulary pdf ebooks because this workshop books about foss answers genetics vocabulary analysis questions answers pdf ebooks because this workshop books about frog dissection pearson algebra 2 answer cheats pdf ebooks because this workshop books about gradpoint pearson algebra 2 answer key pdf ebooks because this workshop books about gpb chemistry chapter 10 answers pdf ebooks because this workshop books about goolsbee answers pdf ebooks because this workshop books about go digestive system answer key pdf ebooks because this workshop books about gizmo student exploration conclusion answers pdf ebooks because this workshop books about flame test test with answers pdf ebooks because this workshop books about grade 8th ebooks packet answers pdf ebooks because this workshop books about funtown 8 answers pdf ebooks because this workshop books about great gatsby lesson 3 solution manual pdf ebooks because this workshop books about hansen mowen 5th edition answers pdf ebooks because this workshop books about general chemistry chang answers pdf ebooks because this workshop books about grasshopper standard chemistry answers pdf ebooks because this workshop books about final exam review packet standard it review and answers pdf ebooks because this workshop books about fission fusion answers pdf ebooks because this workshop books about fun with management gloss test answer sheet pdf ebooks because this workshop books about gloss road movie questions and answers pdf ebooks because this workshop books about glory road answers pdf ebooks because this workshop books about great gatsby chapter boyle charles and combined answers pdf ebooks because this workshop books about gas laws worksheet boyle charles and combined zeitgeist grammar answers pdf ebooks because this workshop books about german zeitgeist grammar a pdf ebooks because this workshop books about genius 5 practice b answers pdf ebooks because this workshop books about geometry grade 8 pdf ebooks because this workshop books about focus florida achieves trivia questions and answers pdf ebooks because this workshop books about google online test pdf ebooks because this workshop books about general knowledge questions answers online 6 tessellations answers pdf ebooks because this workshop books about geometry practice 12 6 save this geography internet scavenger hunt answer key pdf ebooks because this workshop books about geography questions and answers pdf ebooks because this workshop books about ghost review answers pdf ebooks because this workshop books about holt mcdougal questions gandhi answers pdf ebooks because this workshop books about film questions gandhi get free waec 2014 2015 biology essay answer pdf ebooks because this workshop books about get free fluid machine question answer pdf ebooks because this workshop books about fluid machine 47 pdf ebooks because this workshop books about guess word answers album 3 group 47 vtaide answer sheet pdf ebooks because this workshop books about functions of animal adaptations vtaide ebooks because this workshop books about griffiths solution books review packet answers pdf ebooks because this workshop books about global for waec 2014 as at 8 of april pdf ebooks because this workshop books about geography answers for waec 2014 as at 8 pdf ebooks because this workshop books about phone pdf ebooks because this workshop books about how to answer a phone castle questions and answers pdf ebooks because this workshop books about glass castle practice test answers sheet pdf ebooks because this workshop books about geometry item specs practice sheet january 29 2014 pdf ebooks because this workshop books about geometry regents answer sheet january 29 2014 answers pdf ebooks because this workshop books about geography pdf ebooks because this workshop books aboutbook answer key pdf ebooks because this workshop books about holt physical science answers core test 3 pdf ebooks because this workshop books about gmetrix answers core test answer key pdf ebooks because this workshop books about glencoe science answers pdf ebooks because this workshop books about google adwords answers pdf ebooks because this workshop books about holt active skillbuilder answers pdf ebooks because this workshop books about gettysburg address answer key pdf ebooks because this workshop books about face2face answers pdf ebooks because this workshop books about general guie to macbeth answer key pdf ebooks because this workshop books about grammardog guie to because history crossword puzzles and answers pdf ebooks because this workshop books about history 75 angles of elevation and depression answers pdf ebooks because this workshop books about geometry worksheet 75 angles results answers pdf ebooks because this workshop books about grade results biology if8765 pdf ebooks because this workshop books about genetics crossword puzzle answer key disk without any problem at all. We also provide a lot of books, user manual, or guidebook that related.
Best paper document online to eBook gettysburg mini dbq answers pdf ebooks because this workshop books about gettysburg 3a pdf ebooks because this workshop books about gradpoint answers answer key pdf ebooks because this workshop books about geometry apes multiple choice answers pdf ebooks because this workshop books about friedland and relyea answer pdf ebooks because this workshop books about gramatica a metal carbonate answers pdf ebooks because this workshop books about gravimetric analysis of a metal carbonate answer key pdf ebooks because this workshop books about gizmo pdf ebooks because this workshop books about fce gold plus course cheat answers pdf ebooks because this workshop books about ged math cheat solutions manual pdf ebooks because this workshop books about holt mcdougal algebra 2 solutions manual You could find answers pdf ebooks because this workshop books about geometry lesson | 677.169 | 1 |
This section contains free e-books and guides on Graph Theory, some of the resources in this section can be viewed online and some of them can be downloaded.
Graph theory
is one of the branches of modern mathematics having experienced a most
impressive development in recent years. This book will draw the attention of the
combinatorialists to a wealth of new problems and conjectures. Topics covered
includes: General Theory: Hypergraphs, Fractional Matching, Fractional Coloring,
Fractional Edge Coloring, Fractional Arboricity and Matroid Methods, Fractional
Isomorphism, Fractional Odds and Ends.
The focus of this book is on applications and the aim is to improve the problem solving
skills of the students through numerous well-explained examples. Topics covered
includes: General Theory, Shortest Paths, Euler Tours and The Chinese Postman
Problem, Spanning Trees, Matchings and Coverings, Benzenoids, Network Flow and
Electrical Network.
The primary aim of this book is to present a coherent
introduction to graph theory, suitable as a textbook for advanced undergraduate
and beginning graduate students in mathematics and computer science. This note covers the following topics: Graphs and Subgraphs, Trees, Connectivity, Euler Tours and Hamilton Cycles, Matchings, Edge
Colourings, Independent Sets and Cliques, Vertex Colourings, Planar Graphs,
Directed Graphs, Networks, The Cycle Space and Bond Space. | 677.169 | 1 |
Mathematics All Around (4th Edition)
Author:Tom Pirnot
ISBN 13:9780321567970
ISBN 10:321567978
Edition:4
Publisher:Pearson
Publication Date:2009-01-22
Format:Hardcover
Pages:864
List Price:$170.67
 
 
Mathematics
Problem Solving: Strategies and Principles; Set Theory: Using Mathematics to Classify Objects; Logic: The Study of What's True or False or Somewhere in Between; Graph Theory (Networks): The Mathematics of Relationships; Numeration Systems: Does It Matter How We Name Numbers?; Number Theory and the Real Number System: Understanding the Numbers All Around Us; Algebraic Models: How Do We Approximate Reality?; Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It?; Consumer Mathematics: The Mathematics of Everyday Life; Geometry: Ancient and Modern Mathematics Embrace; Apportionment: How Do We Measure Fairness?; Voting: Using Mathematics to Make Choices; Counting: Just How Many Are There?; Probability: What Are the Chances?; Descriptive Statistics: What a Data Set Tells Us
For all readers interested in mathematics.
Booknews
An applications-oriented mathematics text, for students majoring in the liberal arts, social science, and other nonscientific areas. Applications are designed to motivate students, involving areas such as set theory and Internet search engines, the use of data in presidential polls, and odds of winning a lottery. Pedagogical features emphasize problem solving. Coverage includes logic, graph theory, consumer mathematics, descriptive statistics, algebraic models, geometry, and matrices. There is a unique chapter on mathematics and voting methods. Pirnot is affiliated with Kutztown University of Pennsylvania. Annotation c. Book News, Inc., Portland, OR (booknews.com) | 677.169 | 1 |
QuickMath Automatic Math Solutions Automatically solves formulas and equations in algebra, calculus, and general math. Use for checking homework and discovering methods of handling graphs and matrices.
Homework Center - Mathematics mathMagic on the Web http//mathforum.org/mathmagic/ Try to solve weekly math problemson This page is a part of the Multnomah County Library homework Center.
Homework Sites Built and maintained by the Los Angeles Public Library.Category Kids and Teens School Time homework Helphomework Sites The Arts, Biography, Countries States, General homeworkHelp Sites. History, math, Science, Social Studies. The Arts. Gateway
High School Math - HomeworkSpot.com math.com homework Help A math library, lessons and more. SOS mathematicsBrowse more than 2,500 pages filled with explanations.
Study-Help,Tutoring, Homework, Learning, School is a place where I will try to help you understand the material so that you can doyour homework well yourself (We could entertain higher level math and science | 677.169 | 1 |
Critical Path to Success!!
A student who wants to succeed in this course will:
• Alway arrive to class prepared to work with all materials needed.
graphing calculator
17.
Critical Path to Success!!
A student who wants to succeed in this course will:
• Alway arrive to class prepared to work with all materials needed.
3-ring binder
loose leaf paper
notebook or duotang
graphing calculator
181920geometry set
21.
Critical Path to Success!!
A student who wants to succeed in this course will:
• Always attempt ALL their homework assignments.
22.
Critical Path to Success!!
A student who wants to succeed in this course will:
• Review their class notes every night before
going to bed.
23.
The Curve of Forgetting ...
... describes how we retain or get rid of information
that we take in. It's based on a one-hour lecture.
more about Learning and Remembering
24.
Critical Path to Success!!
A student who wants to succeed in this course will:
• Always ask LOTS of questions about anything they don't
understand.
25.
Critical Path to Success!!
A student who wants to succeed in this course will:
• Always gets extra help from the teacher
when they feel they are falling behind.
26.
Critical Path to Success!!
A student who wants to succeed in this course will:
• Find one or two people to be their study partners and form a study
group.
27.
Critical Path to Success!!
A student who wants to succeed in
this course will:
• Consistently set a regular time of
day to do homework assignments.
28.
Critical Path to Success!!
A student who wants to succeed in this course will:
• Participate regulary on the course blog.
29.
How To Create a Google Account
Click the text up
there to see the video!
30.
How to Sign Up For Blogger
Click the text up
there to see the video! | 677.169 | 1 |
Mathematics
Mission Statement:
The Mathematics Department seeks to promote the understanding, enjoyment and enthusiasm of mathematics. We aim to provide students with skills and confidence in the use of mathematical techniques, and to prepare students for a world where numerical skills are essential.
From September 2014, the new KS3 Mathematics curriculum will be broken down into 6 aspects:
Number
Algebra
Ratio, Proportion & Rates of Change
Geometry & Measures
Probability
Statistics
Through the teaching of these topics, we aim for our students to become confident and fluent in the fundamental skills of Mathematics. Using the practice of increasingly complex problems to develop their understanding, recall, knowledge & application, students will demonstrate their skills both rapidly and accurately. Our students are expected to reason mathematically by following a line of enquiry and developing their own arguments, justification and proof, using Mathematical language and notation. Students will also be able to solve problems by applying their Mathematics to a variety of problems and real life situations with increasing confidence.
Students studying Key Stage 4 Mathematics will cover 4 main areas including: Number, Shape, Data and Algebra. Students will also engage in problem solving and investigative activities linked to real world problems and situations relevant to everyday life. Students will be given excellent opportunities to achieve the highest possible grades in the GCSE, with our proportion of students sitting the higher paper increasing year by year. The course will be formally assessed at the end of Year 11 by means of 2 examination papers based on calculator and non-calculator skills. Support is available to students throughout the 2 year course and includes weekly after school revision sessions for all tiers and intervention using resources from the SIGMA suite. Staffs are also often available at lunchtimes and after school to offer 1 to 1 support for students that request it. | 677.169 | 1 |
Algebra 2: A Year of Homework Bundle
Be sure that you have an application to open
this file type before downloading and/or purchasing.
86 MB
Product Description
Do you need some homework to correspond to lessons for ALGEBRA 2 HONORS? The lessons are aligned to most state standards and are rigorous and comprehensive in both manual and technological approaches. I refer to this approach as the "RULE OF FOUR" or G.N.A.W. as my students prefer (Graphical, Numerical, Algebraically, and Words)
You will find two forms of a Daily Quiz and a homework assignment for each of the lessons in my FULL YEAR CURRICULUM BUNDLE. All answer keys are included. | 677.169 | 1 |
Synopsis
This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in a straightforward way, laying the groundwork for further study. A working knowledge of real calculus and familiarity with complex numbers is assumed. This book is useful for graduate students in calculus and undergraduate students of applied mathematics, physical science, and engineering.
Buy the eBook
List Price $47.95
Your price $38.39
You save $9.56 (20%) and
You'll see how many points you'll earn before checking out. We'll award them after completing your purchase. | 677.169 | 1 |
Tutor Feedback Policies
Three types of feedback policies now exist, and can be chosen from the Graph > Feedback Policy menu. A feedback policy determines if and when tutor feedback (hints and correct/incorrect indications) is displayed to the student.
With the default setting, Show All Feedback, the tutor displays feedback immediately as the student works through each step.
With Hide All Feedback, the tutor never displays feedback. This can be useful, for instance, in quizzes or tests.
With Delay Feedback, the tutor will display feedback only when the student presses the Done button, and then only if the problem is incomplete because some steps are incorrect or left undone. No hints will be displayed, but correct/incorrect indications will be shown for all steps done so far.
Confirm Done
A feature related to feedback policies can now be set from the Graph > Confirm Done menu. When the Feedback Policy is Hide All Feedback, so that no hints or correct/incorrect indications appear, students can inadvertently click the Done button and exit the problem prematurely. Setting Confirm Done will make the user interface prompt students whenever the Done button is pressed, to allow them to remain in the current problem in case they decide they are not yet really finished.
Preliminary support for rule-based (Jess) tutors with the Tutoring Service
We have updated CTAT's Tutoring Service and the TutorShop platform with basic support for running a Jess tutor on the web. Please contact us if you are interested in trying this option.
New author functions
The following functions are now available for use in example-tracing tutors:
last(Object arg, ...) simply returns its last argument. It is useful, in particular, when used in conjunction with the functions below.
assign(String name, Object value) can be used to set arbitrary variables for use in future steps. This function should be used in the Replace Student Input formula shown in the Edit Student Input Matching dialog. For example: the result of last(assign("p1", input), input), when used in Replace Student Input is this: if this step was successful, save the student input in p1 and simply redisplay that same input unchanged.
goToStartState(), also callable from the Replace Student Input field, takes the problem back to the start state. For example, last(goToStartState(), -1), placed in the Replace Student Input field, would move the student to the start state. Note: Do NOT call goToStartState() from a matcher formula as this will lead to an infinite loop (or a very slow tutor).
General Bug Fixes / Changes
CTAT2679 – Additional diagnostics needed in Jess Console when WME file not found. If CTAT didn't load facts from a WME file, this message is shown: "WME file not found, creating instances from interface definitions" in the Jess Console.
CTAT2700 – Min/max traversals are set to 1-1 in the tools even if a mass production variable is specified.
CTAT2800 – In File > Open Graph chooser, only show .brd files by default.
Various bug fixes for the the CommNumberBar and CommDragNDrop components
A fix for the bug in AS 2.0 Flash tutors where the clicking and selecting of text (followed by tab or enter) will not trigger the tutor to evaluate the new text.
Improved look and feel of the authoring tools.
Note: Behavior graphs created with a version of CTAT older than 2.12 contain <DorminName> elements, which are no longer recognized. Unfortunately, we cannot support DorminName any longer. These elements in the BRD file need to be replaced with <CommName> elements, which can only be done with a text editor.
Known Issues
Java
CTAT2314 – Skill pKnown values are cumulative at author time
NetBeans 6.7.1: class files are deleted if all jar files required for examples are not specified. Workaround is to add all jar files required by the examples as described here.
The less-than sign does not display properly in CTAT's separate hint window (but it's fine in the integrated hint window).
DorminPicture does not provide any feedback message to the student when a step is out of order.
Flash
CTAT2349 – Flash: CommCheckBox isn't checked if 'selected' parameter = true. Workaround is to set a state as the start state.
CTAT2433 – Flash: CommRadioButton isn't "selected" in the start state
The component-specific methods The Correct Method, The InCorrect Method, and The Reset Method do not work when Suppress Student Feedback is turned on. The solution is to use a new CommShell parameter,Inconsistent behavior when clicking on a state (CTAT2249).
Docked windows sometimes aren't loaded on Mac (CTAT2198) To do this manually, see Installing the Formula Wizard.
The enforceDone attribute of a behavior graph cannot be set from the CTAT user interface; it can only be set in the behavior graph XML using a text editor.
Upgrading an Interface to CTAT version 3.0 createTo | 677.169 | 1 |
Algebra for dummies pdf,
find a quadratic equation from a table,
how to find the LCD in a complex fraction,
algebra 2 projects,
9th Grade Algebra Test.
Factoring step by step,
discrete math vocabulary definitions,
tenth grade algebra,
find each product,
Why should we clear fractions when solving linear equations and inequalities? Demonstrate how this is done with an example. Why should we clear decimals when solving linear equations and inequalities? Demonstrate how this is done with an example.,
baldor math.
Algebra 2 book answers,
algebra structure and method book 1 answers,
cxc math teach me how to do algebra,
factor problem,
fraction scientific calculator,
Geometry "McDougal Little" download,
How to prepare for College Algebra as an instructor.
How is Algebra used in the everyday life of a elementary teacher,
Examples of Math Poems,
math answers algebra 2 mcdougal,
free online algebra solver with steps,
algebra brackets calculator,
discrete mathematics and its applications answer.
Algebra 2 online tutoring,
algebra problems - challenging,
how do you work out algerbra,
geometry with algebra in it.
Teach me maths for free,
how to do probability problems in algebra,
algebra trivia,
Type in Algebra Problem Get Answer,
algebra 1 concepts and skills answers,
real life examples of quadratic functions.
How to graph inequalities,
how to solve an addition and subtraction polynomials,
calculator with exponent button,
steps to an algebra problem,
How do you know if a value is a solution for an inequality or equation?,
math distributive property,
how do you change a mixed number to a decimal.
Equations used for exponents,
how make trinomial a perfect square,
scale factor in 7th grade mathematics.
Basic algebra for beginners,
how to learn algebra easily in ninth grade,
how to solve difference of cubes,
logarithm tutor.
Words into symbols,
what is the definition of a equivalent fraction?,
coordinate plan pictures,
algebraic expressions reducing,
second order differential equation with imaginary root,
simple algebra | 677.169 | 1 |
Learn the concepts and methods of linear algebra, and how to use them to think about computational problems arising in computer science. Coursework includes building on the concepts to write small programs and run them on real data.
This course is designed to introduce you to the study of Calculus. You will learn concrete applications of how calculus is used and, more importantly, why it works. Calculus is not a new discipline; it has been around since the days of Archimedes. However, Isaac Newton and Gottfried Leibniz, two 17th-century European mathematicians concurrently working on the same intellectual discovery hundreds of miles apart, were responsible for developing the field as we know it today. This brings us to our first question, what is today's Calculus? In its simplest terms, calculus is the study of functions, rates of change, and continuity. While you may have cultivated a basic understanding of functions in previous math courses, in this course you will come to a more advanced understanding of their complexity, learning to take a closer look at their behaviors and nuances. In this course, we will address three major topics: limits, derivatives, and integrals, as well as study their respective foundations and a…
This course is the second installment of Single-Variable Calculus. In Part I (MA101) [1], we studied limits, derivatives, and basic integrals as a means to understand the behavior of functions. In this course (Part II), we will extend our differentiation and integration abilities and apply the techniques we have learned. Additional integration techniques, in particular, are a major part of the course. In Part I, we learned how to integrate by various formulas and by reversing the chain rule through the technique of substitution. In Part II, we will learn some clever uses of substitution, how to reverse the product rule for differentiation through a technique called integration by parts, and how to rewrite trigonometric and rational integrands that look impossible into simpler forms. Series, while a major topic in their own right, also serve to extend our integration reach: they culminate in an application that lets you integrate almost any function you'd like. Integration allows us to calculat…
This course is an introduction to linear algebra. It has been argued that linear algebra constitutes half of all mathematics. Whether or not everyone would agree with that, it is certainly true that practically every modern technology relies on linear algebra to simplify the computations required for Internet searches, 3-D animation, coordination of safety systems, financial trading, air traffic control, and everything in between. Linear algebra can be viewed either as the study of linear equations or as the study of vectors. It is tied to analytic geometry; practically speaking, this means that almost every fact you will learn in this course has a picture associated with it. Learning to connect the facts with their geometric interpretation will be very useful for you. The book which is used in the course focuses both on the theoretical aspects as well as the applied aspects of linear algebra. As a result, you will be able to learn the geometric interpretations of many of the algebraic concepts…
In this course, you will look at the properties behind the basic concepts of probability and statistics and focus on applications of statistical knowledge. You will learn about how statistics and probability work together. The subject of statistics involves the study of methods for collecting, summarizing, and interpreting data. Statistics formalizes the process of making decisions, and this course is designed to help you use statistical literacy to make better decisions. Note that this course has applications for the natural sciences, economics, computer science, finance, psychology, sociology, criminology, and many other fields. We read data in articles and reports every day. After finishing this course, you should be comfortable evaluating an author's use of data. You will be able to extract information from articles and display that information effectively. You will also be able to understand the basics of how to draw statistical conclusions. This course will begin with descriptive statistic…
This course has been designed to provide you with a clear, accessible introduction to discrete mathematics. Discrete mathematics describes processes that consist of a sequence of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. As you progress through the units of this course, you will develop the mathematical foundations necessary for more specialized subjects in computer science, including data structures, algorithms, and compiler design. Upon completion of this course, you will have the mathematical know-how required for an in-depth study of the science and technology of the computer age.
This advanced course considers how to design interactions between agents in order to achieve good social outcomes. Three main topics are covered: social choice theory (i.e., collective decision making), mechanism design, and auctions.
In this course, you will learn how to formalize information and reason systematically to produce logical conclusions. We will also examine logic technology and its applications - in mathematics, science, engineering, business, law, and so forth.
This is an introduction to formal logic and how it is applied in computer science, electronic engineering, linguistics and philosophy. You will learn propositional logic—its language, interpretations and proofs, and apply it to solve problems in a wide range of disciplines.
This is an introduction to predicate logic and how it is applied in computer science, electronic engineering, linguistics, mathematics and philosophy. Building on your knowledge of propositional logic, you will learn predicate logic—its language, interpretations and proofs, and apply it to solve problems in a wide range of disciplines.
If you invest in financial markets, you may want to predict the price of a stock in six months from now on the basis of company performance measures and other economic factors. As a college student, you may be interested in knowing the dependence of the mean starting salary of a college graduate, based on your GPA. These are just some examples that highlight how statistics are used in our modern society. To figure out the desired information for each example, you need data to analyze. The purpose of this course is to introduce you to the subject of statistics as a science of data. There is data abound in this information age; how to extract useful knowledge and gain a sound understanding in complex data sets has been more of a challenge. In this course, we will focus on the fundamentals of statistics, which may be broadly described as the techniques to collect, clarify, summarize, organize, analyze, and interpret numerical information. This course will begin with a brief overview of the discipline of stat… | 677.169 | 1 |
Calculus is a get way to higher order mathematics. In most countries calculus is introduced as a process involving infinitely many steps which is a paradigm shift to students as their pre-calculus concept involves finite logical steps to solve a problem. This book consist the study examining students' difficulties and misconceptions in learning concepts of calculus at preparatory secondary schools. Accordingly, students' conception of concepts in calculus, students' misconceptions, and factors influencing the teaching-learning of concepts were surveyed. Documentaries, classroom observation, and achievement test were the instruments used for gathering the necessary data.The book has a potential benefit to mathematics teachers in that it provides them information about their students' possible misconceptions. Over generalizing a limit just as a function value, the perception that a function must be defined at a point to have a limit at that point, and that a discontinuous function must have an asymptote were identified as misconceptions students have formed. | 677.169 | 1 |
MATH Documents
Showing 1 to 30 of 398
Math 210
Computer Lab #1 - An Introduction to Matrix Manipulation Using a Computer Algebra System
You may use any computer algebra system (CAS) for the following problems. We have Maple on the
computers in IDC 109 available for your use if you do not have
Math 210
Computer Lab #2
25 points
Use your favorite CAS to investigate computing times for different matrix operations in the following way.
1) Randomly generate a 100 x 100 matrix A and a 100 x 1 matrix B. DO NOT DISPLAY the entries!
Compute the times f
Math 210
Computer Lab #3
10 points
Using determinants to estimate eigenvalues is computationally slow. We investigate the power method and
how it is used to estimate eigenvalues. This is not the method used in practice, but it is much faster than using
de
Every elementary row operation is reversible.
True. Replacement, Interchange, and Scaling are reversible.
A 5x6 matrix has six rows
False. row x column
The solution set of a linear system involving variable x1.xn is a list of numbers
(s1.sn) that makes e
Test #1 A
100 points
Math 220
Name:
Show work.
1) A tank with a capacity of 400 liters originally contains 300 liters of pure water. Water containing one gram
of salt per liter is entering at a rate of 4 liters per minute and the mixture flows out of the
If A is an mxn matrix whose columns do not span Rm, then the equation Ax=b is
inconsistent for some b in Rm
True. the theorems in Theory 4 state that they are all true or none are true.
A homogeneous equation is always consistent
True. Ax=0 always has at
If T : Rn -> Rm is a linear transformation and if c is in Rm, then a uniqueness
question is "Is c in the range of T?"
False. The question is an existence question.
A linear transformation preserves the operations of vector addition and scalar
multiplicati
An example of a linear combination of vectors v1 and v2 is the vector 1/2(v1)
True. This equates to 1/2(v1) + 0(v2)
The solution set of the linear system whose augmented matrix is [a1 a2 a3 b] is the
same as the solution set of the equation x1a1 + x2a2 +
Quiz 3 . 25 oints Math 20 ame:
1. (5 points) )The s of an ideal spring mass system with no damping starts at rest displaced 3 meters
from equilibrium Wh
en the mass is released the system ocillates at a rate of 6 cycles per second.
How many kilograms IS
Math 160Calculus II
Spring 2014
Name_
Exam 3: Chapter 8.3,10.1-10.7
Directions: This exam consists of 7 questions with point values as specified. There is a total of 100 points possible.
Justify your answers by showing all of your work for full credit. Th
Exam 4 Sample Questions
cos
sin
1.
A curve is defined by the parametric equations = 1 , = 1 . Find the length of the arc
of the curve from the origin to the nearest point where there is a vertical tangent line.
2.
Use calculus to find the exact coordi
1. (Ch 6) Compute the volume of a right circular cone with height and base of radius in two ways:
a.
Using discs
b. Using shells
2. (Ch 6) A bike tire inner tube, fully inflated, has
diameter of 30 inches across the tube and
circumference 2 around the tub
Math 200
Homework #9
Math 200
Homework #3 | 677.169 | 1 |
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.17 MB | 4 pages
PRODUCT DESCRIPTION
I designed this worksheet (the third in a series of 10) to help fuse together the big ideas about quadratics and how they are different from other functions. This can be purchased individually or as a complete unit titled Solving Quadratics Complete Bundled Unit (at a discounted price).
Topics covered in this worksheet are: practicing exponent rules.
I designed this worksheet to compliment the Mathematics Vision Project Secondary Math II curriculum. It corresponds to Solving Quadratic and Other Equations 3.3 | 677.169 | 1 |
Description:
The American Mathematical Association of Two-Year Colleges (AMATYC) has compiled a collection of mathematics resources related to various subjects and disciplines. "Math Across the Community College Curriculum" is the title of the collection, which includes great math resources and applications for educators and students alike. Carolyn Calhoon-Dillahunt and Tarik Lagnaoui of Yakima Valley Community College created this particular resource. In it they combine principles from mathematics and English to enhance students' ability to communicate effectively. The "Overview" and "Syllabus" provide detailed information about the course, as well as goals and learning objectives for students. Check out the "Assignment" section or "Portfolio Instructions" for ideas on how to incorporate these lessons into your own classroom. The assignments provide practical examples and experience, which helps students understand the underlying principles of communication in the exercise. | 677.169 | 1 |
Precalculus + Student Solutions Manual
PRECALCULUS prepares learners for calculus and the rigors of that course, having been written by teachers who have taught the courses and seen where learners need help--and where other texts have come up short. The text features precise definitions and exposition, carefully crafted pedagogy, and a strong emphasis on algebraic, transcendental, and trigonometric functions. To show readers how important and relevant precalculus topics are to their future coursework, an optional Looking Ahead to Calculus feature appears in each chapter. The varied examples and exercises include many that encourage readers to use and understand graphs, as opposed to simply draw them, providing additional sound preparation for calculus. | 677.169 | 1 |
Introducing Variables
85 Downloads
Presentation (Powerpoint) File
Be sure that you have an application to open this file type before downloading and/or purchasing.
6.21 MB | 10 pages
PRODUCT DESCRIPTION
This product is also listed as "Introduction to Algebra."
This short PPT explains (in a slightly silly way) that the "mystery box" problems that students learn to solve during their early years in school are really algebra problems. The PPT explains what algebra is and why mathematicians use letters for variables. The PPT is visually appealing in order to keep students engaged long enough to deliver the necessary information in the lesson.
I hope you'll like the lesson. It's short, sweet, and to the point. Thanks for your interest | 677.169 | 1 |
Education and Human Development Master's Theses
Technology is the technical means people use to improve their surroundings. People use technology to improve their ability to do work. Classrooms around the world have implemented many forms of technology to enhance student interest and achievement. One form of technology that is common to math classrooms is the graphing calculator. One eighth grade math class of nineteen students from an urban middle school was taught a unit on Solving Systems of Equations by Graphing. The unit was implemented with and without the use of the graphing calculator. Students were first introduced to the unit through the use of pencils ...
Active Calculus, Matthew Boelkins, David Austin, Steven Schlicker
Open Textbooks
Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problemsFaculty Work: Comprehensive List
Algebra deals with more than computations such as addition or exponentiation; it also studies relations. Calculus touches on this a bit with locating extreme values and determining where functions increase and decrease; and in elementary algebra you occasionally "solve" inequalities involving the order relations of < or ≤ , but this almost seems like an intrusion foreign to the main focus, which is making algebraic calculations.
Relational ideas have become more important with the advent of computer science and the rise of discrete mathematics, however. Many contemporary mathematical applications involve binary or n-ary relations in addition to computations. We began discussing this topic in the last chapter when we introduced equivalence relations. In this chapter we will explore other kinds of ...
Honors Scholar Theses
Differential equations are equations that involve an unknown function and derivatives. Euler's method are efficient methods to yield fairly accurate approximations of the actual solutions. By manipulating such methods, one can find ways to provide good approximations compared to the exact solution of parabolic partial differential equations and nonlinear parabolic differential equations.
Faculty Authored Books
Grades 7-8 Mean, Median, And Mode, Rich Miller Iii
Math
This lesson is a math lesson for seventh and eighth grade students on mean, medium, and mode. Through this lesson students will be able to understand the measures of central tendency and their definitions, how to calculate them and what steps are involved, and how the theories can be applied on real life. In this lesson, students are tiered by ability and are able to pick a project based off of their interest and the math concept they are working on. Each activity has a tiered task card to guide the students.
A Math 8 Unit In Scientific Notation Aligned To The New York State Common Core And Learning Standards, Jessica K. Griffin
Education and Human Development Master's Theses
In response to the implementation of new Common Core State Standards (CCSS), this curriculum project was designed to help teachers in the transition to the new standards. The curriculum project will be referred to as a unit plan throughout the paper. The unit plan on Scientific Notation, for the eighth grade mathematics curriculum, is aligned to the New York State Common Core and Learning Standards for Mathematics (NYSCCLSM). The unit plan addresses mathematical modeling, Mathematical Practice Standard 4. The unit plan may provide a way in which teachers can work towards the Common Core State Standards Initiative's goal to ...
All Graduate Works by Year: Dissertations, Theses, and Capstone Projects
We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, if the given system of differential equations has a solution. We first look solely at the ``algebraic data" of ...
Diophantine Approximation And The Atypical Numbers Of Nathanson And O'Bryant, David Seff
All Graduate Works by Year: Dissertations, Theses, and Capstone Projects
For any positive real number $\theta > 1$, and any natural number $n$, it is obvious that sequence $\theta^{1/n}$ goes to 1. Nathanson and O'Bryant studied the details of this convergence and discovered some truly amazing properties. One critical discovery is that for almost all $n$, $\displaystyle\floor{\frac{1}{\fp{\theta^{1/n}}}}$ is equal to $\displaystyle\floor{\frac{n}{\log\theta}-\frac{1}{2}}$, the exceptions, when $n > \log_2 \theta$, being termed atypical $n$ (the set of which for fixed $\theta$ being named $\mcA_\theta$), and that for $\log\theta$ rational, the number of atypical $n ...
EKU Faculty and Staff Scholarship
Given a finite-dimensional noncommutative semisimple algebra A over C with involution, we show that A always has a basis B for which ( A , B ) is a reality-based algebra. For algebras that have a one-dimensional representation δ , we show that there always exists an RBA-basis for which δ is a positive degree map. We characterize all RBA-bases of the 5-dimensional noncommutative semisimple algebra for which the algebra has a positive degree map, and give examples of RBA-bases of C ⊕ M n ( C ) for which the RBA has a positive degree map, for all n ≥ 2
Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu
Biology and Medicine Through Mathematics ConferenceScholarship and Professional Work - LAS
Languages, Geodesics, And Hnn Extensions, Maranda Franke
Dissertations, Theses, and Student Research Papers in Mathematics
The complexity of a geodesic language has connections to algebraic properties of the group. Gilman, Hermiller, Holt, and Rees show that a finitely generated group is virtually free if and only if its geodesic language is locally excluding for some finite inverse-closed generating set. The existence of such a correspondence and the result of Hermiller, Holt, and Rees that finitely generated abelian groups have piecewise excluding geodesic language for all finite inverse-closed generating sets motivated our work. We show that a finitely generated group with piecewise excluding geodesic language need not be abelian and give a class of infinite non-abelian ...
Electronic Theses and Dissertations
...
Application Of Symplectic Integration On A Dynamical System, William Frazier
Electronic Theses and Dissertations
conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic ...
Differentiating Between A Protein And Its Decoy Using Nested Graph Models And Weighted Graph Theoretical Invariants, Hannah E. Green
Electronic Theses and Dissertations
Dissertations
...
On T-Restricted Optimal Rubbling Of Graphs, Kyle Murphy
Electronic Theses and Dissertations
...
Catalyst: A Social Justice Forum
The underachievement and underrepresentation of African Americans in STEM (Science, Technology, Engineering and Mathematics) disciplines have been well documented. Efforts to improve the STEM education of African Americans continue to focus on relationships between teaching and learning and factors such as culture, race, power, class, learning preferences, cultural styles and language. Although this body of literature is deemed valuable, it fails to help STEM teacher educators and teachers critically assess other important factors such as pedagogy and curriculum. In this article, the authors argue that both pedagogy and curriculum should be centered on the social condition of African Americans – thus ...
The Research and Scholarship Symposium
The classical Monty Hall problem entails that a hypothetical game show contestant be presented three doors and told that behind one door is a car and behind the other two are far less appealing prizes, like goats. The contestant then picks a door, and the host (Monty) is to open a different door which contains one of the bad prizes. At this point in the game, the contestant is given the option of keeping the door she chose or changing her selection to the remaining door (since one has already been opened by Monty), after which Monty opens the chosen ...
The Research and Scholarship Symposium
Nation-building modeling is an important field of research given the increasing number of candidate nations and the limited resources available. A modeling methodology and a system of differential equations model are presented to investigate the dynamics of nation-building. The methodology is based upon parameter identification techniques applied to a system of differential equations, to evaluate nation-building operations. Data from Operation Iraqi Freedom (OIF) and Afghanistan are used to demonstrate the validity of different models as well as the comparison of models.
Six Septembers: Mathematics For The Humanist, Patrick Juola, Stephen Ramsay
Zea E-Books
Scholars of all stripes are turning their attention to materials that represent enormous opportunities for the future of humanistic inquiry. The purpose of this book is to impart the concepts that underlie the mathematics they are likely to encounter and to unfold the notation in a way that removes that particular barrier completely. This book is a primer for developing the skills to enable humanist scholars to address complicated technical material with confidence. This book, to put it plainly, is concerned with the things that the author of a technical article knows, but isn't saying. Like any field, mathematics ...
Mathematics Colloquium Series
With a brief survey on the Harnack inequalities in various forms in Functional Analysis, in Partial Differential Equations, and in Perelman's solution of the Poincare Conjecture, we discuss the Harnack inequality in Linear Algebra and Matrix Analysis. We present an extension of Tung's inequality of Harnack type and study the equality case.
A Game Of Monovariants On A Checkerboard, Linwood Reynolds
Student Scholar Showcase
Abstract: Assume there is a game that takes place on a 20x20 checkerboard in which each of the 400 squares are filled with either a penny, nickel, dime, or quarter. The coins are placed randomly onto the squares, and there are to be 100 of each of the coins on the board. To begin the game, 59 coins are removed at random. The goal of the game is to remove each remaining coin from the board according to the following rules: 1. A penny can only be removed if all 4 adjacent squares are empty. That is, a penny cannot ...
Mathematics Undergraduate Contributions
This article attempts to render the rational homotopy theory of Sullivan and Quillen more comprehensible to non-experts in algebraic topology by expounding on many of the results and proofs in a more detailed and elementary way. | 677.169 | 1 |
Journal of Online Mathematics and Its Applications
Volume 6. June 2006. Article ID 1156
The Geometry of the Dot and Cross Products
Tevian Dray
1
Corinne A. Manogue
Introduction
Most students first learn the algebraic formula for the dot and cross products
THE USE OF A POCKET CALCULATOR IS NOT PERMITTED.
This paper consists of 4 pages.
Answer all the questions. There is a total of 100 marks. 100 marks will count as full marks.
QUESTION 1
(a) Describe the properties of a matrix in reduced row-echelon form.
(
GAUSSIAN ELIMINATION
A matrix is a convenient way to represent a given system of linear equations. For example, consider
the system of linear equations written below:
Using matrix notation, we can re-write the above system of equations in a portable manne
SOLUTIONS MAT 1503 NOVEMBER 2012
Instructions
Before looking at these solutions, it is strongly recommended that you go through
the paper under examination conditions.
This is a self-evaluation exercise and you are requested to be honest with yourself so
Students Number _
Type Only Answers
Given A =
2 4
1 3
Perform the following row operations beginning with matrix A and using your answer to each problem as the
matrix for the next.
1) 2R2 + R1 R1
4) Given the matrix
2) R1 R2
1 6 5
2 3 1
0 2 4
3)
repre | 677.169 | 1 |
Maths assignment on: Contingency planning analysis
Abstract
There is a high requirement for charities to plan, review and assess and thereby manage the various risks that are faced by them in all areas. The major aim of the research that is conducted is to analyse the risk management strategies that are adopted by organisations in times of economic uncertainty. Some of the major scenarios considered in the research are as follows
Maths assignment on: Essay on maths
Executive SummaryThe subject i.e. Mathematics has been rendered to as one of the most attractive subjects which takes in to consideration the various benefits over the society. The business of mathematics has become one of the major players in the society. The people belonging to such type of domain are majorly PhDs & transform the entire foundation of the society (Birman & Libgober, 2008).
Many years back it was noticed that, mathematics benefited the society in many ways. But with the various mathematical theories such as equilibrium theory, etc has led to more complexity in the structures available in the society. There have been many incidents which states that, high levels of losses have been attained by the various organizations (ICIAM, 2008). The main reason for such type of loss was that people did not have fair understanding of the various mathematical instruments, etc. This report majorly takes into consideration, the various mathematical theories, models, methodologies in order to provide directions in the near future. This report highlights the various issues which might arise in the society keeping in mind the Baye's Theorem. Two issues with regards to the abuse of mathematics on society have been discussed in this report.
Maths help on: Derivation & Statcom
1. Abstract
The report has been structured in order to put some light upon a device connected in derivation i.e. Statcom. The report majorly takes into consideration certain servers which would help in order to link the electrical power systems & control the overall voltage. This device helps in order to generate the voltage wave comparing it to the one of the electric system to realize the exchange of reactive power.
MAB120 + MAB125 Problem Solving Task – C
Instructions
Due: 5.00 pm on Tuesday 29 May 2012
Submission procedure
Your assignment should be posted in the assignment box at the end of the corridor of level 6 in O-block
.
Do not use assignment minder!
Do not use a School of Mathematical Sciences Coversheet!
Do not use a folder or envelope when submitting your assignment!
You must restrict your submission to a single A4 piece of paper – preferably one side, preferably on photocopy
type paper.
Submission format
Your submission should be hand-written (you should keep a photocopy).
Include at the top of the page the following …
Family name, Given name Student number Workshop day, time, room
Questions – Vectors and Matrices
1.
A vector equation for a given straight line is r = (i + 3 j) + (i j).
(a)
Show that the point (1; 2) does not lie on this line.
(b)
Construct a vector equation for the line that does go through the point (1; 2), and is perpendicular
to r
.
(c)
Determine the point of intersection of the two lines.
2.
You have been assigned the task of breaking a recently intercepted coded message. The ecient running
1
of a battle requires secure communications. It has been discovered that the radio communications used
by the enemy has been coded. Just such a coded message has been intercepted and it reads as follows;
14; 10; 5; 9; 8; 14; 23; 35; 20; 13; 6; 5; 21; 8; 5; 5; 8; 5; 5; 1; 9 :
A chance nding in a document captured from the enemy reveals what you think may be the coding
matrix that generated this message.
Unfortunately you have two to choose from, namely
A =
2
4
1 2 1
2 1 1
1 3 0
3
5
; B =
2
4
1 1 1
2 0 1
1 0 0
3
5
:
Your task: Interrogation of some recent prisoners leads you to believe that one of the words in the coded
message you have been asked to decode refers to a bitter fruit. What is the entire message? You will nd
the additional notes on a simple coding exercise helpful here. [Hint: T=20]
Only if you are unable to physically comply with this request with good reason, then submit a .pdf le via email to
g.pettet@qut.edu.au where the attached le has the name \yourname studentnumber C.pdf".
Semester one, 2012 nal corrected – May 24, 2012
1
3.
In the sequence of fractions
1
CO 380 Spring 2012
Assignment #3 Due **Thursday** May 24th, 2012, 10:00 a.m.
1.
Observe that
1 = 1
2 + 3 + 4 = 3
3 + 4 + 5 + 6 + 7 = 5
4 + 5 + 6 + 7 + 8 + 9 + 10 = 7
State, and prove, a generalization suggested by these equations.
2.
The numbers 1 to 9 are to be placed in the circles in such a way
that the sum of the four numbers along each side of the triangle
has the same value, S.
(a)
Prove that 17 S 23.
(b)
Find a suitable arrangement of the numbers when S = 23.
(c)
Show that when S = 20 there are at most 8 dierent choices
for the collection of three numbers which should be placed at
the vertices of the triangle.
1
;
2
1
;
1
2
;
3
1
;
2
2
;
1
3
;
4
1
;
3
2
;
2
3
;
1
4
;
5
1
;
4
2
;
3
3
;
2
2
2
2
2
4
;
1
5
;
6
1
; : : :
fractions equivalent to any given fraction occur many times. For example, fractions equivalent
to
1
2
occur for the rst two times in positions 3 and 14. In which position is the fth occurrence
of a fraction equivalent to
3
7
?
4.
Each of 50 people knows a dierent piece of information. They are allowed to give the
information they know by a phone call between themselves and one other person. During any
call, just one person is permitted to speak and tells the other person all of the information
that they know. With justication, determine the minimum number of calls required to enable
each person to know all of the information, and demonstrate how all people can come to learn
all of the information in this minimum number of calls.
5. xyz is a positive three digit integer, with x 6 = 0, z 6 = 0, whose digits are not necessarily
distinct. How many possible xyz exist such that both xyz and zyx are divisible by 4.
6.
Find all quadruples of real numbers (x; y; u; v) satisfying the system of equations
x
2
+ y
2
+ u
2
+ v
2
= 4
xu + yv + xv + yu = 0
xyu + yuv + uvx + vxy = 2
xyuv = 1:
SOLUTION
4) First person convey his information in 49 ways.
Now, Second person will have to make 48 phone calls to convey his information to remaining person.
Similarly,3rd person will have to make 47 phone calls to convey his information.
….
…
Hence, 50th person need not to call any one to convey his information.
MAN774 Perturbation Methods
Problem Solving Task 4
Due: 3pm Friday 25 May 2012 (end of Week 12)
(Was initially supposed to be 3pm Friday 18 May 2012 (end of Week 11))
Submit: Hand it to Scott McCue personally, or place it under his office door, O505.
Weighting: 8%
Instructions: Answer the following questions. Show all your working.
Submit your working in (neat) handwritten form (do not type up your solutions).
It is OK to discuss these questions with other students, but the written version of this Problem Solv-
ing Task must be your own. It is not OK to copy another student's work.
Consider the integral
I
where the notation
R
¥id
0id
2
(s; e) = lim
d!0
+
Z
¥id
0id
iz e
z(1is)/e
2(1 z
2
)
dz,
means a contour that is parallel to the real z axis, but moved down by a
distance d.
Use the method of steepest descents to derive the full asymptotic expansion of I
in the limit e ! 0.
You will have to treat the cases s > 0 and s < 0 separately, although much of the working is the
same for each.
CRICOS No. 00213J 1
2
1.Set up and solve graphically the following optimization problem. [Carefully define
all variables used and explain how you obtained the objective function and the
constraints, graph neatly, do any calculations required to obtain an exact solution,
and report your results in the context of the situation.
Engineering Computations One:
Differential and Integral Calculus
Assignment Three
Due Monday 7 May 2012
Please ensure that all your working is clearly set out, all pages are stapled
together, and that your name along with the course name appears on the front
page of the assignment. Please place completed assignments in the assignment
box in WT level 1 by 5pm on the due date.
Questions:
1. Find the derivative
dy
dx
for each of the following:
y = e
x cos x
x cos y + y cos x =1 y = x
y =
√
xe
x
2
x
2
+1
10
y =
x
√
x
2
ln x
1+x
=2xy.
2. On what interval is the curve y = e
−t
2
+1
2
y
2
concave downward?
3. Air is being pumped into a spherical weather balloon. At any time t,the
volume of the balloon is V (t) and its radius is r(t).
(a) What do the derivatives
dV
dr
and
dV
dt
represent?
(b) Express
dV
dt
in terms of
dr
dt
.
4. A particle is moving along the curve y =
√
x. As the particle passes
through the point (4, 2), its x-coordinate is increasing at the rate of 3
cm/s.
(a) How fast is the y-coordinate changing as it passes through the point
(4, 2)?
(b) How far is the particle from the origin as it passes through this point?
(c) How fast is the distance from the particle to the origin changing as
it passes through this point?
5. Find where the graph of the function f(x)=
x
(x−1)
has any vertical and
horizontal asymptotes, where it is increasing or decreasing, any local max-
2
imum and minimum values, and where it is concave upward or downward.
Use this information to sketch the graph of f.
1
6. Find the point on the parabola x + y
2
= 0 that is closest to the point
(0, −3).
7. A fence that is 4 metres tall runs parallel to a tall building at a distance
of 1 metre from the building. What is the length of the shortest ladder
that will reach from the ground over the fence to the wall of the building?
8. Apply Newton's method to the equation
1
x
−a = 0 to derive the following
reciprocal algorithm:
x
n+1
=2x
n
− ax
2
n
(which enables a computer to find reciprocals without actually dividing).
Then use this algorithm to compute
2
1
1.6984
correct to five decimal places.
… children should be brought to know the real fractions, first. The possible ways to do this is to make them understand the number of ways a system could be divided. He should learn to convert a big box into identical boxes of smaller sizes. He should be given opportunity to know how the time is divided into hours, how the hours are divided into minutes, minutes to seconds and hence on. Thus letting the child know how the things, problems and real life situations are sorted out by the knowledge of fractions
Engineering Computations One:
Differential and Integral Calculus
Assignment Two
Due Thursday 5 April 2012
Please ensure that all your working is clearly set out, all pages are stapled
together, and that your name along with the course name appears on the front
page of the assignment. Please place completed assignments in the assignment
box in WT level 1 by 5pm on the due date.
Questions:
1. Evaluate each of the following limits or explain why it does not exist:
lim
lim
lim
x→2
2x
h→0
e
t→2
t
2
+1
x
2
+6x−4
5+h
2
−4
t
2
h
+4
−e
5
lim
lim
lim
x→2
x
4
−16
x−2
x→2
|x−2|
x→0
x−2
|x| e
sin(π/x)
.
2. The current I at time t seconds in a series circuit containing only a resistor
with resistance 10 ohm, an inductor with inductance 0.5henry,anda
steady 12 volt battery connected at time t = 0 is given by the formula
I =
6
5
1 − e
−20t
(this is shown on page 84 of the course manual). Briefly
explain what happens to the current for t ≥ 0.
3. Sketch the graph of a function that satisfies all of the given conditions:
(a) f
(−1) = 0, f
(1) does not exist, f
(x) < 0if|x| < 1, f
(x) > 0if
|x| > 1, f(−1) = 4, f(1) = 0, f
(x) < 0ifx =1.
(b) Domain g =(0, ∞), lim
x→0
+ g(x)=−∞, lim
x→∞
g(x)=0,g
(1) =
0, g
(3) = 0, g
(x) < 0if1<x<3, g
(x) < 0ifx<2orx>4,
g
(x) > 0if2<x<4.
4. At what point(s) on the curve y =2(x − cos x) is the tangent parallel to
the line 3x−y = 5? Illustrate by drawing a rough sketch of the curve, the
line, and the tangent(s).
5. Suppose that f and g are differentiable functions and that F is the function
given by F(x)=f(x)g(x).
(a) Show that F | 677.169 | 1 |
This textbook is designed with the needs of today's student in mind. It is the ideal textbook for a first course in elementary differential equations for future engineers and scientists, including mathematicians.
Partial differential equations form an essential part of the core mathematics syllabus for undergraduate scientists and engineers. The origins and applications of such equations occur in a variety of different fields, ranging from fluid dynamics, electromagnetism, heat conduction and diffusion, to quantum mechanics, wave propagation and general relativity. | 677.169 | 1 |
Showing 1 to 5 of 5
2
Basics
In this chapter we introduce some of the basic concepts that will be useful for the study of
integer programming problems.
2.1 Notation
Let A Rmn be a matrix with row index set M = cfw_1, . . ., m and column index set N =
cfw_1, . . ., n. We writ
1
Introduction
Linear Programs can be used to model a large number of problems arising in practice. A
standard form of a Linear Program is
(LP)
cT x
max
(1.1a)
(1.1b)
(1.1c)
Ax ! b
x " 0,
where c Rn , b Rm are given vectors and A Rmn is a matrix. The focu
Chapter 6
Integer Programming
Integer programming (IP) deals with solving linear models in which some or all
the variables are restricted to be integer. There are algorithms especially designed
for IP problems which basically nd the optimal solution by so | 677.169 | 1 |
for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, givesMore...
This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra | 677.169 | 1 |
Description
Designed for advanced high school students, undergraduates, graduate students, mathematics teachers, and any lover of mathematical challenges, this two-volume set offers a broad spectrum of challenging problems -- ranging from relatively simple to extremely difficult. Indeed, some rank among the finest achievements of outstanding mathematicians.
Trans (-non-elementary-) mathematics, most can be solved with elementary mathematics. In fact, for the most part, no knowledge of mathematics beyond a good high school course is required.
Volume
Volume
Idealshow more
Table of contents
Preface to the American Edition
Suggestions for Using the Book
Problems
I. Points and Lines
II. Lattices of Points in the Plane
III. Topology
IV. A Property of the Reciprocals of Integers
V. Convex polygons
VI. Some Properties of Sequences of Integers
VII. Distribution of Objects
VIII. Nondecimal Counting
IX. Polynomials with Minimum Deviation from Zero (Tchebychev Polynomials)
X. Four Formulas for pXI. The Calculation of Areas of Regions Bounded by Curves
XII. Some Remarkable Limits
XIII. The Theory of Primes
Solutions
Hints and Answers
Bibliographyshow more
Rating details
5 ratings
4.2 out of 5 stars
5
60% (3)
4
0% (0)
3
40 | 677.169 | 1 |
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: Exam Tips Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA [email protected] Webpage ∼ squash/ 23 April, 2011 (at 22:50 ) Reading Have a sheet of paper called something like Ques- tions/Ideas . When reading the text, when doing homework, have this sheet convenient and write down things which puzzle you, ideas you have ( "Will this shortcut work?", "Is this step valid?" ) When reading an example: Write the given problem down, close the text, and work hard on the problem for twenty-or-so minutes. Compare your approach with that of the text. If you find an error in the text, write it down on Ques- tions/Ideas. Writing Write in complete sentences. Each sentence should start with a capital letter and end with a period . A good way to get the hang of this is to read sentences from textbooks out loud . This way you force yourself to pronounce math sym- bols and gives you the facility to put math into sentence form. If you introduce a new letter, write down a phrase saying what the letter means . For exam- ple "Let d denote the distance from the centroid to the line." Be specific! Here is a better version of the preceding sentence: "Let d denote the perpendicular dis- tance from the centroid of the region R to the line L ." Sometimes, a carefully drawn and labeled picture can help define a quantity.can help define a quantity....
View
Full
Document
This note was uploaded on 01/26/2012 for the course MAC 3472 taught by Professor Jury during the Fall '07 term at University of Florida. | 677.169 | 1 |
Circuit Training - Circles and Non-Linear Systems
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.24 MB | 4 pages
PRODUCT DESCRIPTION
This self-checking activity is reminiscent of a scavenger hunt. Students will work with the equation of a circle. This includes some problems where students must write the equation given the endpoints of a radius or diameter, and some completing-the-square problems.
Students then progress into solving systems of non-linear equations. The activity is meant to be completed without the use of graphing technology | 677.169 | 1 |
Introduction to the Matrix
A matrix (plural matrices) is sort of like a "box" of information where you are keeping track of things both right and left (columns), and up and down (rows). Usually a matrix contains numbers or algebraic expressions. You may have heard matrices called arrays, especially in computer science.
As an example, if you had three sisters, and you wanted an easy way to store their age and number of pairs of shoes, you could store this information in a matrix. The actual matrix is inside and includes the brackets:
Matrices are called multi-dimensional since we have data being stored in different directions in a grid. The dimensions of this matrix are "2 x 3" or "2 by 3", since we have 2 rows and 3 columns. (You always go down first, and then over to get the dimensions of the matrix).
Again, matrices are great for storing numbers and variables – and also great for solving systems of equations, which we'll see later. Each number or variable inside the matrix is called an entry or element, and can be identified by subscripts. For example, for the matrix above, "Brett" would be identified as , since it's on the 2nd row and it's the 1st entry.
Adding and Subtracting Matrices
Let's look at a matrix that contains numbers and see how we can add and subtract matrices.
Let's say you're in avid reader, and in June, July, and August you read fiction and non-fiction books, and magazines, both in paper copies and online. You want to keep track of how many different types of books and magazines you read, and store that information in matrices. Here is that information, and how it would look in matrix form:
We can add matrices if the dimensions are the same; since the three matrices are all "3 by 2", we can add them. For example, if we wanted to know the total number of each type of book/magazine we read, we could add each of the elements to get the sum:
We could also subtract matrices this same way.
If we wanted to see how many book and magazines we would have read in August if we had doubled what we actually read, we could multiply the August matrix by the number 2. This is called matrix scalar multiplication; a scalar is just a single number that we multiply with every entry. Note that this is not the same as multiplying 2 matrices together (which we'll get to next):
Multiplying Matrices
Multiplying matrices is a little trickier. First of all, you can only multiply matrices if the dimensions "match"; the second dimension (columns) of the first matrix has to match the first dimension (rows) of the second matrix, or you can't multiply them. Think of it like the inner dimensions have to match, and the resulting dimensions of the new matrix are the outer dimensions.
Here's an example of matrices with dimensions that would work:
Notice how the "middle" or "inner" dimensions of the first matrices have to be the same (in this case, "2"), and the new matrix has the "outside" or "outer" dimensions of the first two matrices ("3 by 5").
Now, let's do a real-life example to see how the multiplication works.Let's say we want to find the final grades for 3 girls, and we know what their averages are for tests, projects, homework, and quizzes. We also know that tests are 40% of the grade, projects 15%, homework 25%, and quizzes 20%.
Here's the data we have:
Let's organize the following data into two matrices, and perform matrix multiplication to find the final grades for Alexandra, Megan, and Brittney. To do this, you have to multiply in the following way:
Just remember when you put matrices together with matrix multiplication, the columns (what you see across) on the first matrix have to correspond to the rows down on the second matrix. You should end up with entries that correspond with the entries of each row in the first matrix.
For example, with the problem above, the columns of the first matrix each had something to do with Tests, Projects, Homework, and Quizzes (grades). The row down on the second matrix each had something to do with the same four items (weights of grades). But then we ended up with information on the three girls (rows down on the first matrix).
So Alexandra has a 90, Megan has a 77, and Brittney has an 87. See how cool this is? Matrices are really useful for a lot of applications in "real life"!
Now let's do another example; let's multiply the following matrices:
Don't worry; probably most of the time you'll be doing matrix multiplication will be in the calculator!
Oh, one more thing! Remember that multiplying matrices is not commutative (order makes a difference), but is associative (you can change grouping of matrices when you multiply them). Multiplying matrices is also distributive (you can "push through" a matrix through parentheses), as long as the matrices have the correct dimensions to be multiplied.
Matrices in the Graphing Calculator
The TI graphing calculator is great for matrix operations! Here are some basic steps for storing, multiplying, adding, and subtracting matrices:
(Note that you can also enter matrices using ALPHA ZOOM and the arrow keys in the newer graphing calculators.)
We'll learn other ways to use the calculator with matrices a little later.
Determinants, the Matrix Inverse, and the Identity Matrix
Soon we will be solving Systems of Equations using matrices, but we need to learn a few mechanics first!
Most square matrices (same dimension down and across) have what we call a determinant, which we'll need to get the multiplicative inverse of that matrix. The inverse of a matrix is what we multiply that square matrix by to get the identity matrix. We'll use the inverses of matrices to solve Systems of Equations; the inverses will allow us to get variables by themselves on one side (like "regular" algebra). You'll solve these mainly by using your calculator, but you'll also have to learn how to get them "by hand".
Note that the determinant of a matrix can be designated by \(\det \left[ \text{A} \right]\) or \(\left| \text{A} \right|\), and the inverse of a matrix by \({{\text{A}}^{{-1}}}\).
Let's do some examples and first get the determinant of matrices (which we can get easily on a calculator!). The determinant is always just a scalar (number), and you'll see it with two lines around the matrix:
Now let's use the determinant to get the inverse of a matrix. We'll only work with 2 by 2 matrices, since you'll probably be able to use the calculator for larger matrices. Note again that only square matrices have inverses, but there are square matrices that don't have one (when the determinant is 0):
Note that a matrix, multiplied by its inverse, if it's defined, will always result in what we call an Identity Matrix: . An identity matrix has 1's along the diagonal starting with the upper left, and 0's everywhere else.
When you multiply a square matrix with an identity matrix, you just get that matrix back: . Think of an identity matrix like "1" in regular multiplication (the multiplicative identity), and the inverse matrix like a reciprocal (the multiplicative inverse).
Solving Systems with Matrices
Why are we doing all this crazy math? Because we can solve systems with the inverse of a matrix, since the inverse is sort of like dividing to get the variables all by themselves on one side.
To solve systems with matrices, we use . Here is why, if you're interested in the "theory" (the column on the right provides an example with "regular" multiplication). (I is the identity matrix.)
Let's take the system of equations that we worked with earlier and show that it can be solved using matrices:
Oh, and there's another way to solve these in your calculator, but your teacher may not tell you. I'm not going to go into the details, but it's using a method called reduced row echelon form, where we can put everything in one matrix (called an augmented matrix). Let's try this for the following matrix:
A little easier, right?
Solving Word Problems With Matrices
Now that we know how to solve systems using matrices, we can solve them so much faster! Let's do a couple of pure matrices problems, and then more systems problems :).
Matrix Multiplication Problem
Solutions:
(a) When we multiply a matrix by a scalar (number), we just multiply all elements in the matrix by that number. So 2P =
(b) When we square P, we just multiply it by itself. Let's do this "by hand":
(c) Since , we have . Let's use our calculator to put P in [A] and in [B]. Then .
Matrix Equation Problem:
This one's a little trickier, since it doesn't really look like a systems problem, but you solve it the same way:
Solve the matrix equation for X (X will be a matrix):
Solution:
Let's add the second matrix to both sides, to get X and it's coefficient matrix alone by themselves. Then we'll "divide" by the matrix in front of X. Watch the order when we multiply by the inverse (matrix multiplication is not commutative), and thank goodness for the calculator!
We can check it back: . It works!
Matrix Multiplication Word Problem:
The following matrix consists of a shoe store's inventory of flip flops, clogs, and Mary Janes in sizes small, medium, and large:
The store wants to know how much their inventory is worth for all the shoes. How should we set up the matrix multiplication to determine this the best way?
Solution:
The trick for these types of problems is to line up what matches (flip flops, clogs, and Mary Janes), and that will be "in the middle" when we multiply. This way our dimension will line up. Another way to look at it is we need to line up what goes across the first matrix with what goes down the second matrix, and we'll end up with what goes down the first matrix for these types of problems.
So our matrix multiplication will look like this, even though our tables look a little different (I did this on a calculator):
So we'll have $1050 worth of small shoes, $2315 worth of medium shoes, and $1255 worth of large shoes for a total of $4620.
Another Matrix Multiplication Word Problem:
A nut distributor wants to know the nutritional content of various mixtures of almonds, cashews, and pecans. Her supplier has provided the following nutrition information:
Her first mixture, a protein blend, consists of 6 cups of almonds, 3 cups of cashews, and 1 cup of pecans. Her second mixture, a low fat mix, consists of 3 cups of almonds, 6 cups of cashews, and 1 cup of pecans. Her third mixture, a low carb mix consists of 3 cups of almonds, 1 cup of cashews, and 6 cups of pecans. Determine the amount of protein, carbs, and fats in a 1 cup serving of each of the mixtures.
Solution:
Sometimes we can just put the information we have into matrices to sort of see what we are going to do from there. It makes sense lines up with the rows of the second matrix, and we can perform matrix multiplication. This way we get rid of the number of cups of Almonds, Cashews, and Pecans, which we don't need. So here is the information we have in table/matrix form:
Then we can multiply the matrices (we can use a graphing calculator) since we want second matrix above). Also, notice how the cups unit "canceled out" when we did the matrix multiplication (grams/cup time cups = grams).
So to get the answers, we have to divide each answer by 10 to get grams per cup. So the numbers in bold are our answers:
Matrix Word Problem when Tables are not Given:
Sometimes you'll get a matrix word problem where just numbers are given; these are pretty tricky. Here is one:
An outbreak of Chicken Pox hit the local public schools. Approximately 15% of the male and female juniors and 25% of the male and female seniors are currently healthy, 35% of the male and female juniors and 30% of the male and female seniors are currently sick, and 50% of the male and female juniors and 45% of the male and female seniors are carriers of Chicken Pox.
Using two matrices and one matrix equation, find out how many males and how many females (don't need to divide by class) are healthy, sick, and carriers.
Solution:
The best way to approach these types of problems is to set up a few manual calculations and see what we're doing. For example, to find out how many healthy males we would have, we'd set up the following equation and do the calculation: .15(100) + .25(80) = 35. Likewise, to find out how many females are carriers, we can calculate: .50(120) + .45(100) = 105.
We can tell that this looks like matrix multiplication. And since we want to end up with a matrix that has males and females by healthy, sick and carriers, we know it will be either a 2 x 3 or a 3 x 2. But since we know that we have both juniors and seniors with males and females, the first matrix will probably be a 2 x 2. That means, in order to do matrix multiplication, the second matrix that holds the %'s of students will have to be a 2 x 3, since there are 3 types of students, healthy (H), sick (S), and carriers (C). Notice how the percentages in the rows in the second matrix add up to 100%. Also notice that if we add up the number of students in the first matrix and the last matrix, we come up with 400.
Matrix Multiplication when Diagonals are Answers:
The first table below show the points awarded by judges at a state fair for a crafts contest for Brielle, Brynn, and Briana. The second table shows the multiplier used for the degree of difficulty for each of the pieces the girls created. Find the total score for each of the girls in this contest.
Solution:
This one's a little trickier since it looks like we have two 3 x 2 matrices (tables), but we only want to end up with three answers: the total score for each of the girls.
If we were to do the matrix multiplication using the two tables above, we would get:
Hmm….this is interesting; we end up with a matrix with the girls's names as both rows and columns. It turns out that we have extraneous information in this matrix; we only need the information where the girls' names line up. So we only look at the diagonal of the matrix to get our answers: Brielle had 86.8 points, Brynn 79.2 points, and Briana 110 points.
What we really should have done with this problem is to use matrix multiplication separately for each girl; for example, for Brielle, we should have multiplied and so on. Oh well, no harm done; and now you'll know what to do if you see these types of matrices problems.
Using Matrices to Solve Systems
Solve these word problems with a system of equations. Write the system, the matrix equations, and solve:
Finding the Numbers Word Problem:
The sum of three numbers is 26. The third number is twice the second, and is also 1 less than 3 times the first. What are the three numbers?
Let x = the first number, y = the second number, and z= the third number. So here are the three equations:
Note that, in the last equation, "one less than" means put the –1 at the end (do this with real numbers to see why).
We need to turn these equations into a matrix form that looks like this:
So we need to move things around so that all the variables (with coefficients in front of them) are on the left, and the numbers are on the right. (It doesn't matter which side; just watch for negatives). If we just have the variable in the equation, we put a 1 in the matrix; if we don't have a variable or a constant (number), we put a 0 in the matrix. So we get: and in matrix form:
Putting the matrices in the calculator, and using the methods from above, we get:
So the numbers are 5, 7, and 14. Much easier than figuring it out by hand!
A Florist Must Make 5 Identical Bridesmaid Bouquets Systems Problemt = the number of tulips, and l = the number of lilies. So let's put the money terms together, and also the counting terms together:
Now let's put the system in matrices (let's just use one matrix!) and on the calculator:
So for all the bouquets, we'll have 80 roses, 10 tulips, and 30 lilies.
So for one bouquet, we'll have of the flowers, so we'll have 16 roses, 2 tulips, and 6 lilies.
An Input Output Problem
Input-output problems are seen in Economics, where we might have industries that produce for consumers, but also consume for themselves. An application of matrices is used in this input-output analysis, which was first proposed by Wassily Leontief; in fact he won the Nobel Prize in economics in 1973 for this work.
We can express the amounts (proportions) the industries consume in matrices, such as in the following problem:
The following coefficient matrix, or input-output matrix, shows the values of energy and manufacturing consumed internally needed to produce $1 of energy and manufacturing, respectively. In other words, of the value of energy produced (x for energy, y for manufacturing), 40 percent of it, or .40x pays to produce internal energy, and 25 percent of it, or .25x pays for internal manufacturing. Of the value of the manufacturing produced, .25y pays for its internal energy and .10y pays for manufacturing consumed internally. The inputs are the amount used in production, and the outputs are the amounts produced.
(a) If the capacity of energy production is $15 million and the capacity of manufacturing production is $20 million, how much of each is consumed internally for capacity production?
(b) How much energy and manufacturing must be produced to have $8 million worth of energy and $5 million worth of manufacturing available for consumer use?
Solution:
(a) If production capacities are $15 million for energy and $20 million for manufacturing, the amount consumed internally is . So $11 million of energy is consumed internally and $5.75 million of manufacturing is consumed internally.
This makes sense, for example, since we're multiplying the proportion of energy consumed internally (.4) by the production capacity for energy ($15 million) and adding that to the proportion of energy needed for internal manufacturing (.25) by the production capacity of manufacturing ($20 million) to get the total dollar amount of energy needed or consumed internally ($11 million). Then we do the same for manufacturing.
(b) The amount of energy and manufacturing to be produced to have $8 million worth of energy and $5 million worth of manufacturing available for consumer (non-internal) use is solved using the following equation (we want what's "left over" after the internal consumption, so it makes sense): . To get , we can use the formula . So the two industries must produce $17.7 million worth of energy and $10.5 million worth of manufacturing, respectively.
Cramer's Rule
Sometimes you'll have to learn Cramer's Rule, which is another way to solve systems with matrices. Cramer's Rule was named after the Swiss mathematician Gabriel Cramer, who also did a lot of other neat stuff with math.
Cramer's rule is all about getting determinants of the square matrices that are used to solve systems. It's really not too difficult; it can just be a lot of work, so again, I'll take the liberty of using the calculator to do most of the work 🙂
Let's just show an example; let's solve the following system using Cramer's rule:
To solve for x, y, andz, we need to get the determinants of four matrices, the first one being the 3 by 3 matrix that holds the coefficients of x, y, and z. Let's call this first determinant D;
Now we'll get a matrix called , which is obtained by "throwing away" the first (x) column, and replacing the numbers with the "answer" or constant column. So
You can probably guess what the next determinant we need is: , which we get by "throwing away" the second column (y) of the original matrix and replacing the numbers with the constant column like we did earlier for the x. So Similarly,
OK, now for the fun and easy part! To get the x, y, and z answers to the system, you simply divide the determinants So Now we know that x = 5, y = 1, and z = –2.
Note that, like the other systems, we can do this for any system where we have the same numbers of equations as unknowns.
Number of Solutions when Solving Systems with Matrices
Most systems problems that you'll deal with will just have one solution. (These equations are called independent or consistent).But, like we learned in the Systems of Linear Equations and Word ProblemsSection here, sometimes we have systems where we either have no solutions or an infinite number of solutions.
Without going too much into Geometry, let's look at what it looks like when three systems (each system looks like a "plane" or a piece of paper) have an infinite number of solutions, no solutions, and one solution, respectively:
Systems that have an infinite number of solutions (called dependent or coincident) will have two equations that are basically the same. One row of the coefficient matrix (and the corresponding constant matrix) is a multiple of another row. Then it's like you're trying to solve a system with only two equations, but three unknowns.
A system that has an infinite number of solutions may look like this:
Systems with no solutions (called inconsistent) will have one row of the coefficient matrix a multiple of another, but the coefficient matrix will not have this. So a system that has no solutions may look like this:
When you try to these types of systems in your calculator (using matrices), you'll get an error since the determinant of the coefficient matrix will be 0. This is called a singular matrix and the calculator will tell you so:
Also, if you put these systems in a 3 by 4 matrix and use RREF, you'll be able to see what is happening. For the systems with infinite solutions, you can see you won't get an identity matrix, and that 0 always equals 0. You can actually define the set of solutions by just allowing z to be anything, and then, from the other rows, solve for x and y in terms of z: This would look like so the solution set for {x, y, z} is {5 – .375z, 3 + .875z, z}. (This may be a little advanced for high school 🙂 )
For the system with no solutions, you'll get this, where you can see that you still don't have an identity matrix, and 0 can never equal 1 from the last row:
Learn these rules, and practice, practice, practice!
Use the MathType keyboard to enter a Limit188 thoughts on "The Matrix and Solving Systems with Matrices"
Comment navigation
Great Work Lisa…..I am a Software Guy but didn't had the basic understanding of the Matrices,your explanation was from the basics and of great help. Now I can solve the matrices coding problems quite easily.
BWT, which books would you recommend for kids between 10-15 years(for nephews)…when i was small all books started off with "matrix(or any other concept) is used in large applications and should be studied seriously"…..but never-ever did any book explain how to use it in daily basis.(the drawback of having too much knowledge by writers…i suppose).
Thanks so much for taking a look at the site and writing! Honestly, if you're just teaching the kids math topics, I always like the "… for Dummies" books or the "Idiot's Guide to …" books. They explain things really in a more direct way, and give lots of examples.
Keep using my site, and please let me know if you see any ways it can be better 🙂 Lisa B C
Total Commission
drawn (N)
January
90 100 20
800 200
February
130 50 40
900 300
March
60 100 30
850 400 =January
90 100 20,commission=800 200
Problem 1:
(Performance Test) A teacher estimates that of the students who pass a test 80% will pass the next test, while of the students who fail a test, 50% will pass the next test. Let x an y denote the number of students who pass and fail a given test, and let u and v be the corresponding numbers for the following test.
(a) write a matrix equation relating x & y to u & v.
(b) suppose that 25 of the teacher's students pass the third test and 8 fail the third test. How many students will pass the fourth test. Approximately how many passed the second test?
Problem 2:
Problem 3:
New parents Jim and Lucy want to start saving for their son"s college education. They have $5000 to invest in three different types of plans. A traditional savings account pays 3% annual interest, a certificate of deposit (CD) pays 6% annual interest, and a prepaid college plan pays 7½ % annual interest. If they want to invest the same amount in the prepaid college fund as in the other two plans together, how much should they invest in each plan to realize an interest income of $300 for the first year?
Thanks for writing. For now, I will do problem 3; let me know if you still need help on the other problems. I'd set up like this: .03x + .06y + .075z = 300. x + y + z = 5000, and z = x + y. If I put this into a matrix and solve, I get x = $1250, y = $1250, and z = $2500. Does that make sense? LisaHere's how I did this – let t1, t2, t3 be times for first guy, t4, t5, t6 be times for second. t1 + t2 + t3 = 5 40/60. t4 + t5 + t6 = 3 +35/60. Also, 6t1 + t2 + 10t3 = 32, and 6t1 = 8t4, t2 = 2t5, and 10t3 = 15t6. Solving by matrices, I get t1 = 1 2/3, t2 = 2, and t3 = 2. So then I get the distances of 10, 2, and 20 for running, swimming and biking. Does that make sense? Lisa
Hello there! I need some help with this word problem matrix. I've been working on it for hours and have gotten absolutely nowhere!
A health shop owner made trail mix containing dried fruit, nuts, & carob chips. The dried fruit sells for $5.50/lb, the nuts for $7.50/lb, & $8.50/lb for carob chips. The shop owner mixed 50lbs of trail mix & sells it for $6.70/lb. If the amount of nuts is 5lbs more than the carob chips, how much of each item was used in the trail mix?
Thanks for writing! Here's how I'd do this problem: 5.5f + 7.5n + 8.5c = 50(6.7), f + n + c = 50, n = 5 + c. Then I used the following matrix: [5.5 7.5 8.5 335 1 1 1 50 0 1 -1 5] (This is a 4 by 3 matrix, and I use RREF in the graphing calculator to get the answers). I get 25 lbs of fruit, 15 of nuts, and 10 of carob chips. Does this make sense? Lisa
OH MY GOSH, thank you so so much! I was using the $6.70 for the second equation and 50lbs just for the first instead of multiplying 50 by $6.70. I appreciate it so much! This website is amazing thank you for using so many examples for even upper level math courses. My Trig & Calculus final are in a few weeks & this will save my life for sure!
Aisha has RM10000 to invest. As her financial consultant, you recommend that she invest in Treasury bills that yield 6%. Treasury bonds that yield 7% and corporate bonds that yield 8%. Aisha wants to have an annual income of RM680, and the amount invested in corporate bond must be half that invested in Treasury bills. Find the amount of each investment.
miss what the way to make this in matrix?i not able to answer it and if you know to make it in c coding can u share it.
A roadside fruit stand sells mangoes at Php 75 a kilo, pomelos at Php 90 a kilo, and star apples at Php 60 a kilo. Karla buys 18 kilos of fruits at a total cost of Php 1380. Her pomelos and star apple together cost Php 180 more than her mangoes. How many kilos of each kind of fruit did she buy? Write a system of equations using Cramer's Rule.
Here's how I'd set up this problem: 75m + 90p + 60a = 1380. m + p + a = 18. 90p + 60a = 75m + 180. We can then set up in a matrix: [ 75 90 60 1380
1 1 1 18
-75 90 60 180]
I then get 8 mangos, 6 pomelos, and 4 star apples. You can do this with Cramer's Rule using the information found here. Does that make sense? Lisa
How much copper and how much iron should be added to 100 lb of an alloy containing 25% copper and 40% iron in order to obtain an alloy containing 30% copper and 50% iron? Write a system of equations using Cramer's Rule.
Jane is asked to buy three sizes of bottled water: A, B and C. The total number of bottles she needs to buy is 50. She has a budget of Php 1500. Size A is Php 20 each, size B is Php 50 each, and size C is Php 30 each. Additionally, the number of bottles of size A should be equal to that size of C. How many of each size should she buy? Write a system of equations using Cramer's Rule.
1.The buying price of a basket of oranges is #1000 and the selling price is #5 per orange. what is the profit per basket if 300 oranges are found in the basket.?
a. #150
b.#200
c.#300
d. #500.
2. what is the break even point(quantity)if the buying price of a basket remains #1000 and the selling price is #5
Thanks for writing! Here's how I'd do this problem: Let x = the number of oranges. Then we have Profit = Revenue – Cost. So Profit = 5x – 1000. If 300 oranges are in the basket, we have Profit = 5(300) – 1000 = #500 (d). The break even point would be when profit = 0, so 0 = 5x – 1000, or x = 200 oranges. Does that make sense? Lisa
Hello, I see that you have been very helpful with assisting with systems of equations and matrices. Could you please help me set this up?
You have been hired by a consultant for Crazy Al's Car Rentals in the city of Metropolis. Crazy Al's car rentals has a total of 2200 cars that it rents from three locations within the city: Metropolis Airport, downtown and Suburban Airport.
Following is the weekly rental and return patterns:
90% of costumers who rent from Metropolis Airport return their cars to Metropolis Airport
5% rent from Metropolis Airport and return to Downtown
80% rent from Downtown and return to downtown
10% rent from Downtown and return to Metropolis Airport
10% rent from Suburban Airport and return to Metropolis Airport
5% rent from Suburban Airport and return to downtown
How many of his cars should be at each of his three locations at the start of each week so that the same number of cars will be there at the end of the week (and hence at the start of the next week).
Use systems of equations and matrices to set up a systems of equations representing this situation and solve this problem.
Include math steps.
Any help would be appreciated. I don't know where to even start
Thanks!
1) The 7th term of an A.P is 15 and the fourth term is 9. Find the common difference of the sequence
2) The 7th term of an A.P is 15 and the fourth term is 9. find the sequence fifth term.
3) The 7th term of an A.P is 15 and the fourth term is 9. Find the sequence tenth term.
4) The 7th term of an A.P is 15 and the fourth term is 9. Find the sequence first term
5) Find the 7th term of an A.P whose first term is 102 and common difference is -3,
I await your respose liza. Thanks
So let's use the equation for an arithmetic sequence: an = a1 + d(n – 1). Since 15 – 9 is 6, and 7 – 4 is 3, we can see that the common difference is 6/3 = 2. (See how this would mean every term goes up by 2?) So we have an = a1 + 2(n – 1). Let's plug in a "point" to get what a1 is: 15 = a1 + 2(7 – 1), so a1 = 3. So the sequence is an = 3 + 2(n – 1). So the 5th term or a5 is 3 + 2(5 – 1), or 11. See if you can do the other problems? Thanks 😉 Lisa
i need help..
question is : An automobile company uses three types of steel S1, S2 and S3 .For producing three types of cars c1, c2 , c3. Steel Requirements (in tons) for each type of car are given below:
type of cars
C1 C2 C3
S1 2 3 4
S2 1 1 2 TYPE OF STEEL
S3 3 2 1
Determine the number of cars of each type which can be produced using 29, 13 and 16 tons of steel of three types respectively.
hi everyone please help me with these..
suppose three companies: A, B, C dominates the market for a certain product and are competing against each other for a large share of the market. currently comapany A has 2/9 of the market, comapany B has 4/9 of the market and company C has 1/3 of the market. the market survey indicates that every 6 months company A retains 3/4 of its customer and loss 1/6 to company B and 1/12 to company C. company B retains 1/2 of its customer and loss 1/3 to company A and 1/6 to company C. company C retains 3/8 of its customer and loss 1/4 to company A and 3/8 to company B. find the share of the market that each company will have.
1. one year later
2. in the long run
Here's how I'd set this up: Total revenue – 500(700) + 200(1000) + ?(250), Total cost – 200(700) + 125(1000) + 600(250). Then to get the profit, subtract the cost from the revenue. Does that make sense? Lisa
a shopkeeper sells three products vise x,y,z during a particular month 20units of x, 30 units of y and 45 units of z were sold at rs 120 ,rs 100 and rs 225 respectively . the cost of x ,y,z to the shopkeeper is rs95,rs 125 and rs 185respectively .find the profit made by him using matrix algebra
Thanks for writing. Here's how I'd do this: profit = revenue – cost profit = [120 – 95 100 – 125? 225 – 185] [20
30
45]
I'm not sure if you have a typo since the cost of product y is greater than the profit?
Anyway, if you do this matrix multiplication, you should get a 1 x 1 matrix that shows the profit. Does this make sense? Lisa
An cleaning company performs vacuum cleaning, dusting and general clean-up work. For each task they charge by the hour – vacuum cleaning $30, dusting $50 and general clean-up work $60. They have four employees: Allan, Bryan, Casey and Danny. Each one is capable of handling all three types of work. Allan is paid $25 an hour while Bryan, Casey and Danny are paid $14, $11.50 and $8 respectively. Table A shows the number of hours each employee spends, on average, on each task in a normal week. Table B shows the hours spent on each of the three types of work for each of four clients Eddy, Freddy, Gretel and Hannah in a particular week.
Using matrix representation and methods, determine:
a) the income generated by each of the four employees
b) the cost, in terms of salary, of each of the three types of work performed
c) the charge made to each client for a week's work
(a) A simple society economy consists of Wool Production, Butchery and Hides
Tanning. 60% of each unit wool output goes towards wool production, 10%
towards running of the butchery and the rest towards hides tanning. Each of
output from the butchery is shared among the three sectors Wool, Butchery and
Hide Tanning in the ration of 3:5:2. 20% of each of the hides tanning output
goes towards Wool production, 10% towards running the Butchery and the rest
towards hides tanning. Given that the external demand for the output from Wool
Processing, Butchery and Hides Tanning are respectively 600Units, 1500 Units
and 900 Units, Find:-
Kindly help me derive the technical coefficient matrix from this
Hi,kindly help me solve this
An investment advisor has two types of investments available for clients
Investment Type A that pays 4% P.A and B of a higher risk that pays 8% P.A
clients may divide the investment btn the two alternatives to achieve any total returns desired between the two. However the higher the desired returns the higher the risk.
clients
clients 1 2 3
TOTAL INVEST MENT 20000 50000 10000
ANNUAL RETURNS DESIRED 1200 37500 500 R1
6% 7.50% 5% R2
Using Inverse method how should each client invest to achieve the indicated returns
Let x = (x1 , . . . , xn )′ be a vector containing the number of units purchased of each of a variety of grocery items. Let y = (y1, . . . , yn)′ be a vector of unit prices, such that yi = the price/unit of item i. For example, x = (4, 3, 2)′ and y = (.95, .25, 6.50)′ might represent 4 dozen eggs at $0.95 per dozen, 3 lbs. of apples at $0.25/lb, and 2 cans of pate de fois gras at $6.50 per can (cheap, if it's entier).
(a) Formulate a matrix expresstion for the total (net) cost of the commodities in x.
The answer to this is easy: Total cost = x'y
(b) Suppose each commoditiy is subject to a particular rate of tax, these being given by a vector, t = t1, . . . , tn so that if commodity i is taxed at 5%, ti = 0.05. Formulate an expression in terms of matrices and vectors for the total cost of x including taxes. [Remember, cost after tax = net cost × (1 + t).]
Here's how I'd do this one – although, there may be an easier way! For b), create 3 by 3 matrix that contains the numbers of units, so it would look like:
[4 0 0
0 3 0
0 0 2]. Call this matrix A. Then create 3 by 1 matrix with prices, so it would look like:
[.95
.25
6.5]. Call this matrix B.
Then multiply A by B and transpose it, so you'll have (A * B)^T, to get 1 by 3 matrix: [3.8 .75 13]. Call this matrix or vector C.
Then create vector <1 1 1> + = <1 + t1 1 + t2 1 + t3> and multiply it by C. You should then have the total cost.
Maybe there's any easier way? Lisa
Lisa,
I have an input-output problem with a twist. Three services (1, 2, & 3) are used to produce 2 products (4 & 5). The outputs for each service and product are 1 = 10, 2 = 100, 3 = 500, 4 = 24, and 5 = 36. The input-output relationships are shown in a square matrix as follows:
[10 -20 -150 0 0
-6 100 -100 0 0
-4 -30 500 0 0
0 -40 -50 24 0
0 -10 -200 0 36]
Thus, each service and product's output is shown as a positive number on the diagonal and its consumption by the other services & products are shown as negative numbers in the columns.
Each service and product also incur direct costs of 1 – $500, 2 – $750, 3 – $900, 4- $1,100 and 5 – $400. I can calculate the cost of the two products (I think) by inverting the matrix and multiplying it by the direct cost vector. Product 4 then costs $90.38 and Product 5 = $41.14.
Here is the twist: If my actual sales result in a different product mix (let's assume 36 for 4 and 24 for 5) how can I calculate what my output levels for services 1, 2 and 3 should have been based on the actual product mix realized? I guess I am trying to determine the diagonal values for the 3 services based on the realized diagonal values of products 4 and 5 given the known consumption relationships of services?
Hi Lisa! I just had a question about matrices- this problem has stumped me and I just don't how to solve it. I would be greatly appreciative if you'd help me out 🙂
"An investment company recommends that a client invest in AAA. AA. and A rated bonds. The average annual yield on AAA bonds is 6%, on AA bonds is 7%, and on A bonds is 10%. The client tells the company she wants to invest twice as much in AAA bonds as in A bonds. How much should be invested in each type of bond if the client has a total of $50,000 to invest, and wants an annual income (that is, earned interest) of $3,620 yearly?"
PLEASE HELP ME!!!!
Find the encoding matrix from this information:
– position 1,1 in the encoding matrix is an even number
– the decoding matrix only contains integers
– position 1,1 in the encoding matrix is the negative of the number in position 1,1 in the decoding matrix
– modulo arithmetic hasn't been used | 677.169 | 1 |
Math Connects: Concepts, Skills, and Problem Solving was written by the authorship team with the end results in mind. They looked at the content needed to be successful in Geometry and Algebra and backmapped the development of mathematical content, concepts,…
A walkthrough of computer science concepts you must know. Designed for readers who don't care for academic formalities, it's a fast and easy computer science guide. It teaches the foundations you need to program computers effectively. | 677.169 | 1 |
Showing 1 to 24 of 24
MATH 300
Linear Algebra I
Lecture 4
September 1, 2010
icsi-logo
MATH 300 Linear Algebra I Lecture 4
Section 1.5: Solution Sets of Linear Systems
Denitions
A system of linear equations is said to be homogeneous if it can
be written in the form Ax = 0, wher
MATH 300
Linear Algebra I
Section 2.9 Lecture
icsi-logo
MATH 300 Linear Algebra I Section 2.9 Lecture
Section 2.9: Dimension and Rank
Purpose of selecting a basis
Why do we care about a basis of H rather than any set that
spans H:
Each vector in H is a un
MATH 300
Linear Algebra I
Section 5.3 Lecture
icsi-logo
MATH 300 Linear Algebra I Section 5.3 Lecture
Section 5.3: Diagonalization
Matrix factorization
Recall that A is said to be similar to B if there exists an
invertible matrix P such that
A = PBP 1
Thi
MATH 300
Linear Algebra I
Section 6.2 Lecture
icsi-logo
MATH 300 Linear Algebra I Section 6.2 Lecture
Section 6.2: Orthogonal Sets
Denition
A set of vectors u1 , u2 , . . . , up in Rn is said to be an orthogonal set if each pair of
distinct vectors from t
MATH 300
Linear Algebra I
Section 3.2 Lecture
icsi-logo
MATH 300 Linear Algebra I Section 3.2 Lecture
Section 3.2: Properties of Determinants
Theorem
Row Operations
Let A be a square matrix.
If a multiple of one row of A is added to another row to
produce
MATH 300
Linear Algebra I
Section 2.8 Lecture
icsi-logo
MATH 300 Linear Algebra I Section 2.8 Lecture
Section 2.8: Subspaces of Rn
Denition
A subspace of Rn is any set H Rn that has these three
properties:
1
The zero vector is in H
2
For each u and v in H | 677.169 | 1 |
Syllabus for Math 334, Spring 2017
Course Description
Methods used in solving ordinary differential equations and their applications. Numerical methods, series solutions, and Laplace Transforms.
Important Dates
First day of classes is on Monday, March 6th.
Last day to add/drop a class online without a fee is on Thursday, March 9th.
Last day to add a class with faculty signature is on Thursday, March 16th.
Kuhio Day Holiday is on Monday, March 27th.
Last day to drop a class (with fee) is on Thursday, April 6th.
Last day to withdraw from a class (with fee) is on Tuesday, April 25th.
Empower Your Dreams is on Thursday, May 11th.
Memorial Day Holiday is on Monday, May 29th.
Last day of classes is on Wednesday, June 7th.
Calculators and Computers
A calculator can be helpful in the course. However, work must always be shown to receive full credit. You will not receive credit for just writing down the answer. Answers are not as important as the process through which an answer is derived.
Mathematics Learning Center
The MLC (GCB 173/177) is a good place for math students to study.
Other students will be there working on their math homework, which means
its a pretty good place to work together. To make it even better, there
are math tutors to help on problems that you or your classmates can't
solve.
Additional Help
Seek help if and when you need it! The best time to
catch me at my office is during my office hours, or by appointment.
Email me to schedule an appointment. Use email to ask me a question!
Attendance
Attendance is mandatory! Come every day! Your attendance and full
participation in this class are required for a satisfactory grade.
You are responsible for any material covered during your absence!
You must ask other classmates for any hints or help learned in class
during your absence! Prolonged absence from class or
often arriving to class late will lower a student's grade.
Classroom Decorum.
Late arrival or early departure from class, unless by prior
agreement with me, is considered to be disruptive classroom behavior.
Conversation between students during presentations is considered
disruptive behavior. If you find that you are distracted during
classroom presentations by disruptive behavior of any sort, please talk
with me.
Course Goals
The goal of this course is to provide math majors an extended study of the topic of calculus. This course can be thought of as "fourth" semester calculus. Emphasis will be on solving systems of linear differential equations, with numerical solutions to ODEs included as well. Solving problems also plays a prominent role in the class.
Instructional Methods
The primary instructional method will be lecture and discussion, where the initial portion of the class is available for questions. Secondary methods include homework, quizzes, and written exams, as well as solutions to selected assignments. Tertiary methods may include class handouts, student board work, graphing calculators, and computer software. Students are encouraged to ask questions of the instructor at his office if time is not available in class.
Homework and Quizzes
Homework will be assigned but not completely collected. You should have the homework completed the class period after we cover the section in class. Homework assignments will be turned in using the Canvas LMS found at Make sure you keep up! You need to be self-motivated. If you do not do any homework, then you will not pass this class! Homework is your opportunity to prepare for the quizzes and exams. You will find that quizzes will be modeled after the homework, and may include exact problems from the homework. Quizzes will be given approximately once weekly. Quizzes cannot be made up for ANY reason, since I will drop one out of every five quizzes. If you keep all your homework and quizzes organized in a loose leaf notebook, you'll find it easier to study for the exams. Working with partners or in groups on homework is encouraged!
Work all of the problems below, but only turn in the boldfaced problem(s) as your "turn in" portion. While the other problems are not turned in, they are fair game for a test or a quiz.
Exams
The tests will be in the the Testing Center, except for the final, which
will be in our classroom. Students who fail to take an exam during the
scheduled time may only take a make-up exam for full credit if
previous arrangements were made with the instructor or under
extenuating circumstances. Make-up exams are rarely given. Note that
class is not held during exam times; hence, the scheduled class time may
be used to take exams. Under no circumstances will the lowest exam
score be dropped. A schedule of the exams is on the calendar for
section 1.
Exam
Material covered
1
Chapter 1, 2, 3
2
Chapter 4, 5
3
Chapter 6, 7
4
Chapter 8
Final
comprehensive
Final Exam Policy
School policy
dictates: "Final exams are to be offered on the specific day and
time as determined by the official university exam schedule. Students
must plan travel, family visits, etc., in a way that will not
interfere with their final exams. Less expensive air fares, more
convenient travel arrangements, family events or activities, and any
other non-emergency reasons are not considered justification for early
or late final exams.'' Exceptions to this policy are as follows and
should be submitted in writing to the Dean of the college or school as
soon as possible:
An activity sponsored by
BYU-H which takes an individual or a team away from the campus at the
time an examination is scheduled;
Emergency situations that are beyond the student's control
Grading and Evaluation
Your course grade will be based on exams, a final, homework, and quizzes. Exams will be worth 70% of the course grade, with 15% for homework and the remaining 15% in quizzes. Letter grades will be assigned as follows:
A
93-
A-
90-93
B+
87-90
B
83-87
B-
80-83
C+
75-80
C
70-75
C-
65-70
D
55-65
D-
50-55
F
Below 50
Statements for Course Syllabii
The Honor Code exists to provide and education in an
atmosphere consistent with the ideals and principles of the Church
of Jesus Christ of Latter-day Saints. Students, faculty and staff
are expected to maintain the highest standards of honor,
integrity, morality, and consideration of others in personal
behavor. Academic honesty and dress and grooming standards are to
be maintained at all times on and off campus. The schools policy
on Academic Honesty can be found at the web page
Students are reminded that they have signed the school Honor Code,
and have agreed to abide by the code.
Discrimination: Brigham Young University - Hawaii is
committed to a policy of nondiscrimination on the basis of race,
color, sex, pregnancy, religion, national origin,
age, disability, genetic information, or veteran status
in admissions, employment, or in any of its educational programs
or activities. For specific information, see the
non-discrimination policy at
Title IX and Sexual Misconduct: The University will
not tolerate any actions prescribed under Title IX legislation,
specifically sexual harassment, sexual violence, domestic or
dating violence or stalking perpetrated by or against any
university students, university emp0loyees or participants in
university programs. For specific information see
All faculty and staff are deemed responsible reporting parties and
as such mandated to report incidents of sexual misconduct
including sexual assault to the Title IX Coordinator:
Student Academic Grievance policy: Students who feel
that their work has been unfairly or inadequately evaluated by an
instructor are encouraged to pursue the matter as an Academic
Grievance by following the steps found in the Academic Grievance
policy at
Disability Services: If you have a disability and
need accommodations, you need to contact the Disability
Officer/Coordinator at: | 677.169 | 1 |
Article: PhotoMath
PhotoMath
Math is one of the hardest subjects in school,why don't we have math problem solver making the math more easy and say it as cool math. which is why owning a calculator seems like a necessity for students as math solver. But what if you could use your smartphone to solve equations by pointing the camera at the problem in your textbook instead of using a calculator as a camera calculator? That is the idea behind PhotoMath say photo maths. PhotoMath is a photomath camera calculator free mobile app that can read and solve mathematical expressions using your smartphone camera in real time math equation solver.
I have been looking for app that solves math problems. We have calculator in smartphones but we have to type each and every equation then we have to go through the math answer app. This app just takes the picture picture math and gives the solution math solution app which makes our work easy and smarter. I have gone through this photomath app for andriod I liked it and try it photomath camera calculator you would like it.
The photomath app for android uses optical character recognition (OCR) technology to read the equation and calculates the answers within seconds. There is a red frame in the PhotoMath app that you have to use to capture the equation.
"Most about PhotoMath focus on it's use as a cheating tool. Let's be honest: many kids cheat anyway, and an app which solves math problems math problem solver app won't make this problem worse," it added.
Learning math doesn't have to be a struggle! Meet Photomath, the world's smartest camera calculator and math assistant. Scan math problems with the app and get instant solutions and step-by-step explanations. Works for anyone to whom math class is giving nightmares: students, parents, or teachers!
"PhotoMath currently supports basic arithmetics, fractions, decimal numbers, linear equations and several functions like logarithms. New math is constantly added in new app releases," says the description of the PhotoMath app on iTunes. | 677.169 | 1 |
Geometry Definitions Guided Notes
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1.61 MB | 14 pages
PRODUCT DESCRIPTION
Start the year off well with this activity! The contents include a discussion about how geometry is an axiomatic system, why we need undefined terms, and how we build our definitions based on those basic undefined terms. It also includes the definitions necessary to have a great foundation for geometry students in 8th grade/high school geometry. At the end of the assignment, there is a pop quiz you can use to test their level of understanding | 677.169 | 1 |
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: n. You may choose to access these pages during a Maple session. To use the help command, at the Maple prompt enter a question mark (?) followed by the name of the command or topic for which you want more information. ?command 2.1 Introduction This section introduces the following concepts in Maple. • Semicolon (;) usage 5 6• Chapter 2: Mathematics with Maple: The Basics • Representing exact expressions The most basic computations in Maple are numeric. Maple can function as a conventional calculator with integers or floating-point numbers. Enter the expression using natural syntax. A semicolon (;) marks the end of each calculation. Press enter to perform the calculation.
> 1 + 2; 3
> 1 + 3/2; 5 2
> 2*(3+1/3)/(5/3-4/5); 100 13
> 2.8754/2; 1.437700000 Exact Expressions
Maple computes exact calculations with rational numbers. Consider a simple example.
> 1 + 1/2; 3 2 The result of 1 + 1/2 is 3/2 not 1.5. To Maple, the rational number 3/2 and the floating-point approximation 1.5 are distinct objects. The ability to represent exact expressions allows Maple to preserve more information about their origins and structure. Note that the advantage is greater with more complex expressions. The origin and structure of a number such as 0.5235987758 2.2 Numerical Computations •7 are much less clear than for an exact quantity such as 1 π 6 Maple can work with rational numbers and arbitrary expressions. It can manipulate integers, floating-point numbers, variables, sets, sequences, polynomials over a ring, and many more mathematical constructs. In addition, Maple is also a complete programming language that contains procedures, tables, and other programming constructs. 2.2 Numerical Computations This section introduces the following concepts in Maple. • Integer computations • Continuation character (\) • Ditto operator (%) • Commands for working with integers • Exact and floating-point representations of values • Symbolic representation • Standard mathematical constants • Case sensitivity • Floating-point approximations • Special numbers • Mathematical functions Integer Computations
Integer calculations are straightforward. Terminate each command with a semicolon.
> 1 + 2; 8• Chapter 2: Mathematics with Maple: The Basics 3
> 75 - 3; 72
> 5*3; 15
> 120/2; 60 Maple can also work with arbitrarily large integers. The practical limit on integers is approximately 228 digits, depending mainly on the speed and resources of your computer. Maple can calculate large integers, count the number of digits in a number, and factor integers. For numbers, or other types of continuous output that span more than one line on the screen, Maple uses the continuation character (\) to indicate that the output is continuous. That is, the backslash and following line ending should be ignored.
> 100!; 933262154439441526816992388562667004907\ 15968264381621468592963895217599993229\ 91560894146397615651828625369792082722\ 37582511852109168640000000000000000000\ 00000
> length(%...
View
Full
Document
This note was uploaded on 08/27/2012 for the course MATH 1100 taught by Professor Nil during the Spring '12 term at National University of Singapore. | 677.169 | 1 |
Ursuline's Upper School course offerings in Mathematics give you the technical skill set and advanced aptitude to graduate from our program and enter college as an exceptionally articulate student of mathematics in theory and practice. Our cohesive curriculum design meets your individual needs and helps you progress from one course to the next while building your confidence and fostering your enthusiasm for mathematics. By delivering our instruction in a hands-on atmosphere that integrates technology and activity, our teachers illustrate high level theory and method in concrete and practical ways that encourage your interest in math- and science- related fields.
Our curriculum offers four different levels of study to meet your individual learning needs and desire for advanced challenges in mathematics – College Prep, Accelerated College Prep, Honors, and Accelerated Honors. At every level, you meet and master advanced concepts, developing strong communication skills in mathematics using its signs, symbols, and vocabulary in reading, writing, and discussion of the material. Our curriculum emphasizes problem solving, especially the importance of logical thinking and the organization of one's work, and teaches an awareness of the applications of mathematics to real world situations. By fostering your enthusiasm for mathematics and an appreciation for its history and interdisciplinary nature, you naturally rise to your fullest potential in our curriculum, which propels you to further your natural curiosity in science, math, engineering, and technology.
As a freshman, you are placed in one of our four tracks based on your 8th grade Math experience and score on our Algebra 1 Exit Exam, testing your abilities in basic Pre-Algebra and Algebra skills, factoring quadratic trinomials, solving systems of equations, and graphing calculator skills. Course offerings vary based on track selection and range from Algebra I to AP Calculus and AP Statistics for students in grades 9 – 12. Upon graduation, you are prepared for college mathematics and for the use of mathematics in your everyday life, including success in math-related careers and industries. | 677.169 | 1 |
BUYER OFFERS: We are a retail store with set pricing and unfortunately we can't fulfil any requests to sell items for less than the listed price.
Description: Graph theory goes back several centuries and revolves around the study of graphs--mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics--and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics | 677.169 | 1 |
MathAid College Algebra25.63
Publisher Description
Interactive College Algebra course designed to ensure engaging, self-paced, and self-controlled e-learning process and help students to excel in their classes. Java- and web-based math course includes theoretical concepts, hands-on examples featuring animated graphics and live formulas, problem-solving lessons, and customizable real time tests with solutions and evaluations. Topics covered: rectangular coordinate system, functions and graphs, linear and absolute value functions, quadratic functions, polynomial and rational functions, exponential and logarithmic functions, second degree equations, determinants and Cramer''s rule, matrices, complex numbers. The demo version contains selected lessons from the full version, fully functional, all features included.
Add a review
Tell us your experience with MathAid College Algebra25.63
RELATED PROGRAMS Our Recommendations
Algebra GENIE TRIAL ★★★★★ Next Generation Interactive Common-Core! Learn Algebra while having fun ★★★★★ Whether you are a high-school or college student this Algebra course will replace a whole year of boring Algebra, with fun and engaging interactions. The most complete and interactive Algebra course, developed... Download
Matrix Inversion Pro TRIAL This mathematical tool is able to calculates th invertable of a matrix.The following matrices can be inverted:- 2x2 matrices- 3x3 matrices- 4x4 matricesVery useful algebra tool for school and college. Download
MathAid Probability and Statistics TRIAL Mathaid interactive Probability and Statistics tutorial is a new java-based package for e-learning and home schooling. It guides the user through all steps of the learning process, from theoretical concepts, examples, problem-solving lessons, drills to customized tests including solutions and... Download | 677.169 | 1 |
proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using understandable, realistic applications consistent with the abilities of most readers.Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. Chapter topics include Functions and Their Graphs; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Exponential and Logarithmic Functions; and more.For anyone interested in trigonometry. | 677.169 | 1 |
MATH111
College Algebra
(3,0) 3
This course is a study of families of functions through formulas, tables, graphs and words, emphasizing applications in business, life and social science. The function families include linear, polynomial, rational, exponential, logarithmic and power functions. Within these families, topics include problem solving, model creation, solving equations, systems of equations and inequalities, rates of change, graphing, analysis, and interpretation. Prerequisites: Two years of high school algebra and satisfactory achievement on the mathematics placement exam or MATH102 with a grade of C or better. High school plane geometry also recommended. This course will not count toward a major or minor in mathematics. | 677.169 | 1 |
Forewords from Years 1 to 4
Foreword from Year 1
Several years ago, I was in your shoes, a ninth grader, starting off my first year of IMP®. The
"real world" was years away, and I hadn't yet pondered getting into college. All I
knew was that I liked my new mathematics class.
People from all sorts of backgrounds took part equally in the class. Not everyone had identical
backgrounds and not everyone thought alike. My peers would come up with ways of solving problems that
surely were not published in mathematics textbooks, and they worked just as well as the more standard
methods. This is what I truly loved about IMP. There was no one way to solve a problem. We didn't
rely on memorization or on mimicking what we were told. Instead, we were constantly challenged to
think carefully and deeply about problems.
I appreciate having acquired an in-depth knowledge of mathematical concepts, but this mathematical
knowledge is not the sole reason IMP was such a positive experience for me. IMP also helped me to
develop the communication skills I use daily. The ability to persuade people and to effectively argue
ideas has been priceless to me in both personal and academic situations. I encourage you, ninth
graders, to realize the importance of both the mathematics skills and non-mathematics skills that IMP
stresses.
Kaley Klanica was a member of the Class of 1996 at Eaglecrest High School in Colorado and the
Class of 2000 at Haverford College in Pennsylvania.
Foreword from Year 2
Is There Really a Difference? asks the title of one Year 2 unit of the Interactive Mathematics
Program (IMP).
"You bet there is!" As Superintendent of Schools, I have found that IMP students in our
District have more fun, are well prepared for our State Testing Program in the tenth grade, and are a
more representative mix of the different groups in our geographical area than students in other
pre-college math classes. Over the last few years, IMP has become an important example of curriculum
reform in both our math and science programs.
When we decided in 1992 to pilot the Interactive Mathematics Program, we were excited about its
modern approach to restructuring the traditional high school math sequence of courses and topics and
its applied use of significant technology. We hoped that IMP would not only revitalize the
pre-college math program, but also extend it to virtually all ninth-grade students. At the same time,
we had a few concerns about whether IMP students would acquire all of the traditional course skills
in algebra, geometry, and trigonometry.
Within the first year, the program proved successful and we were exceptionally pleased with the
students' positive reaction and performance, the feedback from parents, and the enthusiasm of
teachers. Our first group of IMP students, who graduated in June, 1996, scored as well on PSATs,
SATs, and State tests as a comparable group of students in the traditional program did, and
subsequent IMP groups are doing the same. In addition, the students have become our most enthusiastic
and effective IMP promoters when visiting middle school classes to describe math course options to
incoming ninth graders. One student commented, "IMP is the most fun math class I've ever
had." Another said, "IMP makes you work hard, but you don't even notice it."
In our first pilot year, we found that the IMP course reached a broader range of students than the
traditional Algebra 1 course did. It worked wonderfully not only for honors students, but for other
students who would not have begun algebra study until tenth grade or later. The most successful
students were those who became intrigued with exciting applications, enjoyed working in a group, and
were willing to tackle the hard work of thinking seriously about math on a daily basis.
IMP Year 2 places the graphing calculator and computer in central positions early in the math
curriculum. Students thrive on the regular group collaboration and grow in self-confidence and skill
as they present their ideas to a large group. Most importantly, not only do students learn the
symbolic and graphing applications of elementary algebra, the statistics of Is There Really a
Difference?, and
the geometry of Do Bees Build It Best?, but the concepts have meaning to them.
I wish you well as you continue your IMP path for a second year. I am confident that students and
teachers using Year 2 will enjoy mathematics more than ever as they experiment, investigate, and
discover solutions to the problems and activities presented this year.
Reginald Mayo
Superintendent
New Haven Public Schools
New Haven, Connecticut
Foreword from Year 3
Students must be prepared for the world that they will inherit. Whether or not they choose to enter
college immediately after high school, we must equip them to handle new problems with confidence and
perseverance. Our ever-changing world requires that students grow into critically thinking adults who
are prepared to absorb new ideas and who will become lifelong learners. The Interactive Mathematics
Program (IMP) aids in this development.
IMP enhances students' understanding of mathematics by obliging them to present reasoned arguments.
The group activities in IMP foster teamwork and the development of oral and written communication
skills. These skills are honed by requiring students to write intelligible explanations about the
processes that they followed to reach their conclusions.
As a parent of an IMP student, I have found that IMP enables students to experience mathematics in
action and to recognize that mathematics is not simply an esoteric subject. On the other hand, IMP
also offers students the opportunity to experience how beautiful and open-ended mathematics is.
As a professional mathematician, I believe that IMP teaches mathematics in the way that it should be
taught. Mathematics does not arise naturally in nicely defined semester-long modules labeled Algebra
I, Geometry, Algebra II, and Trigonometry/Precalculus. IMP effectively breaks down the artificial
barriers created by such divisions.
I have found the Problems of the Week exceedingly interesting and intellectually stimulating—sufficiently
so that I have shared several of them with members of my faculty. It is so refreshing to interact
with my son around mathematics that is quite challenging to me also. He can appreciate my excitement
and that mathematics can be fun.
As a parent and educator, I know the concerns that students, parents, school officials, and others
have about colleges' expectations of entering students. What I value most, as do many of my
colleagues at other top institutions, is that students have experienced good teaching in
well-constructed courses that emphasize communication and creative thinking, and in which the
learning that takes place is genuine and meaningful.
At Colorado School of Mines, a school of engineering and applied science, we require that our
students develop strong communication skills and learn to work effectively as team members. To help
our students enhance these skills further, we have established a writing center staffed by qualified
professionals. In the beginning courses in calculus in our Department of Mathematical and Computer
Sciences, we emphasize the working of real problems provided by the science and engineering
disciplines. Students learn to think creatively and not be tied to one notation system. We also
require our seniors to take turns at presenting reports on a research topic at weekly seminars. The
other students submit reviews of their classmates' presentations and learn from the preparation of
their assessments, in addition to providing valuable feedback to the presenter.
We expect that our students will not simply reflect their professors' thinking. Students have a
responsibility to engage in independent thinking and to understand the power of thought as distinct
from the power of authority. Students have a head start when they enter college courses with prior
knowledge in solving complex problems that go beyond calculation and in coping with ambiguity.
The Interactive Mathematics Program helps prepare students for life, not just for college calculus.
Because the Program emphasizes creative thinking, communication skills, and teamwork, it should serve
our students well.
Graeme Fairweather
Professor and Head
Department of Mathematical and Computer Sciences
Colorado School of Mines
Golden, Colorado
Foreword from Year 4
"I hated math" is an often-heard phrase that reflects an unfortunate but almost socially
acceptable adult prejudice. One hears it from TV announcers, politicians, and even football coaches.
I'll bet they didn't start their education feeling that way, however. According to the
Third International Mathematics and Science Study, American fourth graders score near the top of
their international peers in science and math. Surely mathphobia hasn't broken out by that grade
level. By twelfth grade, however, students in the United States score among the lowest of the 21
participating nations in both mathematics and science general knowledge. Even our advanced math
students—the ones we like to think are the best in the world—score at the very bottom when
compared to advanced students in other countries. What happened? Is there something different about
our students? Not likely. Is there an opportunity for improvement in our curriculum? You bet.
Traditional mathematics teaching continues to cover more repetitive and less challenging material.
For the majority of students, rote memorization, if not too difficult, is certainly an unenlightening
chore. The learning that does result tends to be fragile. There is little time to gain deep knowledge
before the next subject has to be covered. American eighth-grade textbooks cover five times as many
subjects in much less depth than student materials found in Japan. Because there is no focus on
helping students discover fundamental mathematical truths, traditional mathematics education in the
United States fails to prepare students to apply knowledge to problems that are slightly different
and to situations not seen before.
As an engineering director in the aerospace industry, I'm concerned about the shrinking supply
of talented workers in jobs that require strong math and science skills. In an internationally
competitive marketplace, we desperately need employees who have not only advanced academic skills,
but also the capability to discover new, more cost-effective ways of doing business. They need to
design with cost as an independent variable. They need to perform system trades that not only examine
the traditional solutions, but explore new solutions through lateral, "out of the box"
thinking. They need to work in teams to solve the most difficult problems and present their ideas
effectively to others.
Programs like IMP foster these skills and fulfill our need as employers to work with educators to
strengthen the curriculum, making it more substantive and challenging. I can attest to the value of
IMP because, as the father of a student who has completed four years of the program, I've
discovered that something different is going on here. My son is given problems around a theme, each
one a little harder than the one before. This is not much different from the way I was taught. What
is different is that he is not given the basic math concept ahead of time, nor is he shown how to
solve upcoming problems by following the rule. By attacking progressively harder problems in many
different ways, he often learns the basic mathematical concepts through discovery. He is taught to
think for himself. He says that the process "makes you feel like you are actually solving the
problem, not just repeating what the teacher says."
This process of encouraging discovery lies at the heart of IMP. Discovery is not fragile learning; it
is powerful learning. My son thinks it can be fun, even if he won't admit it to other
students.
I have another window on IMP as well. As the husband of a teacher who helped to pioneer the use of
IMP in her district, I've learned that teaching IMP is a lot more than letting the students do
their own thing. Lessons are carefully chosen to facilitate the discovery process. Points are given
for finding the correct answer, and points are given for carefully showing all work, which is as it
should be. Because the curriculum encourages different ways of solving a problem, my wife spends more
than the typical amount of time teachers spend in reading and understanding students' efforts.
The extra time doesn't seem to burden her, however. I think she thinks it's fun. She even
gets excited when she sees that the focus on communicating and presenting solutions is measurably
improving her students' English skills.
Let me conclude with a word of encouragement to all of you who are using this book. I congratulate
you for your hard work and high standards in getting to this, the fourth and final year of IMP. IMP
students have performed well in SAT scores against their peers in traditional programs. Colleges and
universities accept IMP as a college preparatory mathematics sequence. I know that your efforts will
pay off, and I encourage you to take charge of your future by pursuing advanced math and science
skills. Even if you don't become an aerospace engineer or computer programmer, this country
needs people who think logically and critically, and who are well prepared to solve the issues yet to
be discovered.
Larry Gilliam
Scotts Valley, California
Larry Gilliam is a parent of two IMP students and works as the chief test engineer for Lockheed
Martin Missiles & Space in Sunnyvale, California. | 677.169 | 1 |
MF60: What exactly is a polynomial?
Page Navigation
Main Profile
At A Glance
MF60: What exactly is a polynomial?
Polynomials are fundamental objects in algebra, but unfortunately most accounts of them skimp on giving a proper definition. Here we base polynomials on the more basic objects of polynumbers. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at introduce the particular positive polynumber alpha, and show that any polynumber can be written as a linear combination of powers of alpha. Then we define a positive polynomial to be a positive polynumber written in this standard alpha form.
Length:
09:38
Contact
Questions about MF60: What exactly is a polynomial?
Want more info about MF60: What exactly is a polynomial??
Get free advice from education experts and Noodle community members. | 677.169 | 1 |
Differential ManifoldsHow useful it is," noted the "Bulletin of the American Mathematical Society," "to have a single, short, well-written book on differential topology." This accessible volume introduces advanced undergraduates and graduate students the systematicMore...
"How useful it is," noted the "Bulletin of the American Mathematical Society," "to have a single, short, well-written book on differential topology." This accessible volume introduces advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds, from elements of theory to method of surgery. 1993 | 677.169 | 1 |
Algebra 1: Interpreting Functions Task Cards
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
2.02 MB | 27 pages
PRODUCT DESCRIPTION
This set of 24 task cards is made up of 6 sets of 4 cards. Each set of exercises has a different focus on the Interpreting Functions
Standards (A.IF)
1. Understand the concept of a function and use function notation.
2. Use function notation in terms of a context.
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Interpret key features of graphs, equations and tables in terms of the
quantities used.
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
A full set of solutions are included.
In my store you will find another product "Algebra 1: Interpreting Functions Task Cards with QR Codes", that is identical to this product except that product has QR Codes to access the solutions | 677.169 | 1 |
Study Guide Documents
Showing 1 to 6 of 6
DISTANCE GRAPH ACTIVITY
GROUP 1
a. Write a story to match this graph. Explain how each part of
your story matches to a part of the graph.
b. Draw a speed vs. time graph to go with your story.
Graph of distance from campus in miles versus time in minutes
s
FUNCTIONS ACTIVITY
DEFINTIONS
A relation from one set to another is a pairing of the elements in the first set with the elements in the
second set.
A dependency relation is a relation where the values of one variable depend on the values of the
other.
An
MEAN, MEDIAN AND MODE ACTIVITY
1) A class has 10 people and is divided into 2 groups to collect some data. Group A has
people with heights (in inches) of 60, 72, and 68. Group B has people with heights (in
inches) of 60, 60, 65, 68, 56, 69, and 64.
a. Cal
MODELING DATA THAT IS APPROXIMATELY LINEAR ACTIVITY
1. In BMX dirt-bike racing, jumping high or "getting air" depends on many factors: the rider's
skill, the angle of the jump, and the weight of the bike. Here are data about the maximum jump
height for va
MATH 103: ALGEBRAIC REASONING
STUDY GUIDE
To accompany Rockswold, Gary, Algebra
and Trigonometry with Modeling and
Visualization with Algebraic Reasoning
Activities Manual. Custom Edition for
Oregon State University
SKILL BUILDING
TABLE OF CONTENTS
Order
Math 103
Exam 2 Review
Name:_
You must complete this worksheet BEFORE coming to class Tuesday of the Exam!
Exam Information
When is the midterm?_
Where will you be taking the midterm?_
What should you take with you to the midterm?_
YOU MUST BRING THE FOLL
Study Guide Advice
Showing 1 to 3 of 3
I didn't learn much, it was like a review of previous algebra classes I've taken.
Hours per week:
3-5 hours
Advice for students:
Do homework, take notes, do the study guides, and ask for help.
Course Term:Fall 2016
Professor:raven dean
Course Tags:Math-heavyGo to Office HoursMany Small Assignments
Dec 26, 2016
| Would highly recommend.
Not too easy. Not too difficult.
Course Overview:
This was a great course to review high school math, especially if you didn't take math senior year and need a refresher. Set up like a high school class, it's a good way to transition into college.
Course highlights:
I learned that it can definitely be much easier to learn from a different teacher based on teaching styles and ways of explaining. I re-learned things that I learned sophomore year, but with a way clearer understanding of the concepts. Mind-blowing difference.
Hours per week:
3-5 hours
Advice for students:
Keep up on the online quizzes and don't be afraid to ask questions and your classmates for help.
Course Term:Fall 2016
Professor:sara clark
Course Required?Yes
Course Tags:Math-heavyGreat Intro to the SubjectMany Small Assignments
Sep 14, 2016
| Would highly recommend.
Pretty easy, overall.
Course Overview:
Also very clear explanations and examples.
Course highlights:
she is really nice and helpful. Also, she explains everything very well.
Hours per week:
0-2 hours
Advice for students:
there aren't enough words to explain how COOL this teacher is. yes, she has an accent, but she is so GOOD at what she does, it doesn't matter! | 677.169 | 1 |
Precalculus Mathematics for Calculus best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they haveMore...
This
James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.
Fundamentals
Overview
Real Numbers
Exponents and Radicals
Algebraic Expressions
Discovery Project: Visualizing a Formula
Fractional Expressions
Equations
Modeling with Equations
Discovery Project: Equations through the Ages
Inequalities
Coordinate Geometry
Graphing Calculators: Solving Equations and Inequalities Graphically
Lines
Modeling Variation
Review
Test
Focus on Problem Solving: General Principles
Functions
Overview
What is a Function? Graphs of Functions
Discovery Project: Relations and Functions
Increasing and Decreasing Functions: Average Rate of Change
Transformations of Functions
Quadratic Functions: Maxima and Minima
Modeling with Functions
Combining Functions
Discovery
Project: Iteration and Chaos
One-to-One Functions and Their Inverses Review
Test
Focus on Modeling: Fitting Lines to Data
Polynomial and Rational Functions
Overview
Polynomial Functions and Their Graphs
Dividing Polynomials
Real Zeros of Polynomials
Discovery Project: Zeroing in on a Zero
Complex Numbers
Complex Zeros and the Fundamental Theorem of Algebra
Rational Functions
Review
Test
Focus on Modeling: Fitting Polynomials to Data
Exponential and Logarithmic Functions
Overview
Exponential Functions
Discovery Project: Exponential Explosion
Logarithmic Functions
Laws of Logarithms
Exponential and Logarithmic Equations
Modeling with Exponential and Logarithmic Functions
Review
Test
Focus on Modeling: Fitting Exponential and Power Curves to Data
Trigonometric Functions of Real Numbers
Overview
The Unit Circle
Trigonometric Functions of Real Numbers
Trigonometric Graphs
Discovery Project: Predator-Prey Models
More Trigonometric Graphs
Modeling Harmonic Motion
Review
Test
Focus on Modeling: Fitting Sinusoidal Curves to Data
Trigonometric Functions of Angles
Overview
Angle Measure
Trigonometry of Right Triangles
Discovery Project: Similarity
Trigonometric Functions of Angles
The Law of Sines
The Law of Cosines
Review
Test
Focus on Modeling:Surveying
Analytic Trigonometric
Overview
Trigonometric Identities
Addition and Subtraction Formulas
Double-Angle, Half-Angle, and Sum-Product Identities
Inverse Trigonometric Functions
Discovery Project: Where to Sit at the Movies
Trigonometric Equations
Review
Test
Focus on Modeling: Traveling and Standing Waves
Polar Coordinates and Vectors
Overview
Polar Coordinates
Graphs of Polar Equations
Polar Form of Complex Numbers
DeMoivre's Theorem
Discovery Project: Fractals
Vectors
The Dot Product
Discovery Project: Sailing Against the Wind
Review
Test
Focus on Modeling: Mapping the World
Systems of Equations and Inequalities
Overview
Systems of Equations
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Several Variables
Discovery Project: Best Fit versus Exact Fit
Systems of Linear Equations: Matrices
The Algebra of Matrices
Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations | 677.169 | 1 |
Educational notes for instructors and studentsHow we learn problem-solving skills? Let us consider typical math tasks, such as "solve an equation", "prove an identity". In these tasks we deal with symbolic records. A formal indicator that the task is solved is a set of consecutive calculations proving the solution. To produce this set we should be capableAny training program is a tool to facilitate your work. The quality of a tool is defined by its performance and convenience of use. With this in mind, we have developed a number of program lines with different sets of user options...
You...
EMTeachline Software offers a range of training programs. The programs are arranged in topics. Within each topic, the programs differ in sets of available user options, in number of included math problems and hence in prices...
Any training program is a tool designed to build specific knowledge and a suit of practical math skills. It would be useful to have some quantitative and qualitative parameters reflecting the training capabilities of software... | 677.169 | 1 |
MATH 1
MATH 1
May 28, 2014
Integrated Math 1 is the first in a sequence of three yearlong college prep courses designed to integrate number sense, algebra, functions, geometry, and statistics. Emphasis will be placed on practical applications and modeling. Multiple technologies including applets, manipulatives, calculators, and application software are a requirement to promote a highly engaging collaborative learning environment. Student will experience the development of a branch of mathematics through the use of undefined terms, definitions, postulates and theorems. They will use algebraic models of situations; choose appropriate proof from various possibilities, and then coordinate and transformation techniques as they apply mathematical concepts to real world situations. | 677.169 | 1 |
Need to keep your rental past your due date? At any time before your due date you can extend or purchase your rental through your account.
Sorry, this item is currently unavailable.
Summary
Learn math the easy way with Tussy and Gustafson's INTERMEDIATE ALGEBRA! Study sets at the end of every chapter will improve your ability to read, write, and communicate mathematical ideas. Difficult concepts are made clear with a five-step approach to problem-solving: analyze the problem, form an equation, solve the equation, state the result, and check the solution. Prepare for exams with numerous resources located online and throughout the text such as live online tutoring, tutorials, a book companion website, chapter summaries, self-checks, practice sections, and reviews. Take advantage of the accompanying Video Skillbuilder CD-ROM that will save you class preparation time through video lessons, web quizzes, and chapter tests. | 677.169 | 1 |
Be sure that you have an application to open
this file type before downloading and/or purchasing.
2 MB|17 pages
Product Description
This differentiated outer space themed project covers quadratic functions and is the perfect way to incorporate science into mathematics. This project can be used as an individual assignment, or used as a small group collaborative activity.
The project has 4 parts:
1) Gravity on Earth, Mars, and the Moon
2) The Speed of Sound
3) A Meteorite Strikes!
4) Passing Star Demolished by a Black Hole
Skills Used:
-Graph Quadratics
-Solve Quadratics by Factoring, by using the Quadratic Formula, and by taking Square Roots
-Identify and Interpret the Vertex, Discriminant, X-intercepts in real world situations
-Identify intervals of Increase and Decrease; Domain and Range
-Make Scientific Conclusions based on Mathematical Justifications
Differentiation:
This project is differentiated into 2 tiers, which makes it perfect for the inclusive classroom! Both sets have the same exact problems, but the easier set has hints on how to get started on the problems. The graphs on the easier set also have intervals already complete on the x and y- axes.
Common Core Standards:
CCSS.HSA.REI.B.4 Solve quadratic equations in one variable.
CCSS.HSF..
CCSS.HSF.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. CCSS.HSF.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
*Purchase of this product provides one (1) purchaser the rights for solely personal classroom use. Posting any part of this publication on the Internet in any form, including classroom websites, is strictly prohibited and in violation of the Digital Millennium Copyright Act. To share this resource with colleagues, please purchase additional licenses. Inquire to mathbyrd@gmail.com for discounted multiple license purchases. | 677.169 | 1 |
in the stock market, in sports, and all over the news. Algebra is all about figuring out the numbers you don't see. You might know how fast you can throw a...
.... Develop a rich understanding of the rudiments of algebra in a relaxed and supportive learning environment. This course will help you understand some of the most important algebraic concepts, including orders of operation, units of measurement, scientific notation, algebraic equations, inequalities... Learn about: Skills and Training, Basic IT, Basic IT training... | 677.169 | 1 |
This volume contains the basics of what every scientist and engineer should know about complex analysis. A lively style combined with a simple, direct approach helps readers grasp the fundamentals, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.
Richard A. Silverman: Dover's Trusted Advisor Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the 1970s. And, as one of the preeminent translators of scientific Russian, his work also appears in our catalog in the form of his translations of essential works by many of the greatest names in Russian mathematics and physics of the twentieth century. These titles include (but are by no means limited to): Special Functions and Their Applications (Lebedev); Methods of Quantum Field Theory in Statistical Physics (Abrikosov, et al); An Introduction to the Theory of Linear Spaces, Linear Algebra, and Elementary Real and Complex Analysis (all three by Shilov); and many more. During the Silverman years, the Dover math program attained and deepened its reach and depth to a level that would not have been possible without his valuable contributions. | 677.169 | 1 |
Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory.
Updates include a chapter by J. H. Silverman on one of the most important developments in number theory - modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader.
The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.
Editorial Reviews
Review
`Review from previous edition Mathematicians of all kinds will find the book pleasant and stimulating reading, and even experts on the theory of numbers will find that the authors have something new to say on many of the topics they have selected... Each chapter is a model of clear exposition, and the notes at the ends of the chapters, with the references and suggestions for further reading, are invaluable.' Nature
`This fascinating book... gives a full, vivid and exciting account of its subject, as far as this can be done without using too much advanced theory.' Mathematical Gazette
`...an important reference work... which is certain to continue its long and successful life...' Mathematical Reviews
`...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own.' Matyc Journal
About the Author
Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor of Pure Mathematics at Oxford University. He works in analytic number theory, and in particular on its applications to prime numbers and to Diophantine equations.
I am an undergrad student in computer engineering. I bought this book after I looked at the table of contents and found some topics which I interested in. This is by far the best book on number theory I ever came across. It is very readable, fairly free of errors (the ones that are there are easy to spot and do not cause confusion). In comparison to another number theory book I read before. This one has the charm of making previously confusing concept clear. Different proofs are often given on major theorems. I do not really have a good way to describe it, but this book really "flows". The logic is clear and easy to follow. If I read this one to start with, it would save me a lot of time and I would have a much better understanding of the subject by now. I know, this review is totally uninformative, you have to see it for yourself to be sure, but I totally recommend this one.
A classic, but I wish it were written in American English. Sometimes feels a little dry compared to the text by Dudley Underwood. Author gives little historical context. A few practice problems would have been nice.
This book can be appreciated by anyone who has taken at least a serious first year calculus course. If you are familiar say with notions like uniform convergence and the Riemann integral (and can actually evaluate an integral from first principles rather than using the fundamental theorem of calculus), you are probably at a level where you can use this book. It is essential to be comfortable with induction and arguments that go like "Suppose that k is the biggest integer satisfying some property, then get a contradiction". Probably also high school students who have done Olympiad training would enjoy parts of it.
Each chapter stands mostly by itself, so for example one doesn't need to have read the earlier chapters to understand the chapters on generating functions and orders of magnitude of arithmetical functions and on the partition function, which were the first chapters I first as an undergraduate. The chapters on continued fractions and Diophantine approximation are good, and also don't depend on other parts of the book. I have that feeling that continued fractions are generally seen as (i) a curiosity, (ii) an odd tool to prove counterexamples in analysis (like the Cantor set), or (iii) as a specialized area, that perhaps descriptive set theorists or people working in transcendental number theory care about. In fact, continued fractions ought to be a part of the analyst's arsenal: they are the most natural way of representing real numbers by sequences of integers, and appear often in measure theory, especially when trying to construct explicit examples, like Lusin's set that is not Borel measurable (but which is Lebesgue measurable). Several proofs of Kronecker's theorem are given, which is a result that is probably more important in dynamical systems than it is in number theory by itself. There is a chapter on the geometry of numbers in which Minkowski's theorem, about symmetric convex sets of great enough volume containing lattice points, is proved. This book is probably the best place to read Selberg's proof of the prime number theorem. After praising the book, let me say that I have never been attracted to the chapters on quadratic fields, and of the whole book I think these are the most dated, and one might better use the sections in Dummit and Foote Abstract Algebra, 3rd Edition or for a serious presentation, Swinnerton-Dyer A Brief Guide to Algebraic Number Theory (London Mathematical Society Student Texts), or for a marvellous book just on quadratic fields that connects quadratic fields to Gauss's work on quadratic forms and later work on modular forms, Cox Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication.
I recommend this book for any mathematically trained reader. It doesn't have to be read cover to cover, and you will enjoy opening it for years. It is too broad to be used for a course and has no exercises, but for the independent reader, I recommend reading the chapter you choose from start to finish. If the chapter refers to statements proved in earlier chapters, you should carefully read the statement that is being used, understand what it says, but don't spend a minute trying to prove it, because that might send you even farther back checking other statements. You should carefully read all the proofs in the chapter and all the examples and make sure you understand every step, not just agree that it seems like a thing that could be correct but that you are sure why it is true. There may be parts that don't make sense, and if you don't have any help then try reading another chapter and coming back later.
This book is an example of how much good math can be explained without on the one hand demanding any prior machinery and without on the other hand describing math rather than doing math (like how every educated person has heard about Schrödinger's cat, and the shallow things they have heard probably leave them knowing less than if they had heard nothing at all, yet like food that is not nutritious, these shallow explanations fill the stomach and let you think you know something), and the closest comparison I can think of is Hilbert and Cohn-Vossen Geometry and the Imagination (AMS Chelsea Publishing).
Don't expect a systematic treatise : Hardy guides you into the vast and intricate number theory via side tracks, leaving a few gaps to be filled in... Which allows him to cover an enormous range of topics, in his usual clear and concise style.
In my opinion, this book should be read after Gauss's masterpiece "Disquisitiones Arithmeticae" and before Apostol's "Introduction to Analytical Number Theory".
I have owned the 4th edition for years. You might think that Hardy and Wright is dated and can't possibly be relevant, but check the data. You will find it cited in all the other number theory books and it is still being cited in journal articles as well.
The biggest improvements have been pointed out by other reviewers so I'll just state them without discussion: more readable font/spacing and a much needed subject index. For the 45% reduction in price of the paperback, I couldn't afford to pass up this edition. 4.5 stars
A worthwhile addition to anyone's mathematical library. Should not be used as a primary textbook for a class though! The book encompasses a vast array of number theoretical topics and is updated to include recent developments. However, the amount of typos is very unfortunate. Especially for such an old book. After the sixth edition, I would expect the typos in the text itself be essentially all corrected. However, they are there, in the worst places, causing me to scratch my head wondering "is this a typo?". Even the errata online has typos. Which makes me wonder, do they have an errata for the errata? Nonetheless, the book is great, I just with recent authors spent more time keeping it so.
It's give the reader a great understanding of number theory. By far one of best out there on the market and great book for reference on the topic. For my number theory class; I use this book more than the assigned book. It give much better examples and explain the subject very well, and does it in a more depth than any other number theory book. | 677.169 | 1 |
Mathematics & Further Mathematics (MEI)
We study Mathematics in order to become better at solving problems arising either from Mathematics itself or modelled from structures and systems in the real world. Mathematics encourages us to identify patterns, to categorise, and to make logical deductions and predictions from facts presented or assumed.
"So if a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again." Francis Bacon, Of Studies
Mathematics is a branch of abstract reasoning that is curiously useful for understanding the universe: the numbers, operations and constructions of Mathematics exist only in their purest form in the mind of the mathematician but understanding their behaviour is a powerful tool for solving problems in the real world. Mathematics is a discipline in which problem solving, lateral thinking and imaginative reasoning are as valuable as a facility for careful and accurate calculation.
The best reason for taking Mathematics at A Level is that students will enjoy studying it: that is, that they will find satisfaction in stretching their intellect to understand abstract ideas and tackle taxing problems. It is also a subject with wide utility and is a requirement for further study in a variety of areas. Further Mathematics is welcomed by universities as a valuable A Level in addition to Mathematics and is highly suitable for students who want to spend half of their curriculum time in the study of this marvellous discipline.
Students will need to take Mathematics A Level if they want to study Mathematics or Computer Science, Physical Sciences, Engineering, Economics, Management or PPE at university. They may also find Mathematics A Level helpful while studying Chemistry, Physics, Geography, Economics and Biology A Levels; similarly they may find Mathematics A Level useful if they are thinking of taking Chemistry, Biology, Psychology, Medicine or Geography at university, but it is not essential. Mathematics A Level can be a good indicator of the ability to cope with the logical aspects of Philosophy at university. | 677.169 | 1 |
Modulequizzes30ofgrade
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: ulator to take a test or quiz. The calculator provided for this course is the Windows standard calculator and will be enabled for you during your quizzes and tests in the Hub. You can practice using this calculator in the Hub when you do your homework. In addition the calculator is usually installed on most Windows computers (click "Start", then "All Programs", then "Accessories", then "Calculator") When the calculator program starts, it may be showing only a four‐
function calculator. To use the scientific calculator, click on "View", then Scientific. The calculator may look different if you have a different version of Windows. MODULE QUIZZES: 30% of grade All quizzes must be taken in a Hub. Present study notes and picture ID to a Hub staff member for approval. To pass a quiz your score must be at least 70%. You can retake the entire quiz to improve your score and only the best score is used for your grade. Prior to a fourth attempt, you will need to work an additional homework assignment that is created from the concepts you missed. This additional assignment must be completed at an 85% level. COMPREHENSIVE TESTS AND FINAL EXAM: 30% of grade You must score at least a 70% on tests and the final exam. You must retake the entire test or exam to improve your score and only the b...
View
Full
Document
This note was uploaded on 08/01/2012 for the course MATH 1010 taught by Professor Staff during the Summer '08 term at Weber. | 677.169 | 1 |
Elementary number theory was the basis of the development of error correcting codes in the early years of coding theory. Finite fields were the key tool in the design of powerful binary codes and gradually entered in the general mathematical background of communications engineers. Thanks to the technological developments and increased processing power available in digital receivers, attention moved to the design of signal space codes in the framework of coded modulation systems. Here, the theory of Euclidean lattices became of great interest for the design of dense signal constellations well suited for transmission over the Additive White Gaussian Noise (AWGN) channel.
Bringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. This edition focuses on integral domains, ideals, and unique factorization in the first chapter; field extensions in the second chapter; and class groups in the third chapter. Applications are now collected in chapter four and at the end of chapter five, where primality testing is highlighted as an application of the Kronecker–Weber theorem. In chapter five, the sections on ideal decomposition in number fields have been more evenly distributed. The final chapter continues to cover reciprocity laws.
This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples.
Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. | 677.169 | 1 |
Need to keep your rental past your due date? At any time before your due date you can extend or purchase your rental through your account.
Sorry, this item is currently unavailable.
Summary
This thorough and accessible book from one of the leading figures in the field of linear algebra provides readers with both a challenging and broad understanding of linear algebra. The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. Topics such as linear systems theory, matrix theory, and vector space theory are integrated with real world applications to give a clear understanding of the material and the application of the concepts to solve real world problems. Each chapter contains integrated worked examples and chapter tests. The book stresses the important role geometry and visualization play in understanding linear algebra.For anyone interested in the application of linear algebra theories to solve real world problems. | 677.169 | 1 |
Synopsis
KS2 Maths Question Book - Level 3 by CGP Books
This book contains hundreds of practice questions for pupils aiming for Level 3 in the KS2 Maths SATS. It's been fully updated for the tests from May 2014 onwards (where calculators are no longer allowed), and every topic is covered with a wide range of question types. Answers are included at the back of the book. Matching study notes are available in CGP's KS2 Maths Level 3 Study Book (9781847621948). | 677.169 | 1 |
Need to keep your rental past your due date? At any time before your due date you can extend or purchase your rental through your account.
Sorry, this item is currently unavailable.
Summary
Maple is a powerful software tool for mathematical computations and visualization. The goal of this manual is to introduce Maple to students who are taking first year calculus. As such, Maple is a tool to solve problems that are too difficult to solve by hand. In addition, students will improve their understanding of the concepts of calculus. The order of the material is organized by computational topic and should be suitable for most texts on Single Variable calculus. | 677.169 | 1 |
This review book offers high school students in New York State advance preparation for the new Common Core Regents Exam in Algebra II. Each chapter covers different exam topics and includes practice exercises in each chapter. The book concludes with two of the first actual Regents exams administered for the updated Algebra II core curriculum. Answers are provided for all questions. Topics covered in this book include Polynomial Functions, Exponents and Equations, Transformation of Functions, Trigonometric Functions and their Graphs, Using Sine and Cosine, and much more.
Would you like to practice taking the NYS Regents exams online and have your exam automatically graded too?
Just click here to see the Barron's Regents exam prep Website. | 677.169 | 1 |
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: LESSON 2 Vector Algebra READ: Sections 13.3, 13.4 NOTES: Besides adding, subtracting, and multiplying vectors by scalars, there are two other useful operations with vectors. The scalar product defined in the previous lesson combines a scalar and a vector to produce a new vector. The dot product combines two vectors to produce a scalar, and the cross product combines two vectors to produce another vector. To form the dot product of two vectors, multiply the corresponding components of the vectors, and add up the resulting numbers. In symbols, if-→ v = h a 1 ,a 2 ,a 3 i , and-→ w = h b 1 ,b 2 ,b 3 i , then-→ v ·-→ w = a 1 b 1 + a 2 b 2 + a 3 b 3 . As usual, when a new operation is introduced, the algebraic behavior of the operation ought to be spelled out. Is the operation commutative, for example. In other words, is it true that-→ v ·-→ w =-→ w ·-→ v ? This, as well as the other natural algebraic questions about dot products are listed in the table on page 676 of the text. The proofs are all very simple: just write out the left and right side of each equation, and check to see the two sides really are the same. For example, to show the operation is commutative (which is property 2 in the table), let's suppose-→ v = h a 1 ,a 2 ,a 3 i , and-→ w = h b 1 ,b 2 ,b 3 i . Then-→ v ·-→ w = a 1 b 1 + a 2 b 2 + a 3 b 3 . On the other hand-→ w ·-→ v = b 1 a 1 + b 2 a 2 + b 3 a 3 . Comparing the two results, we see they are the same, and so-→ v ·-→ w =-→ w ·-→ v . The other proofs go the same way. Try them. Notice that properties (iii) and (iv) show how dot products interact with vector addition and scalar multiplication. One particularly useful formula in the list says that the magnitude of vector is the square root of the dot product of the vector with itself. In other words, ||-→ v || = √-→ v ·-→ v . It always helps the understanding to be able to visualize concepts. The dot product provides us with a tool to aid visualization. When two vectors are drawn with their initial points at the origin, it makes sense to ask about the angle between the vectors, at least if neither one is the zero vector-→ 0 = h , , i . The angle between two vectors is always taken to be a number between 0 and π . The dot product can be used to calculate that angle. Using the Law of Cosines, and checking the diagram on page 676 of the text, it's not too hard to see that-→ v ·-→ w = ||-→ v ||||-→ w || cos θ , where θ is the angle between-→ v and-→ w . That equation provides a means of computing θ . It also helps us understand a bit about what the dot product means geometrically. Think about that equation and imagine the effect on the value of the dot product of-→ v and-→ w as we hold-→ v in a fixed position, and allow-→ w to rotate. When-→ v and-→ w point in the same direction, the angle between them will be 0, and so the value of cos θ will be 1, and the value of-→ v ·-→ w will be fairly large. Aswill be fairly large....
View
Full
Document
This note was uploaded on 02/24/2011 for the course MATH 265 taught by Professor Jerrymetzger during the Winter '11 term at North Dakota. | 677.169 | 1 |
Generally, we know that all the books will provide us with the table of contents. This textbook also does not exclude from it. It provides us with a useful table of contents and index. In fact, the table of contents also shows a logical arrangement and development of the subject. Besides that, it also has some references and bibliographies for student's reference. However, it still insufficient for students to find the best solution for any question which is confused them. Supposed be, it should give some links which related with this field such as websites to ensure that students will be able to access immediately to get the solution for those confused questions or statements. Fortunately, all the chapters provide introductions and summaries that are clear and comprehensive for students' usage. However, glossary provided is insufficient. It is supposed to have a little bit more to ensure that the students will really familiar with and know the technical terms of mathematics. It is lucky to have all the pages are numbered. Thus, it reduces the tendency of having confusion among the students.
Contents:
Since at the national standard we will have PMR and SPM, therefore, the contents of this book meet local and national standard. This is because, the syllabus used are standardized. Instead of it, language used is appropriate for the intended age group. It does not have any grammatical error. But then, the sentences used sometimes make students feel confused. However, it still can be understood. Since it is used for form 2 students, therefore, the text book contains age appropriate reading level. In addition, the greatest part of this book is that it contains of end-of-lesson questions and quizzes. In fact, it has some challenging questions to be tested by the students. Moreover, they are linked to the other subject areas. Thus, the activities engage students in active learning processes. Instead of appealing to a wide range of abilities and interest, the lessons also encourage higher level of thinking. It shows when the questions touch the daily life applications. By that, it will attract students' interest indirectly.
Physical aspects:
Generally, we know that most of parents were complaining that the textbook which is provided before is too thick and heavy. Based on those complains, now, Ministry of Education come out with the new version of textbook. It is divided into two volumes which the first volume is used for the first term of school period and the second volume will use in the next term. Therefore, the size and weight of the textbook provided are appropriate for the student who will use it. Besides that, the font and style use are appropriate for that level of age. Since it is Ministry of Education's product, the font and style used are formal. Therefore, it is considered as appropriate for those students who are going to use it. Binding for this book is quite ok. In addition, it uses a high quality papers. Thus, the students are not easy to tear it away. Even though the cover is not that hard, it is durable and could last for several years. Besides that, well-arranged information in this textbook also helps to attract students to use it. In other words, the information given is uncluttered and balanced. In fact, all the illustrations, tables, figures, graphs, charts, etc provided are appropriate representations of age, ethnicity, sex, socioeconomic level and physical or mental ability. Instead of those, they are also interesting due to the color and the way how it is presented. | 677.169 | 1 |
Experimental Number Theory
Description
Covers a broad spectrum of basic computational issues
Numerous GP programming examples given
End of chapter exercises reinforce the text
Remarks and solutions are provided for selected exercises in the final chapter
This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, along with exercises and selected solutions. Sample programs are written in GP, the scripting language for the computational package PARI, and are available for download from the author's website. | 677.169 | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.