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MATHEMATICS CURRICULUM
Required: Three Units Recommended: Three - Four Units for college prep
Elementary Algebra I
Grade: 9,10 Duration: Year Prerequisite: None
An algebra course which will provide the student with a very methodical approach to signed numbers, subtraction, reciprocals, solving linear equations, and polynomials.
Elementary Algebra II
Grades: 10,11,12 Duration: Year Prerequisite: Elementary Algebra I
An algebra course designed to reinforce the studies of Elementary Algebra I and extend the concepts of linear equations, polynomials, and radicals. This two year sequence is the equivalent of Algebra I.
Algebra I
Grades: 9,10,11 Duration: Year Prerequisite: None
Algebra I will provide strong emphasis on linear solutions, polynomials, radicals, and factoring including an integration of available technology. Interpretation of word problems will be stressed.
Geometry
Grades: 9,10,11,12 Duration: Year Prerequisite: Algebra I or equivalent
The course begins with an introduction to the basic concepts of Euclidean Geometry. The course progresses by integrating algebra into the study of different shapes and their relationships through deductive and inductive reasoning.
Honors Geometry
Grades: 9,10 Duration: Year Prerequisite: Algebra I and instructor's approval
A power Geometry class which is intended to challenge students by covering the topics of Geometry in an accelerated fashion and with the use of additional supplemental materials.
Advanced Algebra
Grades: 10,11,12 Duration: Year Prerequisite: Geometry(for students who have successfully completed a year of Algebra and Geometry.)
Emphasis is given to the structure of Algebra and the nature of proofs. Manipulative skills needed to perform algebraic operations with competence are stressed along with developing the student's power to think logically. This course covers quadratic equations, complex numbers, analytic geometry, exponential and logarithmic functions, and trigonometry. Suggested for college prep.
Honors Advanced Algebra is a power course intended to challenge students by the use of an accelerated course.
Statistics I & II
Grades 11, 12
Prerequisite: Advanced Algebra
Duration: Year Long
Statistics is a course that covers the topics of producing data, organizing data, chance, and inference. There will be motivational, hands-on activities that allow students to explore statistical concepts and examples from a variety of fields. The graphing calculator will be utilized. Concurrent enrollment in math classes will be allowed, and students must maintain quality efforts and work in both classes.
Math Analysis is a course which covers the topics of symbolic logic, analytical geometry, sequences and series, limits, trigonometry, and polynomial functions (Binomial Theorem). The graphing calculator will be utilized. Suggested for college prep. Concurrent enrollment in math classes will be allowed for special cases only, and students must maintain quality efforts and work in both classes.
This course is a continuation of Math Analysis beginning with trigonometry and introduces the topics of limits, derivatives, integration, and exponential functions. This course will provide an introduction to college Calculus for math or science majors. The graphing calculator will be utilized. Suggested for college prep. Concurrent enrollment in math classes will be allowed for special cases only, and students must maintain quality efforts and work in both classes.
AP Calculus will prepare the student to take the AP Calculus exam. Limits, derivatives and its applications, integration and its applications, exponential and logarithmic functions, and inverse functions will be studied. An AP approved graphing calculator is required. This course is divided into semesters with credit given each semester. The second semester must be taken in the same school year. Concurrent enrollment in math classes will be allowed for special cases only, and students must maintain quality efforts and work in both classes. | 677.169 | 1 |
Mathematics – Further
Students who take this course:
Students will have at least a 7 in GCSE mathematics. They will need to be confident in the application of algebraic and other mathematical skills and have an interest in solving real life problems using these skills together with logical mathematical argument. Further Mathematics is required by many universities as a prerequisite to study mathematics at degree level. It is also useful for accounting, financial subjects, law, engineering and sciences.
Course Description:
Maths at this level consists of the study of pure maths and the study of the application of mathematics to the physical world through:
Pure mathematics;
Statistics (understanding and interpreting information);
Mechanics (understanding how and why physical objects move and behave as they do);
Decision Maths (uses discrete mathematics to construct mathematical models to arrive at an optimal solution to real life problems). | 677.169 | 1 |
Note that there are two ways to learn calculus: the high-school way, without proofs (Stewart is a good example) and the college-level way, with epsilon-delta proofs (Spivak is this kind.) You should decide what fits your needs best. You don't necessarily need to learn high-school-style calculus first -- my first intro to calculus was Serge Lang's book, which is similar to Spivak but more compressed -- but if you're just getting started computing derivatives it may help to do some physics problems to build intuition.
I think I'll stick to Spivak, then. Technically I've been taught the high-school style calculus twice, once in high-school and once in college, but the former was mediocre and the latter was ridiculously abridged and compressed, and I usually employed the "study one day before exam" strategy. The high-school style calculus would be most likely adequate for me but I think I should try at least once a Rigorous Math Textbook. | 677.169 | 1 |
Module 1 Preparation & Learning ResourcesTextbook/ Flexbook Pages
This first unit is one of my own design so information is scattered around. The flexbook on function notation is good and the .pdf on representing functions will be a good reference. I am including the dimensional analysis chapter for review if you need it.
This video shows the basic shapes of the graphs we will see over and over again in science.
Web Pages
An introduction to functions can be found HERE. A page showing the graphs of the eight basic types of functions is located HERE. *There is a GREAT reference page of the metric base units and many derived units for physics HERE.* Be sure to check out the definitions and the historical context of the base units.
Concept Map
Here is a concept map that shows my interpretation of the relationship between SI base units and mathematical functions. | 677.169 | 1 |
21-118: Calculus of Approximation
Description
In previous courses of the calculus sequence, functions were dealt with
just as they were presented. As a result, all of the answers obtained were
exact. Sometimes, however, an approximate answer is all that is needed.
In Calculus of Approximation, we investigate techniques that may be used
when an exact answer is not necessary. There are two issues involved here.
The first is finding a convenient way to approximate the desired information.
The second is measuring the errors we create by our approximations. We will
deal with both of these topics in this course. | 677.169 | 1 |
Chapter1Preliminaries
A certain amount of mathematical maturity is necessary to find and study applications of abstract algebra. A basic knowledge of set theory, mathematical induction, equivalence relations, and matrices is a must. Even more important is the ability to read and understand mathematical proofs. In this chapter we will outline the background needed for a course in abstract algebra. | 677.169 | 1 |
Search
ALGEBRA II 6(K)
The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Specific Skill:
determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation | 677.169 | 1 |
Math Math MATH!
I was thinking of a career in engineering, but now that i think of it , not anymore, i love physics, i can do physics with no problems, but math....thats a different story, i dont know wut the hell is wrong with me, i'v had a calculus test on Limits yesterday and i studied the night before four about 5 hours (reading over notes, mostly practicing lots of problems), and then i get 70% on the test.... this is really getting on my nerves and im thinking of dropping the course, we are now doing derivatives and im doing that fine, but today my teacher introduced the chain rule, and now my head is about to explode from trying to figure that out. I do lots of problems so i can be ready for my tests. My teacher puts questions similar to the ones she assigns for homework, but puts about 3 questions that are really hard, and she makes those questions worth more than all of the other questiosn put togther... its not like i cant do them, but they confuse me because i'v been practicing something and something like that comes in and messes me up...
Is there anything i can do to better help me prepare for math tests, or is math just not for me.... i mean i like math, and i love physics, im good at physics, but i suck at math...how would this effect my choice of career in engineering...
If you can do physics problems, then I assume you can do unit conversions, right? The chain rule isn't really much more than doing unit conversions. Item A changes by a certain amount in response to a change in B, except you don't want your answer in terms of B. So you have to have to multiply your first answer by the rate that B changes in response to C - the term you want your answer in. And so on, sometimes, just like unit conversions can be several steps.
For example:
You want to find out how fast your radius is changing in meters per second along an elliptical orbit. Unfortunately, you have to find out how much the radius changes per degree first (the derivative of your radius with respect to angle). Then you need to find out how fast your angle is changing in degrees per second or radians per second (the derivative of your angle with respect to time). When you multiply them together, you have meters/degree times degrees/second. Since degrees are on both the top and bottom, they cancel out, leaving you with meters/second.
It's actually pretty unusual to be good at physics without being good at math. Thats like saying you are terrible at dribbling and shooting, but you are a good basketball player. I suggest you strengthen your algebra skills, since that's what i'm beginning to suspect your troubles stem from, since calculus in itself is not very difficult; in fact that reminds me of a quote I heard about someone claiming he could teach a fifth grader calculus, but its really the algebra that would kill them.
I agree with the tutor suggestion. If you're taking classes at a college, you should check to see if they offer free tutoring. If so, give it a shot. The worst that happens is that you waste a little time. It might really help.
I tutor and I hear your complaints at the beginning of every semester. The chain rule takes time and practice to master. Once you do it a zillion times it will come second nature. Just practice that's the only thing I'd recommend. Do all the problems in your book. If you still have trouble go to a library and grab a calc book and start doing the problems. Eventually a little light will come on or a bell will ring and from that point on you'll apply the chain rule without a probelm (and without realizing it).
You can applly the chain rule from the outermost function inward or the innermost function outward. I recommend the latter because it follows the rules you apply from algebra anyway.
example:
[tex]
f(x)=\sqrt{x^2+9}
[/tex]
In this case if you where to substitute a valu in for x then solve it where would you begin? You replace the x with said value, square it and add 9 so why not start there with your derivative?
The chain rule will come as second nature. Also, don't sweat limits either. You need to understand what is going on with a limit because that concept eventually builds into the concept of a derivative but you'll eventually learn this theorem called L'Hopitals rule which will make finding limits much easier--in fact if you find it in your text you could use it on your final to "verify" your answer when doing limits the conventional way.
Well, good luck and may the [itex] \lim_{\Delta x \rightarrow 0} \frac{f(x+\delta x)-f(x)}{\Delta x} [/itex] be with you.
thx faust and everyone else for advice and help...i think you are right, my problem is with the algebra, i have reviewed my tests, and my biggest source of error is the algebra, i understand the concepts well, and now how to apply them, i just have to learn to apply them right. Any suggestions to help me in my "weak" algebra skills?
Resist the temptation to do algebra in your head. Always write down every step no matter how easy or insignificant. You're less likely to mess up and when you do you can usually spot it. Make you negative signs big and pronounced. Not distributing a negative is a big offender. If you spot a mistake don't try and squeeze a correction in (ie write a negative near the top of a number because you forgot it). Erase or put a light line through the error and start writing in another location. Keep your work neat and organixed. I still do this:
Code (Text):
(x-2)(x-4)=
x^2-4x
-2x +8 = x^2-6x+8
keep your work neat and organized. Make the radian/degree equivilents second nature. When someone says 30 degrees you should immediatly say
[tex]
\frac{\pi}{6},\sin{\frac{\pi}{6}}=\frac{1}{2},\cos{\frac{\pi}{6}}=\frac{\sqrt{3}}{2},\tan{\frac{\pi}{6}}=\frac{\sqrt{3}}{3}
[/tex]
Verify the solution to every function which involves a quotient is a valid solution. I've seen this a lot where people will determin the domain of a function write said domain down but never verify the soultions are in the domain. | 677.169 | 1 |
Lady Lumley's 6th Form Courses - Page 19
MATHEMATICS (FURTHER)
What does the course involve?
The course develops skills in four areas of mathematics; pure maths, statistics, mechanics and
decision mathematics. Pure maths extends the core maths covered at A level, whilst introducing new
topics such as complex numbers. Statistics and mechanics also extends the concepts covered at A
level, while decision maths studies algorithms and networks.
There are six units and we usually cover the following modules, but these can vary according to the
interests of the students in the group;
AS
Further Pure 1
Decision Mathematics 1
Decision Mathematics 2
A2
Further Pure 2
Statistics 2
Mechanics 2
The course covers the Edexcel specification, which you can access at
What qualifications do I need?
This course is suitable for students who have achieved a grade 'A' or above in GCSE Mathematics.
You must also be studying A-level Mathematics to follow this course.
Equipment
A scientific calculator is essential for most units. Some students enjoy using graphic calculators, the
department has a class set of these for use in lessons. We also have maths specific software, which
can enhance students' understanding, installed on a number of computers around school.
Assessment
All units are assessed by a written examination. Each module carries equal weighting towards the final
result.
General Comments
Further mathematics extends students mathematical knowledge and understanding. It is an enjoyable
and rewarding subject which explores new concepts and ideas to a high level. It provides an
additional challenge for any students who enjoy maths and are confident in their ability in the subject. It
develops students' understanding of mathematical processes and enables them to model real life
problems.
Future Prospects
Further Mathematics is a requirement for most Mathematics degrees. Many degrees like Physics,
Chemistry, Engineering or Computer Science also require Further Mathematics to at least AS Level.
The Further Maths Support Programme has excellent information regarding which Universities or
courses require Further Mathematics: | 677.169 | 1 |
Baker's Choice - An alternative unit on linear equations and inequalities for high school mathematics
On this page, you will find an electronic portfolio of my work and reflections on a unit of high school mathematics called Baker's Choice. Baker's Choice is an 18 day unit on linear programming as part of the Interactive Mathematics Program (IMP).
Cover letter
The central problem presented in the Baker's Choice unit is one of a small bakery owned by the Woos. The Woos make two types of cookies at their bakery, plain cookies and cookies with icing. They need a mathematician to look at their business and decide how many cookies they should make for the following day in order to maximize their profits, like any small business would want. Maximizing their profits involves looking at many different variables and constraints of the business. The constraints of the problem (i.e. the bakery) are as followed:
One dozen of their plain cookies requires a pound of cookie dough, 0.1 hours of preparation time, cost $4.50 to make, and sells for $6.00.
One dozen of their iced cookies requires 0.7 pounds of cookie dough, 0.4 pounds of icing, 0.15 hours of preparation, cost $5 to make, and sells for $7.00.
They have only 110 pounds of cookie dough and 32 pounds of icing on hand.
They only have enough oven space to make a total of 140 dozen cookies for tomorrow.
The have 15 hours of total preparation time.
The central problem of Baker's Choice may seem overwhelming to a high school algebra student, but the unit does a great job breaking down the required concepts and skills needed to solve the problem into smaller, more digestible tasks in order to build the knowledge necessary to tackle the central problem of the unit. Through several homework assignments and problems of the week, the students will learn how to express and interpret constraints using inequalities, graph linear inequalities, find the maximum of a linear function in a polygonal region, examine parameters in a problem, draw feasible regions of inequalities, and solve linear programming problems with two variables.
In order to better teach an interactive and engaging unit like this in my future high school mathematics class, I participated in the problem solving process of the Baker's Choice unit. Below are links to selected works and activities assigned throughout the unit that demonstrate some of the concepts and skills listed above and a personal growth statement reflecting on the unit. | 677.169 | 1 |
Hello people . How do you people do permutations on ti graphing calculatorI find these routine queries on almost every forum I visit. Please don't misunderstand me. It's just as we advance to high school , things change suddenly . Studies become challenging all of a sudden. As a result, students encounter trouble in doing their homework. permutations on ti graphing calculator in itself is a quite complex subject. There is a program named as Algebrator which can help you in this situation.
You must go through Algebrator. I had always thought math to be a difficult subject but this program made it very easy to learn . You can type in the question and it provides you the answer, just like that! It is so user friendly that learning becomes a fun experience.
Thanks for the detailed information , this seems awesome. I wished for something exactly like Algebrator, because I don't want a software which only solves the exercise and gives the final result, I want something that can actually show me how the exercise needs to be solved. That way I can learn it and after that solve it without any help , not just copy the answers . Where can I find the software?
I am a regular user of Algebrator. It not only helps me finish my assignments faster, the detailed explanations offered makes understanding the concepts easier. I recommend using it to help improve problem solving skills. | 677.169 | 1 |
Mathematics & Science
Learning Center
Computer Laboratory
Mathematica Basics—Algebraic Operations II
Introduction
In this notebook we will continue to cover Mathematica's algebraic abilities.
So far we have covered the four basic arithmetic operations, along with factoring
and substitution. We now move on to one of the more problematic topics in
algrabra—the solving of equations.
Evaluating Commands
Remember, as we said in the introduction to the first notebook, in order to
tell Mathematica that you want it to actually evaluate what you have
typed, hit the ENTER key over on the extreme right side of your keyboard on the
numeric keypad. Again, don't confuse this with the RETURN key, which merely
starts a new line of text.
You can now switch to an actual Mathematica practice notebook by
clicking on the icon on the left. It may take a while to start up! Don't forget to come back
here when you're done! (You can also return here just to reread the instructions.) See you in a few
minutes.
Welcome back! You may be wondering how well you did. Click on the icon on the left to see the answers you should have gotten. (Only the answers are given, so if you don't match our results you need to figure out what you did wrong.) | 677.169 | 1 |
Friends , I am in need of aid on powers, equivalent fractions, least common measure and graphing equations. Since I am a newbie to Algebra 1, I really want to understand the bedrocks of Pre Algebra completely. Can anyone suggest the best place from where I can begin reading the basics? I have an exam next week.
Welcome aboard friend . This subject is very interesting, but you need to know your concepts and techniques first. Algebrator has guided me a lot in my course. Do give it a try and it will work for you as well .
function definition, converting fractions and angle complements were a nightmare for me until I found Algebrator, which is truly the best algebra program that I have ever come across. I have used it frequently through several algebra classes – Basic Math, Algebra 2 and Intermediate algebra. Simply typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my algebra homework would be ready. I highly recommend the program. | 677.169 | 1 |
More than a study of shapes and angles, geometry reflects an amalgamation of discoveries over time. This book not only provides readers with a comprehensive understanding of geometric shapes, axioms, and formulas, it presents the field's brilliant minds—from Euclid to Wendelin Werner and many in between—whose works reflect a progression of mathematical thought throughout the centuries and have helped produce the various branches of geometry as they are known today. Detailed diagrams illustrate various concepts and help make geometry accessible to all. | 677.169 | 1 |
SAT prep and applying to college
Function Fear
Of all the topics on the math section, my students seem to have the most trouble with functions. Did your heart rate increase when you read the word "function"? Okay – maybe not. But a lot of students get frazzled by function questions, so here's some help:
Image via Wikipedia
Let's start with the psychology. I like to ask my students "what was the first grade in which you ever leaned a math function"? Their answers typically run from 7th to 11th grade. Wrong! You learned your first function in 1st grade. Addition and subtraction are functions, as are many other concepts you learned throughout grade school.
A mathematical function is simply a set of instructions that tells you what to do with one or more values. Addition is actually a hard one, since you have to memorize all of those combinations (you're not born knowing what 8 + 3 is).
First grade teachers like to make things simple. They just show you a chart that says something like 8 + 0 = 8, 8 + 1 = 9, 8 + 2 = 10, etc. But high school teachers can't make things that simple, because they know you'd laugh at them. So they show you something like
f(x,y) = x + y
…and say "here's an easy one." Who's laughing now?
But wait…the only thing that's new there is f( ). Your teacher tells you that f( ) means "eff of." But I don't know what "eff of" means either. So I say that it means "start with."
So f(x,y) = x + y means "start with x and y, and end up with their sum."
And f(3,4) means "start with 3 and 4, and end up with their sum," which is obviously 7.
Let's look at one more:
f(x) = 2x + 4 means "start with x, and end up with twice x plus 4."
f( ) looks scarier than + or √, because it looks like 3 symbols. Just think of it as one symbol.
Okay, that was pretty elementary stuff. But my point is that overcoming "function fear" is the first step toward mastering function problems. More tips on functions will follow shortly. | 677.169 | 1 |
that you can use and download from the internet. Just visit the site sign in to be able to download books.
Teaching Strategy:
Learning Mathematics , in my opinion, is like learning swimming. You can not swim if you just listen, and watchyour trainer without trying to apply what he(she)
teaches you.In order to do that you should follow the following rule
1.On each lecture, I will give you a task to do like reading the next lesson or solve some problems to discuss. You should do that to be able to follow us in the lecture.
2.Do not go to the training section without trying to solve the problems in advance.
The instructor's mission is to help you to solve the problems you could not solve not to solve all the problems of the sheets.
3-Do not hesitate to ask about any thing you do not understand or missed in the lecture. Otherwise you may not be able to follow the remaining part of the course.
Assessments:
Quizzes: There will be a regular quiz every two weeks in additionsto "Pop" quizzesor 4-minute paper quizzes.
Mid-Term Exams: There are two mainmid-term exams: each one of 20 degrees. If you have any excuse for absence. You should bring an official excuses. Pleasebe advised that the alternative exams are done only for one time and no excuses can be accepted if a student does not attend thealternative exam. | 677.169 | 1 |
Math: Organizations: Mathematics Foundation of America
Math: Organizations: Mathematics Foundation of America
Description: The purpose of MFOA is to ensure that the mathematically talented high school student receives mathematics education appropriate for a future mathematician by providing suitable summer programs and mentors. | 677.169 | 1 |
Get Discrete Mathematics Assignment Help Now
What is Discrete Mathematics?
Discrete Mathematics can be defined as the study of finite systems. As the name suggests, discrete mathematics involves mathematical structures that are "discrete" rather than "continuous". Rational numbers and real numbers are examples of continuous systems, as between any two such numbers a third number can be found. On the other hand examples of discrete objects include graphs, integers and logical statements that can have only separated and distinct values.
With the increasing use of computers in every field, the importance of discrete math has grown rapidly since the dawn of the computer age. The properties and functionality of a digital computer can be understood through the use of finite mathematical systems.
Discrete mathematics involves the study of various topics such as set theory, relations, functions, probability, graphs, binary trees and Boolean algebra.
Email Based Homework Assignment Help in Discrete Mathematics
Transtutors is the best place to get answers to all your doubts regarding your discrete mathematics homework assignment online math.
Live Online Tutor Help for Discrete Mathematics
Transtutors has a vast panel of experienced discrete math tutors who can explain the different concepts to you effectively. You can also interact directly with our discrete math tutors for a one to one session and get answers to all your problems in your school, college or university level discrete mathematics homework. Our tutors will make sure that you achieve the highest grades for your discrete math assignments. We will make sure that you get the best help possible for exams such as the AP, AS, A level, GCSE, IGCSE, IB, Round Square etc. | 677.169 | 1 |
Maths for Chemistry
4.11 - 1251 ratings - Source
Maths for Chemistry recognizes the challenges faced by many students in equipping themselves with the maths skills needed to gain a full understanding of chemistry, offering a carefully-structured and steadily-paced introduction to the essential mathematical concepts all chemistry students should master.Maths for Chemistry recognizes the challenges faced by many students in equipping themselves with the maths skills needed to gain a full understanding of chemistry, offering a carefully-structured and steadily-paced introduction to the ...
Title
:
Maths for Chemistry
Author
:
Paul Monk, Lindsey J. Munro
Publisher
:
Oxford University Press - 2010-04 | 677.169 | 1 |
calc. N° de ref. de la librería BZ038542
calculate tips. focusing on mathematical theory and real life contact. intuitive and easy to understand. easy to understand. in line with the characteristics of liberal arts students; through clever Use the history of mathematics. scientists discussed the original literature. mathematical theory and real life contact. so that the historical background and theoretical knowledge seamlessly ext | 677.169 | 1 |
402: PRE-ALGEBRA
Course Description
This course covers operations with integers, fractions, decimals and associated applications, ratio, proportion, geometry, and measurements with the emphasis on critical thinking and applications. Elementary algebra topics such as variables, expressions, and solving equations are introduced. This is a pass/no pass course where pass is given for mastery of the above topics. The mastery level is set by the department. PREREQUISITE: Completion of Math 400 with a grade of 'C' or better OR completion of Math 400 with a grade of 'P' OR appropriate assessment test score.
Learning Outcomes
Perform basic operations with whole numbers, integers , fractions, and decimals without the aid of a calculator.
Analyze a variety of problems, decide on a correct method or strategy of solution, implement the strategy to solve the problems, and evaluate solution to determine if it is reasonable using estimation skills.
Simplify algebraic expressions and solve equations involving integers, fractions, and decimals without the aid of a calculator. | 677.169 | 1 |
Discrete Mathematics:
an open introduction
Welcome
Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.
A second edition is now available. You can download it for printing or tablet use, or browse the interactive online version. In addition to rearranging some content and adding exercises, the new edition is available as an interactive website, thanks to the PreTeXt project (previously called Mathbook XML).
The previous version (Fall 2015 edition) will remain available. If you downloaded this edition prior to July 15, 2016, grab a new copy as I have corrected quite a few typos.
I intend to continue improving the text, and very much encourage anyone using it to email me their feedback and suggestions. If you decide to use the book in your course, please let me know.
Download or Purchase
This is a free textbook. You can dowload the 2nd edition to read on your computer or tablet. If you want other editions (including one suitable for two-sided printing), please see the downloads page. There you can also find information about obtaining the LaTeX source code in case you want to remix the book.
There is also an inexpensive print edition available through Amazon.com. This should be quite a bit cheaper than printing the book yourself.
About
This text was written to be used as the primary text for the class Discrete Mathematics (Math 228) at the University of Northern Colorado. The course serves as the role of a transitions course (introduction to proof), as well as an introduction to topics in discrete mathematics. While we have a few students each semester who will go on to study computer science, pure mathematics or applied mathematics, the majority of students are studying to be elementary or secondary math teachers. For this reason, most of the standard discrete textbooks are not appropriate for us. For many years we used Discrete and Combinatorial Mathematics by Richard Grassl and Tabitha Mingus. This is a very nice book in many ways (Grassl taught at UNC) but the print-on-demand publishing was expensive for students and some sections needed updating and (as I saw it) rearranging.
While the book began as a set of lecture notes, it now contains a number of features that should support its use as a primary textbook:
363 exercises, including 233 with answers or full solutions, as well as 130 more involved problems suitable for homework.
Investigate! activities throughout the text to support active, inquiry based learning.
A full index and list of symbols.
Consistent and (hopefully) helpful page layout and formatting (i.e., examples are easy to identify, important definitions and theorems in boxes, etc.)
License
Discrete Mathematics: An Open Introduction by Oscar Levin is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. You are free to download, use, print, and even sell this work as you wish to. You can also modify the text as much as you like (create a custom edition for your students, for example), as long as you attribute the parts of the text you use to the author.
If you are interested in using parts of the book combined with another text with a similar but different license (GFDL, for example), please contact me to get permission to modify the license. | 677.169 | 1 |
This course aims at providing basic concepts in linear algebra and foundation knowledge for computing problem solving by numerical methods. After successful completion of this course, the student will be able to understand the concepts and relationships among linear systems, matrix equations, and vector spaces on linear mapping and transformation and the basic operating principle of matrices, vectors, linear transformations, and numerical methods.
The course aims at providing knowledge for the basic concepts of probability and statistics and the techniques for solving mathematical problem for probability analysis. Provide knowledge for the basic concepts of probability and statistics and the techniques for solving mathematical problem for probability analysis.
To learn the basic concept and applications of electronic circuits. This course aims at providing the students with fundamental knowledge and concepts of electronic circuits and the students will learn the application of electronic circuits and gain foundation knowledge for advanced level computer hardware subjects.
Give an introduction to symbolic logic and set theory; Provide the techniques in solving problems with discrete structures. The focus is to apply the techniques to problems in computer science. Give an introduction to symbolic logic and set theory and provide the techniques in solving problems with discrete structures. The focus is to apply the techniques to problems in computer science.
This course aims at giving an introduction to numerical methods for solving computational problems using methods such as error analysis. We will study the practical aspects of the use of numerical methods especially by computer and introduce the concepts of applications of numerical methods. After successful completion of this course, students will be able to understand the iterative methods to solving computational problems and the error analysis, rate of convergence, stability and other practical aspects.
The aim of this course is to provide a basic concept of the theory and application of differentiation and integration. After successful completion of this course, students will be able to understand the iterative methods to solving computational problems and the Error analysis, rate of convergence and other practical aspects.
This course aims at providing advanced concepts in multi-variable calculus. After successful completion of this course, students will be able to understand the theory and applications of multi-variable calculus.
This course aims to provide basic concepts in Newtonian mechanics and the foundation knowledge for mechanics, rotational mechanics and fluid mechanics. After successful completion of this course, the student will be able to understand the concepts Physics concepts of Newtonian mechanics and electricity and the application of mechanics and electricity in our daily life.
This course aims at providing foundation knowledge for Electricity and Magnetism. After successful completion of this course, the student will be able to understand the concepts Physics concepts of Newtonian mechanics and electricity and the application of mechanics and electricity in our daily life.
Basic concepts in computers; Foundation knowledge for programming, database and computer networking subjects. After successful completion of this course, the student will be able to understand: The concepts of development of computer; The basic operating principle of input/output, information processing, data communication and storage device in computer system.
Develop a basic concept and applications of C programming language; Provide foundation knowledge of computer programming. Upon completion of this course, the students will learn how to write C/C++ programs and how to develop applications for data input/output and data processing.
Develop a basic concept and applications of C/C++ programming language. Upon completion of this course, the students will learn how to write C programs and how to develop applications for data input/output and data processing.
To provide knowledge in developing web applications including database processing; To provide foundation knowledge for advanced level networking and programming subjects. Upon completion of this course, the student have learnt the basic Internet programming techniques and is able to Write applications for the WWW and understand what can and cannot be done over the Internet.
To provide knowledge of the concepts and operating principles of the UNIX system.To understand concepts, commands and functions in UNIX system. To be able to develop simple applications including scripts in UNIX environment.
Provide an introduction to basic data structures, and algorithms for manipulating them, using C/C++ programming language; Give an introduction to the underlying concepts of abstract data types and data structures used for storing and handling information in computers; Provides foundation for advanced level database subjects. Upon completion of the course, the students will have learnt; The technique of analyzing the efficiency of different types of data structures; The technique of applying the theory of data structures to develop database and implementation technique of data structure.
Provide an overview of system administration, maintenance and automation; Provide knowledge for efficient use of system resource by familiarizes tools available and sharing of resources. To provide an overview of API of UNIX and Windows, to teach the practical techniques of programming in operating system level.
To Understand the basic design concept of different layer of computer network. To introduce the concepts and functions of data communication; To teach the framework of a computer network / reference model; To describe the details of TCP/IP; To understand routed and routing protocols, error detection and monitoring methods; To provide the knowledge about the configuration and maintenance of router; To provide the basic knowledge for a network administrator in LINUX.
To provide concepts of the network and system administration. To understand the advanced features of UNIX network and system.To understand the operations of the web/Internet network services.To gain hands on experiences of administrating computer system and network. Topics include Bootstrapping, kernel and driver, Backup, Network connections and managemen, DHCP, NIS, NFS and Samba, Apache Web Serve,DNS and BIND,Email systems.
To provide knowledge of the basic concept of computer organization and architecture design. Upon completion of this course, the student will learn: The basic concept of the computer architecture; How the memory of the computer is organized; How the computer handles I/O and interrupt routines from a low-level hardware point of view; The basic concept of micro-programming.
To allow the students to develop independent ability and organization of thought to solve and analyze abstract and complex problems. The student projects aim to achieve the objectives: Development of critical and logical thinking; Actual 141B Final Year Project II1 Term, 3 Credits
To allow the students to develop independent ability and organization of thought to solve and analyze abstract and complex problems. Development of critical and logical thinking:Actual 152 Algorithms and Complexity 1 Term, 3 Credits
To give an introduction to the design and analysis of algorithms and discuss various design techniques and topics of complexity. To give an introduction to the design and analysis of algorithms; To understand the techniques of complexity analysis.
To provide basic concept of theory of computation and formal language theory. To introduce the foundations of formal language theory, computability, and complexity; To teach the relationship between automata and various classes of languages.
This course aims to provide an understanding of the theoretical and practical issues underlying the production of two-dimensional and three-dimensional graphics. The objectives of the course are for students to understand: the hardware and software elements of computer graphics systems; the relevant graphics languages and standards; the concept of output primitives and attributes and to be able to apply these in the context of a graphics API; the basis of the viewing pipeline for geometrical primitives, including the roles of 2D and 3D geometrical transformations, raster conversion, and clipping algorithms; the use of color models; and the basic image transformation and filtering operations.
The aim of this course is to provide theoretical knowledge and implementation concepts of database systems. To introduce students the essential topics in modern database management systems; To provide the context of database analysis and modeling; To provide database design and implementation techniques; To teach the database administration.
The aim of this course is to provide theoretical knowledge and implementation concepts of database systems. To introduce students the essential topics in modern database management systems; To provide the context of database analysis and modeling; Toprovide database design and implementation techniques; To teach the database administration.
This course aims to provide students the knowledge of the principles and practice underlying the design of distributed systems, with emphasis on the Internet, the Web and middleware. To understand the issues to be resolved in the design of distributed systems; To be able to evaluate and criticize design for distributed systems; To appreciate the design and implementation of some of the widely-used distributed systems.
The aim of this course is to give students a basic understanding of the technologies underlying multimedia systems and their key applications. The objectives of the course are for students to understand: the properties of different media that are used to compress the digital representation for text, images, audio and video; the hardware constraints affecting the transmission and presentation of multimedia; andthe various multimedia features explored in advanced applications.
To give students a basic understanding of network security and its applications. The students will learn the concept of cryptography, hashing and secure data transmission.
Keyword Syllabus
Cryptography, information theory and the development of secured data transmission such as DES standard, public key, private key, hashing
Prerequisite
CSC 113, CSC 21, CSC 152
CSCC 165 Fault Tolerant Systems and Design1 Term, 3 Credits
To introduces the concepts in reliable computing and design methods for fault-tolerant systems. The students will learn the design concept of fault tolerant system in term of system architecture and system recovery.
The aim of this course is to provide a basic theoretical and implementation concept of object oriented programming. To develop a basic concept of the object oriented programming; To teach OOP languages: C++ and Java.
To introduce the information theory with an emphasis on those ideas and methods that are most useful in computer science applications. To understand the concepts of data compression, arithmetic coding and noise channel coding theorem.
The aim of this course is to provides the basic theoretical concept of computer simulation. The student will learn the techniques of forming mathematical and statistical models and their implementation techniques.
The aim of this course is to introduce the basic concept of image processing by computer and pattern recognition. Upon completion of the course, the students will learn the basic mathematical concept of image processing and the implementation of pattern recognition algorithms by computer.
To introduce the basic concepts involved in E-commerce environment and the implementation techniques to a successful system. To learn the design concepts, standard, software and hardware development environment of E-commerce systems.
The aim of this course is to learn the basic concepts and the major techniques of information retrieval. To learn the information retrieval techniques for document ranking, indexing, searching, visualizing multimedia objects, and searching the Web.
To provide a basic concept of operating principle of micro-controller and its applications. To learn the software programming and hardware design concepts of micro-controllers; To learn the programming techniques for practical micor-controller applications.
The aim of the course is to provide the basic concepts and techniques in parallel computing, with emphasis on applications on practical problems. To learn the theory and architecture design concept of parallel computing system.
The aim of the course is to provide the basic understanding of Human-computer interaction for computer system design To introduce the process of user centred system design; To introduce the technology of the user interface; To introduce the basic underlying theory of interaction.
To provide a basic theoretical concept of Digital Signal Processing and its applications. To learn the mathematical concept of digital signal processing algorithm and the implementation techniques of DSP algorithm.
To provide knowledge in Software Engineering approaches to the design and maintenance of software. To introduce the models of software development; To teach the various design tools; To introduce the techniques of comprehensive testing; To introduce the tools for version control, documentation and CASE (Computer Aided Software Engineering).
Understand the basic functions and design concept of operating system. The objectives of this course are to provide an in-depth understanding of: Roles of operating system in modern computer system; Interfaces of operating system to different hardware and application program; Algorithms that can be applied in operating system; Reasons behind the design of different operating systems.
The aim of this course is to provide basic concept and theoretical understanding of neural networks. To introduce the artificial neural networks in problem solving such as pattern recognition, functional mapping and prediction.
The aims of the course is to provide the basic concepts of system analysis techniques. To introduce the models of software development; To teach the various design tools; To introduce the techniques of comprehensive testing.
To provide a basic concept of management information system. To introduce the usage and importance of information system in business organization; To investigate the reasons for success or failure of a information system from the real world examples; To introduce the concept of E-Commerce and its benefits. | 677.169 | 1 |
It consists of two 10pt halves, running in parallel: Fields and Vector Calculus and Waves and Fourier Analysis, and provides a suitable preparation for core MP in JH, in particular Electromagnetism and Relativity, and Quantum Dynamics.
- Develop a working knowledge of the elements of vector calculus, in differential and integral form, and the use of index notation and summation convention.
- Understand the application of vector calculus to the flow of ideal fluids, and problems in electrostatics and magnetostatics.
- Develop a working knowledge of the elements of Fourier Series and Fourier Transforms, and their application to a variety of linear systems.
- Understand a wide range of physical phenomena involving waves: reflection and refraction, dispersion, interference and diffraction, wave-particle duality.
- Devise and implement a systematic strategy for solving a simple problem by breaking it down into its constituent parts.
- Use the experience, intuition and mathematical tools learned from solving physics problems to solve a wider range of unseen problems.
- Resolve conceptual and technical difficulties by locating and integrating relevant information from a diverse range of sources. | 677.169 | 1 |
Wednesday
Thursday
Quiz 8-1
Friday
Review for AP Exam
Pre-Calculus
Monday
4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant Objective: be able to generate the graphs for the tangent, cotangent, secant, and cosecant functions and to explore various transformations of these graphs. Pg 366, #35-49 odds Content Expectation P6.2
Tuesday
4.6 Graphs of Composite Trigonometric Functions Objective: be able to graph sums differences, and other combinations of trigonometric and algebraic functions. Pg 375, #1-37 odds
Wednesday
4.6 Graphs of Composite Trigonometric Functions Objective: be able to graph sums differences, and other combinations of trigonometric and algebraic functions. Pg 375, #39-79 odds | 677.169 | 1 |
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
Eddington's The Mathematical Theory of Relativity is arguably the first comprehensive treatise on the mathematical and physical foundations of general relativity. As Prof. Ashtekar explained it in his excellent and informative Foreword "it is comprehensive on three fronts: Eddington systematically introduces the tools of differential geometry, explains the (then known) physical consequences of the theory with admirable clarity, and discusses in detail the conceptual underpinning of general relativity." The new publication of Eddington's book is justified not only by its historical value, but also by the fact that it still provides an original and detailed introduction to the deep physical ideas of general relativity and its mathematical formalism, whose "treatment throughout the monograph is clear, sharp and at the same time pedagogical" (from the Foreword). Eddington's enlightening exposition of general relativity "carries interesting lessons for contemporary researchers in gravitational science at all stages of their career. It is therefore fortunate that the Minkowski Institute Press is making this historic monograph easily available once again" (from the Foreword). NOTE: This book is not a re-publication of the scanned pages of the original publication; the text has been typeset in LaTeX can't be less than 5 stars for a book on relativity, written by Eddington...
Some readers may find it very, I mean very, mathematical... But hey, that's what the title says and what Eddington just does.
The difficulties that a reader may encounter are not so much due to Eddington's way of using tensors -- which is the old/classic way -- but are mainly due to to :
1. The extensive prerequisites such as : mechanics, electrodynamics, electromagnetism...
2. The very dense proofs, where lots of steps are assumed known to the reader or easy to guess...
On the other hand, Eddington does a real effort at explaining the basic concepts and their interconnections as he theory unfolds, i.e. the WHAT, the WHY, the HOW and the WHAT IF... And that is so rare that it must be mentioned.
As a beautiful introduction to this book, I suggest Eddington's "Gravitation", i.e. "Space, Time and Gravitation", which are the same.
For a complete review of relativity books, see my comment on Einstein's "The Principle of Relativity".
I got the ebook from the publisher's site yesterday and was surprised to read the reviews here.... until I saw the time they were written - those reviews are NOT for this book. "The Mathematical Theory of Relativity" published on December 19, 2016 seems to be a very important book (see Description) by a man who writes well for the general public; I have read two of his less advanced and very interesting books.
Just got the book today--it's a ripoff! The "math" is simply unreadable--a bunch of incoherent symbols. Clearly, whoever produced this edition knows no math nor any physics. I am sending the book back. It's simply crap! | 677.169 | 1 |
GCSE Mathematics – Numeracy
'GCSE Mathematics – Numeracy' will build on the levels of numeracy and progress numeracy skills and will assess the mathematics that learners will need in their everyday lives, in the world of work, and in other general curriculum areas.
Content will include number, measure and statistics plus some aspects of algebra, geometry and probability. New topics to include Venn Diagrams, discussion analysis, sampling and box and whisker plots and AER-APR formula.
GCSE specification in Mathematics – Numeracy will enable learners to develop knowledge, skills and understanding of mathematical and statistical methods, techniques and concepts required for everyday life, in the world of work, and in other general curriculum areas
select and apply appropriate mathematics and statistics in everyday situations and contexts from the real world
use mathematics to represent, analyse and interpret information
acquire and use strategies for problem solving and modelling in context
understand that models may need refining and that there may be more than one way to solve a problem
interpret mathematical results and draw and justify conclusions that are relevant to the context
communicate mathematical information in a variety of forms
There will be a focus on literacy and numeracy skills together with developing your knowledge of sustainable issues, citizenship, bilingualism, enterprise and Welsh culture.
All post 16 learners who undertake this course (Welsh Government funded provision over 40 hours) are required to undertake the WEST (Wales Essential Skill Toolkit) Full Diagnostic Initial Assessment for Communication , Application of Number and Digital Literacy within the first four weeks of enrolment | 677.169 | 1 |
FLY Fusion™ Algebra
FLY Fusion™ Algebra Like a personal tutor, the FLY Fusion Algebra software for the FLY Fusion platform coaches middle school students through writing and factoring single variable equations, graphing systems of linear equations, or solving quadratic equations. FLY Fusion Algebra also helps with simplifying and factoring expressions and graphing lines and parabolas.The software also features a FLY Fusion Algebra FLYware control card featuring shortcut buttons, glossary terms, and a quick start guide. This software works only with the FLY Fusion Pentop Computer, and is not compatible with FLY 1.0 (LFC37735, sold separately). Click here for details | 677.169 | 1 |
About this product
Description
Are You Fascinated With Weather And Storms? Test Your Skills With Weather Related Math Equations! Correlates To Emphasis On Students Applying Foundational Math Skills. Correlated To Common Core, Texas Teks, Virginia Sols, And Georgia Performace Standards. Includes Text Features Such As Charts And Graphs. | 677.169 | 1 |
Preparing Students For Algebra
As students in the lower level grades prepare for the shift into higher order math classes, algebra can sometimes be overwhelming and frightening for students who have had no experience with it before. "Math is hard enough with just numbers," many students complain, "now what will we do when they throw letters in there too?!" this is a common worry amongst lower level math students, but there are some things parents, tutors and teachers can do to help prepare these students for success when it comes to algebra.
First of all, preparation for algebra can seem daunting for anyone, but when you focus on the key areas that truly help develop a strong math foundation, it is manageable. Many parents and math professionals focus on improving their child's calculation skills as a major part of preparing for algebra. However, according to a study in the Journal of Educational Psychology, it is more beneficial for students to practice word problems that basic math functions. Being able to read, dissect and solve word problems is a much more cognitive process, and can better prepare students for the real world situations brought up in most algebraic equations.
Problem solving is a skill that is required for success in all areas of math. In algebra, students should feel confident completing one and two-step problems, along with being able to ignore extra information that does not pertain to the problem and filter out what information is important and useful. They should have experience solving problems using a formula given to them.
Teachers, parents and tutors should always incorporate reading practice into every lesson. A student who understands math concepts but has difficulty sounding out words or reading the problem will struggle as much, if not more, than a student who can read fluently but has a weak math understanding. Students should know how to read the question, write their answer, and use and understand statements such as "if-then" when proving their answers and reasoning.
Estimating and reasoning are also two very important skills students should have when preparing for algebra. Things like making sure the units in the answer match the units in the problem.
As students reach higher-level math courses, their understanding of and ability to use a complex calculator becomes very important. Students should be familiar with the functions of a graphing calculator and have the ability to solve simple formulas and create tables.
Algebra doesn't have to be daunting and overwhelming for students. Teachers, parents and tutors can help them feel confident on their first day of algebra class by making sure they are prepared with the basics beforehand. | 677.169 | 1 |
ALEX Lesson Plan Resources
Subject: Mathematics (9 - 12) Title: Parent Functions and Their Children Description: In this lesson, students will be able to identify parent functions of linear functions, absolute value functions, and quadratic functions. Students will be presented with functions and asked to graph them by first identifying the basic curve and then using transformations. The transformations that will be highlighted in this lesson are translation and reflection. These activities will be done in teams of four students.
Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Investigating Parabolas in Standard Form Description: Students explore the coefficients of a quadratic function using a graphing calculator. This is an inquiry lesson to be used as an introduction to translations and dilations of functions.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation. SubjectThinkfinity Lesson Plans
Subject: Mathematics,Science Title: Sound WaveAdd Bookmark Description: This student interactive, from Illuminations, helps students understand the mathematical models used to represent sound. Students come to understand the origins of the terms pitch, tone, frequency, and intensity, as well as explore the dynamics of a sound wave. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: What's the Function?Add Bookmark Description: This lesson allows students to look for functions within a given set of data. After analyzing the data, students should be able to determine what type of function best represents the data. Then, students use regression on a calculator to determine the function that provides the best fit. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 | 677.169 | 1 |
Author: Roland B. Minton Publisher: CRC Press ISBN: 1498706320 Size: 53.55 MB Format: PDF, ePub View: 535 DownloadRead Online
Ideally, users of this book will have enough to choose from to suit whichever version of a sports course is being run." "The book is very appealing to teach from as well as to learn from.
Author: Hope Martin Publisher: Walch Publishing ISBN: 9780825139208 Size: 42.67 MB Format: PDF, ePub, Docs View: 5179 DownloadRead Online
Whether addressing algebra or geometry, probability or statistics, this book is full of great ideas for making the connection between the real world and your classroom.
Author: Rae Simons Publisher: Simon and Schuster ISBN: 1422289206 Size: 26.14 MB Format: PDF, Docs View: 7387 DownloadRead Online
In Sports Math, you'll discover that the math you learn in the classroom is just as important on the soccer field and basketball court.
Author: Robert Kissell Publisher: Academic Press ISBN: 0128052937 Size: 75.17 MB Format: PDF, ePub View: 5788 DownloadRead Online
4.1 INTRODUCTION In this chapter we provide an overview of probability and
statistics and their use in sports modeling applications. The chapter begins with
an overview of the mathematics required for probability and statistics modeling
and ... | 677.169 | 1 |
Objective: The objective of the course is to offer students a motivated introduction to the basic concepts of classical algebra such as integers, congruence classes, congruences equations, and polynomials, with an eye on more abstract topics such as groups and rings. We also present several important applications of these concepts especially in cryptography and number theory. This course takes a rigorous approach initiated in AMAT 299 (Intro to Proofs) - many results discussed in class will be proven in full detail.
Material covered: We will cover the following sections of the text:
Chapters 1-6,8,9,11,12,14,15,16 (time permitting: 20,23,24,28,30.)
Attendance: You are expected to attend class on time everyday .
I reserve the right to lower your course grade for absences.
Examinations: There will be two one-hour exams and the final :
Exam 1 (early October)
Exam 2 (early November)
There will be a cumulative final exam during the final examination period (place and time will be announced in class.) All students are expected to take the examinations at the announced time.
There is no reason to miss an exam other than getting sick (bring note from doctor), being on a team that
has a game at the same time an exam is given
(bring a note from your coach), or a death or serious illness in your family. In the event you can not attend an exam, you need to notify me IN ADVANCE .
You can call me, e-mail me (preferred contact!) or leave a message with the secretaries.
Homework: Writing assignments (aka homeworks) are an essential part of the course. Daily homework
problems will be assigned on each section of material covered in class. Homework will be collected and graded!
If you want to attach your whole problem set together, use a paperclip or staple. Your homework should be nea\
t and legible.
Use of electronic devices:
The use of cell phones is prohibited in class. Ringtones must be turned off in class and, if on, cell phones \
must be in vibrate mode. If there is a need to check for and/or receive a call, the student must inform me in\
advance to excuse him/herself to take an important call. Students must not engage in text messaging in the c\
lassroom. Students who create disturbance with ringing cell phones or text messaging, will be asked to leave \
the class session. Also, I do not allow laptops, tablet devices (iPads, etc.), music players, or any other el\
ectronic devices I deem potentially distracting in class. | 677.169 | 1 |
Course home page
Linear
Programming (LP) problems form
an important class of optimization problems with many practical
applications in production planning, resource allocation, investment
decisions,
scheduling, transportation and logistics, inventory
management, game theory and many other contexts. Solution methods for
Linear Programming
problems such as the Simplex algorithm (Dantzig, 1947) are routinely
used within
optimization packages to solve even very large problems, and form the
basis for
sophisticated algorithms to solve discrete optimization problems with a
wide range of practical applications.
This course presents the general theory
and characteristics of LP problems and some of the main algorithms for their
solution. After completing
this course the student
Can model several
practical optimization problems as linear programming problems
Understands the
mathematical foundations of linear programming and duality theory
Understands and can
apply the main algorithms for solving linear programming problems
Can use optimization software for implementing and solving linear and
mixed-integer linear programs | 677.169 | 1 |
Great Jobs for Math Majors
ISBN-10: 0071448594
ISBN-13: 9780071448598swers the question "What can I do with a major in math?" It isn't always obvious what a math major can offer to the workplace. But it provides you with valuable skills and training that can be applied to a wide range of careers. "Great Jobs for Math Majors helps you explore these possibilities | 677.169 | 1 |
This is a brand new course that works with MyMaths to deliver the new KS3 curriculum, so you can replace your outdated framework materials. With a truly differentiated structure so that all abilities can access the new curriculum, the scheme is underpinned by a learn it once and learn it well philosophy that enables coherent teaching and learning.98383693
Descripción Oxford University Press. Estado de conservación: New. MyMaths for Key Stage 3 is the brand new course that works with MyMaths to deliver the new curriculum. This student book is for middle ability students embarking on KS3. Its unique emphasis on visible progression and visual engagement, along with direct links to the MyMaths site, all help to bring maths alive for your average ability student. Num Pages: 336 pages, Colour. BIC Classification: 4KHN; YQM. Category: (E) Primary & Secondary Education. Dimension: 255 x 195 x 17. Weight in Grams: 792. . 2014. Paperback. . . . . Books ship from the US and Ireland. Nº de ref. de la librería V9780198304487 | 677.169 | 1 |
Use this mathematical drawings and graphs template to create your own math illustrations using the shapes of plane and solid geometric figures as well as trigonometric functions.
"Mathematical visualization or mathematical visualization is an aspect of geometry which allows one to understand and explore mathematical phenomena via visualization. Classically this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century), while today it most frequently consists of using computers to make static two or three dimensional drawings, animations, or interactive programs. Writing programs to visualize mathematics is an aspect of computational geometry." [Mathematical visualization. Wikipedia]
The math illustrations template for the ConceptDraw PRO diagramming and vector drawing software is included in the Mathematics solution from the Science and Education area of ConceptDraw Solution Park | 677.169 | 1 |
3 , correlated to 2005 Lesson 1.3 (pp ) Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions). Lesson 1.4 (pp ) Comparing and Ordering Integers Find an approximate location of a rational number on a number line Compare and order rational numbers 2
4 , correlated to 2005 Lesson 1.5 3
5 , correlated to 2005 Lesson 1.6 Evaluate algebraic expressions when given values for the variable(s) Calculate the mean, median, mode, and range for a data set Choose a measure of central tendency most appropriate to analyze a particular set of data Describe how an individual data point may affect the measures of central tendency Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker). 4
6 , correlated to 2005 Lesson 1.7 (pp ) Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Add, subtract, multiply, and divide integers special multiplication properties of zero Recognize that division by zero is not defined Evaluate algebraic expressions when given values for the variable(s) Calculate the mean, median, mode, and range for a data set Choose a measure of central tendency most appropriate to analyze a particular set of data. 5
7 , correlated to 2005 Lesson 1.8 Graph ordered pairs of rational numbers on a rectangular coordinate system Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Make conjectures from a graphical representation. 6
8 , correlated to 2005 Chapter 2 (pp ) Solving Equations Lesson 2.1 (pp ) Properties and Operations Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication Evaluate algebraic expressions when given values for the variable(s) Graph ordered pairs of rational numbers on a rectangular coordinate system 7
9 , correlated to 2005 Lesson 2.2 (pp ) The Distributive Property Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Add, subtract, multiply, and divide integers Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. Lesson 2.3 (pp ) Simplifying Variable Expressions Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication. 8
10 , correlated to 2005 Lesson 2.4 (pp ) Variables and Equations Add, subtract, multiply, and divide integers Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication Evaluate algebraic expressions when given values for the variable(s) Solve one and two step single variable equations and inequalities Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1mile = 88 ft/sec. 9
11 , correlated to 2005 Lesson 2.5 (pp ) Solving Equations Using Addition or Subtraction Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Recognize absolute value of a rational number as the value of its distance from zero Evaluate numerical and algebraic expressions containing absolute value Evaluate algebraic expressions when given values for the variable(s) Solve one and two step single variable equations and inequalities. Lesson 2.6 (pp ) Solving Equations Using Multiplication or Division Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1mile = 88 ft/sec Add, subtract, multiply, and divide integers Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 10
12 , correlated to 2005 Lesson 2.7 (pp ) Decimal Operations and Equations with Decimals Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication Solve one and two step single variable equations and inequalities Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 11
13 , correlated to 2005 Chapter 3 (pp ) Lesson 3.1 (pp ) Solving Two-Step Equations Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. Lesson 3.2 (pp ) Solving Equations Having Like Terms and Parentheses Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities Graph ordered pairs of rational numbers on a rectangular coordinate system. Lesson 3.3 (pp ) Solving Equations with Variables on Both Sides Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. Lesson 3.4 (pp ) Solve one and two step single variable equations and inequalities. Lesson 3.5 (pp ) Solving Inequalities Using Multiplication or Division Solve one and two step single variable equations and inequalities. 12
14 , correlated to 2005 Lesson 3.6 (pp ) Solving Multi-Step Inequalities Solve one and two step single variable equations and inequalities Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system. 13
15 , correlated to 2005 Chapter 4 (pp ) Lesson 4.1 (pp ) Factors and Prime Factorization Lesson 4.2 (pp ) Greatest Common Factor Lesson 4.3 (pp ) Equivalent Fractions Make predictions and describe the limitations of the predictions when using data samples Make conjectures from a graphical representation Recognize and create equivalent forms of a rational number Find an approximate location of a rational number on a number line Recognize absolute value of a rational number as the value of its distance from zero Evaluate numerical and algebraic expressions containing absolute value. Lesson 4.4 (pp ) Least Common Multiple Evaluate algebraic expressions when given values for the variable(s) Describe simple patterns using a mathematical rule or algebraic expression Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers). Lesson 4.5 (pp ) Rules of Exponents Evaluate algebraic expressions when given values for the variable(s) Recognize and create equivalent forms of a rational number Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers). 14
16 , correlated to 2005 Lesson 4.6 (pp ) Negative and Zero Exponents Recognize and create equivalent forms of a rational number Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers). Lesson 4.7 (pp ) Scientific Notation Solve one and two step single variable equations and inequalities Recognize and create equivalent forms of a rational number 15
17 , correlated to 2005 Chapter 5 (pp ) Lesson 5.1 (pp ) Rational Numbers Recognize and create equivalent forms of a rational number Find an approximate location of a rational number on a number line Find a rational number between any two rational numbers. Lesson 5.2 (pp ) Adding and Subtracting Like Fractions Compare and order rational numbers Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares. Lesson 5.3 (pp ) Adding and Subtracting Unlike Fractions Solve one and two step single variable equations and inequalities Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Check the reasonableness of results using estimation Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication. 16
18 , correlated to 2005 Lesson 5.4 (pp ) Multiplying Fractions Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions. Lesson 5.5 (pp ) Dividing Fractions Solve one and two step single variable equations and inequalities 17
19 , correlated to 2005 Lesson 5.6 (pp ) Using Multiplicative Inverses to Solve Equations Lesson 5.7 (pp ) Equations and Inequalities with Rational Numbers Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. 18
20 , correlated to 2005 Chapter 6 (pp ) Lesson 6.1 (pp ) Ratios and Rates Lesson 6.2 (pp ) Writing and Solving Proportions Lesson 6.3 (pp ) Solving Proportions Using Cross Products Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Solve problems using simple proportions Recognize and create equivalent forms of a rational number Represent very large and very small numbers using scientific notation Solve problems using simple proportions. Lesson 6.4 (pp ) Similar and Congruent Figures Classify two and three dimensional objects according to the defining characteristics Recognize and create equivalent forms of a rational number Solve problems using simple proportions Identify congruent and similar shapes Find missing lengths of similar plane figures using proportions Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Measure angles, perimeter, area, and volume using the correct size and type of units Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 19
21 , correlated to 2005 Lesson 6.5 (pp ) Similarity and Measurement. Lesson 6.6 (pp ) Scale Drawings Measure inaccessible heights or distances using similar triangles Solve problems using simple proportions Describe simple patterns using a mathematical rule or algebraic expression Identify congruent and similar shapes Find missing lengths of similar plane figures using proportions Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Create and interpret scale drawings Determine an approximate distance between two points using map scales Solve problems involving scale factors using ratios and proportions. 20
22 , correlated to 2005 Lesson 6.7 (pp ) Probability and Odds Measure inaccessible heights or distances using similar triangles Conduct a survey or experiment to collect data Derive the probability of an event mathematically, e g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle. Lesson 6.8 (pp ) Represent the probability of an event as a fraction, percent, ratio, or decimal. 21
23 , correlated to 2005 Chapter 7 (pp ) Lesson 7.1 (pp ) Percents and Fractions Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Recognize and create equivalent forms of a rational number. Lesson 7.2 (pp ) Percents and Proportions Make conjectures from a graphical representation Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Check the reasonableness of results using estimation Make predictions and describe the limitations of the predictions when using data samples. 22
24 , correlated to 2005 Lesson 7.3 (pp ) Percents and Decimals Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Check the reasonableness of results using estimation Recognize and create equivalent forms of a rational number Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Compute with percents, including those greater than 100% and less than 1% Solve problems using simple proportions Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Make conjectures from a graphical representation Make predictions and describe the limitations of the predictions when using data samples. Lesson 7.4 (pp ) The Percent Equation Lesson 7.5 (pp ) Percent of Change Represent the probability of an event as a fraction, percent, ratio, or decimal Recognize and create equivalent forms of a rational number Compute with percents, including those greater than 100% and less than 1% Check the reasonableness of results using estimation Compute with percents, including those greater than 100% and less than 1% Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication. 23
25 , correlated to 2005 Lesson 7.6 (pp ) Percent Applications Check the reasonableness of results using estimation Recognize and create equivalent forms of a rational number Compute with percents, including those greater than 100% and less than 1%. Lesson 7.7 (pp ) Simple and Compound Interest Evaluate algebraic expressions when given values for the variable(s) Compute with percents, including those greater than 100% and less than 1% Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 24
26 , correlated to 2005 Chapter 8 (pp ) Lesson 8.1 (pp ) Relations and Functions Compute with percents, including those greater than 100% and less than 1%. Lesson 8.2 (pp ) Linear Equations in Two Variables Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Compute with percents, including those greater than 100% and less than 1% Solve problems using simple proportions Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Describe simple patterns using a mathematical rule or algebraic expression Evaluate algebraic expressions when given values for the variable(s) Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system. 25
27 , correlated to 2005 Lesson 8.3 (pp ) Using Intercepts Evaluate algebraic expressions when given values for the variable(s) Identify the horizontal and vertical intercepts of a linear relation from a graph or table Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system. 26
28 , correlated to 2005 Lesson 8.4 (pp ) The Slope of a Line Recognize that division by zero is not defined Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 27
29 , correlated to 2005 Lesson 8.5 (pp ) Slope-Intercept Form Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 28
30 , correlated to 2005 Lesson 8.6 (pp ) Writing Linear Equations Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Make predictions and describe the limitations of the predictions when using data samples. 29
31 , correlated to 2005 Lesson 8.7 (pp ) Function Notation) Evaluate algebraic expressions when given values for the variable(s). 30
32 , correlated to 2005 Lesson 8.8 (pp ) Systems of Linear Equations Represent very large and very small numbers using scientific notation. 31
33 , correlated to 2005 Lesson 8.9 (pp ) Graphs of Linear Inequalities Graph ordered pairs of rational numbers on a rectangular coordinate system Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system. 32
34 , correlated to 2005 Chapter 9 (pp ) Lesson 9.1 (pp ) Square Roots Lesson 9.2 (pp ) Simplifying Square Roots Lesson 9.3 (pp ) The Pythagorean Theorem Lesson 9.4 (pp ) Real Numbers Recognize and create equivalent forms of a rational number Compute with percents, including those greater than 100% and less than 1% Recognize and create equivalent forms of a rational number Evaluate algebraic expressions when given values for the variable(s) Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication Find an approximate location of a rational number on a number line Compare and order rational numbers Evaluate algebraic expressions when given values for the variable(s) Determine the slope of a linear relation from a graph or ordered pairs. Lesson 9.5 (pp ) The Distance and Midpoint Formulas Lesson 9.6 (pp ) Special Right Triangles Lesson 9.7 (pp ) The Tangent Ratio Lesson 9.8 (pp ) The Sine and Cosine Ratios Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Compare and order rational numbers Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Solve problems using simple proportions Measure angles, perimeter, area, and volume using the correct size and type of units Measure inaccessible heights or distances using similar triangles Measure angles, perimeter, area, and volume using the correct size and type of units. 33
35 , correlated to 2005 Chapter 10 (pp ) Measurement, Area, and Volume Lesson 10.1 (pp ) Triangles Lesson 10.2 (pp ) Polygons and Quadrilaterals Classify two and three dimensional objects according to the defining characteristics Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system. Lesson 10.3 (pp ) Areas of Parallelograms and Trapezoids Classify two and three dimensional objects according to the defining characteristics Classify two and three dimensional objects according to the defining characteristics Measure angles, perimeter, area, and volume using the correct size and type of units Develop formulas for calculating the circumference of circles and the areas of triangles, parallelograms, and trapezoids. Lesson 10.4 (pp ) Circumference and Area of a Circle Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Classify two and three dimensional objects according to the defining characteristics 34
36 , correlated to 2005 Lesson 10.5 (pp ) Surface Areas of Prisms and Cylinders Classify two and three dimensional objects according to the defining characteristics Calculate surface area and volume of right prisms and cylinders using appropriate units. Lesson 10.6 (pp ) Surface Areas of Pyramids and Cones Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Classify two and three dimensional objects according to the defining characteristics Measure inaccessible heights or distances using similar triangles Calculate surface area and volume of right prisms and cylinders using appropriate units Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 35
37 , correlated to 2005 Lesson 10.7 (pp ) Volumes of Prisms and Cylinders Determine the slope of a linear relation from a graph or ordered pairs Classify two and three dimensional objects according to the defining characteristics Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Estimate measurable quantities in both standard and metric units, e.g., a vase holds a little less than a quart or about a liter; a 10K run is about 6 miles Calculate surface area and volume of right prisms and cylinders using appropriate units. Lesson 10.8 (pp ) Volumes of Pyramids and Cones Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Find missing lengths of similar plane figures using proportions Classify two and three dimensional objects according to the defining characteristics Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects. 36
38 , correlated to 2005 Chapter 11 (pp ) Data Analysis and Probability Lesson 11.1 (pp ) Stem-and-Leaf Plots and Histograms Determine the slope of a linear relation from a graph or ordered pairs2 (pp ) Box-and-Whisker Plots Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker) Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker). 37
39 , correlated to 2005 Lesson 11.3 (pp ) Using Data Displays4 (pp ) Collecting Data Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker) Conduct a survey or experiment to collect data Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Calculate the mean, median, mode, and range for a data set. Lesson 11.5 (pp ) Interpreting Data Evaluate reported inferences or predictions based on a data set Make conjectures from a graphical representation Make predictions and describe the limitations of the predictions when using data samples Evaluate reported inferences or predictions based on a data set. 38
40 , correlated to 2005 Lesson 11.6 (pp ) Permutations) Derive the probability of an event mathematically, e g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle. Lesson 11.7 (pp ) Combinations Represent the probability of an event as a fraction, percent, ratio, or decimal). Lesson 11.8 (pp ) Probabilities of Disjoint and Overlapping Events Derive the probability of an event mathematically, e g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle Conduct a survey or experiment to collect data Conduct experiments to approximate the probability of simple events Identify mutually exclusive events Recognize that the sum of the probability of an event and the probability of its complement is equal to one Determine whether a game or process is fair. 39
41 , correlated to 2005 Lesson 11.9 (pp ) Independent and Dependent Events Represent the probability of an event as a fraction, percent, ratio, or decimal Recognize that the sum of the probability of an event and the probability of its complement is equal to one Determine whether a game or process is fair. 40
43 , correlated to 2005 Lesson 12.7 (pp ) Exponential Growth and Decay Recognize and create equivalent forms of a rational number Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Solve one and two step single variable equations and inequalities Create a table, graph, or algebraic expression to represent the relationship between two variables. Lesson 12.8 (pp ) Sequences Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Describe simple patterns using a mathematical rule or algebraic expression Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Solve one and two step single variable equations and inequalities Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 42
44 , correlated to 2005 Chapter 13 (pp ) Lesson 13.1 (pp ) Angle Relationships Lesson 13.2 (pp ) Angles and Parallel Lines Lesson 13.3 (pp ) Angles and Polygons Lesson 13.4 (pp ) Translations Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Classify two and three dimensional objects according to the defining characteristics Graph ordered pairs of rational numbers on a rectangular coordinate system. Lesson 13.5 (pp ) Reflections and Symmetry Translate a geometric shape a given distance on a coordinate plane and identify the vertices Reflect a geometric shape across a line in a coordinate plane and identify the coordinates of the vertices Translate a geometric shape a given distance on a coordinate plane and identify the vertices. 43
45 , correlated to 2005 Lesson 13.6 (pp ) Graph ordered pairs of rational numbers on a rectangular coordinate system Reflect a geometric shape across a line in a coordinate plane and identify the coordinates of the vertices. Lesson 13.7 (pp ) Dilations Translate a geometric shape a given distance on a coordinate plane and identify the vertices Graph ordered pairs of rational numbers on a rectangular coordinate system Create and interpret scale drawings Solve problems involving scale factors using ratios and proportions. 44
Variables and Expressions Problem Solving: Using a Problem-Solving Plan Use a four-step plan to solve problems. Choose an appropriate method of computation. Numbers and Expressions Use the order of operations
Grade 7 Math Course Lesson Plan: 34 weeks Welcome to Thinkwell s 7th Grade Math! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan is meant to be a guide
2012-2013 Math Content PATHWAY TO ALGEBRA I Unit Lesson Section Number and Operations in Base Ten Place Value with Whole Numbers Place Value and Rounding Addition and Subtraction Concepts Regrouping Concepts
MATH Activities ver3 This content summary list is for the 2011-12 school year. Detailed Content Alignment Documents to State & Common Core Standards are posted on NOTE: Penda continuesAlgebra I COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics, with an emphasisAlgebra I Pacing Guide Days Units Notes 9 Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order
Prep for Calculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular
New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and The lessons that address each Performance Indicator are listed, and those in which the Performance IndicatorAlabama Course of Study: Mathematics (Grades 9-12) NUMBER AND OPERATIONS 1. Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots,
Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
Standard: Number, Number Sense and Operations Number and Number C. Develop meaning for percents including percents greater than 1. Describe what it means to find a specific percent of a number, Systems
A Correlation of Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013 to the Topics & Lessons of Pearson A Correlation of Courses 1, 2 and 3, Common Core Introduction This document demonstrates
Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards
Understanding the Progression of Math Courses in NEISD According to House Bill 1 (HB1), students in Texas are required to obtain credits for four courses in each subject area of the foundation curriculum
SOL 8.1 exponents order of operations expression base scientific notation Represents repeated multiplication of the number. 10 4 Defines the order in which operations are performed to simplify an expression.
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
Pre-Algebra IA Pre-Algebra IA introduces students to the following concepts and functions: number notation decimals operational symbols inverse operations of multiplication and division rules for solving
High School Mathematics Algebra This course is designed to give students the foundation of understanding algebra at a moderate pace. Essential material will be covered to prepare the students for Geometry.
Chapter 3 Vocabulary equivalent - Equations with the same solutions as the original equation are called. formula - An algebraic equation that relates two or more real-life quantities. unit rate - A rate
MAT 0950 Course Objectives 5/15/20134/27/2009 A student should be able to R1. Do long division. R2. Divide by multiples of 10. R3. Use multiplication to check quotients. 1. Identify whole numbers. 2. Identify | 677.169 | 1 |
In this course, you learn how to apply fundamental mathematical tools and techniques used in most fields of science, engineering and mathematics. You first strengthen and extend your existing skills in algebra, graphing, geometry and trigonometry, and then explore differential calculus, essential for the development of many technologies. Your skills in the recall, use and communication of the mathematics presented in this course provide the foundation for further studies in mathematics | 677.169 | 1 |
Download and read online McGraw Hill Math Grade 5 in PDF and EPUB NowDownload and read online Math Connects Grade 2 Consumable Student Edition in PDF and EPUB It's All Connected Math Connectsis intended for use in all elementary math classes as a balanced basal approach to teaching mathematics. Math Connects is the elementary portion of the vertically aligned PreK to 8 Math Connects program from Macmillan/McGraw-Hill and Glencoe. This program is designed to excite your students about learning mathematics while at the same time providing you, the teacher, with all the tools and materials you will need to teach the program. Your students will be motivated as they solve real-world problems such as creatures under the sea; emperors of the ice; and roller coaster physics. A variety of teacher materials are available to meets the needs of all your students, from early finisher to English learner
Download and read online Everyday Mathematics in PDF and EPUB These consumable books provide lesson support material for students to analyze and complete. They provide a long-term record of each student's mathematical development.
Download and read online McGraw Hill s Math Grade 8 in PDF and EPUB Now | 677.169 | 1 |
Switched On 5 Sub Set Grd 7 2007 Edition
Description
Combined in one complete set, the SOS 7th Grade 5-Subject Set conveniently contains all the subjects you need, and costs less than ordering the subjects individually. Designed with five core subjects, this curriculum set creates a solid educational foundation while giving your student an engaging, interactive learning environment.<br /><br /><br /><br />Subjects Include:<br /><br /><br /><br />Bible<br /><br />History & Geography<br /><br />Science<br /><br />Language Arts<br /><br />Mathematics<br /><br /><br /><br />In this step-by-step, comprehensive curriculum, your student will build his knowledge of the five core subjects. Each subject contains nine major topics and a review to guide the learning process. In addition, the SOS 7th Grade 5-Subject Set includes personalized progressive lessons and time-saving administration features like automatic grading. With this curriculum set, you can be assured your student will learn the essential Christ-centered material he needs to know. <br /><br />show more | 677.169 | 1 |
books.google.com - This... Review
Let's Review: Math A
This ways. The author also includes new Regents question types dealing, for instance, with motion problems and mathematical systems defined by tables. New contextualized word problems further enhance the presentation. The totally rewritten chapter on problem-solving offers students a core set of strategies that apply to a variety of curriculum-related exercises. In addition to subject review, demonstration examples, and practice exercises with answers, the book includes several complete recent Math A Regents exams with answers.
About the author (2007)
Lawrence S. Leff has helped make mathematics and tests more accessible to students through his work and his writing. Leff is assistant principal and math supervisor at Franklin D. Roosevelt High School in Brooklyn, New York. His writing is centered primarily on examination preparation guides. His books, which target high school students, have included, Let's Review: Sequential Mathematics, a teacher planning and student review and math test preparation guide, and Preparation for the CLEP--College-Level Examination Program. Some of Leff's math review guides originally were intended for New York area high school students participating in the three-year mathematics curriculum there. Lawrence Leff has also published mathematics materials not strictly for test-taking, including Geometry the Easy Way. | 677.169 | 1 |
Principles of Mathematics
We dont often think of math in terms of being presented with a Christian Worldview, but Master Books and author, Katherine A. Loop, have done just that. Using a Biblical lens, this comprehensive, two-year, junior high math course will cover the basics of arithmetic and pre-algebra and thoroughly prepare your student for algebra.
This curriculum is intended to be used for two years for 7th and 8th grades, although advanced 6th graders could also complete it. It is designed to be used before the student starts Algebra (in the curriculum of your choice). This curriculum would also work well for high schoolers who need a review of basic concepts and beginning algebra. The table of contents topical format allows you to use this text as a reference or extra practice for someone who might be struggling.
There are two books for each level of the program: a student text and a teacher guide. The teacher guide also holds student worksheets. Book 1 reviews basic arithmetic and teaches problem-solving skills and mental math through a Biblical lens. Book 2 is considered the pre-algebra portion of the program, so students need to be competent in basic functions of fractions, decimals, percent, and basic geometry. Book 2 assumes the knowledge of content presented in Book 1; so if you arent sure where to begin, have your student take the placement tests available on our website.
The Student Book (textbook) is the instruction, divided into chapters, then into lessons. Important notes about the curriculum and its use are found in the front of the book. Students will read the lesson in the Student Book and complete the activity page found in the Teacher Guide (more about that in a bit). Thats how easy it is to use this curriculum. Dont confuse easy-to-use with over-simplified content. After comparing the content of this course with that of Bob Jones, Saxon, Alpha Omega etc., Principles of Mathematics stays with the pack. It covers all pertinent topics for algebra preparation. While there is quite a bit of reading, the language is fairly easy to read and comprehend (conversational). The text is black and white with examples and illustrations, so may not appeal to your more visual learner. Calculator instruction is included, beginning with lesson 4.5, but parent/teacher can discern the amount of calculator use allowed. Lessons that have recommended calculator use are marked with a calculator symbol.
The Teacher Guide is a very important part of this program. You will find a course schedule, student worksheets for each lesson, answer keys (a mix of answers and solutions), quizzes, and tests. Also included in the worksheets are math problems from historical text books, such as Applied Mathematics for Junior High Schools and High Schools and Secondary Arithmetic: Commercial and Industrial for High, Industrial, Commercial, Normal Schools, and Academics and Practical Algebra: First Year Course. These problems help students understand the role of math throughout history, but they are also good thinking math problems. There are two versions of the schedule two-year and one-year. The two-year schedule is basically one lesson per day using both books to equal two years of junior high math. If you have a student who is really motivated and wants to finish both books in one year, there is a schedule for that. In this option, students complete about 2 to 3 lessons per day depending on the length. The Student Workbook is consumable (not reproducible); pages are perforated with plenty of space for students to show their work and answer questions.
The Principles of Mathematics Sets include a student text and the teacher guide.
Supplies suggested for this course are the student textbook and workbook, binder with notebook paper, abacus, blank index cards, calculator, graph paper, compass, measuring tape with Metric and US measure, ruler with Metric and US measure, and a protractor.
There is no separation of math and God: this text strives to teach students math and its connection to God and the Bible. The first 3 sections of chapter one are full of information to debunk misconceptions about math; explain math from a Biblical foundation; and expose the spiritual battle in math: all to lay a solid foundation for studying math with a Biblical Worldview. I have read a lot of articles and books on the relationship of math and God, but have never seen an actual curriculum that incorporates the two. ~ Donna | 677.169 | 1 |
Business Math and Statistical Measures Advice
Showing 1 to 3 of 3
This course helps refresh you on high school level math you haven't done is quite some time and it helps teach you how to invest and save and show you how much money you can potentially have with specific formulas. This course helps with the adult life.
Course highlights:
The highlights in this course were learning about present value, future value and funds. I learned what I need to save per month with a simple interest rate and that could get me a great deal of money for my future.
Hours per week:
3-5 hours
Advice for students:
Read the chapters and follow the examples.
Course Term:Fall 2016
Professor:Rudilee Gabel
Course Required?Yes
Course Tags:Background Knowledge ExpectedAlways Do the ReadingMany Small Assignments
Jul 05, 2016
| Would highly recommend.
Not too easy. Not too difficult.
Course Overview:
I needed this class it will help with my future career and it is a great refresher. Anyone in business can use this and will use the skills you learn.
Course highlights:
Just getting back into math and the swing of things. I realized how we use math in everything we do
It is a great class, difficult. But if you put the time and effort into the course and take the offered help from the professor, you will pass!
Course highlights:
Statistical analysis and business operations, financial calculations. At the end of the semester you have to do a PowerPoint presentation of a restaurant that you are starting and have to break down all the financial calculations and percentages of the operations.
Hours per week:
6-8 hours
Advice for students:
Don't fall behind, and do every assignment. It will guarantee and A for you. | 677.169 | 1 |
AS/SC/MATH3410.03F
Complex Variables
Some polynomials, such as,
have no roots if
we confine ourselves to the real number system. The complex numbers
can be defined as the set of all numbers of the form
,
where and b are real,
i is a new kind of number satisfying
, and the operations of arithmetic
are carried out in a
fairly obvious way. The complex numbers include the reals (case),
and the extended system has the desirable property that not only
but every polynomial now
has a root. In the
system of complex numbers certain connections are seen between otherwise
apparently unconnected real numbers. A striking example is Euler's
formula. This is actually a
very simple consequence of the
extension to complex variables of the familiar exponential and
trigonometric functions. The concepts and operations of calculus
(differentiation, integration, power series, etc.) find their
most natural setting in complex (rather than real) variables. In
addition, some physical problems such as those involving
electrical circuits and certain two-dimensional potential
problems (arising in fluid dynamics, airfoil theory,
electrostatics, etc.) are most easily analysed in the context of
complex numbers and functions.
The present course is intended to give the student a basic
knowledge of complex numbers and functions and a basic facility
in their use. The subject is a vast one, however, and its study
can be continued in MATH4210.03 (Complex Analysis). | 677.169 | 1 |
Modern Algebra
Spring 2011 This course will be based on proofs, and you will have to write many proofs.
COURSE OBJECTIVES:
Upon successful completion of this course, you will be able to prove theorems in abstract algebra, in particular, concerning groups, rings, and fields. You will know, understand, and be able to apply, prove, and explain major results in this area.
Textbook:
Contemporary Abstract Algebra, Joseph Gallian, Parts 1-4.
We may skip some chapters, as announced in class.
The textbook is required at all class meetings.
Required Reading:
Read each chapter that we cover in class, both before and after class.
Skim the chapter before class, even if you don't understand it fully,
to have some idea of what we'll be doing in class. Read it more
carefully after class to clarify and fill in details you missed in
class.
Warning:
Sometimes, we will not "cover" all the material from a chapter, but
instead focus on a particular aspect of the chapter. In such cases, I
will point out in class (and at this
website) which other
parts of the chapter I expect you to read on your own.
GRADES:
Participation (5%)
A significant portion of class time will be devoted to discussions and problem-solving. Your active engagement with the material is required at all times, whether you are presenting, participating in the audience, or working on a problem with a group. You will not be able to get a good participation grade if you are absent too much.
Computer exercises (5%)
Computer exercises from the textbook will be assigned regularly. These use web applets you can run from any browser, and which are available
here.
For each exercise, turn in a record of your observations and conjectures. These will be graded largely on effort.
Individual homework will be assigned weekly, and will be due Thursdays (with exceptions as announced in class). You are allowed to work together on homework (in fact, I
encourage you to do so), but the paper you turn in you must write yourself. Homework (including computer exercises) is due at the beginning of class (1:30 sharp); if you cannot make it to class, arrange to either deliver the homework to me early, or have someone else bring it to class for you. Your lowest homework score will be dropped.
Midterm (20%)
The midterm will cover all material we have discussed to that point. The midterm will be on
Thu., 24 Mar.
Final (30%)
The final exam will be comprehensive over all material we discuss in class. The
final will be on
Thu., 12 May, 1:00-3:45 p.m.
Makeup exams can be given only in extraordinary and unavoidable circumstances, and with advance notice. 1.3.1 AprilDisabilities:
If you have, or suspect you have, a disability and need an accommodation, you should contact the Disabled Student Services Office (DSSO) at 747-5148, dss@utep.edu, or Union East room 106. You are responsible for presenting to me any DSS accommodation letters and instructions.
Exceptional circumstances:
If you anticipate the possibility of missing large portions of class time, due to exceptional circumstances such as military service and/or training, or childbirth, please let me know as soon as possible. | 677.169 | 1 |
Edekit has developed over 10 year 7 Maths units that support the commencement of the Australian Curriculum in 2014. Other units for year 7 and year 9 are currently being developed and will become progessively available during the second half of 2013.
Click on the button Available Program Units for details of available units.
A Sample Program Unit is also available for review.
Rationale*
Mathematics is a reasoning and creative activity employing abstraction and generalisation to identify, describe and apply patterns and relationships.
It is a significant part of the cultural heritage of many diverse societies. The symbolic nature of mathematics provides a powerful, precise and concise means of communication.
Mathematics incorporates the processes of questioning, reflecting, reasoning and proof. It is
a powerful tool for solving familiar and unfamiliar problems both within and beyond mathematics. As such, it is integral to scientific and technological advances in many fields of endeavour.
In addition to its practical applications, the study of mathematics is a valuable pursuit in its own right, providing opportunities for originality, challenge and leisure. | 677.169 | 1 |
This article brings you the chapterwise tips and strategies along with important questions for CBSE Class 9 Mathematics and Science which will help you prepare effectively for the changed assessment structure that includes three periodic tests and one annual examination at the end of the year CBSE Class 9 Mathematics chapter 13, Surface Areas and Volumes: Important topics & questions to prepare for Class 9 Mathematics Examination, 2017-2018. All the questions have been prepared to cover most of the important topics included in chapter-Surface Areas and Volumes. The questions and terms mentioned in this article will surely help to make your preparation easy and organised.
In this article you will get CBSE Class 9 Mathematics chapter 11, Constructions: Important topics & questions to prepare for Class 9 Mathematics Examination, 2017-2018. All the questions have been prepared to cover most of the important topics included in chapter- Constructions. The questions and terms mentioned in this article will surely help to make your preparation easy and organised.
In this article you will get CBSE Class 9 Mathematics chapter, Probability: Important topics & questions to prepare for Class 9 Mathematics Examination, 2017-2018. All the questions have been prepared to cover most of the important topics included in chapter- Probability. The questions and terms mentioned in this article will surely help to make your preparation easy and organised.
In this article you will get CBSE Class 9 Mathematics chapter 1, Number Systems: Important topics & questions to prepare for Class 9 Mathematics Examination, 2017-2018. All the questions have been prepared to cover most of the important topics included in chapter- Number Systems. The questions and terms mentioned in this article will surely help to make your preparation easy and organised completed | 677.169 | 1 |
It might happen so that you have come to this page in search
for a freeware Windows graphing utility to use it for you homework
or lesson. If so, there is one - GraphSight Junior.
GraphSight Junior is a freeware small graphing utility for Windows
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Testimonials
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"I'm a teacher in an Agronomy course in South Brazil and my purpose with GraphSight Junior is didact. I and my students employ the program to visualize the shape of mathematic equations or models. I consider the facility the most interesting feature of the program. I don't have any suggestion at this moment, but I intent it in the future. Best regards! " - A. P.
"Using GraphSight Junior for college Algebra II course for graphing functions. It helps by being much faster and more readable than the graphing calculators currently on the market. Most of my work doing graphs is for homework and a portable calculator is not needed. The most useful features are the abilities to 1) control line width and color for multiple graphs 2) being able to do multiple graphs 3) it is extremely easy to use with an intuitive user interface. " - D. J.
"I use GraphSight Junior only to print out simple algebraic and trigonometric functions. It would be helpful to print out functions expressed in terms of a parameter. For this purpose I still use Mallard Basic and GSX on my old Amstrad 8256, but of course, it would be unreasonable to expect GSJ to match the power of Mallard Basic. SketchCalc used to have movable axes whereby the pairs of co-ordinates for any point could be determined easily. " - N. H.
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"
I currently use GraphSight Junior primarily in a grade seven classroom
setting in Thailand and secondarily in my school office. I have not yet
used it for instructional purposes. I spent some time playing with it to
learn some of its idiosyncrasies.
I then installed it on the two classroom computers. We do not have an LCD
projector but we do have a 29" TV connected to the computer in each
classroom.
There are a few students in my classes who, to put it mildly appear less
than well motivated.
While the class is working at a project or assigned problems, I sometimes
load the program and fiddle with a few graphs. It is somewhat akin to
fishing - and I caught a few big ones!
One or two of them were almost begging me to let them try it. (They don't
have all the math yet that they should have to really use the program
properly - but they NOW SHOW INTEREST!!! I gave them the web address and
they have downloaded their own copies already. After a little bit of input
instruction, they were off and running.
The last graph I put up for them was "y = xsinx". I did it in red and then
spun the wheel on the wheel mouse, shrinking and expanding the x-axis. The
changing patterns fascinated them - and me too!
Almost every day one or two students ask me when we can start using the
program. (We haven't even started graphing straight lines yet, but it looks
like that topic will have to jump the queue.)
As I mentioned above, we are in Thailand. I am a retired Canadian College
math prof teaching here in an English Program. We are not a particularly
wealthy institution, so the fact that the program is free is greatly
appreciated.
On behalf of the school, I thank you!
" - J. M.
"GraphSight Junior helps me to show how straight lines are drawn - changing slope / intercepts and predicting what the line will look like. The Smooth curve rendering is great." - S. K.
"Ok, GraphSight Junior I use in my school, I need make some Graps and the excell is no good for this details." - M. R.
"I use GraphSight Junior to help me representing a function in math homework. I personally think there is nothing special with this program, except if you just want to make a curve." - J-P. P.
"I'm a lecturer in Mathematics of Pedagogical University Hanoi 2. I used GraphSight Junior to present to our students on usefullness of a mathematical software. It seem very usefull in my lectures." - T. M. T.
"Hello, my name is Martina and I would like to get your GraphSight Junior to my computer because I feel I need it to understand better the maths as I'm studying it at school.I have read the review of it in one computer magazine I subscribe to.Thanks for your understanding." - M. M.
"GraphSight Junior is interesting in using for maths lessons in UK middle school, as simple alternative to cabri geometry or geometers sketchpad, also considerably cheaper!" - R. O.
"GraphSight Junior is very good! I appreciate it is a very important for my kids is very usefull for trigonometric class. Thank you." - J. D.
"I am a parent although happy with Maths, want to find a tool to reinforce graphs to solve equations etc. Trying to plot graphs early in KS3 - such as Y=X2 (sq). This will also then aid more complex graphs. I have found GraphSight Junior on the ask.co.uk site. Thank you." - N. B.
"Thanks for a great little GraphSight Junior! I use it just to see graphs of calculus problems before I jump into them." - A. W.
"Im in school grade 11 university math and have high hopes of someday being an engineer. GraphSight Junior is simply wonderful in allowing me to explore graphing functions." - J. M.
"I find GraphSight Junior to be a very simple, but quite handy little program. I have recommended it to a number of my highschool math students." - H. D. | 677.169 | 1 |
Mathematics 6 - Saxon Pre-Algebra - Live Online Course 2017-2018
Quick Overview
In this Live Online Course students will cover an introduction to geometry and discrete mathematics.
Details
This pre-algebra course provides an introduction to geometry and discrete mathematics. Topics covered include fraction, decimal, and mixed number operations, scientific notation, prime and composite numbers, order of operations, coordinates, exponents, square roots, ratios, algebraic expressions, solving equations with one variable, working with signed numbers, scientific notation, ratios, geometry fundamentals, probability, the Pythagorean Theorem and more. This course will solidify basic mathematics skills and prepare the student for success in Algebra I. Homework will average 3 - 4 hours per week.
Mathematics 6 - Pre-Algebra Saxon is taught by an expert instructor in the Veritas Virtual Classroom and is limited to only 20 students per course.
A Digital Tablet, a protractor and a ruler with inches and mm/cm are also recommended, but unfortunately, this item is not available through Veritas Press. ClickHERE | 677.169 | 1 |
An application of mathematics to modeling real world problems from the behavioral, computational, managerial, and social sciences. Includes such topics as probability, descriptive and inferential statistics, financial management, voting systems, codes and data storage.
Functions (including exponential and logarithmic functions), limits, derivatives and rates of change, applications of derivatives including graphing and optimization, and indefinite and definite integrals with applications.
Functions, rates of change, limits, derivatives of algebraic functions, applications including maxima and minima, exponential and logarithmic functions, and indefinite and definite integrals with applications.
Vector functions and their derivatives, motion in two and three dimensions, lines, planes, and parametric surfaces, spherical and cylindrical coordinates. Partial derivatives and multiple integrals in two and three dimensions. Vector fields, line and surface integrals.
Overview of mathematical topics from a perspective appropriate for early and middle childhood educators. Prime numbers and factorization, the operation of division on whole and rational numbers, ratio and proportion, probability, and data analysis.
Overview of mathematical topics from a perspective appropriate for early and middle childhood educators. Introductory geometry in two and three dimensions, transformational geometry, and concepts of measurement.
Introduction to logic and techniques used in mathematical proofs. Students gain experience in constructing proofs as they study sets, relations, functions, algebraic structures, and the properties of real numbers. Integrated Writing course.
Differential equations, axiomatics, probability theory, matrix algebra, simulation, and game theory, and their use in a variety of models in the social sciences, life sciences, and humanities. Includes deterministic models, probabilistic models, simulations.
Linear first order equations, method of characteristics. Classification of second order equations. Solution techniques for the heat equation, wave equation and Laplace's equation. Maximum principles. Green's functions and fundamental solutions.
Algebraic principles and linear, polynomial, rational, exponential, logarithmic, and trigonometric functions from a perspective appropriate for middle school teachers. Uses technology to explore how properties of functions appear in various representations.
Explores the big ideas in calculus -- limit, derivative, and integral -- with the goal of a solid conceptual understanding. Emphasizes applications, connections to algebra, and how these concepts appear in middle school math classrooms.
Infinite series, sequences and series of functions, power series, Taylor series, uniform convergence, topology of R^n, real-valued and vector-valued functions of several variables, derivatives and integrals of functions of several variables.
Learning to think quantitatively through solving pure and applied mathematics problems and modeling real world problems. Focuses on working with the steps involved in modeling real-life situations and understanding how modeling and problem solving differ.
nfinite series, sequences and series of functions, power series, taylor series, uniform convergence, topology of R^n, real-valued and vector-valued functions of several variables, derivatives and integrals of functions of several variables. Department Managed Prerequisite(s): Undergraduate lev | 677.169 | 1 |
Does your maths need to be refreshed and refocused for engineering or science?
Are there some elements of school maths you have forgotten or never quite mastered?
With clear explanations, lots of examples and a friendly, encouraging style, Fundamental Maths is a short, easy-to-follow textbook that makes maths accessible and manageable for all.
Written for students entering HE or FE courses in engineering or science, the author covers all the core topics and breaks them down into easily digestible chunks, keeping explanations clear and concise throughout.
Put past anxieties about maths or gaps in your knowledge behind you!
"synopsis" may belong to another edition of this title.
About the Author:
MARK BREACH is Principal Lecturer in Engineering Surveying at Nottingham Trent University, UK, where he also teaches mathematics to engineers. He is the author of several textbooks.
Book Description Palgrave Macmillan 2011-01-1173 | 677.169 | 1 |
Mathtopper Class 11 1.0
Mathtopper brings you a first of its kind Maths Learning Course that meets all your Mathematics requirements from the comfort of your home.
5
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Measure It 3.3
Build whole number and fraction computation skills. Number by number problem exercises. Includes whole number math facts, addition, subtraction, multiplication and division of whole numbers and fractions. Also includes English and Metric
5
Demo
The Lucent Calculator 2.0 2.0
The calculator can calculate and plot formulas with variables. Tooltip-Help for all functions of the calculator are available. The plotter can calculate null, intersection of functions, minima and maxima. The statisic can calculate average and
DreamCalc Standard Edition 3.5.1
DreamCalc is more powerful than many dedicated graphing packages. Graph functions and plot list data simply & quickly!
DreamCalc is ideal for teaching environments and is widely used in schools. The software includes a comprehensive User Guide
Cartesius Grapher 1
Cartesius Grapher 1 is an application for navigating your way via functions by panning and zooming with your mouse.
5
Freeware
Geometry Calculator 2.1.2w
Geometry Calculator is a program for calculating the area of circles, rectangles, squares, triangles with surface Area and Volume of cubes, prisms, cylinders, pyramids, cones and spheres, not only can you get the area calculation with this program. | 677.169 | 1 |
Date and Time
About Praveen Parmar
About the Course
In this course the student would learn the concept and short tricks. This course includes 5 live sessions, 30 videos, 10 documents and 10 online test
Topics Covered
Course Outline of Vedic Math Part I Basic Level 1. Miscellaneous Simple Method a. Squaring of number ending with '5' b. Squaring a number between 50 and 60 c. Multiplication of numbers with a series of 9's d. Multiplication of numbers with a series of 1's e. Multiplication of numbers with a series of similar digits in multiplier f. Subtraction using the rule 'All from 9 and the last from 10' 2. Criss-Cross System of Multiplication a. Two digit numbers b. Three digit numbers c. Four digit numbers 3. Squaring Numbers a. By Criss-Cross Technique b. By Formula Method 4. Cube Roots of Perfect Cubes 5. Square Roots of Perfect Squares Part II Intermediate Level 6. Base Method of Multiplication a. When the number of digits in RHS exceeds number of zeros in the base b. Multiplying a number above the base with a number below the base c. Multiplying numbers with different bases d. When base is not a power of 10 7. Base Method for Squaring 8. Digit-Sum Method 9. Magic Squares 10. Dates and Calendars 11. General Equations 12. Simultaneous Linear Equation Part III Advanced Level 13. Square Roots of Imperfect Squares 14. Cubing Numbers 15. Base Method of Division
Who should attend
This course may attend the students of Class 4th and onwards, Ideal for students preparing for Bank PO, IIT-JEE & Competitive Exams like CPT, CET, CAT, etc.
Pre-requisites
For the students of 4th onwards.
What you need to bring
Should have broadband connection for live class
Key Takeaways
Methods taught were simple and could be mentally solved which will help the students to attain confidence. Workshop to be organized from school to school at all levels.The methods will help the students to check their answers which will build their confidence. Maths phobia hopefully will disappear. | 677.169 | 1 |
Wikipedia in English (1)
The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained - no background in complex numbers is assumed - and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more. | 677.169 | 1 |
Wednesday, September 9, 2015
Geometry: A Comprehensive Course by Dan Pedoe PDF Download
Professor Pedoe is widely known as a fine teacher and a fine
geometer. His abilities in both areas are clearly evident in this
self-contained, well-written, and lucid introduction to the scope and
methods of elementary geometry. It covers the geometry usually included
in undergraduate courses in mathematics, except for the theory of convex
sets. Based on a course given by the author for several years at the
University of Minnesota, the main purpose of the book is to increase
geometrical, and therefore mathematical, understanding and to help
students enjoy geometry.
Among the topics discussed: the use
of vectors and their products in work on Desargues' and Pappus' theorem
and the nine-point circle; circles and coaxal systems; the
representation of circles by points in three dimensions; mappings of the
Euclidean plane, similitudes, isometries, mappings of the inversive
plane, and Moebius transformations; projective geometry of the plane,
space, and n dimensions; the projective generation of conics and
quadrics; Moebius tetrahedra; the tetrahedral complex; the twisted cubic
curve; the cubic surface; oriented circles; and introduction to
algebraic geometry.
In addition, three appendices deal with
Euclidean definitions, postulates, and propositions; the
Grassmann-Pluecker coordinates of lines in S3, and the group of circular
transformations. Among the outstanding features of this book are its
many worked examples and over 500 exercises to test geometrical
understanding. | 677.169 | 1 |
Sitemap
Case Study: My Experience With Calculators
An Introduction to Math. There are various types of qualifications that are required in various fields. The kind of skill needed should be able to match the available position. This is to ensure that the individual can be able to handle the task arising from the job. This is to ascertain that the individual has full capability of working there. One of the main qualifications is the education. The level of teaching helps to indicate the reliability of the person when it comes to that job. There are different disciplines that an employer usually looks at in the education level. This is in accordance with the issues that the individual has learned in school. The subject may be science or languages related. For an employee to be able to decide whether or not he should hire a person he usually looks at the education level. This is to a certain whether the person is qualified for the job or not before embarking on other fields that will either qualify or disqualify him. Math is the primary unit that an employer looks for as one of the qualifications. Math shows the ability of a person to deal with the arithmetic and the calculations relating to a particular discipline. An employer, therefore, looks a person with the ability to deal with mathematical problems and complex calculations that might arise in the course of the work. Math, therefore, turns out to be an essential discipline that relates to the way people work and how they can solve problems that are numerical or that requires calculations. People have therefore tried to establish ways in which they can be able to solve math problems. this has involved inventing different math stuff that can help us address some questions. Calculator is one of the tools that have been invented. The modern calculators are as a result of continuous improvement of the previous gadgets. The calculators are fed with formulas and can generate the required answers when the user is in need. This has enabled the math to be step ahead and be easier in solving problems. Why not learn more about Lessons?
The computer has been another invention that has significantly assisted in solving the math problem. A computer can be used to address some of the most complex math problems that are known to man because of their efficiency and reliability. They help us in dealing with the complex calculations regarding the organization. These are just some of the tool that man has come up with in helping him solve the problems relating to calculations. Math has been encouraged by many people since they help us solve life questions. The solving of the problems can be handled by the use of the formulas that have been put in place by the scholars. The problems can be easily solved since the formulas are standard.Education – Getting Started & Next Steps | 677.169 | 1 |
Sketch.g., physical temporal phenomena) or to mathematical phenomena (e.g., a function with three extrema). Moving students beyond plotting and reading points to interpreting the global meaning of graphs and the functional relationships that they describe has been identified as a major goal of mathematics education.
Tools like Sketch2Go enable the bypassing of algebraic symbols as the only channel into mathematical representation, and motivate students to experiment with a given situation, analyze it, and reflect upon it, even when the situation is too complicated for them to approach symbolically. The visual analysis that emerges from work with such tools is different from that which arises from work with algebraic symbols or numerical tables.
Features
Sketch2Go is a qualitative graphing tool. Graphs are sketched using seven icons representing constant, increasing, and decreasing functions that change at constant, increasing, or decreasing rates. It is based on original R&D carried out by Schwartz and Yerushalmy (1995) and Shternberg & Yerushalmy (2001), who propose an intermediate bridging representation based on the function and its vocabulary. The seven graphic icons describe the change in both the function and its rate of change. Sketch2Go is a version of the Qualitative Derivative Grapher programmed by Alexander Zilber for CET (Centre for Educational Technology).
Mathematical modeling cannot be fully accomplished by this qualitative sign system of constant, increasing, and decreasing functions. But the set of seven signs supports forming a mathematical construction with language developed from acquaintance with physical scenarios, helping lay the foundations of learning pre-calculus and calculus. Sketch2Go supports the abstraction of everyday phenomena using a small set of mathematical signs that can be manipulated on screen as semi-concrete objects.
Suggested Activities
a modeling problem
a car is moving at a speed of 20 meters per second when the driver sees a ball rolling on the road. The driver's reaction time is one second (reaction time is the time that passes between identifying the ball and pressing the brakes.) During that time the car continues at its constant speed. After the driver presses the brakes, the car decelerates for 7 seconds until it stops.
* Describe in a graph the distance the car traveled during from the time the driver saw the ball until the car stopped.
* What does the lower graph describe in this story?
* How would your graph change in each of the following situations: (1) the driver drove faster; (2) the driver was drunk; (3) it was a rainy day.
Using sketches to prove derivative rules
Sketch examples of functions that would fulfill the constraints listed below.
Write the properties that the functions represent or argue why you could not find such functions:
* Continuous functions whose derivatives are increase monotonically
* Continuous functions that have derivative functions with exactly a single maximum
* Continuous functions with derivative functions that have a discontinuity or some sort
* Functions with discontinuity that have continuous derivative functions
* Functions that have continuous derivative functions and a second derivative with discontinuitymPustak Add (320x240 360x640) MPustak Add Hindi is a Mathematics Practice app in Hindi language that helps you learn with a lot of fun Practice simple addition questions and compete against yourself for score and time
Please note that the current version supports 240x320 and 320x240 screen sizes only. For owners of phones with larger screen sizes, we request you to wait for another update to this applicationEquation Solver Equation Solver is intended to solve systems of linear algebraic equations with real coefficients of the second and third order (with two and three unknown).
a1*x+b1*y=c1
a2*x+b2*y=c2
a1*x+b1*y+c1*z=d1
a2*x+b2*y+c2*z=d2
a3*x+b3*y+c3*z=d3 | 677.169 | 1 |
Read the opening extract of the brand new A. J. Finn book before its publication on 22/01/2018
Maths for engineers books
See below for a selection of the latest books from Maths for engineers category. Presented with a red border are the Maths for engineers books that have been lovingly read and reviewed by the experts at Lovereading.
With expert reading recommendations made by people with a passion for books and some unique features Lovereading will help you find great Maths for engineers books and those from many more genres to read that will keep you inspired and entertained. And it's all free!
Handbook of Software Engineering Kyo-Chul Kang
Here is a complete overview of software engineering with a focus on historical perspective and a description of technology evolution that provides a crucial context for researchers as well as engineers to develop new solutions in a rapidly advancing area. Format: Hardback - Released: 11/10/2017
Differential Equations for Engineers The Essentials David V. Kalbaugh
This book surveys the broad landscape of differential equations, including elements of partial differential equations (PDEs), and concisely presents the topics of most use to engineers. It introduces each topic with a motivating application drawn from electrical, mechanical, and aerospace... Format: Hardback - Released: 05/09/2017
Understanding Engineering Mathematics John Bird
Studying engineering, whether it is mechanical, electrical or civil relies heavily on an understanding of mathematics. This new textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them to solve real-life engineering problems. It deliberately starts... Format: Hardback - Released: 30/08/2017
Basic Engineering Mathematics John Bird
Now in its seventh edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in... Format: Hardback - Released: 11/08/2017
Other books in this genre
Engineering Mathematics, 7th ed John Bird
A practical introduction to the core mathematics required for engineering study and practice Now in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based... Format: Hardback - Released: 02/08/2017
Basic Engineering Mathematics, 6th ed John Bird
Introductory mathematics written specifically for students new to engineering Now in its sixth edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples... Format: Hardback - Released: 02/08/2017
Higher Engineering Mathematics, 7th ed John Bird
A practical introduction to the core mathematics principles required at higher engineering level John Bird?s approach to mathematics, based on numerous worked examples and interactive problems, is ideal for vocational students that require an advanced textbook. Theory is kept to... Format: Hardback - Released: 28/07/2017
Engineering Mathematics John Bird
Now in its eighth edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. Mathematical theories are explained in a straightforward... Format: Hardback - Released: 27 Hardback - Released: 07 Paperback - Released: 07/07/2017 | 677.169 | 1 |
Customer Reviews
Great book for math majors
This lovingly written and exquisitely crafted book provides a detailed introduction to abstract algebra. First published in 1964, it is still an excellent textbook and will probably never go out of date.
The text does not assume any background beyond high school math, but the mathematics it covers is intense and detailed. This is a book for college math majors, not for someone who is looking for a casual introduction to | 677.169 | 1 |
Quantitative Reasoning
(minimum of 6 credits) [QR]
Students must complete a minimum of two QR courses. One must be a course with the MA (mathematics) prefix and completed within the first 60 credits of study (exceptions to this time frame may be necessary for transfer students). All students must pass the Math Placement Test at the stipulated level in order to register for a MA course.
Courses in this area:
Acquaint students with formal systems, procedures, and sequences of operations.
Strengthen students' understanding of variables and functions.
Apply mathematical techniques to the analysis and solution of real-life problems.
Develop an understanding of and facility with statistical analysis, including an understanding of its applications and limitations. Courses meeting these criteria must emphasize why statistical inference works and not simply how to use statistical techniques.
Strengthen understanding of the relationship between algebraic and graphical representations.
Emphasize the importance of accuracy, including precise language and careful definitions of mathematical concepts.
Understand both underlying principles and practical applications of one or more fields of mathematics. | 677.169 | 1 |
Polynomials I Tutoring Videos
0step viewsSeptember 15, 2015
High School ACT Prep Videos
"In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents." | 677.169 | 1 |
MATH 350 Calculus III
3 Credits
In this continuation of MATH 251, students learn to work with infinite series and power series, as well as vectors and vector-valued functions. By solving a variety of problems using calculus, students enhance their ability to communicate mathematical concepts in both an oral and written format. | 677.169 | 1 |
This volume presents a full high-school course in elementary algebra and contains all the topics given in the standard year-and-a-half courses. It is adapted to the prevailing practice of teaching elementary algebra in two courses - a full-year course followed by a half-year course. The first twenty-three chapters contain all the work required in any standard one-year course, and the remaining ten chapters comprise a subsequent half-year course, reviewing and extending the elementary processes, fractions, factoring, exponents, and methods of solving equations, before any new topics are given. The result is a single volume adapted to a continuous one-and-a-half-year course, or to a course in which geometry intervenes between first-year and second-year algebra. It is especially suited to the latter plan, because Chapters XXIV and XXV furnish the review necessary for those pupils who take the divided course. Moreover, the treatment of quadratic equations, radicals, exponents, ratio, proportion, variation, and graphs in the second as well as in the first year's work, gives the greatest flexibility to the use of the book. For example, if, for the purposes of a short course, one or more of the later chapters were omitted from the first year's work, the chapters in the second year's work would supply material on the subjects omitted.
In whatever manner the study of geometry and algebra is alternated, the student acquires little knowledge of the metrical properties of geometry during the first year. For this reason, the authors have used in their problems only the most obvious of these properties, and have given in a carefully prepared supplement the more difficult properties to which algebra may be applied Brand New Book ***** Print on Demand *****.Ex269329 | 677.169 | 1 |
Introduction to Graph Theory
We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them.
In this course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible!
By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics.
As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
From the lesson
Flows and Matchings
This week we'll develop an algorithm that finds the maximum amount of water which can be routed in a given water supply network. This algorithm is also used in practice for optimization of road traffic and airline scheduling. We'll see how flows in networks are related to matchings in bipartite graphs. We'll then develop an algorithm which finds stable matchings in bipartite graphs. This algorithm solves the problem of matching students with schools, doctors with hospitals, and organ donors with patients. By the end of this week, we'll implement an algorithm which won the Nobel Prize in Economics! | 677.169 | 1 |
About this product
Description
his book is designed to give students a broad understanding of the basics of algebra. Algebra fundamentals are essential for solving problems in other parts of mathematics as well, such as algebraic geometry. The Facts On File Algebra Handbook delivers algebra made easy and accessible to everyone. | 677.169 | 1 |
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PowerPoint Slideshow about 'College Algebra: An Overview of Program Change' - irWest Virginia University (WVU) established the Institute for Math Learning (IML) within the Department of Mathematics in January 2001. The goal of the IML is to develop, evaluate, and implement new and successful approaches to mathematics teaching and learning.
The IML was formed partly in response to results from the Third International Mathematics and Science Studies (TIMSS), which showed that the United States trailed most developed countries in the world on this assessment (Mullis et al., 1998).
Through the course changes, faculty members have tracked the number of students receiving a D, an F, or withdrawing (called the DFW rate). Most IML courses historically had DFW rates of 40%-60%. Since Spring 2001, there has been a decline in the DFW rate for College Algebra, which has been significantly restructured since the creation of the IML.
WVU offers two versions of on-campus College Algebra and only the on-campus version that is part of the IML is included. Students are placed into College Algebra by completing an algebra workshop, by passing a placement test, or by having scored at least a 23 on the math ACT test. Many IML courses, including College Algebra, have 200-student sections.
A Personal Response System (PRS) has been used in some sections since Fall 2004. A PRS is a combination of hardware and software that allows instructors to poll students with multiple choice questions during class. The students use handheld wireless transmitters to respond. Software immediately aggregates the answers and displays a frequency chart for each answer choice.
In Fall 2005 a lecture guide was introduced into the course. The guide gives students outlines of definitions and examples, which are discussed in class. Students fill in the definitions and work out the examples, either in class with the instructor, working in class on their own, or outside of class using their text.
A web-based College Algebra course has also been offered through WVU. Primary goals of the course are to increase the college attendance rate in West Virginia (West Virginia Higher Education Policy Committee, 2002) and to increase the ACT scores for West Virginia students (WVDE, 2001).
The WvEB course is web-enhanced, has a university professor instructor of record, and has a high school mathematics teacher facilitator. Since Fall 2003, the two courses have used the same syllabi and assessments.
For example, in WvEB Algebra final course evaluations for the 2002-2003 academic year, 82% of respondents indicated that the online quizzes helped them learn the course material, with half of these students reporting that the quizzes were the course component that most helped them learn.
In the Fall 2004 semester, students were repeatedly reminded in class that they were required as stated on the course syllabus to work on Quizzes 1 and 2 to prepare for the first exam. The first exam was taken by 498 students and the average grade was a 63.1%. At 10:00 am on the morning of this exam, only 381 students had completed Quiz 1 at least once and only 252 students had completed at least one attempt on Quiz 2 (Butler & Zerr, 2005).
During the Fall 2004 semester, a study was conducted to investigate differences in performance results between the 3 sections of College Algebra. One section used PRS and PowerPoint presentations; a second section used only the PowerPoint presentations, while the third section served as a control.
It was found that the quizzes were the course component that had the greatest impact on the difference in the final grades between the sections. There was no significant difference between sections on the ACT tests, but all students gained an average of 1 scaled point.
It is important to note that the mean scaled math ACT pretest score for students in all three sections was 19.93, which is close to the 2005 West Virginia average of 19.3 in 2005 (Average ACT Scores by State, 2005). However, this score is substantially below the math ACT score of 23 required to take the course. Furthermore, even the mean scaled posttest score of 22.17 is lower than the entrance requirements.
A survey on PRS was also given to students in the section which used PRS. While there were some difficulties using the new technology in the classroom, it was found that approximately 66% of students wanted to use PRS in future classes and overall written responses were positive. There was, however, a notable difference in the amount of class time students wanted to spend on PRS, which led to other research in the course.
While conducting the PRS survey research in the course, it was noted that some students thought that PRS questions were not worth the class time and that there was a discrepancy in the amount of time that students thought should be spent on PRS questions.
It was decided to study learning styles in College Algebra in the Fall 2005 semester. One goal of the research was to see if particular learning styles correlate with student grades on course components, and if there are any learning styles which are not addressed by any of the current course components.
Students were given a learning styles inventory to complete outside of class on WebCT for a small amount of bonus points. The Center for Innovative Teaching Experiences (C.I.T.E.) Learning Styles Inventory by Babich, Burdine, Albright, and Randol (1976) consists of 45 questions, and was formulated at the Murdoch Teachers Center in Wichita, Kansas to help teachers determine the learning styles preferred by their students (WVDE, 2006).
Survey results from the section where the instructor had the most experience using PRS and used the lecture guide to lead the course are interesting. Approximately 48 students returned surveys that were at least partially completed. In this section, 42 students picked the lecture guide as a helpful course component, and 31 students picked the lecture guide as the most helpful course component (over 63% of students responding). Of the students in this section, 25 picked PRS as a helpful course component, and 2 picked PRS as the most helpful course component. When asked if the lecture guide and PRS worked well with their learning style, 36 and 22 students, respectively, said yes. Only 3 students said that the lecture guide did not work well with their learning style, while 10 said this about PRS.
Preliminary research into College Algebra and WvEB Algebra led the researchers to question why the WvEB Algebra students seemingly outperform the on-campus students so significantly, with higher course grade averages and lower DFW rates. To study this question, in the Fall 2004 semester 50 WvEB Algebra students were paired with on-campus students based on age, gender, high school background, and ACT scores. Preliminary results show that, when matched, on-campus students perform as well on pre to post-ACT measures as the WvEB students. | 677.169 | 1 |
2014 UPDATE: the hot version (released in April, 2014) comprises those updates:
The up to date version numbers the questions and answers. This is helping to simply locate the proper solutions at the back of the book.
100% of the solutions to the up to date variation were independently verified either by means of laptop and via a global math whiz.
AUTHOR: Chris McMullen earned his Ph.D. in physics from Oklahoma country collage and presently teaches physics at Northwestern nation collage of Louisiana. He built the Improve Your Math Fluency sequence of workbooks to aid scholars turn into extra fluent in simple math skills.
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NOTE: the reply key makes use of commonplace shape. Fractions are expressed as diminished fractions and ideal squares are factored out of squareroots. for instance, should you obtain a solution of one over root eight, the reply key will in its place exhibit root 2 over four; either solutions are a similar, however the resolution key makes use of average shape.
This biography makes an attempt to make clear all aspects of Zermelo's existence and achievements. own and clinical elements are saved separate so far as coherence permits, so one can let the reader to keep on with the single or the opposite of those threads. The presentation of his paintings explores motivations, goals, reputation, and impression. chosen proofs and data gleaned from unpublished notes and letters upload to the research.
An creation to the traditional perform of rune crypt because it applies in glossy lifestyles. There are step by step directions to utilizing runes for healthiness, occupation, love existence and kinfolk existence. perform packing containers let readers to check their figuring out and there are case experiences of runes in motion. | 677.169 | 1 |
This richly detailed overview surveys the evolution of geometrical ideas and the development of the concepts of modern geometry from ancient times to the present. Topics include projective, Euclidean, and non-Euclidean geometry as well as the role of geometry in Newtonian physics, calculus, and relativity. Over 100 exercises with answers. 1966 edition.
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. | 677.169 | 1 |
AP Calculus Optimization Discovery Project with M&Ms!
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Optimization is a tricky topic in calculus. This one-day activity allows students to discover how calculus can help them.
Each student (or small group) starts with an index card, which will be cut and folded up to form a box. First they calculate what would happen if the box is made various ways, and see that the volume changes depending on the size of the cuts.
Next students develop an equation and apply calculus to determine how to create a box with maximum volume - so that they can fill it up with the most candy! | 677.169 | 1 |
Discrete and Computational Geometry
Discrete and Computational Geometry
Joseph O'Rourke, Satyan L. Devadoss
Language: English
Pages: 270
ISBN: 0691145539
Format: PDF / Kindle (mobi) / ePub
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems.
* The essential introduction to discrete and computational geometry
* Covers traditional topics as well as new and advanced material
* Features numerous full-color illustrations, exercises, and unsolved problems
* Suitable for sophomores in mathematics, computer science, engineering, or physics
* Rigorous but accessible
* An online solutions manual is available (for teachers only). To obtain access, please e-mail: [email protected]
page intentionally left blank POLYGONS Polygons are to planar geometry as integers are to numerical mathematics: a discrete subset of the full universe of possibilities that lends itself to efficient computations. And triangulations are the prime factorizations of polygons, alas without the benefit of the "Fundamental Theorem of Arithmetic" guaranteeing unique factorization. This chapter introduces triangulations (Section 1.1) and their combinatorics (Section 1.2), and then applies these
are collinear, then any triangulation of S has exactly 2k + h − 2 triangles and 3k + 2h − 3 edges. Proof. Let T be a triangulation of the point set S, and let t be the number of triangles of T. We know T subdivides the plane into t + 1 faces, t triangles inside the hull and the face outside the hull. Each triangle has three edges, and the outside face has h edges. Since each edge touches exactly two faces, (3t + h) double counts edges; so there are exactly E = (3t + h)/2 edges. Applying Euler's
Figure 3.13. (a) The flip graph of a convex pentagon and (b) the 3D associahedron. 75 76 CHAPTER 3. TRIANGULATIONS Theorem 3.39. There exists a convex n-dimensional polytope1 called the associahedron whose vertices and edges form the flip graph of a convex (n + 3)-sided polygon. The k-dimensional faces of this polytope are in one-to-one correspondence with the diagonalizations of the polygon using exactly n − k diagonals. Notice that the vertices of this polytope (the "faces" of dimension
− p ≤ x − q }. If S has numerous sites, then we need to compare the distances of points between p and all other sites of S. This yields the following result: Theorem 4.1. The Voronoi region Vor( p) is the intersection of all halfplanes H( p, q), where q is any other site in S. One of the fundamental results of discrete geometry is as follows: 99 100 CHAPTER 4. VORONOI DIAGRAMS Theorem 4.2. The intersection of any (not necessarily finite) set of convex objects is convex. Proof. Let {Xi | i ∈ | 677.169 | 1 |
Featured Book
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Some Applications of Geometric Thinking is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a ``course'' in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The goal of Some Applications of Geometric Thinking is to help teachers see that geometric ideas can be used throughout the secondary school curriculum, both as a hub that connects ideas from all parts of secondary school and beyond--algebra, number theory, arithmetic, and data analysis--and as a locus for applications of results and methods from these fields. Some Applications of Geometric Thinking is a volume of the book series ``IAS/PCMI--The Teacher Program Series'' published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest | 677.169 | 1 |
About this title:
Synopsis: Written for students who are struggling in math, Math Tutor: Mastering Algebra Skills is an excellent tool for providing additional concept reinforcement. Each lesson in this book contains an "Absorb" section to instruct and simplify math concepts, as well as an "Apply" section to help students grasp concepts on their own. Topics covered include fractions, order of operations, expressions and equations with variables, solving linear equations, polynomials, and more! It is great for use in the classroom or at home and fully supports NCTM standards!Book Description Twain Media, Incorporated Publishers, Mark. Paperback. Book Condition: Good. Book has a small amount of wear visible on the binding, cover, pages. Bookseller Inventory # G1580372589I3N006IM_ns | 677.169 | 1 |
Magical Book On Quicker Maths is a book that helps its readers tackle the mathematics sections in all competitive exams with minimum effort.
In Magical Book On Quicker Maths, M. Tyra provides a new and speedier approach to problem solving, one that is simple to understand and easy to apply. It is aimed at aspirants of all competitive exams conducted by banks, the Union Public Service Commission (UPSC), the Staff Selection Commission (SSC), LIC, CPO, UTI, GIC, and similar organizations.
With this book, M. Tyra aims to fulfil the need for faster and more effective methods of solving mathematical problems. The book begins with an introduction on tips for preparing for mathematics examinations, followed by chapters on various mathematical concepts. Some of the topics covered include fractions, surds, profit and loss, ratio and proportion, time and work, simple and compound interest, trigonometry, and data analysis.
The book is meant to help students from all streams, including science, commerce and arts.
The concepts involved are explained clearly and concisely so that students will find them easier to understand, regardless of whether or not they have good prior grounding in mathematics. The book also contains several illustrations, lending visual clarity to the concepts explained. It covers all the possible types and variations of problems that have appeared in competitive exams in recent times.
The author has put in two years of rigorous effort and research to come up with this book. He has derived many of the ideas from Vedic mathematics, number theory, and also through suggestions from his readers and other study resources on the subject.
About M. Tyra
M. Tyra or Manoj Tyra is an instructor of mathematics. He writes books on problem solving and quantitative aptitude, with a special focus on Vedic mathematics.
He has written Magical Book On Quicker Maths. Also, he has co-authored the book, Practice Book On Quicker Maths, with K. Kundan. This book can be used for practicing problem solving and strengthening one's understanding of the concepts from Magical Book On Quicker Maths. He started his own publication with Banking Services Chronicle, a monthly magazine. He has also developed study material for correspondence courses for IIT, CAT, and banking examinations.
He graduated in 1990, with a degree in Mathematics from Delhi University. He has taught and mentored several students, helping them prepare for various competitive exams.
this is exactly what the publishers say - magical....miraculous....i have used this book....it is perhaps the best book available in the market with such a large number of detailed solved questions, quicker methods, explanations and short cut formualaes....if you can work out this book, then for sure maths @ any competitive exam in the world is gonna be a cake walk for sure......this book is just great....if you work on it ....u will win....if you buy it and look at it...you'll lose....so get...
This book is good. You can by this book and practice, but remember YOU MUST HAVE A GOOD GRIP OVER MATH...why??....because there are some areas which require a little pre-occupied knowledge in order to understand. There are some areas which are described in a clumsy way and could have been made better but the number of such are very few. Recommended to Use----Provided you have a nice base already!!!
Its a mediocre book on Q.A./Maths. In the market lots of books are available with the title "Quicker" & "Quickest" books on mathematics. But, ask an experienced person who've used these kinds of books before. Don't purchase them on the basis of cover or attractive promises made by the slogans.
They consist of a single formula of a particular question. So its better not to mug up these formulae and move on to a standard book on Q.A. For this book the rating must be 3/5.
guys, the qicker maths by m tyra is one f d best books for ppreparing 4 banking xavs w.r.t. tyv vanagement. i referred dis book nd got vany f short cut tricks wic helped me a lot in banking xsms.... now i m a P.O. in Union bank of india nd i helped by this book a lot... so my suggestion u must have tis book nd r.s . agarwal bok for preparation..
Questions in quant which are coming in the current papers are based on concept. Those days of tricks are gone. Unless your concept is clear you cant do anything.so try to solve questions rather than following this book. Practice from 10 rd sharma .agarwal etc. Moreover this book is useless for those who are beginers and somewhat average. To utilize the tricks given in this book first ur concept should be crystal clear.
this book contain lots of formula , you have to learn it , moreover when ...
My Kind advice is please dont buy this book. which is gud for nothing. After buying this book i am repenting now. This book does not contain any speed increasing tips. if ur looking for increasing your speed there are lot number of blogs in net. Mk Tyra has done nothing special in this book, He simply solved the problems like others authors. Shame on BSC publications. | 677.169 | 1 |
Description: The principles of Analytical Geometry are developed in the first two chapters of this book. The remainder of the book is occupied in applying the principles and methods of Analytical Geometry to the straight line, circle, parabola, etc.
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Mathematics Papers Answers Grade 11
This comprehensive compendium of questions and answers, compiled by an expert team of maths educators, is designed for exam revision. The purpose, however, has been to extend mathematical thinking and expertise beyond the norm. | 677.169 | 1 |
Course MAT199
Math Alive
Mathematics has profoundly changed our world, from the way we communicate with each other and listen to music, to banking and computers. This course is designed for those without college mathematics who want to understand the mathematical concepts behind important modern applications. The course consists of individual modules, each focusing on a particular application (e.g., digital music, sending secure emails, and using statistics to explain, or hide, facts). The emphasis is on ideas, not on sophisticated mathematical techniques, but there will be substantial problem-set requirements. Students will learn by doing simple examples.
In past semesters there have been modules on the following topics:
Cryptography
Error correction & compression
Probability & Statistics
Birth, Growth, Death & Chaos
Graph Theory
Voting & Social Choice
Description of classes
Grading:
Problem Sets count for 40% of the course grade
Class Participation counts 10% of the course grade.
The midterm paper counts for 25% of the course grade.
The final paper counts for the remaining 25% of the course grade.
Additional Important Notes:
In order to obtain a passing grade, you MUST have obtained at least half of the points on EACH component.
Problem sheets will be made available each week except for spring break which is set aside for work on the midterm paper. Problem sets will be collected at the beginning of the lecture on Thursday (11am) following the week when the material was covered in class (the first problem set being due on Week 2 on Thursday at 11). Exact dates will be posted on the course web page.
Late homework will NOT be accepted except by prior arrangement with the instructor.
Of the 12 problem sets to be turned in, only the highest 11 will be used to compute the grade. That is to say, the lowest problem set grade will be dropped. | 677.169 | 1 |
Eighth Edition of this highly dependable book retains its best featuresaccuracy, precision, depth, and abundant exercise setswhile substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers.Chapter topics include Graphs; Polynomial and Rational Functions; Conics; Systems of Equations and Inequalities; Exponential and Logarithmic Functions; Counting and Probability; and more.For individuals with an interest in learning algebra as it applies to their everyday lives. | 677.169 | 1 |
Targeted especially towards students who struggle with their core math program, Modern Curriculum Press M Mathematics uses a traditional drill and practice format with a predictable, easy-to-use lesson format that's flexible and adaptable to your schedule and needs. Each two-page lesson focuses on one main objective; the first page begins with a developmental model and the second provides practice. Reinforcing basic math skills, extensive practice will help students learn and retain new concepts while preparing a wide range of ability levels for success on standardized tests. Level E covers adding, subtracting, multiplying, and dividing fractions and decimals; geometry; ratios and percents; graphs, statistics and probability; equations, integers and graphs. 378 indexed pages, softcover...
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Description Can be scripted using an advance motion control language MCP has several user definable I/O High performance motion control intelligence Can also change direction during full throttle without damage The MCP2160 Dual 160A 60VDC Advanced Motor Controller can be scripted using an advance motion control language. At the heart of the MCP is a 32Bit high performance Cortex M4 processor with DSP and FPU. The MCP has several user definable I/O. This includes integration of limit switches and high current control I/O to control contactors, relays, braking systems and more. In addition I2C and SPI are supported to connect to external sensors. The MCP programmable language and mix of control I/O eliminate the need for a secondary control system in most all applications. With the MCP...
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Description New Swiftech MCP35X 12 VDC Pump by Swiftech Product Description The MCP35X pump is a substantial evolution from the long established MCP355 series. It differentiates itself from its sibling by two primary features. The MCP35X Swiftech pump housing has been redesigned to provide considerably enhanced hydraulic performance is compatible with multiple tubing options thanks to the adoption of the G1/4 port standard can host an optional built- in reservoir is also sold separately, and remains compatible with all MCP3XX series pumps. The motor is now PWM compatible, allowing variable speed control thru the motherboard from 1300 to 4500 rpm. Part Number: MCP35X-BK. Product Dimensions: 5.9 x 3.9 x 5 inches Item Weight: 13.1 ounces Shipping Weight: 13.1 ounces Manufacturer: Swiftech...
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:: eBay Listing Template :: Home About Us Feedback Newsletter Blade Stock Canopy: mCP X BL Item Description Blade Stock Canopy: mCP X BL, BLH3909 Main Features Stock Canopy: mCP X BL Specification Manufacturer: Horizon Hobby Shipping Weight (pound) : 0.0 Shipping Dimensions: Width: 3.20 Length: 4.60 Height: 0.70 are typically shipped withing 24 hours after...
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Manufacturer ... Model ... Blade MCP X BL BLH3908YE Yellow Hi-Performance Main Blade Set MCPX BL Item Specifics: Item #: BLH3908YE Item Condition: Brand New in Factory Packaging Manufacturer: Blade Warranty: Full Manufacturer Warranty UPC Code: 605482092231 Shipping Time: In Stock Ships Within 24hrs Item Details: Blade MCP X BL BLH390YE Yellow Hi-Performance Main Blade Set This is Blade Yellow Hi-Performance Main Blade Se and is intended for use with the Blade 130X helicopter. S hipping | 677.169 | 1 |
Customize Your VideoText Interactive Algebra Module A
It is generally understood that the study of Algebra is the study of relations. Relations of first-degree should be mastered first and are addressed in this Module A. In fact, as instructors, we all understand that relations of any degree other than one must be "reduced" to relations of first-degree, or "factored" into linear or first-degree factors, before they can be resolved. The impact of this understanding on the scope and sequence of Algebra content, is to organize the various types of relations, by degree. In this course, first-degree relations are examined exhaustively before higher-order relations are encountered. | 677.169 | 1 |
AS/SC/MATH4160.03W
Combinatorial Mathematics
Combinatorics is an important branch of both pure mathematics and
modern applied mathematics. Faced with finite discrete
structures (such as graphs, combinatorial designs, geometric
configurations, etc.) basic questions arise:
Existence: given a set of prescribed properties, do any
such objects exist?
Enumeration: If they exist, how many are there?
Algorithms: Are there efficient methods to construct some
(all) such objects?
Such combinatorial questions arise in many areas, ranging through
logic, algebra, geometry, probability and statistics, operations
research, computer science and modeling in the social sciences,
physical and natural sciences and engineering. Students have
probably also encountered combinatorial questions on mathematical
contests and mathematical aptitude tests!
We will study some central techniques in this field. Topics
covered in this course will include introduction to
enumeration;
relations and partitions; combinatorial identities; algebraic
counting techniques; ordered sets.
Additional topics, for projects and presentations, will be based
on the interests of the students.
The text will be K. Bogart, Introductory Combinatorics, (HBJ).
The prerequisites are a solid background in linear algebra
(MATH2222.03, or MATH2022.03) and
mathematical maturity, indicated by completion of at least two
courses at the 3rd or 4th year level and a course emphasizing
mathematical or logical proofs. Students who lack this
background need permission of the instructor.
The final grade will be based on assignments, class tests, and
projects/presentations.
Prerequisites: AS/SC/MATH2022.03 or AS/SC/MATH2220.03; a major
MATH\- course (6 credits) at the 3000 level; or permission of the
Course Coordinator. | 677.169 | 1 |
Featured ProductsHelp students make the transition from arithmetic to algebra and geometry! Perfect for use as full units of study, as supplements to the curriculum, or as tutorial resources at home. Each book includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, and answer keys. 128 pages. | 677.169 | 1 |
This book provides a comprehensive introduction to linear programming which encompasses all the major topics students will encounter in courses on the subject. The authors aim to teach both the underlying mathematical foundations and how these ideas This book provides a comprehensive introduction to linear programming which encompasses all the major topics students will encounter in courses on the subject. The authors aim to teach both the underlying mathematical foundations and how these ideas are implemented in practice. The book illustrates all the concepts with both worked examples and plenty of exercises. In addition, Windows software is provided with the book so that students can try out numerical methods using the examples and exercises and hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time. Authors'note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States. The new version of Formula One, when ready, will be posted on WWW. ...Continua Nascondi | 677.169 | 1 |
Basic Concepts in Modern Mathematics
Basic Concepts in Modern Mathematics
An in-depth survey of some of the most readily applicable essentials of modern mathematics, this concise volume is geared toward undergraduates of all backgrounds as well as future math majors. By focusing on relatively few fundamental concepts, the text delves deeply enough into each subject to challenge students and to offer practical applications. The opening chapter introduces the program of study and discusses how numbers developed. Subsequent chapters explore the natural numbers; sets, variables, and statement forms; mappings and operations; groups; relations and partitions; integers; and rational and real numbers. Prerequisites include high school courses in elementary algebra and plane geometry. | 677.169 | 1 |
here's something about calculus.
Mathematicians turn misty-eyed at its very mention. Students cringe.
It's been praised as the highest intellectual edifice created by
humankind, and dismissed as an absurdity that computes only "ghosts of
departed quantities."
Physicists will tell you it's the mathematical scaffolding behind our
entire technological society; former students will tell you it's used for
calculating the volumes of bananas. A philosopher might say it's the
mathematics behind counting the number of angels that can fit on the head
of a pin.
In ever-more frantic efforts to bridge this gap, mathematicians are
putting out dozens of new books and CDs designed to sell their favorite
subject. These new approaches couldn't come at a better time.
These days, calculus is required for almost every even vaguely
quantitative profession, from architecture to economics. Yet as many as a
third of first-year undergraduates fail the course, according to
mathematician Colin Adams of Williams College, one of the authors of the
new book "How to Ace Calculus." The book is dedicated to "all the
students whose lifelong ambitions were dashed on the cliffs of calculus."
Among those dropping over the edge, Adams says, are "a ton of students
who have their sights set on, say, being a doctor. They take calculus,
and then suddenly, boom, that's the end."
The calculus crisis has set off what UCLA math chairman Tony Chan
calls a "war" among mathematicians over how to teach this essential
subject. Yet more than a decade of reform has not solved the problem.
A Constantly Shifting World What is it about calculus that causes such fear and loathing in some,
and ardor in others?
What is calculus, anyway?
In a nutshell, calculus is the mathematics of moving targets. Most
mathematics deals with things that hold still: numbers and triangles and
points and quantities.
But the real world shifts constantly. Blood and electricity flow,
temperatures rise, wind rushes, galaxies collide, empty space expands,
continents drift. "Still life exists only in an art gallery," says
mathematician Keith Devlin, dean of sciences at St. Mary's College of
Moraga and creator of the CD and book "Electronic Companion to Calculus,"
as well as other popular interpretations.
Yet, until calculus was invented, mathematics couldn't get a grip on
change.
Pinning down motion might not seem to be that much of a problem. But
the very idea presented countless paradoxes to the ancient Greeks. "Some
things were Greek, even to Greeks," David Berlinski opens his charming
and instructive book, "The Tour of the Calculus."
The Greeks couldn't make mathematical sense of how a chicken could
cross the road, for example. Obviously, chickens do cross roads, but
ancient Greek mathematicians reasoned that a chicken has to cross half
the road, then half of the half that's left, then half of that half, and
so on and so forth, ad infinitum. It will always have half of some
interval left to traverse. To be sure, the steps the chicken takes in
this scenario will get infinitely small. But there are also infinitely
many steps to take. Ipso facto, you can't get there from here. You can't
get anywhere.
The flaw in the Greeks' logic was the assumption that you can't add up
an infinite number of things and get a finite answer. Calculus showed
that you can.
And once you can add infinite sums, you can do all sorts of amazing
things--for example, calculate how an infinite number of angels can sit
on the head of a pin.
"That alone is one reason mathematicians find it incredible," Devlin
says. "It's the human, finite mind finding ways to handle the infinite.
To me that's just staggering."
But the idea of adding up an infinite number of infinitely small
pieces still boggles the mind. What does it mean, after all, to be
infinitely small? What is the difference between infinitely small and
nonexistent? "That was a really hard concept for people to deal with,"
Adams says. "Are [these infinitesimally small subdivisions] here or are
they not here? Are they real or are they not?" These "infinitesimals"
seemed so spooky to 18th-century British philosopher Bishop Berkeley that
he dismissed them sarcastically as "ghosts of departed quantities."
Actually, calculus tames the infinite in two different, complementary,
ways. First, it can pin down instantaneous rates of change--for example,
how fast is your car moving down the freeway? Further, it can pin down
rates of change of rates of change--for example, how fast is your car
accelerating or slowing down?
By adding the total of an infinite number of infinitesimal changes,
calculus also can compute the total amount of change. How much weight
have you gained in your lifetime--despite all those ups and downs? Or,
how much did you earn on that investment? Most important, calculus gives
you a handle on how one thing changes as a function of something else. As
master math expositor Martin Gardner puts it, calculus keeps track of how
the number of toes in a family changes as a function of the number of
persons the family contains.
Gardner explains all this in the recently reissued best-selling 1910
book, "Calculus Made Easy," by Silvanus Phillips Thompson, which Gardner
still considers the best introductory calculus text on the market. The
two faces of calculus grasp both the instantaneous flicker and the
holistic sum.
The Symmetry of the Whole Taken together, "there's a beautiful symmetry to it," UCLA's Chan
says. "You can go back and forth, from one view to the other, and always
get back where you started."
Why, then, don't students see the light?
"Calculus means different things to different people," Devlin says.
Students facing their first calculus courses tend to see it as a
mismatched jumble of techniques for solving problems they'll probably
never need in real life: slopes of graphs, areas under curves, velocity,
acceleration, volumes.
Students get so lost struggling through the underbrush that they can't
see the broader view, experts say. "It's like telling a joke without the
punch line," says mathematician Deborah Hughes Hallett of the University
of Arizona, who worked on the Harvard Calculus Reform program.
"Generations of students have studied calculus without ever seeing its
power."
Indeed, one of the reasons U.S. students do so poorly on standardized
math tests in general, according to Hughes Hallett, is that they cover
more topics more superficially than their foreign counterparts.
"One thing that makes students not enjoy a subject is the sense that
they don't know what it means," she says.
These days, introductory calculus books try to cram in so much,
Gardner says, that they typically weigh 5 pounds, are 3 inches thick and
cost close to $100.
Are students being asked to cover too much too quickly? Isaac Newton
was one of the inventors of calculus, and even he knew a lot less about
the subject than students are required to learn today, Devlin says.
Newton, Devlin says, "would probably be lucky to get a C" in today's
typical calculus class. "If I were grading Newton's explanation of
calculus now, I would put red ink all over it."
Because it took 200 years for the best minds in math to work out the
details, he says, "we shouldn't be surprised if it takes students more
than a semester."
Educators trying to inspire as well as instruct get caught between two
sometimes contradictory goals. Teaching equations without context leaves
calculus stuck in students' throats like dry crackers. On the other hand,
preaching the magic of calculus without the often difficult mathematics
that makes it work provides no substance.
In the end, Devlin says, any effective approach for bridging the
calculus gap will have to appeal to aesthetics.
Fewer bananas, more angels. | 677.169 | 1 |
best selling, the same as found in James Stewart's market-leading Calculus text, is what makes this text the market leader. | 677.169 | 1 |
Very good, but I just want to emphasize that Level 1, as I've defined it, doesn't necessary involve equations; it just means that you get the right answers somehow, as long as it's not cheating. (So I think the "calculate" part in its name is a bit misleading and I should probably pick a different one.)
To put it another way: for purposes of determining whether you have type I understanding, ad hoc is okay, but post hoc is not. | 677.169 | 1 |
Chemical Engineering Syllabus For Gate 2016An...
Platforms: Mac
There are lots of things to remember as a student. The date of a famous battle or a complex equation, and that's on top of remembering where you're meant to be and when and what assignments you're meant to be working on. Syllabus looks after all that for you, leaving your memory free for other...
Platforms: MacThe Matlab CAPE-OPEN Unit Operation is a unit operation implementation for which the calculations can be entered in Matlab.
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Number Press is the perfect solution for printshops, organizations, clubs or any type of business that need to number their documents. Ideal to number forms, raffles, NCR, Slips, Multiple-Up or anything that needs to be numbered. Choose any font, style, size or color Place up to 32 Numbers...
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Geometry Express is the newest addition to Praeter Software's award-winning line of educational mathematic calculation and teaching software for students and teachers.
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Platforms: Mac | 677.169 | 1 |
Welcome to Math IGCSE 607, a two-year course that will prepare you for the IGCSE exam in May of 2015 but will also set the stage for IB courses. Be prepared to learn lots, question lots, work lots, and enjoy lots!
Please note that as of this year, ALL 9th grade students will be required to own and use a TI-84 or TI-84+ graphing calculator. Put your name on the calculator and take good care of it because you will most likely be using it for the rest of your High School career and beyond! | 677.169 | 1 |
This is an introduction to stochastic integration and stochastic
differential equations written in an understandable way for a wide
audience, from students of mathematics to practitioners in biology,
chemistry, physics, and finances. The presentation is based on the
naïve stochastic integration, rather than on abstract theories
of measure and stochastic processes. The proofs are rather simple
for practitioners and, at the same time, rather rigorous for
mathematicians. Detailed application examples in natural sciences
and finance are presented. Much attention is paid to simulation
diffusion processes.
The topics covered include Brownian motion; motivation of
stochastic models with Brownian motion; Itô and Stratonovich
stochastic integrals, Itô's formula; stochastic
differential equations (SDEs); solutions of SDEs as Markov
processes; application examples in physical sciences and finance;
simulation of solutions of SDEs (strong and weak approximations).
Exercises with hints and/or solutions are also provided.
"Thus, the book is a welcome addition in the effort to
make stochastic integration and SDE as accessible as possible to
the greater public interested in or in need of using
them." (Mathematical Reviews, 1 February
2013)
"If I have a chance to teach (again) a course in
stochastic financial modelling, I will definitely choose this to be
among two or three sources to use. I have all the reasons to
strongly recommend it to anybody in the area of modern stochastic
modelling." (Zentralblatt MATH, 1 December | 677.169 | 1 |
(back cover) Barron's Review Course Series Let's Review: Integrated Algebra An ideal companion to high school math textbooks, this new book covers all required Integrated Algebra topics prescribed by the New York State Board of Regents. For Students: Easy-to-follow topic summaries designed for rapid learning Step-by-step demonstration examples Thorough preparation for classroom and Algebra Regents examinations Many practice exercises with answers Graphing calculator approaches For Teachers: A valuable lesson planning aid A helpful sources of practice, homework, and test questions
Designed with New York State high school students in mind. CliffsTestPrep is the only hands-on workbook that lets you study, review, and answer practice Regents exam questions on the topics you're learning as you go. Then About the contents: Inside this workbook, you'll find sequential, topic-specific test questions with fully explained answers for each of the following sections: Number Sense and Operations Algebra Geometry Measurement Statistics and Probability A full-length practice test at the end of the book is made up of questions culled from multiple past Regents exams. Use it to identify your weaknesses, and then go back to those sections for more study. It's that easy! The only review-as-you-go workbook for the New York State Regents examIntermediate algebra for college students has been writing in one form or another for most of life. You can find so many inspiration from Intermediate algebra for college students also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Intermediate algebra for college students book for free.
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As in previous editions, the focus in PREALGEBRA & INTRODUCTORY ALGEBRA remains on the Aufmann Interactive Method (AIM). Students are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. Student engagement is crucial to success. Presenting students with worked examples, and then providing them with the opportunity to immediately solve similar problems, helps them build their confidence and eventually master the concepts. Simplicity is key in the organization of this edition, as in all other editions. All lessons, exercise sets, tests, and supplements are organized around a carefully constructed hierarchy of objectives. Each exercise mirrors a preceding objective, which helps to reinforce key concepts and promote skill building. This clear, objective-based approach allows students to organize their thoughts around the content, and supports instructors as they work to design syllabi, lesson plans, and other administrative documents. New features like Focus on Success, Apply the Concept, and Concept Check add an increased emphasis on study skills and conceptual understanding to strengthen the foundation of student success. The Third Edition also features a new design, enhancing the Aufmann Interactive Method and making the pages easier for both students and instructors to follow. Available with InfoTrac Student Collections Important Notice: Media content referenced within the product description or the product text may not be available in the ebook versionAlgebra is fundamental in the learning of mathematics. In Singapore, students begin the learning of formal algebra in primary six (Singapore Ministry of Education, 2006a). In secondary school, algebra features prominently in the curriculum (Singapore Ministry of Education, 2006b). Prior to learning formal algebra, primary school students use the model method as one of the methods to solve word problems. The model method is one of the most recognised features of the Singapore mathematics curriculum (Singapore Ministry of Education, 2009). It has been found that the model method has allowed primary school students without access to formal algebra a means to represent and solve algebraic word problems (Ng & Lee, 2009). Research has indicated that students encounter a variety of difficulties in formal algebra. These include understanding the meaning of letters used in formal algebra (Kuchemann, 1981) and translating information in text into algebraic equations (e.g. Stacey & MacGregor, 2000). The use of concrete and pictorial representations has been found to help students in solving word problems (e.g. Lewis, 1989; Willis & Fuson, 1988). While the model method has helped students solve word problems using pictorial representations, such representations are seldom harnessed for beginning students in formal algebra to acquire skills in algebraic manipulation. This book aims to do the latter. There has been much evidence that the model method can be integrated with the algebraic method (Kho, 1987, 2005, 2007; Beckmann, 2004). Secondary school teachers have been trained to show the relationship between the model method and the algebraic method (Kho, 2007). This book fleshes out this approach using topics in lower secondary algebra. This book focuses on helping students develop a strong foundation in algebraic manipulation. Basic algebraic manipulations including writing, evaluating, expanding, simplifying, and factorising algebraic expressions and solving algebraic equations are introduced pictorially. While it is not the intention that students to always rely on pictorial representations when doing algebra, the model method serves as a good starting point for students to learn algebraic manipulation meaningfully. It is hoped that this book will provide teachers with a resource to help students make the transition from the model method to formal algebra. As for students who find formal algebra daunting, this book serves as a bridge. | 677.169 | 1 |
February 19, 2008
Algebra 2/19 - 2/22
Algebra learners,
We just finished chapter 7...what a chapter! You have learned all about the slope and y=mx + b. What a treat! This week we are beginning our preparation for the MCA tests by completing a pre-assessment to gauge your understanding of the material.
Plus, on Thursday and Friday, I am offering a one time offer of a retake day for the chapter 7 test. If you are interested in retaking the chapter 7 test, A-day retakes are Thursday and B-Day retakes are Friday. Please let me know ASAP so I know how many tests to make | 677.169 | 1 |
Mr. John Kriegl's Lesson Plans
10-9-17
AP Calculus
Monday
Review for Chapter 2 Test
Tuesday
Chapter 2 Test
Wednesday
101, #1-10 all
Thursday
102, #11-17
Friday
Pre-Calculus
Monday
1.2 Functions and Their Properties Objectives: be able to represent functions numerically, algebraically, and graphically, determine the domain and range for functions, and analyze function characteristics such as extreme values, symmetry, asymptotes and end behavior. Pg 95, #43-63 odds Content Expectation P1.1
Tuesday
Quiz 1.1-1.2
Wednesday1-28 all Content Expectation P1.1
Thursday29-51odds Content Expectation P1.1
Friday | 677.169 | 1 |
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This can be a sophisticated textual content for the only- or two-semester direction in research taught essentially to math, technology, machine technological know-how, and electric engineering majors on the junior, senior or graduate point. the elemental thoughts and theorems of research are awarded in this type of method that the intimate connections among its quite a few branches are strongly emphasised.
This insightful e-book combines the heritage, pedagogy, and popularization of algebra to give a unified dialogue of the subject.
Classical Algebra offers a whole and modern point of view on classical polynomial algebra in the course of the exploration of ways it used to be built and the way it exists this present day. With a spotlight on well-known components comparable to the numerical recommendations of equations, the systematic research of equations, and Galois conception, this publication allows an intensive knowing of algebra and illustrates how the innovations of contemporary algebra initially built from classical algebraic precursors.
This e-book effectively ties jointly the disconnect among classical and smooth algebraand presents readers with solutions to many desirable questions that sometimes cross unexamined, including:*
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The writer solutions those questions and extra, laying off mild on a wealthy background of the subject—from historic and medieval occasions to the current. based as 11 "lessons" which are meant to offer the reader additional perception on classical algebra, each one bankruptcy comprises thought-provoking difficulties and stimulating questions, for which whole solutions are supplied in an appendix.
Complemented with a mix of ancient comments and analyses of polynomial equations all through, Classical Algebra: Its Nature, Origins, and makes use of is a superb publication for arithmetic classes on the undergraduate point. It additionally serves as a useful source to an individual with a basic curiosity in mathematics.
Selection thought offers a proper framework for making logical offerings within the face of uncertainty. Given a suite of possible choices, a suite of effects, and a correspondence among these units, selection concept deals conceptually easy approaches for selection. This e-book offers an summary of the basic strategies and results of rational determination making below uncertainty, highlighting the consequences for statistical perform.
Richard A. Silverman's sequence of translations of remarkable Russian textbooks and monographs is recognized to humans within the fields of arithmetic, physics, and engineering. the current ebook is one other very good textual content from this sequence, a precious addition to the English-language literature on Fourier sequence.
One of many values y1 or y2 may possibly consistently be taken because the significant worth of the inverse trigonometric functionality. instance thirteen. three Write expressions for the overall price of (a) arcsin half, (b) arccos (–1), and (c) arctan (–1). (a) The valuable price of arcsin 0.5 is π/6, and a moment worth (not coterminal with the crucial worth) is 5π/6. the overall worth of arcsin half is given through the place n is any confident or unfavourable integer or 0. (b) The primary price is π and there's no different price no longer coterminal with it. hence, the final worth is given by way of , the place n is a good or unfavourable integer or 0. (c) The vital price is –π/4, and a moment worth (not coterminal with the central worth) is 3π/4. therefore, the overall price is given by way of the place n is a favorable or adverse integer or 0. SOLVED difficulties thirteen. 1 locate the central price of every of the next. (a) Arcsin (b) Arccos (c) Arctan (d) Arccot (e) Arccos (f) Arccsc (g) Arccos (h) Arcsin (i) Arctan (j) Arccot (k) Arccos (l) Arccsc thirteen. 2 convey the primary price of every of the next to the closest minute or to the closest hundredth of a level. (a) Arcsin or 19. forty seven° (b) Arccos or sixty six. forty two° (c) Arctan or fifty six. 31° (d) Arccot or forty. 10° (e) Arccos or 14. 39° (f) Arccsc or forty-one. fifty three° (g) Arcsin or –40. 08° (h) Arccos or 116. 87° (i) Arctan or –55. 22° (j) Arccot or 126. 28° (k) Arccos or a hundred forty five. ninety seven° (l) Arccsc or –13. eighty° thirteen. three make sure all of the following. thirteen. four make certain all of the following. thirteen. five evaluation all of the following: (a) cos (Arcsin 3/5), (b) sin [Arccos (–2/3)], (c) tan [Arcsin (–3/4)] (a) permit ; then , θ being a first-quadrant perspective. From Fig. thirteen. 2(a), Fig. thirteen. 2 (b) enable ; then , θ being a second-quadrant attitude. From Fig. thirteen. 2(b), (c) permit ; then , θ being a fourth-quadrant attitude. From Fig. thirteen. 2(c), thirteen. 6 evaluation . allow and Then and , θ and φ being first-quadrant angles. From Fig. thirteen. 3(a) and (b), Fig. thirteen. three thirteen. 7 overview . permit and Then and , θ and φ being first-quadrant angles. From Fig. thirteen. 4(a) and (b), Fig. thirteen. four thirteen. eight evaluation sin (2 Arctan 3). allow ; then , θ being a first-quadrant attitude. From Fig. thirteen. five, Fig. thirteen. five thirteen. nine exhibit that . enable after which and every attitude terminating within the first quadrant. we're to teach that or, taking the sines of either participants, that . From Fig. thirteen. 6(a) and (b), Fig. thirteen. 6 thirteen. 10 express that . allow θ = Arctan 0.5 and φ = Arctan 4/3; then and . we're to teach that or, taking the tangents of either participants, that . Now . thirteen. eleven express that . allow θ = Arcsin 77/85, φ = Arcsin 3/5, and ψ = Arccos 15/17; then , , and , every one attitude terminating within the first-quadrant. Taking the sine of either participants of the given relation, we're to teach that . From Fig. thirteen. 7(a), (b), and (c), Fig. thirteen. 7 thirteen. 12 express that Arccot 43/32 - Arctan 1/4 = Arccos 12/13. enable θ = Arccot 43/32, φ = Arctan 1/4, and ψ = Arccos 12/13; then , , and , each one perspective terminating within the first-quadrant. Taking the tangent of either individuals of the given relation, we're to teach that . From Fig. thirteen. eight, . Fig. thirteen. eight thirteen. | 677.169 | 1 |
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Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.
This undergraduate text takes a novel approach to the standard introductory material on groups, rings, and fields. At the heart of the text is a semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. Avoiding excessive abstraction whenever possible, the text focuses on the central problem of studying the solutions of polynomial equations. Highlights include a proof of the Fundamental Theorem of Algebra, essentially due to Euler, and a proof of the constructability of the regular 17-gon, in the manner of Gauss. Another novel feature is the introduction of groups through a meditation on the meaning of congruence in the work of Euclid. Everywhere in the text, the goal is to make clear the links connecting abstract algebra to Euclidean geometry, high school algebra, and trigonometry, in the hope that students pursuing a career as secondary mathematics educators will carry away a deeper and richer understanding of the high school mathematics curriculum. Another goal is to encourage students, insofar as possible in a textbook format, to build the course for themselves, with exercises integrally embedded in the text of each chapter.
The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.
This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The reader will find the focus of attention shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.
This book presents interesting applications of abstract algebra to practical real-world problems. Especially for those whose interest in algebra is not confined to abstract theory, the text makes the study of abstract algebra more exciting and meaningful. The book is appropriate as either a text for an applied abstract algebra course or as a supplemental text for a standard course in abstract algebra. While fully developed, the algebraic theory presented is just what is required for the applications discussed in the book. This book is included in the Brooks/Cole Series in Advanced Mathematics (Series Editor: Paul Sally, Jr.).
Suitable for second to fourth year undergraduates, this title contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space.
This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. The student will develop a solid foundation in the following topics *Gaussian elimination and other operations with matrices *basic properties of matrix and determinant algebra *standard Euclidean spaces, both real and complex *geometrical aspects of vectors, such as norm, dot product, and angle *eigenvalues, eigenvectors, and discrete dynamical systems *general norm and inner-product concepts for abstract vector spaces For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable. Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory.
This work is intended as an upper-division laboratory supplement for courses in abstract algebra. It consists of several Mathematica packages that the authors have programmed as a foundation with two collections of labs for group theory and ring theory built on this base. Additionally, there is a "users guide" which illustrates the functionality of the underlying code. The lab portion of the book reflects the contents of the Mathematica-based electronic notebooks. Students interact with both the printed and electronic versions of the material in the laboratory, and the students can look up details and reference information in the Users Guide. Exercises occur in the stream of the text of the lab, which provides a context within which to answer. Questions are designed so that they either be written into the electronic notebook, or on paper, whichever the instructor prefers. The notebooks are available for all versions of Mathematica and run across all platforms for which Mathematica exists. Exploring Abstract Algebra with Mathematica is a very timely addition to the undergraduate abstract algebra curriculum. This work is unique, filling a tremendous void in the literature. It offers an environment for studying algebraic structures using Mathematica, to write computer labs in which students can explore the ideas in abstract algebra computationally and visually, and it provides a Users Guide for the data structures and commands of this package. Flexibility of use, and the intention of the authors to make this work highly visual, e.g., with the inclusion of a fullcolor insert of significant algebraic concepts/images, make this publication pedagogically useful to both instructors and students alike. For more information on the underlying software packages, please go to the website | 677.169 | 1 |
80618851874
ISBN: 0618851879
Edition: 5
Publication Date: 2007
Publisher: Houghton Mifflin Company College Divisio
AUTHOR
Edwards, Bruce H., Larson, Ron
SUMMARY
Written by the author, this manual offers step-by-step solutions for all odd-numbered text exercises as well as Chapter and Cumulative tests. In addition to Chapter and Cumulative tests, the manual also provides practice tests and practice test answers.Edwards, Bruce H. is the author of 'Precalculus with Limits a Graphing Approach Study and Solutions Guide 5th Edition', published 2007 under ISBN 9780618851874 and ISBN 06188518 | 677.169 | 1 |
Geometric Series Exam Questions
A collection of videos, solutions, activities and worksheets that are suitable for A Level Maths.
A-Level Maths Edexcel C2 January 2007 Q10(a)
Worked solution to the above Core 2 question on the geometric series.
A-Level Maths Edexcel C2 January 2007 Q10(b)
Worked solution to the above Core 2 question on the geometric series
A-Level Maths Edexcel C2 January 2008 Q2b
This question is on the geometric series.
A-Level Maths Edexcel C2 January 2008 Q2c
This question is on the sum of a geometric series | 677.169 | 1 |
Designed for undergraduate mathematics majors, this rigorous and rewarding treatment covers the usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Author Daniel J. Velleman focuses on calculus as a tool for problem solving rather than the subject's theoretical foundations. Stressing a fundamental understanding of the concepts of calculus instead of memorized procedures, this volume teaches problem solving by reasoning, not just calculation. The goal of the text is an understanding of calculus that is deep enough to allow the student to not only find answers to problems, but also achieve certainty of the answers' correctness. | 677.169 | 1 |
Mathematics Education BookChapter 3 of this resource can be used to supplement Section IV: Research on Student Learning for topics in the Numbers and Operations Category. The Chapter includes information about 1) Student difficulties, confusion, and misconceptions and 2) Factors contributing to students' difficulties, confusion, and misconceptions.
This book illustrates the development of studentsí understanding of statistical concepts. The author gives many examples that highlight how students think about important statistical concepts and supports findings based on research. Student thinking is explained in relation to a variety of tasks based on sampling, graphical representations, averages and chance. This resource could be used to supplement the readings from section I, II, III and IVA collection of essays which offer insights into the emphasis on statistics in the K-12 mathematics curriculum. Through the investigation of several projects, the authors explore the enhancement and assessment of student learning in the areas of collection, presentation and interpretation of data. The essays cover content, teaching, learning and assessment. The statistics content, the extent of coverage recommended for various grade levels as well as student understandings are highlighted. This resource could be used in conjunction with the readings from section I and II | 677.169 | 1 |
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