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"MATH classes, seminars, workshops, tutoring, and mentoring in the field of mathematics; Teaching, training, tutoring and courses of instruction at the undergraduate, graduate and post-graduate level in the field of mathematics; Conducting after-school tutoring programs in the field of mathematics; Educational services, namely, providing online classes and online seminars in the field of mathematics; Educational services, namely, providing online instruction in the field of mathematics; Educational services, namely, providing web-based instruction in the field of mathematics; Educational services, namely, providing instruction in the field of mathematics via online interactive software applications; providing online web-based instruction in the field of mathematics via wireless mobile devices | 677.169 | 1 |
Ideal math trouble solver That will Make you a better Scholar
In some classes, all it's going to take to move an test is note getting, memorization, and recall. Even so, exceeding inside a math course will take a unique variety of effort. You can not just clearly show up to get a lecture and look at your teacher "talk" about calculus and . You learn it by executing: being attentive in class, actively researching, and resolving math issues - regardless if your teacher has not assigned you any. When you end up struggling to perform effectively within your math course, then stop by most effective website for fixing math complications to see the way you may become a much better math student.
Inexpensive math experts on-line
Math programs abide by a normal progression - each builds upon the expertise you've received and mastered with the earlier program. Should you are finding it challenging to observe new ideas at school, pull out your old math notes and assessment previous materials to refresh by yourself. Make sure that you fulfill the conditions right before signing up for any class.
Review Notes The Evening Ahead of Class
Hate any time a instructor phone calls on you and you have forgotten tips on how to clear up a certain dilemma? Steer clear of this moment by reviewing your math notes. This could assist you to determine which principles or issues you'd love to go above at school the subsequent working day.
The thought of accomplishing homework every night time could seem irritating, however, if you wish to achieve , it really is important that you continually follow and master the problem-solving procedures. Use your textbook or online guides to work by way of best math troubles over a weekly basis - even if you have got no research assigned.
Make use of the Dietary supplements That come with Your Textbook
Textbook publishers have enriched modern publications with excess content (such as CD-ROMs or on-line modules) which can be used to support learners obtain additional observe in . Many of these elements may additionally contain an answer or explanation guidebook, which can assist you to with performing as a result of math troubles all by yourself.
Browse In advance To stay Ahead
If you would like to reduce your in-class workload or perhaps the time you devote on research, make use of your spare time following school or around the weekends to study in advance towards the chapters and ideas that could be covered the next time that you are in school.
Review Previous Tests and Classroom Illustrations
The operate you do at school, for research, and on quizzes can present clues to what your midterm or closing exam will search like. Make use of your aged exams and classwork to create a own research manual for the upcoming exam. Glance in the way your instructor frames concerns - this is almost certainly how they are going to show up on the examination.
Figure out how to Perform With the Clock
This can be a well-known review tip for persons taking timed tests; specially standardized tests. For those who have only 40 minutes for your 100-point take a look at, you'll be able to optimally spend four minutes on each individual 10-point concern. Get details regarding how extensive the check are going to be and which styles of questions are going to be on it. Then prepare to attack the easier questions very first, leaving you sufficient time and energy to devote about the more complicated types.
Improve your Methods to obtain math research assistance
If you are acquiring a tough time being familiar with concepts at school, then you should definitely get aid outside of course. Inquire your pals to make a research group and stop by your instructor's business office hrs to go more than tricky problems one-on-one. Go to analyze and overview periods when your teacher announces them, or employ a non-public tutor if you need a person.
Chat To By yourself
If you are reviewing problems for an test, check out to elucidate out loud what technique and methods you utilized to get your remedies. These verbal declarations will occur in handy during a examination any time you need to remember the measures you ought to acquire to find a alternative. Get further practice by hoping this tactic using a mate.
Use Study Guides For Extra Observe
Are your textbook or course notes not encouraging you recognize what you need to be mastering in class? Use study guides for standardized exams, like the ACT, SAT, or DSST, to brush up on old substance, or . Study guides typically occur equipped with complete explanations of how you can resolve a sample issue, , and you simply can typically obtain wherever may be the superior purchase | 677.169 | 1 |
Algebra tutorials for beginners
With an emphasis on images and interactives, our math tutorials make learning math easier. Go to and get the complete course and more. Follow the steps and get the answer. (DUMMY PROOF). Can be used for Pre-Algebra. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies algevra this website. See our User Agreement and Privacy Policy.Slideshare uses cookies to improve functionality and performance, algebra tutorials for beginners to provide you with relevant advertising. | 677.169 | 1 |
Using this textbook enables readers to design digital systems using the modern HDL approach, but they have a broad foundation of knowledge of the underlying hardware and theory of their designs.
This textbook introduces readers to the fundamental hardware used in modern computers. The only pre-requisite is algebra, so it can be taken by college freshman or sophomore students or even used in Advanced Placement courses in high school. | 677.169 | 1 |
Math: CPM
CPM began as a grant-funded mathematics project in 1989 to write textbooks to help students understand mathematics and support teachers who use these materials. CPM Educational Program is now a nonprofit educational consortium of middle and high school teachers and university professors that offers a complete mathematics program for grades 6 through 12 (Calculus) designed to engage all students in learning mathematics through problem solving, reasoning, and communication. | 677.169 | 1 |
Description
CliffsQuickReview course guides cover the essentials of your toughest subjects. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. Whether you're new to limits, derivatives, and integrals or just brushing up on your knowledge of the subject, CliffsQuickReview Calculus can help. This guide covers calculus topics such as limits at infinity, differential rules, and integration by parts. You'll also tackle other concepts, including* Differentiation of inverse trigonometric functions* Distance, velocity, and acceleration* Volumes of solids with known cross sections* Extreme value theorem* Concavity and points of inflection CliffsQuickReview Calculus acts as a supplement to your other learning materials. Use this reference in any way that fits your personal style for study and review - you decide what works best with your needs. You can flip through the book until you find what you're looking for - it's organized to gradually build on key concepts. Here are just a few other ways you can search for topics:* Use the free Pocket Guide full of essential information.*
Get a glimpse of what you'll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapter.* Use the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to know.* Test your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource Center.* Tap the glossary to find key terms fast. With titles available for all the most popular high school and college courses, CliffsQuickReview guides are comprehensive resources that can help you get the best possible grades.show more
Back cover copy
We take great notes -- and make learning a snapWhen it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core Calculus concepts -- from functions, limits, and derivatives to differentials, integration, and definite integrals -- and get the best possible grade.Master the basics--fastComplete coverage of core conceptsAccessible, topic-by-topic organizationFree pocket guide for easy referenceshow more | 677.169 | 1 |
Basic course description
Math 100a is the first quarter of UCSD's three-quarter abstract algebra course. It is aimed to prepare students
for graduate study in mathematics. Compared to Math 103a-b, which is a more basic two-quarter sequence in algebra, Math 100a-c
will move more quickly, cover more material, and feature more difficult homework and exams.
The text will be Beachy and Blair, "Abstract Algebra", 3rd edition.
Please follow the links at the right to read the syllabus and to find the course calendar and homework assignments. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
Real-life examples encourage students to connect math to their
own experiences
Full scope of math curriculum in 16 books means students can work
on specific areas for review
Every Number Power book targets a particular set of math skills. Students
can work on as many or as few concepts as they need. Diagnostic tests and
performance-based prescriptions target problem areas. Short, manageable
lessons and step-by-step examples assure success. Each book includes
quick-reference pages for using calculators, mental math, formulas,
measurements, and estimations.
Reading Level 5-7
Synopsis
Every Jamestown's Number Power book targets a particular set of math skills with straightforward explanations, easy-to-follow, step-by-step instruction, real-life examples, and extensive reinforcement exercises. Use these texts across the full scope of the basic mathematics curriculum, from whole numbers to pre-algebra and geometry.Skills-Correlated Number Power books cover basic computation to the fundamentals of algebra and geometry and other math skills needed for taking standardized tests. Books include evaluation and skills correlation charts to track progress in mastering math skills.
Synopsis
Real-life examples encourage students to connect math to their own experiences
Full scope of math curriculum in 16 books means students can work on specific areas for review
Every Number Power book targets a particular set of math skills. Students can work on as many or as few concepts as they need. Diagnostic tests and performance-based prescriptions target problem areas. Short, manageable lessons and step-by-step examples assure success. Each book includes quick-reference pages for using calculators, mental math, formulas, measurements, and estimations. | 677.169 | 1 |
Homework help for 7th grade and pre algebra
Homework help for 7th grade and pre algebra
Practice for free to find out exactly what - you need. "My daughter is in the . We are using the website for tutoring in conjunction with the Glencoe book. What a great ! I also use it for myself to argumentative essay topics for college refresh my memory so that I can them with . I plan toI also use it for myself to refresh my memory so that I can them with . I plan to renew my subscription. I have also highly recommended the website to friends." Donna. "I am the parent of two students, one in - () and the other in Algebra II (9th grade). Both girls have enjoyed using your site,Learn math for free—proportions, basics, arithmetic with negative numbers, probability, circles, and more. Full curriculum of exercises and videos.GO Math: Middle School . GO Math: Middle School . GO Math: Middle School . Saxon Math Course 3. Saxon Math Course 2. Glencoe MATH Course 3 (Volume. Glencoe MATH Course 2 (Volume. Saxon Math Course 1. Big Ideas Math: Accelerated. SpringBoard Mathematics Course 3 /. SpringBoard Free Worksheets. Personalized one on one online tutor, and test prep . Free Trail available.Welcome to IXL;s math page. Practice math online with unlimited questions in more than 200 - math skills.CPM Home Textbook CC3 . Chapter 1 Lessons. 1.1.11.1.21.1.31.1.41.2.11.2.2. Chapter 2 Lessons. 2.1.12.1.22.1.32.1.42.1.52.1.62.1.72.1.82.1.9. Chapter 3 Lessons. 3.1.13.1.23.1.33.1.43.1.53.1.63.1.73.2.13.2.23.2.33.2.43.2.5. Chapter 4 Lessons. 4.1.14.1.24.1.34.1.44.1.54.1.64.1.7. Chapter 5 Lessons.Free math lessons and math from basic math to , geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly.Javascript and Cookies MUST be enabled for this site to function properly. Core Connections. CC Course 1. CC Course 2. CC Course 3. CC . CC
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Geometry. CC 2. CC Integrated College Transitions. Calculus Third Edition. Precalculus Third Edition. Calculus. -Calculus. CC Integrated 1. CC Integrated 2.Aug 03, 2012. Rating star, Whatever;s best. by: Anonymous I;m going into Algebra 1 honors in , but I heard someone who;s going into 8th grade and has to take -. If he;s up to doing hard , but also a high school class, he should go for it! If he doesn;t feel ready for algebra, take -.Get Free Math Help from the Best Online Tutor of Math. Solve Math Problems and get Instant Answers and Grade 7 from Experts. All basic topics and their sub-topics including , geometry, mensuration and their sub-topics are added in this syllabus. Grade 7 Math is a foundationVirtual Nerd;s patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to pre take whatever path through the material best serves their needs. These unique features make Virtual Nerd aa bungee jumper jumps 5 feet ever 0.5 second. let "s" be the toy;all number of seconds in a jump and "h" be the height of the jump. Write and equation to find"s". Use your equation to Dec 17 Tiffany from Marrero, LA 1 Answer 0 Votes. MathTextbooks and . FCPS 24/7 - Blackboard. FCPS 24/7 Math Textbook for Math 7Honors. Prentice Hall 1. Math Textbook 1 and 1 Honors pre Social Studies. The American Journey: Modern Times. Social Studies Textbook. Civics Today: Citizenship, Economics You.Online - Tutoring. What is -? - is the term given to mathematics that is typically studied in the , 8th and 9th grades in most schools in the United States. However there are students who have opted to take this course as early as the 5th and 6th . - serves as an introductionMay 27, 2017 Math Tutor plus Includes: a) Free k-12 math practice skills, including -, Algebra, Geometry, Statistics, Trigonometry, Pre-calculus, and Calculus. b) Access to 16 million learning resources, including instructional videos, webpages, interactives, and more that can you understand any math-, Algebra I, Algebra II, Geometry: by free math tutors, solvers, lessons. Each section has solvers (calculators), lessons, and a place where you can submit your problem | 677.169 | 1 |
CS 915 - Constructive Commutative Algebra
University of Western Ontario Computer Science Department
Date: September 11, 2009
Outline.
This reading course introduces the student to fundamental
and modern tools for computing with polynomial ideals and affine varieties.
The aim is to give fundamental notions and also to show to the student
how to navigate in the latest discoveries of the field.
This proceeds in three steps
Then we study in a seminar format some recent adavances on another
tool and let the student get the fundamental notions
by herself.
This year we study fast technqiues for computing characteristic sets.
Finally, the student is given a little research project where she
has to reuse recent ideas of one topic into another area.
This year the student has to adapt the fast computation techniques
of characteristic sets to Gröbner bases.
The goal is not necessarily to make new discoveries but to
show investigation techniques to the student. | 677.169 | 1 |
This volume provides a basic understanding of Fourier series, Fourier transforms, and Laplace transforms. It is an expanded and polished version of the authors'' notes for a one-semester course intended for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. The material is self contained with numerous exercises and various examples of applications. Allan Pinkus, Samy Zafrany, Books, Science and Nature, Fourier Series And Integral Transforms Books>Science and Nature, Cambridge University Press
Cambridge University Press. PAPERBACK. 0521597714 1997-09-28., Cambridge University Press, 1997-09-28 | 677.169 | 1 |
Activity sections are included in almost all the chapters. Nearly all the activities
involve Mathcad (version 5.0 for Windows). Several activities also require Maple V
(release 3 for Windows).
as a self-study guide:
Homework Help sections are designed to allow the student to use technology while
solving homework problems from the text (Calculus with Analytic Geometry,
Larson, Hostetler and Edwards; D.C. Heath, 5th Edition). Some chapters also include
a Questions section, intended to help the student assess the insight he or she gained
into the visual and numerical aspects of the calculus concepts discussed.
as a reference:
While this guide is not intended to be a software manual, it provides useful
information to aid the student in the use of the software during the calculus course(s),
as well as afterwards. Software-related information, most of which is given in the course
of the activities, is fully indexed for convenience. Appendix A contains a summary of
Mathcad operations and functions. Appendix B includes a list of common problems
encountered by students while working with Mathcad.
Because of the large amount of
graphics and various fonts, we have used the Adobe Acrobat Portable Document Format
(PDF) to allow users of different types of computers to view and print the
document without distortion. You will need the Adobe Acrobat Reader software
(version 2.1 or higher recommended), which is available without charge at the
Adobe Web site. If you have a fast
connection, then you may want to download the zipped archives containing all
the files:
If you do not have a fast connection, we recommend that you access the
PDF files using the Table of Contents below (each of these files contains
either one or two chapters of the manual). Links to individual Mathcad and
Maple files have also been placed there. | 677.169 | 1 |
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In this live Grade 12 Mathematics show we take a look at Functions & Inverses. In this lesson we revise definitions and terminology used to describe functions. We also define the inverse of a function. | 677.169 | 1 |
Click on the Google Preview image above to read some pages of this book!
Stochastic Programming is the science that provides us with tools to design and control stochastic systems with the aid of mathematical programming techniques. It is on the border line of statistics and mathematical programming. This book is a comprehensive introduction to the field and its basic mathematical tools. While its mathematics is of high level, the developed models offer powerful applications, demonstrated by a large number of examples. The presented material ranges from basic linear programming to algorithmic solutions of sophisticated system problems and applications in water resources and power systems, ship manufacturing, inventory control, etc. Students and researchers in operations research, mathematics, statistics, various fields of engineering, economics, insurance, finance, biology and environmental protection may find the book a useful aid to study and solving practical and theoretical problems. | 677.169 | 1 |
20 effective study tips and techniques for students of mathematics and engineering courses
Being an engineering or mathematics students can be very cumbersome and stressful due to lots of brain racking calculations that you will be encountering during your course of study but engineering and mathematics is very vital and important to the society that we cant do without it, it may be a bit complicated but when "the going gets tough the tough gets going" and thats why we will be offering twenty effective study tips for mathematics and engineering students to encourage and help them for the good work that they are doing to make the society a better place to live in.
Tip #1: Take good notes, and keep them all
after your classes are over.
Engineering textbooks can be dense, but
endure through the tedium. Do your reading –
all of it – and keep a highlighter and page
markers handy. After the class is over, keep
your most useful and well-written textbooks
as reference. Your notes, annotations, and
highlighting will be invaluable later on. You
may even want to keep a "Rules of Thumb"
notebook, allowing you quick access to your
most-used formulas.
Tip #2: Get to know your professors.
Develop a relationship with your professors so
you feel comfortable approaching them and
asking for help. Get to know one or two key
professors particularly well, and turn to them
for help with your homework, insight into the
industry, and even job or program references.
Tip #3: Ask questions, both in class and out.
Your professors want you to learn. But if the
only thing you ever ask is, "Will this be on the
test?" then you are not taking advantage of
their knowledge or willingness to help. Ask for
additional examples to clarify difficult
equations and concepts. More often than not,
your fellow students will thank you for
speaking up, and your professor will
appreciate your active investment in the
material.
Tip #4: Try to solve a problem before asking
for help.
No one wants to do your homework for you.
You'll be more likely to get help if you've
already begun the effort. Even if you're totally
lost, make a legitimate, prolonged effort to
solve a problem before asking for help. When
you do seek help, be prepared to discuss what
you tried already, and bring your scratch paper
showing your attempts.
Tip #5: Form a study group.
Working alone can get exasperating if you find
yourself stuck on a problem. Working with
others will not only introduce other viewpoints
to approaching a problem, it will also provide
encouragement and camaraderie in the face of
frustration.
Tip #6: Teach someone else.
One of the most effective ways of ensuring you
understand something is by explaining it to
someone else. Before you move past a subject,
make sure you not only answered the question
but also can replicate and explain the process.
Each new subject and concept will build on
the last, so don't move on until you've
mastered each new idea.
Tip #7: Diversify your engineering classes.
Take classes in all sorts of engineering, even if
they are not your concentration.
Understanding not only the subject matter,
but also how other types of engineers
approach and solve problems, will lend insight
into your own field, from biomedical to
mechanical to chemical to environmental
engineering and beyond.
Tip #8: Take classes outside engineering,
particularly design classes.
The most successful engineers are insatiable
learners, so seek to broaden your skill set
generally. A design class can teach you how
to represent information visually and how to
talk about an idea from a big picture
perspective. A writing class can hone your
skills for communicating your ideas to others.
A business class can prepare you for
organizational tasks and leadership roles later
in your career.
Tip #9: Hone your communications skills,
including conversation, writing, and
presentation.
The best and most innovative ideas in the
world have no hope of growing past the
drawing board if you are unable to
communicate them effectively. And today,
most technical communication between team
members and leadership happens over email,
which is a form of writing. Learn to present an
argument simply and without agenda, and
always read your emails through once or twice
before sending.
[ also read 10 tips on how to graduate with a very good
result in school
advice from nairalanders on how to make a
good result in school ]
Tip #11: Build your portfolio.
Participate in as many hands-on projects as
possible, especially those outside the
classroom. Future employers look for both
coursework and relevant experience, and a
well-organized and articulate portfolio will be
invaluable during your job search. Your
practical project experience will also reinforce
the "in theory" knowledge you gain in class.
Tip #12: Get a summer internship.
One of the best portfolio buildings blocks is
the summer internship. Internships do more
than build your resume; they demonstrate to
potential employers that you can commit to a
long-term role and work as part of a team.
Tip #13: Build your network.
Do not wait until you need a job to start
building professional relationships. In addition
to getting to know your professors and peers,
attend extracurricular lectures, workshops, and
networking events, and get to know as many
people working or studying in your field as
possible. Take a genuine interest in the work
of others, ask lots of questions, and don't be
afraid to seek guidance or advice from those
of advanced experience. They were once
neophyte engineers too!
Tip #14: Scour the resources of professional
engineering associations and companies.
Professional engineering associations, such as
the National Society of Professional Engineers,
are an invaluable resource for jobs, advice,
and networking. Identify organizations that
share your values and interests, and make as
many contacts as possible.
Tip #15: Skip the honors class.
In the engineering field, your GPA matters. If
you struggle in calculus, don't kill yourself in
Honors Calc; take the easier class, learn the
material thoroughly, and take the higher
grade.
Tip #16: Learn when to lead and when to back
down.
Engineers often work in teams, and every team
has one or more leaders. You should feel
comfortable in both leading and following the
directions of others. Hone your leadership
skills and learn how to effectively influence
group decisions, but recognize when your
contribution should be to take orders and
follow direction.
Tip #17: Work on the problem before the team
meets.
The best results occur when a group discusses
ideas that have already been fleshed out by
individual members. Learn to do your own
work and self-motivate. Always arrive at the
team meeting with ideas in mind.
Tip #18: Be a perfectionist.
In the words of one engineer, "In the working
engineer world, a 99% correct product can
cost millions of dollars in damages." Adopt
the mindset of practicing something until it is
perfect, as opposed to going as quickly as
possible and settling for a B. When your work
is 100%, even if it is slower, it is valuable.
Tip #19: Identify your inspiration.
What made you decide to study engineering?
Who do you look up to in your chosen field?
Learn about how individuals and companies
have sought and found success, and replicate
their behaviors.
Tip #20: Take heart and persevere.
Engineering is a difficult course of study for
everyone, no matter their IQ or test scores.
Frustration can lead to feeling like an
imposter. Every future engineer has struggled
through seemingly impossible problem sets,
cranky professors, and gut-wrenching exams.
In the face of inevitable small failures,
recognize that you are challenging yourself
like never before, and push on through the
difficult experiences. | 677.169 | 1 |
Study Zone
Formulae Guides Of XII
Hello folks. NCERT publishes two Textbooks for Maths, Part I and Part II for the students of class XII. Maths Part I of NCERT covers six chapters whereas Maths Part II of NCERT includes seven chapters; in total we have to study 13 chapters. Followings are the List Of Important Formulae based on all the Topics Of NCERT Textbooks of class 12. The presentation of each topic has been done in an illustrative format. Covering all the aspects of the concerned topic, these Formulae Guides will be quite helpful for all | 677.169 | 1 |
The present practice book for JEE Main and Advanced Mathematics contain over 8000 questions which have been divided into 32 chapters namely Complex Numbers, Theory of Equations, Sequences and Series, Permutations and Combinations, Binomial Theorem, Determinants, Matrices, Logarithms and Their Properties, Probability, Functions, Limits, Continuity and Differentiability, Differential Coefficient, Application of Derivatives, Monotonicity, Rolle's and Mean Value Theorems, Maxima and Minima, Indefinite Integration, Definite Integration, Areas, Differential Calculus, The Straight Lines, Pair of Straight Lines, Circle, Parabola, Ellipse, Hyperbola, Three Dimensional Geometry, Trigonometric Ratios and Identities, Trigonometric Equations, Inverse Circular Functions, Solution of Triangles and Vectors. This is a Master Practice Book consisting of innovative objective problems like MCQs with Single Correct Option, Multiple Correct Options, Assertion-Reason, Linked Comprehension Based, Matrix Matching and Single Integer Answer Type. This is a Master Practice Book that consists all formats of JEE questions like MCQs with Single Correct Option, Multiple Correct Options, Assertion-Reason, Linked Comprehension Based, Matrix Matching and Single Integer Answer Type. The different types of objective questions provided in the book will help in sharpening the comprehension and analytical abilities in the students. All the questions are supplemented by hints and step-by-step explanatory solutions at the end of each chapter. The book also contains Solved Paper last three years' (2014-2016) JEE Main and Advanced which will help aspirants get an insight into the recent examination pattern and the types of questions asked therein.
As the book contains ample number of mathematics objective questions on the basis of the new examination pattern and syllabi for JEE Main and Advanced, it will help students learn in depth about the various concepts and subjects covered under the syllabi of mathematics for JEE Main and Advanced Exam 2018. | 677.169 | 1 |
"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.
Michael Th. Rassias is a brilliant young mathematician and son of a highly regarded author and acclaimed mathematician, Themistocles Rassias. He has received several awards in competitive mathematical problem solving. He received first prize in the Jozef Wildt International Mathematics Competition for three consecutive years in 2004, 2005 and 2006. He was also the silver medalist at the 44th International Mathematics Olympiad of 2003 held in Tokyo, Japan.
Rassias's last book with Springer is entitled "Problem-Solving and Selected Topics in Number Theory" and was published Nov. 23, 2010.
S.E. Louridas does not hold a present affiliation but has written 6 olympiad related books and has trained young people in math olympiads for several years in Greece.
"Sotirios E. Louridas and Michael Th. Rassias, the authors of the book at hand, put together an excellent collection of problems for practice. They provide detailed solutions following the masters of that skill. … an active reader would greatly benefit from reading the book; while working out the problems is bound to sharpen his or her problem solving skills. … it's a worthy addition to a library of a problem solver."
—Alex Bogomolny, MAA Reviews, December, 2013
"The book is a wonderful presentation of the essential concepts, ideas and results of Euclidean Geometry useful in solving olympiad problems of various level of difficulties. The theoretical part is excellently illustrated by challenging olympiad problems. The complete solutions to these problems are carefully presented, most of them together with several interesting comments and remarks. ... All in all the text is a highly recommendable choice for any olympiad training program, and fills some gaps in the existing literature in Euclidean Geometry. The book is a very useful source of models and ideas for students, teachers, heads of national teams and authors of problems, as well as for people who are interested in mathematics and solving difficult problems."
—Mihaly Bencze, EMS Newsletter, November 2013
"A subject of high interest for problem-solving in Euclidean Geometry is the application of geometric transformations ... The authors have succeeded to study with great accuracy these transformations. Additionally, they have applied them in order to obtain very nice solutions for some quite challenging problems ... The book is full of new and challenging ideas that will provide guidance and inspiration for future study in the fundamental area of Euclidean Geometry. The large collection of problems in this book provides a valuable recourse for advanced high school students, university undergraduates, instructors, and Mathematics coaches preparing students to participate in mathematical Olympiads...."
—Nicusor Minculete, Gazeta Matematică, Seria B., 10/2013
"This book provides an essential presentation of concepts and ideas as well as problems with their solutions in Euclidean Geometry, a traditional and still challenging part of Geometry.
—Dorian Andrica, Zentralblatt
"The book is mainly devoted to several very interesting problems, some of which constructed by the authors, that have been presented in a rigorous and self-contained manner. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. The book will be of particular interest to students and teachers who train them for Mathematical Olympiads and other Mathematical Contests. Additionally to everyone who enjoys studying some of the jewels of Euclidean Geometry and has some special love for good problems and beautiful ideas. ... The Foreword of the book has been written by Michael H. Freedman (Fields Medal in Mathematics, 1986) ... The authors deserve congratulations for their excellent effort and success to provide a high quality service in fundamental mathematics. "
—Jose Luis Diaz Barrero, Octogon Mathematical Magazine, October 2013
"Sixty-five problems and their solutions are arranged in three parts: problems based on basic theory, problems based on advanced theory, and geometric inequalities. Some problems were included in International Mathematical Olympiads (IMOs) or proposed in short lists in IMOs ... the problem part of the book ... contains a collection of interesting problems. ... Chapter 4 seeks to "present some of the most essential theorems of Euclidean Geometry". Some of these theorems (Pythagoras', Ceva's, Menelaus') are important indeed and applicable to many problems."
—Yury J. Ionin, Mathematical Reviews, January 2014
"There are many excellent books on plane Euclidean geometry, exploring the subject at various levels. The book under review, which is foreworded by Michael H. Freedman (Fields Medal, 1986), adds yet another facet to this colorful subject. This delightful book presents a collection of problems in plane Euclidean geometry in the spirit of mathematical olympiads, along with their solutions. Additionally, it provides essential theory of plane Euclidean geometry, with proofs of some fundamental theorems. As such, this monograph is an excellent training manual to use in preparation for mathematical competitions and olympiads. Hence, this is a book that belongs in all academic libraries, from high school through graduate level." | 677.169 | 1 |
The Physics 163 Internet Problems assignments are intended to
provide students with opportunities to individually apply
problem-solving strategies to current topics in order to better
internalize the mathematical relationships and improve
problem-solving skills. The emphasis on the problem sets is to
provide students with individual practice.
Many Physics 163 students occassionally or regularly have
difficulty getting started on a problem or simply get stuck
once they have started. For such students, there is a need for help
in order for them to sustain the individual application of
problem-solving in Physics. The Audio Help section is intended to
meet that need for individual help in order to get a student started
or un-stuck. Each problem set is accompanied by a collection
of audio files for strategicly chosen problems. The audio files
provide explanations, suggestions, hints, diagrams and at times
animations for solving the problems. The ultimate goal is to help
students become more confident of their problem-solving habits and
more independent in their approach to problem sets. The links below
lead to the Audio Help pages. | 677.169 | 1 |
Express Review Guide: Algebra I by LearningExpress Editors
February 28, 2017 @ 12:06 am
By LearningExpress Editors
Show evaluate courses: Algebra I is helping scholars collect functional talents with speedy, exact classes. All key issues are coated. Readers will make the most of math suggestions, concepts for fending off universal pitfalls, sidebars of math definitions, and an in depth word list. furthermore, pre and posttests support scholars gauge either their vulnerable components in addition to their development.
How do you draw a immediately line? How do you establish if a circle is actually around? those may possibly sound like easy or perhaps trivial mathematical difficulties, yet to an engineer the solutions can suggest the variation among luck and failure. How around Is Your Circle? invitations readers to discover the various related basic questions that operating engineers take care of each day--it's tough, hands-on, and enjoyable.
This publication, designed for complex graduate scholars and post-graduate researchers, introduces Lie algebras and a few in their purposes to the spectroscopy of molecules, atoms, nuclei and hadrons. The booklet includes many examples that aid to explain the summary algebraic definitions. It offers a precis of many formulation of useful curiosity, resembling the eigenvalues of Casimir operators and the size of the representations of all classical Lie algebras.
This complete, best-selling textual content specializes in the examine of many various geometries -- instead of a unmarried geometry -- and is carefully sleek in its procedureBoth of these solutions are true. The solution set of this equation is all real numbers. An equation that is true for all real numbers is called an identity. Following are several inequalities and their descriptions. Again, look carefully at each solution set. 1), . . } For expression 3, {x| x > 3} means all real numbers x that satisfy x > 3. 39 40 Express Review Guides: ALGEBRA I PRACTICE LAP DIRECTIONS: Use scratch paper to solve the following problems. You can check your answers at the end of this chapter.
Associative For any three numbers For any three numbers a, b, property a, b, and c, the expression and c, the expression a • b • c a + b + c can be interpreted can be interpreted either as either as (a + b) + c or as (a • b) • c or as a • (b • c), and a + (b + c), and these two these two products are equal. sums are equal. The identity For any number a, a + 0 = a. For any number a, a • 1 = a. a. Zero, added to any number, One, multiplied by any number, the leave-it-alone leaves that number alone. | 677.169 | 1 |
Algebra… The study of the one and only 'x', the ever unknown variable. Just kidding, algebra is much more than just all this. Although many books differ in what they classify algebra as, I am going to use algebra to basically cover the theory of equations, complex numbers, matrices, sequences and series, and a few minor chapters. Time's of prime importance and so, let's be on our way to discuss this essential unit of JEE-Mathematics syllabus.
Let's head up to the second portion of the Calculus portion of JEE Syllabus. The tricks that we have mastered and used while doing the differential part of calculus shall help a lot in Integral Calculus. After all, Integration is just the inverse of Differentiation. However, it gets a bit more interesting than that. Differentiation of functions can be easy, sometimes even implicit. However, Integration for the most part is not elementary. Let's head on to the individual chapters and the books that we are going to need for this high-weightage unit of JEE Maths syllabusI will be very honest with all of you. I didn't start my journey of organic reaction mechanisms with the standard method. Usually, kids start of mechanisms with Hydrocarbons (addition/free radical substitution, etc). I started my journey of Reaction Mechanisms with Nucleophilic Substitution reactions. The chapter was Alkyl Halides and there were a number of concepts to be learned – Sn1, Sn2 and Sni reactions, along with the use of Neighbouring Group Participation (NGP). These are definitely the OST important concepts of this chapter and enough attention must be given on them.
Mechanics is undoubtedly the most conceptual part of JEE Physics. In fact, the entire two year syllabus revolves around mechanics. While the exam paper has about 30% direct questions from mechanics, it is safe to assume that the paper also has another 30-35% questions indirectly involving mechanics. That's a whopping 60-65% of the paper based on one single unit of Physics! Basically, what this means for you, the candidate, is that an absolute mastery over Mechanics is essential for a good rank. Also, keep in mind that mechanics CANNOT be mastered in a month… it needs about 8-10 months of rigorous practice to fully grab the concepts of mechanics. So, if initially, you cannot understand mechanics or solve its questions, don't be disheartened. Most of the kids have trouble understanding mechanics. Continue reading Mechanics – The most conceptual part of JEE Physics→
One of the most prestigious exams at +2 level is KVPY. Now it can be cleared in both 11th(SA) and 12th(SX) and in college as well(SB). I will be talking about SX here, and how to clear it, especially if you are a PCB student
Everyone knows what modernity stands for, right? Speed. Yup, that's the answer. And how do we achieve it…. Well, we use short cuts, tricks, slangs, etc. Everyone knows what "IDK' stands for, right? Such a long line….shortened into three letters. Yeah, that is the new modern generation. Quick, fast and short. Presenting the shortest unit of the enitre JEE syllabus, something as short as its modernity and as quickly understood… Yup, you guessed it right. It is none other than Modern Physics, the most scoring unit of JEE Physics.Continue reading Modern Physics : Quick, simple, and easy→
Here are a few books that I came across during my stay at IIT. These have been recommended to me by a senior of mine. These books have received acclaim from a lot of students and I feel it's best to share the knowledge.
It's the year 2015. PC users receive a notification from Microsoft the likes of which they have never seen. The notification says – Upgrade to Windows 10. For free! (That was serious marketing, Microsoft).Of course, I didn't realise back then how Microsoft was playing us all along. With the excitement of a teenager, I quickly borrowed all the laptops in the house, and upgraded them to Windows 10 the day it was launched. | 677.169 | 1 |
WildLinAlg15: Applications of row reduction (Gaussian elimination) I
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WildLinAlg15: Applications of row reduction (Gaussian elimination) I
This lecture shows how the three main problems of Linear Algebra can be tackled using the algorithm of row reduction, also called Gaussian elimination. The three main problems are: how to invert a linear change of coordinates, how to compute the eigenvalues and eigenvectors of a square matrix, and how to compute the determinant of a square matrix. Each problem is illustrated with examples.This is one of a series of lectures maing a first course in Linear Algebra, given by Assoc Prof N J Wildberger of UNSW, also the discoverer of Rational Trigonometry.CONTENT SUMMARY: pg 1: @00:08 3 main problems of Linear Algebra;pg 2: @01:51 Inverting a linear change of coordinates; example;pg 3:? @05:19 example finished; new idea: introduce a y-sub-i matrix; to obtain the inverse of a matrix;pg 4: @09:17 Theorem concerning an invertible matrix;pg 5: @11:00 Finding eigenvalues and eigenvectors of an nXn matrix; remark about the Homogeneous case;g 6: @14:23 The eigenvalue problem using row reduction; example1; check of result @19:34;pg 7: @20:34 example2 as a reminder of the physical meaning of an eigenvector equation (see WildLinAlg7);pg 8: @24:38 example2 continued; finding the eigenvectors using row reduction; perpendicular eigenvectors;pg 9: @27:52 How to calculate a determinant; characteristics of a? determinant; as the volume of a parallelpiped; properties of a determinant necessary to do row reduction @30:20;pg 10: @31:32 the determinant of an upper triangular matrix;pg 11: @35:11 example:? putting a matrix in upper triangular form to obtain its determinant; remark about this lesson @38:47 ;pg 12: @39:33 exercises 15.(1:2) ; invert some systems using row reduction; find inverse matrices;pg 13: @40:17 exercises 15.(3:4) ; find eigenvalues and eigenvectors; compute determinants; (THANKS to EmptySpaceEnterprise)
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Get free advice from education experts and Noodle community members. | 677.169 | 1 |
Yes, that makes sense and for some odd reason, I thought I understood what you said TeDo and Kathy- both- thank you, Ladies! As always, you amaze me with what a person can learn here!
I'm not doing E's homework for him but said I'd put the question here since he doesn't know anyone here to ask outside of school and we live so far out in the country now, his bus is always late to school in the mornings. I don't know if he's too spent tonight to go over this but he can look at it tonight or tomorrow, and also bookmark that link.
I'm just sitting here in awe of you all able to do HS math.....................or um, the way it's done now. I have issues helping Darrin with his 2nd grade math for pete's sake.......and from what I've seen they seem to do their utter best to make very simple concepts extremely difficult. ugh
I used to love love love algebra way back in the day, looked forward to going to class......I loathed any other math class except algebra. For some odd reason it just "clicked" with me and I caught on easily. Now? Phht.......lol
Hound, it helps that I tutored remedial Algebra in college and now have a 21 year old niece and 18 year old nephew that had to do this recently (with a LOT of explanation/tutoring from auntie here) and that I worked in the math dept at the school here. difficult child 2 finished Algebra 1 this spring and difficult child 1 is starting it next week. It's a good thing I DO know how to do it or all 4 of these kids would have been doomed.
I don't doubt it. My kids either sought help from a teacher or other student or figured it out themselves. Sad thing was not that I'd never done it, it's that I couldn't understand the "instructions" enough to refresh my memory to help them.
I didn't just "remember" it. I had to read their book to remind me how to do it and/or learn how to do it again. It took some time but now I'm just an old hand at it. It really does require a whole different level of thinking. We'll see how soon I forget it again once both of mine are through Algebra 2. LOL
There were times when I was in school and also when I was trying to help E with homeowrk that I couldn't even decipher the instructions from the teacher but if I looked at the problem and figured it out or had it explained to me a different way, or explained it to E a different way, it seemed much easier and I "got it" and learned the concept. I don't know if that means we have a learning disability, we just think differently than most people, or if we are intellectually limited. Or if teachers are typically teaching to one personality type or learning group. I (and E) have gone from clueless to completely understanding just due to a concept being presented differently.
E and I both remembered (this evening) a few times when he was in middle school when he showed me "difficult" homework, I read the instructions, and said WTH!! Then after reviewing the book, I said "this is easy", told him what I could see was being done and asked for, and then he said "oh, no problem- I can do that". Is that a difference in teaching methods or learning styles or IQ????
I think its a different way of learning and doing. See..I come from the dark ages where if you used a calculator to do algebra it was cheating. Now they want you to buy these expensive things and learn to do algebra on them. I think I somewhat understood what Kathy was saying but it made no sense to me because it sounded like more steps. F function? Huh? Why dont I just solve 3e + 5 = 27. (Just using that for example) Please dont actually make me do math because I have lost that ability with the meningitis.
But to me it seems much better to learn the concepts of x + y= z than to enter it into a function button and then into a G button.
difficult child 1 is one of those that needs explained in much different ways but then he IS on the spectrum. Textbooks are typically written to the neurotypical thinking skills of the average student. Then they present this same information/textbook to a kid on the spectrum or who has a learning disability (math, reading, doesn't matter) who is perfectly capable of understanding it if it was explained in basic and simple language. difficult child 1 is better at analyzing examples than having it explained OR from reading the book himself. It's just a different thought pattern/learning style.
Janet, I also come from those dark ages. lol And soon as they start giving instructions for doing the problems with the calculator.......I'm totally lost. I think they're cheating the kids to teach them to do the math that way at the very beginning. We're teaching them to be overly reliant on gadgets to do the real work for them and to not really think about it all the way through.
When mine were young, they weren't allowed a calculator for homework (I didn't give a darn what the teacher did/didn't want) and I refused to buy them one for class. I don't think they even saw one until college.....unless the teacher had some in the classroom.
I watched in my college algebra course grown people reduced to tears because using the calculator only made it ten times more confusing. (didn't help they didn't know how to use the calculator properly either.......which included me) Bff and I had to tutor classmates on the steps worked out on paper (heaven help you if you tried to follow professor skip ten steps) .......and bff tutored all of us on wth the buttons on the calculator did. Not that teaching me a calculator did much good. If I tried to use it I couldn't work the problem. Since the professor had problems worded such you had to use it......well, there is a reason I barely passed the course and it wasn't all Traumatic Brain Injury (TBI) related. (or I don't think it was as I wasn't the only one having issues.)
I'm weird. I learned math pre kindergarden as money. I learned to add/subtract/ and figure in tax percentage before I ever went to school. So, if I'm dealing with numbers........I think in money. (which is why I caught on to the metric system and decimals so easily) There is one hitch to this "talent" or having learned this way. Standing in a store you don't have pencil and paper, not that I could write anyway at the time. lol I got into more trouble for not being able to show my work than anything else in school. I couldn't show my work because it was in my head, and it was automatic.......and I just "knew" the answer. How I got the answer I couldn't explain because I learned to do it so young that honestly, I dunno how I did it........or do it now when it decides to work properly. When I tried to show my work......I usually got the answer wrong because I'd manage to mix myself up. The only thing I could show my work on was algebra.....because of this cool thing the teacher did making a pattern out of the problem that was a smilie face......and I'm weird and liked making the smilie face. lol
My poor grandma was just trying to teach me how to manage money, I'm sure she didn't mean to mess me up with math. Fractions nearly gave me a nervous breakdown until we got to the part where they become decimals then I was like Ohhhh money! But I'm still not that hot with fractions, even worse now after the accidentFractions nearly gave me a nervous breakdown until we got to the part where they become decimals then I was like Ohhhh money
Click to expand...
Lisa, Lisa... I'm having serious flashbacks. In reverse.
difficult child absolutely insisted he could not possibly do fractions. We didn't eat pizza and pie, and he couldn't relate to the examples they were using. No clue at ALL. Until one year the teacher in desperation brought up the issue... and all I did was turn to difficult child and start listing off construction measurments. What's three and three eights plus 4 and a sixteenth? And he knew the answer, but insisted those weren't fractions, they were measurements! Took a bit to broaden his scope, to teach him to generalize, because he was only used to the power-of-two fractions - half, quarter, eighth and so on - the ones you find on... a construction tape measure. After that, he caught on to decimals too, based on it being "money"... but only to two decimal places, because you can't have half a cent...
Cory can do fractions in a snap because of construction. The boy has a 9th grade education....actually he barely spent anytime in a regular classroom past 5th grade. After that he was in a wilderness camp for all of 6th grade, half of 7th then in a self contained emotionally disturbed class from the second half of 7th until he quit school in 9th. In those classes they only had worksheets and no actual teaching. It was a holding pen. I think he went to at least 7 different schools between those years. He quit school at 15I must be a really "bad" teacher; I still show my students long division the way Step does and adding the way Lisa does! Also my 5th graders are not allowed to use calculators (except once in a great while). Doesn't mean I don't show other ways as well but I figure (no pun intended) that I need to reach students in whatever way I can.
No, wiped out, you're an excellent teacher and your students are getting a real education they can understand and will carry them through their lives.
I had college professors who couldn't for the life of them figure out what was wrong with my children's generation that they couldn't do normal equations, most especially without calculators. Obviously, they'd never tried to help their child with homework. The younger the kids got, the worse the problem got. Spelling is no better. Here in younger grades they're encouraged to spell phonetically.....and are not marked wrong if they've done it that way on anything except the spelling list. This is carried out throughout high school. So now, as well as kids who can't do simple math, you have a vast number of kid who have no idea how to spell correctly even some of the simplest words. Nichole had a hard enough time with the dyslexia.......but add in the phonetic spelling junk, and she still has a hard time spelling words correctly. (although now she'll look them up for correct spelling)
Old methods worked and produced people like Einstein. Now granted, some kids have trouble with that method.....but like you Sharon, most good teachers can find an alternate way to help them learn. All this changing curriculum every time they turn around is confusing to the kids, and has got to be a nightmare for teachers to keep up with. And then you have those teachers just teaching for the proficiency tests......and I won't go near my soap box on that one. | 677.169 | 1 |
This market leader is written as an elementary introduction to the mathematical theory of probability for readers in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus.
A major thrust of the Fifth Edition has been to make the book more accessible to today's readers. The exercise sets have been revised to include more simple, "mechanical" problems and new section of Self-test Problems, with fully worked out solutions, conclude each chapter. In addition many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, packaged with each copy of the book, provides an easy to use tool to derive probabilities for binomial, Poisson, and normal random variables. It also illustrates and explores the central limit theorem, works with the strong law of large numbers, and more | 677.169 | 1 |
Writing Math Research Papers 5th Ed.
A Guide for High School Students and InstructorsMathematics research papers provide a forum for all mathematics enthusiasts to exercise their mathematical experience, expertise and excitement. The research paper process epitomizes the differentiation of instruction, as each student chooses their own topic and extends it as far as their motivation and desire takes them. The features and benefits of the research paper process offer a natural alignment with all eight Common Core State Standards for Mathematical Practice. Writing Math Research Papers serves both as a text for students and as a resource for instructors and administrators. The Writing Math Research Papers program started at North Shore High School in 1991, and it received the 1997 Chevron Best Practices in Education Award as the premier high school math course in the United States. Author Robert Gerver's articles on high school mathematics research programs were featured in the National Council of Teachers of Mathematics publication Developing Mathematically Promising Students, the NCTM's 1999 Yearbook, Developing Mathematical Reasoning in Grades K 12, and in the September 2017 issue of the Mathematics Teacher.
Pre-order this eBook
Available Feb 1, 2018
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Methods of Proof in MathematicsMethods of Proof in Mathematics Course Menu
This course is an introduction to abstract mathematics, with an emphasis on the techniques of mathematical proof (direct, contradiction, conditional, contraposition). Topics to be covered include logic, set theory, relations, functions and cardinality.
Prerequisite: Calculus lll
Note: This course is proof based. All homework assignments, exams and the final are graded by the instructor. | 677.169 | 1 |
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February | 677.169 | 1 |
More than 5.000.000 Books
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The revised third edition of this hands-on workbook presents exercises, math problems, sample science passages, and quizzes with answers and detailed solutions as it takes college-bound students through all the math and science requirements for the ACT test. Separate math chapters provide a complete review of the ACT Math test, including:
Pre-algebra, elementary algebra, and intermediate algebra
Plane geometry, coordinate geometry, and trigonometry
The science sections emphasize the scientific method, the analysis of tables and graphs, and the technique for reading scientific passages. A four-step drill is introduced to help students with ACT Science test questions. This edition reviews the three types of passages covered on the ACT Science test:
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Conflicting viewpoints passages
Additional features include a glossary of math formulas and science terms as well as test-taking strategies for success. The workbook concludes with a comprehensive math practice test as well as a comprehensive science practice test | 677.169 | 1 |
This compulsory course is suitable for those students who have previously gained grade E in GCSE Mathematics. Please note that anyone who has achieved a grade E in GCSE Mathematics is automatically enrolled onto this course.
Students will sit two Level 2 exams, one in January and the other in May.
Starting in September students will study for 5 periods per week preparing for the Edexcel Level 2 Award in Number and Measure for which they will sit an exam in January. This qualification focuses on the basic foundations of number work and related topics.
From January to May students will then study for the AQA Higher Level in Financial Calculations. This is a level 2 Free Standing Mathematics Qualification (FSMQ). The course builds on the knowledge gained during the Edexcel Level 2 Award, but has a particular emphasis on money related topics linked to percentages, fractions and decimals, such as calculating costs in a business and retail sale offers.
Skills in numeracy and problem solving are highly sought after by employers and a Mathematics qualification is considered vital for entry to the job market.
If a student is successful in either or both of the level 2 qualifications, or if they display a level of understanding that is above a GCSE grade E, then progression onto the GCSE Mathematics course and hence entry into the GCSE exam will be considered | 677.169 | 1 |
Why read all of them, can't you pick a particular topic. I know math majors generally pick something like topology or something. And normally you wont "Read" the books but actually go through the algorithms and do the proofs.
woot. one of these was my number theory professor (i think he has 4 books on the list). he was tough. he assigned unsolved problems on the final.
strawdog soubriquet
July 25th, 2007 11:36pm
I hate to insult you so much, Rick, but that's a stupid goal. it's a lazy way out to stick to that series. Also, unless you took a lot more math at UBC than you've ever maentioned, most of them will be too advanced. have you already done senior-level analysis courses? multi-variable boundary-value problems? linear algebra? it's unlikely that all those books are the best ones for their topic.
ward on a treo 700p
July 25th, 2007 11:44pm
I took more math courses than I will ever need, if I keep working in this stupid place...
Rick Zeng
July 25th, 2007 11:58pm
Obviously, not any 400 level courss.
Rick Zeng
July 26th, 2007 12:01am
There is no such thing as a PhD comprehensive exam. Maybe one you take en route to getting the PhD, but at the end you demonstrate that you know one thing incredibly well, well enough that at least 3 highly trained people in your field who have had time to rip apart your thesis can't really find any reason to deny you a doctorate. Not only that, you have to have made "a lasting contribution to the body of science".
Aaron
July 26th, 2007 12:02am
I would suggest, if you are serious and I dont think you are. Doing something like bluebeard (with the forex thing), setting up a blog, "math for dummies" or something. "statistics for people who don't know statistics"
I bought a couple of statistics for dummies books thinking I want to do the same thing. I got to about Gaussian distribution or something and that was it.
I think to say of math courses "all they are is proofs" is to somehow underestimate what mathematical proofs should be about. What mathematical proof should be about is coming to a complete understanding of why and how something is true, approaching it from many different directions, seeing the connections with related things, and ultimately being able to write down a proof that is different from the one first learned.
There is some sense in which proving things is the whole of mathematics.
bon vivant
July 26th, 2007 1:52am
Aaron,
"There is no such thing as a PhD comprehensive exam. Maybe one you take en route to getting the PhD..."
Yeah, that's what I meant.
Bot, I agree. "For dummies" books in general don't work for academic subjects. You need to find books written by professionals who know how to explain their subjects.
Rick Zeng
July 26th, 2007 2:29am
Yeah, you are right in doubting my motive.
I still have not finish reading Donald Knuth The Art of Programming volume one. | 677.169 | 1 |
Mathematical Methods in CAD (Summer School 2012)
Schedule
Course content
Geometric design of the physical wold is an ingredient of the solution of many engineering problems. The course gives an introduction into several mathematical concepts and algorithms, which support the design of curves and surfaces. Specifically, we study
Bezier curves
polynomial splines
rational splines (NURBS)
and describe their properties, such as geometric continuity, shape preservation, and refinability. Some insight into interpolation and approximation by spline functions will be given as well. Similar conepts are discussed for surface design.
Prerequisites
Knowledge of Calculus and Linear Algebra
Basic programming skills, preferably Matlab or Maple
Homework
Weekly assignments consist of 3-4 problems. They are due the following Monday at 10 am. | 677.169 | 1 |
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The student will solve, algebraically and graphically,
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b) quadratic equations over the set of complex numbers;
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Lecture 9 - PowerPoint PPT Presentation
Combinatorics. The branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations which characterize these properties. Examples of combinatorial problems: Scheduling classes (or tournament play); Determining cheapest route for a mu 9 | 677.169 | 1 |
Copy Restrictions: You
may make single copies of this document for your own personal use and for the
use of other students, but inclusion in another document, publication or any use
for profit requires my permission. Teachers may make multiple copies of this
document for their students if they first get permission from me. Merely send
me an email (Just click on Webmaster in the navigation bar.) with a one-sentence
explanation of what you're using the document for. I'll give you permission in
a timely manner.
GENERAL: All
keys have at least two functions and some have three. The default function for
a key is the white print on the key. When 2nd is pressed the key
function is as indicated in blue print (gray on some later models) on the panel
immediately above the key. When ALPHA is pressed, the function is the white
label immediately above and, in most cases, near the right end of the
key.
I. BASIC MATH
1. Turning the calculator ON and OFF.
a) To turn on: Press the ON key.
b) To turn off: Press 2nd; then OFF (the second function
for the ON key.)
2. Adjusting the contrast of the screen.
a) To make the screen display darker: Press the 2nd key; then press the
UP arrow
key.
b) To make the screen display lighter: Press the 2nd key; then press
the down
arrow key.
3. Clearing the Calculator Screen.
a) To clear the calculator screen: Press the CLEAR key.
b) Note that CLEAR may also take you to another screen if you are
using one of
the screens that does not permit data entry.
4. To move to another screen:
a) Press 2nd, QUIT.
b) You can also use CLEAR
if you're not using a screen such as Y=, List, or
PRGM where entries can be
made.
5. Correcting errors or changing characters.
a) To replace a character at
the cursor position, just press the new
character.
b) To insert a character in the
position of the cursor, press 2nd, press
the INS key, and then press the key for
the desired character.
c) To delete a character in the
position of the cursor, press the DEL key.
6. Changing the MODE:
(Use the MODE for such things as changing from degrees to radians, displaying numbers as powers of ten, using split screen, and other similar things.)
a) Press the MODE key.
b) Use the arrow keys to move the cursor to the desired item.
c) Press ENTER to highlight the selected item.
d) Press CLEAR or 2nd, QUIT to return to the home screen,
7. Performing numerical calculations,
a) On the graphing calculator screen, the multiplication symbol will
appear
as * and the division symbol will appear as /.
b) Parentheses can be used to denote multiplication or as grouping symbols
to
clarify the order of
operations.
c) To enter an exponent use the ^ key for any exponent. You can also use
the x2
to raise a number
to the second power.
d) Use the (-) key for negative numbers and the - key for subtraction.
8. Raising a number to a power: a) Enter the number.
b) Press the ^ key
c) Enter the number for the power. Enclose
fractional exponents in parentheses.
d) Press ENTER.
e) For an exponent of 2 only, you can use the x2
key after entering the
number that you want to raise to the second power.
f) Alternate method for raising to the third power
only: Enter your number,
press MATH; then 3; then ENTER. (Note that using ^
is more efficient.)
9. Finding the root of a number:
a) Enter the number for the root index.
b) Press the MATH key.
c) Press 5 to paste the unspecified root symbol to
the screen.
d) Enter the number you want to find the root of.
e) Press ENTER.
f) As an alternate method for cube root only, you
can also choose to press
MATH, enter 4 to select item 4, and enter your
number. Finally, press ENTER.
10. Operations with fractions:
a) Use the divide symbol between the numerator
and denominator. Ex: ¼ is
entered as 1÷4.
b) Use the correct operator symbol (divide,
multiply, add, subtract) between
fractions.
c) Pressing ENTER will give you the answer in
decimal format. To get the answer
as a fraction, skip step c) and continue as below.
d) Press MATH to select Frac; then ENTER.
NOTE: You can convert decimals to
fractions using step d), but the decimal
must have 12 decimal places. Example: To convert
the decimal equivalent of
1/3 to a fraction, you must enter this number, .333333333333.
Otherwise the
calculator will just return the decimal you entered.
II. SPECIAL
EXPRESSIONS:
1. To enter the symbols, =, ≠, >, <, ≥, or ≤:
a) Press the 2nd ; then the TEST key.
b) Enter the item number for the desired symbol.
1. Graphing a function.
a) Press the Y= key.
b) Enter the function(s) using the [X,T,Θ] key to enter the
variable X.
c) Press GRAPH to graph the function. (If you don't see your
graph, press
TRACE and use the arrows to find the maximum or minimum value of your
function. Press ENTER.)
d) To leave the screen without graphing: press 2nd,
QUIT.
e) Press CLEAR while the cursor is on the same line as the
function to erase the
function.
f) To deselect a function, move the cursor to the equal sign
and press ENTER.
3. To change the viewing window to a custom size:
a) Press the Window key.
b) Use the arrow keys to move the cursor to the value to be
changed.
c) Enter the new value.
d) Press Graph to see the new graph, or press Quit to return to
the calculations
screen.
e) ZSquare keeps the y-scale the same and adjust the x-scale so
that one unit
on the x-axis equals one unit on the y-axis.
f) ZDecimal makes each movement of the cursor equivalent to
one-tenth of a
unit.
g) ZInteger makes each movement of the cursor equivalent to one
unit.
4. Evaluating a function without going
to the Graph screen..
a) Press 2nd, Y-VARS.
b) Press ENTER.
c) Select the name of a function, e.g., Y1.
d) Enter an x-value as YI (3) or a list of x-values in the format
Y1 ({2,3,4,5}). (In the
last format, make sure the interior grouping symbols are braces rather than
parentheses.)
e) Press ENTER.
5. To change or erase a function:
a) Press the Y= key.
b) Use the arrow keys to move the cursor to the desired location
and make
changes by inserting, deleting, or changing the desired characters.
c) To erase a function, with the cursor on the same line as the
function, press the
CLEAR key.
6. To use the trace function:
a) Press the TRACE key.
b) Use the right and left arrow keys to move the cursor along
the graph. The
coordinates of the cursor location are shown.
c) If more than one graph is on the screen, you can press the up
or down arrows
to jump
between graphs.
7. Finding the maximum and minimum points.
a) Enter the function and graph.
b) Press 2nd; then the CALC key.
c) Press 3 for minimum or 4 for maximum.
d) Move the cursor to the left of the point and press ENTER.
e) Move the cursor to the right
of the point and press ENTER
f) Press Enter again.
g) The maxima or minima will appear at the bottom of the screen.
8. Finding the value of a function at a given value of x.
a) Enter the function and the graph.
b) Press 2nd; then the CALC key.
c) Press 1 to select value.
d) Enter the x-value and press
ENTER.
9. To zoom in using a box.
a) Enter the function and graph.
b) Press the ZOOM key.
c) Press 1 to select ZBox.
d) Move the cursor above and to the left of the location you
want enlarged and
press ENTER.
e) Move the cursor below and to the right of the location you
want enlarged and
press ENTER.
f) The box is then enlarged to fill the screen.
10. Finding the intersection point of two graphs.
a) Press "Y=" and enter
two equations whose intersection you want to find.
b) Press 2nd, CALC.
c) Press 5 to select Intersect.
d) Using the left or
right cursor, move the cursor near the point of intersection if it's not already
there. If it's on the intersection, you might want to move it away
slightly.
e) Press ENTER. The
prompt "First curve" should appear.
f) Press ENTER and
at the prompt "Second curve," press ENTER again.
g) At the prompt "Guess,"
move the cursor near or on the intersection and press ENTER.
f) The point of intersection will appear at the bottom of the
screen.
11. Solving an equation in one variable. (Also
know as finding the roots.)
a) Press "Y=" and enter
the equation you want to solve.
b) Press 2nd, CALC.
c) Press 2 to select root.
d) Move the cursor to the left of the intercept and press ENTER.
e) Move the cursor to the right of the intercept and press
ENTER.
f) Move the cursor
between the above two points and press ENTER again.
g) The "x" and "y"
coordinates of the root will appear at the bottom of the screen.
12.
Graphing inequalities is with the standard TI-82 is tedious. Use my
program, INEQGRAF. The
instructions for using this program are in
Appendix IA of this manual.
IV. SPECIAL
FUNCTIONS:
1. Changing from radian measure to the degree mode.
a) Press the MODE key.
b) Move the cursor to either
Radian or Degree to match the units
of your angle.
c) Press ENTER.
d) Press CLEAR or 2nd, QUIT to return to the
calculator screen.
2. Graphing piecewise functions or functions on an interval.
a) To graph a function on the interval x < a, enter the function
followed by
(x<a).
b) To graph a function on
the interval x > a, enter the function followed by (x>a).
c) To graph a function of the interval a<x<b, enter the function
followed by
(x>a)(x<b).
3.
Graphing trigonometric functions:
a) You must have
the calculator set to radians to graph a trig function. See the MODE
section if
you don't know how to do that.
b) Press "Y=" and
then press the button for the function you want to graph.
c) Enter the
argument of the function, e.g., X, and press GRAPH.
4.
Using the LOGIC functions.
NOTE: You can use the logic functions
such as "and", "or," "xor," or "not(," to do things such as
Boolean algebra and truth tables. Not that you must use "1" for true and
"0" for false. As
a simple example, suppose you wanted to do p ^ q.
a) Press 2nd, LIST
and enter the proper combination of 1s and zeros in for p in the table under
L1.
b) Enter the proper combination of 1s and 0s for q in L2.
c) Press 2nd, QUIT to go
to the home screen.
d) Press 2nd, L1,
2nd, TEST, cursor to LOGIC and press 1.
e) Press 2nd, L2;
the press ENTER.
f) The answer will appear
on the home screen enclosed in braces.
5. Finding terms of
sequences.
a) Press 2nd,
LIST, 5 to paste Seq( to the home screen.
b) Enter the
sequence information in the following format.
Seq(formula, variable, beginning, end, step).
Example: First five terms of : an = 3n +4.
1) Convert variables to 'x'; then enter: Seq(3x+4, 1, 5, 1). Press ENTER to
get the answers.
c) If you
want the answer in fractions rather than decimals do this:
1) After you've entered the information for the sequence, press MATH, ENTER.
That will
paste ►Frac to the end of the sequence information.
2) Press ENTER to get the answer in fractions.
6. Recursion formula:
Let's take this recursion formula:
an = 3an-1 +2, when a1 = 5.
a) Press 5; then
ENTER.
b) Enter the formula as follows: Press 3, 2nd, Ans, +2.
c) You will now get a new term each time you press ENTER.
V. CALCULUS
1. Finding the numerical derivative from a function:
a) Press the MATH key.
b) Press 8 to select nDeriv(.
c) Press 2nd, Y-VARS; select the variable you want
and press ENTER.
d) Enter the name of the independent variable, probably X.
f) Enter the
value where you want to find the variable and press ENTER.
2. Determining the value of the derivative from points on a graph.
a) Enter the function and graph.
b) Press 2nd, CALC.
c) Press 6 to choose dy/dx.
d) Move the cursor to the desired point and press ENTER. The
value of the
numerical derivative
at the point you selected will appear at the bottom of the screen.
3. Drawing a tangent line at a point.
a) Enter the function and graph.
b) Press 2nd, DRAW.
c) Press 5 to select Tangent(.
d) Move the cursor to the point of tangency desired and press
ENTER.
f) To clear the tangent line, press 2nd, DRAW and
then ENTER.
4. Calculating the value of a definite integral:
a) Press the MATH key.
b) Press 9 to select fnInt(.
c) You will now enter an expression in the form Y,X,a,b inside
the parentheses.
In that
expression, Y is the expression you're integrating; for example Y1, X is the
variable of integration, usually X; a is lower limit and b is the upper limit.
d) For the expression to be integrated, you can either choose a
variable entered
into the Y= screen, or you can enter the expression itself. As an example,
you
might have fnInt(Y1,X,1,2 with your expression entered into Y1, or you
might have fnInt( x2,x,1,2
where you have entered the expression x2 yourself.
Notice that you must enter Y1 from the Y-VARS
menu if you use that
method.
e) Press the ENTER key to see the value of the definite
integral.
5. Alternate procedure for finding the value of a definite integral.
a) Press the ZOOM key.
b) Press 4 to select ZDecimal. (You don't have to do this step,
but it probably will be
easier to set your limits if you do.)
c) Press the Y= key.
d) Enter the function you are integrating.
e) Press the GRAPH key.
i) Press 2nd, CALC.
g) Press 7 to select Integral.
h) Move the cursor to the
lower limit of integration and press the ENTER key. i) Move the cursor to the upper limit of
integration and press the ENTER key. j) The integrated region will be shaded, and the value of the
definite integral will
appear at the bottom of the screen.
VI. MATRICES:
1) Entering a matrix:
a) Press MATRIX, move the cursor to EDIT.
b) Move the cursor to the matrix number you want to edit or
enter numbers in,
and press ENTER.
c) Enter the number of rows and press ENTER;
then enter the number of
columns and press ENTER.
d) Enter each value of the matrix and press ENTER after
each value.
e) Press 2nd, QUIT to go to the home screen.
2) Multiplying two matrices [A] * [B]:
a) Enter the data into matrices [A] and [B] and press 2nd,
QUIT to go to the
home screen.
b) Press MATRIX, select the matrix you want as the first
in the product, [A],
and press ENTER.
c) Press the multiply symbol.
d) Press MATRIX, select the matrix you want as the second
in the product,
[B], and press ENTER.
e) Press ENTER to perform the multiplication step.
f) Remember that the numbers of columns in [A] must equal
the number of
rows in [B] or you will get a dimension error.
3) Doing other matrix math:
a) Press MATRIX and cursor over to MATH. There you
will see a list of
operations that you can do. To do find the determinant, use Det. To find
the transpose, use T.
b) After you select the operation you want, press ENTER.
c) Press MATRIX, select the matrix you want to operate
on, and press
ENTER.
d) Press ENTER again to get your answer.
4)
Solving systems of equations:
The TI-82 does not
have the ref and rref functions as the TI-83 Plus and TI-84 do. You can
use my program,
see item 5)
below. Perhaps the easiest way to solve a system of equation with the
TI-82 is to make use of
this equation:
[A][X]
=[K] where [A] is the matrix of coefficients, [X] is the variables, and
[K] is the matrix of coefficeints.
Now, we solve that equation for this:
[X] =[A]-1 [K]
To perform
the math for this, do the following:
a) Enter the
coefficients in matrix [A] or whatever matrix you choose.
b) Enter the
constants in matrix [B] or whatever matrix you choose other than the one you
have the
coefficients in.
c) From the home screen,
press 2nd, MATRIX, and press 1 for matrix [A].
d) Press the inverse
button, x-1.
e) Press the multiply
button.
f) Press 2nd,
MATRIX, 2 for matrix [B]. You should now have [A]-1 *[B] on the home
screen.
g) Press ENTER and the
answer will be displayed
NOTE: You can do any of the elementary row
operations. They are very useful for doing the arithmetic for Gauss or
Gauss-Jordan elimination, but a little time is required to get the hang of
solving a matrix a row at a time. So, since most students don't take the time to use those
functions, I'm not going to include them. Instead, I'll give you my
Website as a reference for finding out how to do those operations if you want
to do them. First go to my Website:
Go to the listing "TI FAQs" in the navigation bar on the left. Click on
the link "More Detailed Page 1". That will take you to a long page of 40 FAQs. Cursor down to the answers
and then down to answer (21). That will give you the procedure for doing the row operations.
Alternately, to find item 21, you can use Find under the Edit menu and enter (21) in the dialog
box. Then click Next to find the answer.
5) Doing rref and ref:
a) You cannot do these
operations on the TI-82 without a program. There
is a program on
my Website for doing this. Go to my Website at the URL listed above.
The program takes about 25 minutes to enter by hand. For STCC students,
as time permits,
I will transfer this
program electronically from a TI-82 that I have the program stored in to
the
student's calculator. To set up a time to have this done, email me at
dkizer@southwest.tn.edu . The instructions for this program are
in Appendix IB of this
manual.
VII. TRANSFERRING PROGRAMS AND DATA:
1) I will assume that both calculators are TI-82: a) Turn both calculators off and plug in
the unit-to-unit cable for both calculators.
b) Turn on both calculators and press 2nd, LINK on both. Cursor over
to
RECEIVE on the receive calculator, the calculator that you're
transferring the
program to.
c) Press ENTER on the receive calculator. The word "Waiting"
should appear.
d) On the sending calculator, cursor down to Prgm and press ENTER.
e) Cursor down to the program you want to transfer and press ENTER.
The program that
you selected will be marked with a square
"dot."
f) Cursor over to TRANSMIT press ENTER.
g) If everything is connected satisfactorily, transmission of the
program should start.
Otherwise, you'll get a transmit error after a
few seconds.
h) If you get a transmit error, rotate the plugs slightly back and forth
and try again.
VIII. PROBLEMS:
a) Problems with trigonometric functions: The most common
problem with trig functions is not having the MODE set to the to the dimension
of the number entered. For example, students may have entered degrees, but have
their calculator MODE set to radians. To correct that, see "Changing the MODE
in section I.
b) If your calculator hangs up and you are unable to correct
the problem, first try online or other places that provide help. If you are
unable to get help, you can reset the calculator. Do that as follows:
1) Press 2nd, MEM, press 3.
2) Decide if you really want to RESET.
Resetting will erase all of your programs.
IX. APPENCES:
Appendix IA:
Graphing Inequalities:
This program, INEQGRAF, may be downloaded from my website
in either text or .82P format. It will graph up to three inequalities on
the same screen. After the calculator has graphed the equation in Y1=, it then
moves on to the equation in Y2=. If you want to interrupt the graphing for some
reason, press the ON button.
Graphing is done as follows: SETTING THE WINDOW:
For many Finite Math problems you will get the best display (the feasible
region) if you set Xmin and Ymin both at 0.
ENTERING EQUATIONS:
1) Put your inequalities in the slope-intercept form, y = ax+b, and enter
the part to the right of the equal
sign into the Y=
screen. Either clear or deselect all other equations on this screen.
2) Press 2nd, QUIT to leave the Y= screen.
RUNNING THE PROGRAM:
1) Press PRGM and select the program INEQGRAG by either pressing the number
before it on the
keyboard or highlighting its number and pressing ENTER.
2) Press ENTER. The menu will appear on the screen and wait for you to choose a
number. If you
press 1, the equation in Y1= will be selected for graphing.
3) Another menu will appear asking what type inequality you want to graph. Press the
appropriate number and press ENTER. All equations will be
graphed and the appropriate graph(s) will
be shaded. The menu will appear again and wait for you to
tell it what to do my selecting a number.
4) When you are done, press the number 3 for DONE, and the calculator will
display the shaded
inequalities. Notice that the calculator does not draw
the dashed line for < or >. It only draws a
solid line.
5) When you are finished with the graph for a particular problem, press ENTER.
The shading will be
erased and the graphs will be redrawn. Be sure to do
this last step because the program keeps
running until you do.
Appendix IB:Doing ref and rref: 1) Enter the matrix data according to Item 1, in
section VI.
2) Press PRGM; then press the number before the program name
RREFREF2. The matrix that you
entered will be displayed for checking for accuracy.
Press ENTER.
3) When the menu appear, select the number for the operation that
you want to perform.
4) The solution will be displayed in decimal form. Note that
you can scroll to the right if the last
columns are not displayed on the screen.
5) Press ENTER to display the matrix in fractions.
6) Finally, press ENTER to quit the program. | 677.169 | 1 |
References
The following is the main text-book for the course. This book provides a comprehensive and modern treatment
of the subject and would be an extremely handy reference for all your years to come. Unfortunately, the
book omits many proofs and has no exercises. This means that attending the lectures regularly would be a
must for every student. | 677.169 | 1 |
Description
"The CliffsStudySolver" workbooks combine 20 per cent review material with 80 per cent practice problems (and the answers!) to help make your lessons stick. "CliffsStudySolver Algebra II" is for students who want to reinforce their knowledge with a learn-by-doing approach. Inside, you'll get the practice you need to factor and solve equations with handy tools such as: straightforward, concise reviews of every topic; practice problems in every chapter - with explanations and solutions; a diagnostic pretest to assess your current skills; and, a full-length exam that adapts to your skill level.Beginning with the rules for exponents and operations involving polynomials, this workbook ventures into quadratic equations, function transformations, rational root theorem, and more. You'll explore factoring by grouping, graphing, complex numbers, and hyperbola, plus details about: solving exponential and logarithmic equations; using a graphing calculator to graph lines and polynomials; dealing with story problems using systems of equations; performing scalar and matrix multiplication; and factoring binomials, trinomials, and other polynomials.
Practice makes perfect - and whether you're taking lessons or teaching yourself, "CliffsStudySolver" guides can help you make the grade.show more | 677.169 | 1 |
traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at minimum a calculator such as the TI 89 with C. A. S. capabilities.Includes "To the Teacher" sections that Draw connections from the number theory or abstract algebra under consideration to secondary mathematics. Provides historical context with "From the Past" sections in each chapter. Features "Worksheets" that outline the framework of a topic in most chapters.A useful reference for mathematics teachers who need to brush up on their abstract algebra skills. An Introduction to Abstract Algebra with Notes to the Future Teacher, 1/E Olympia Nicodemi Melissa A Sutherland Gary W Towsley | 677.169 | 1 |
it by carrying out: being attentive in class, actively studying, and fixing math problems – even when your instructor hasn't assigned you any. When you end up struggling to perform well in the math course, then stop by finest web page for resolving math difficulties to learn the way you may become an even better math student.
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Utilize the Dietary supplements That include Your Textbook
Textbook publishers have enriched modern day publications with extra materials (such as CD-ROMs or on the web modules) which can be utilized to help pupils gain excess apply in . A few of these supplies could also incorporate a solution or explanation information, which often can allow you to with operating via math difficulties yourself.
Go through Forward To remain Forward
In order for you to lessen your in-class workload or maybe the time you invest on research, make use of your free time just after faculty or on the weekends to go through in advance towards the chapters and ideas that could be included the following time that you are at school.
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The get the job done you do in class, for research, and on quizzes can give clues to what your midterm or ultimate examination will seem like. Make use of your old checks and classwork to make a personal examine information to your impending test. Look within the way your instructor frames issues – this is often almost certainly how they're going to show up with your check.
Learn how to Work Via the Clock
This is the well known study suggestion for persons getting timed examinations; specifically standardized assessments. If you have only 40 minutes for any 100-point test, then you can certainly optimally spend 4 minutes on each individual 10-point query. Get facts about how very long the examination will probably be and which forms of questions are going to be on it. Then plan to assault the easier issues first, leaving yourself enough the perfect time to expend about the extra demanding types.
Improve your Resources to have math homework assistance
If you are possessing a hard time comprehending concepts in class, then make sure to get aid outside of class. Ask your pals to make a study group and visit your instructor's place of work hrs to go over challenging difficulties one-on-one. Show up at research and assessment periods when your instructor announces them, or use a personal tutor if you want a person.
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Any time you are examining problems for an test, attempt to clarify out loud what system and approaches you utilized to obtain your answers. These verbal declarations will appear in useful through a take a look at once you ought to recall the steps you must consider to locate a answer. Get added exercise by making an attempt this tactic using a close friend.
Use Analyze Guides For Additional Practice
Are your textbook or course notes not encouraging you comprehend what you must be understanding in class? Use examine guides for standardized tests, including the ACT, SAT, or DSST, to brush up on outdated product, or . Analyze guides generally appear outfitted with extensive explanations of how you can solve a sample challenge, , and you simply can typically locate the place may be the much better obtain mathtroubles. | 677.169 | 1 |
Course Description: Designed for students requiring remediation in intermediate algebra skills. Topics for this course include exponents and polynomials; factoring; rational expressions and functions; and roots and radicals. This course will not apply toward graduation requirements and will not transfer.
Any required prerequisites: Students must have a C or higher in Math 0302 or the appropriate placement test scores.
Student Learning Outcomes
Students will be able to organize and consolidate their mathematical thinking through communication. Success will be measured using a variety of formative assessment strategies in a collaborative learning environment.
Students will be able to analyze and evaluate the mathematical thinking and strategies of others.Success will be measured using a variety of formative assessment strategies in a collaborative learning environment.
Students will apply and adapt a variety of appropriate strategies to solve problems. Success will be measured using a variety of formative and summative assessment strategies.
Students will monitor and reflect on the process of mathematical problem solving. Success will be measured using a variety of formative and summative assessment strategies.
Testing Requirements – Online Students Only
All chapter tests and the comprehensive final exam must be proctored by an approved testing organization. (Ask you instructor for more details.)
Students are NOT allowed to use their book or notes of any kind while taking their proctored tests and exam.
Students are allowed to use a calculator. However, the TI-89, TI-Inspire with CAS or any other calculator with CAS capability are not permitted
Required Access Code: Students must have a Hawkes Learning access code.
Calculators: Calculators are allowed in this course.
Other Policies, Procedures and important dates: Please refer to the WTC Course Catalog for the following:
Campus Calendar
Final exam schedule
How to drop a class
Withdrawal information
Student Conduct/Academic Integrity
Students with disabilities
Course Topics – Below are the main topics covered in this course. Each topic requires prerequisite knowledge; therefore other topics may also be covered to ensure student success. Topics are subject to change. | 677.169 | 1 |
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Are your textbook or class notes not encouraging you fully grasp what you really should be studying in school? Use research guides for standardized tests, such as the ACT, SAT, or DSST, to brush up on previous substance, or . Review guides normally appear geared up with thorough explanations of tips on how to solve a sample problem, , and you simply can generally come across the place would be the much better invest in mathtroubles. | 677.169 | 1 |
eye103
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Created by teachers for teachers, the Math Academy tools and activities included in this booklet were designed to create hands-on activities and a fun learning environment for the teaching of mathematics to the students. This booklet contains the themed program "Are You Game? Math Academy--Explorations in Probability," which teachers can use to enhance their math instruction while staying true to the academic rigor required by the state standards framework. Included in this booklet... Topics: ERIC Archive, State Standards, Educational Games, Probability, Mathematics Instruction, Student...
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This paper reports on a mathematics course in an Austrian high school that focuses on probability distributions. Students in this course used a TI-92 during math classes, at home for doing exercises, and during math tests. The TI-92 was used as a tool for calculations and illustrations making the concepts of probability distributions easy to understand and the problems easy to solve for the students. (Author/KHR) Topics: ERIC Archive, Concept Formation, Foreign Countries, Graphing Calculators, Instructional Design,...
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"The Power of Probability" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) and Common Core State Standards, which gives students opportunities to practice their skills and knowledge of the mathematics of probability. Developed by The Actuarial Foundation, the program's lessons and worksheets motivate students through activities that use mathematics for real purposes. [A poster that accompanies this teaching guide can be viewed and/or retrieved... Topics: ERIC Archive, State Standards, Assignments, Probability, Teaching Guides, Grade 6, Grade 7, Grade...
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Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of probability distributions are given, which exhibit the existence of a continuum of situations interpolating the extreme cases of infinitely and minimally divisible probability distributions. Source:
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In this paper, we observevd the amalgamated free probability of direct product of noncommutative probability spaces. We defined the amalgamated R-transforms, amalgamated moment series and the amalgamated boxed convolution. They maks us to do the amalgamated R-transform calculus, like the scalar-valued case. Source:
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The set of all idempotent probability measures (Maslov measures) on a compact Hausdorff space endowed with the weak* topology determines is functorial on the category $\comp$ of compact Hausdorff spaces. We prove that the obtained functor is normal in the sense of E. Shchepin. Also, this functor is the functorial part of a monad on $\comp$. We prove that the idempotent probability measure monad contains the hyperspace monad as its submonad. A counterpart of the notion of Milyutin map is defined... Source:
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A combinatorial approach to free probability theory has been developped by Roland Speicher, based on the notion of noncrossing cumulants, a free analogue of the classical theory of cumulants in probability theory. We review this theory, and explain the connections between free probability theory and random matrices. We relate noncrossing cumulants to classical cumulants and also to characters of large symmetric groups. Finally we give applications to the asymptotics of representations of... Source:
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The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function, which has all properties of the classical probability function. The logical analog of the Large Number Law is deduced from properties of this function. Source:
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We survey the development of probability from 1900, starting with Bachelier's theory of speculation. Fisher information appears in the theory of estimation. We touch on Brownian motion, and the Wiener integral. The Ito calculus, and its relation to to the heat equation, is mentioned. Quantum theory is introduced as a generalisation of probability, rather than of mechanics. The weakness of attempts to describe quantum theory in terms of hidden variables is explained, by a simple proof of Bell's... Source:
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We construct a sequence of states called m-monotone product states which give a discrete interpolation between the monotone product of states of Muraki and the free product of states of Avitzour and Voiculescu in free probability. We derive the associated basic limit theorems and develop the combinatorics based on non-crossing ordered partitions with monotone order starting from depth m. The Hilbert space representations of the limit mixed moments in the invariance principle lead to m-monotone... Source:
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Using concepts of noncommutative probability we show that the Loewner's evolution equation can be viewed as providing a map from paths of measures to paths of probability measures. We show that the fixed point of the Loewner map is the convolution semigroup of the semicircle law in the chordal case, and its multiplicative analogue in the radial case. We further show that the Loewner evolution ``spreads out'' the distribution and that it gives rise to a Markov process. Source:
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A collection of old and new problems, puzzles, games, and diversions based on probability, geometry, number patterns, magic squares, and the laws of physics Topics: Mathematical recreations, Puzzles, Games, Mathematical recreations, Puzzles, Games
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About forty years ago it was realized by several researchers that the essential features of certain objects of Probability theory, notably Gaussian processes and limit theorems, may be better understood if they are considered in settings that do not impose structures extraneous to the problems at hand. For instance, in the case of sample continuity and boundedness of Gaussian processes, the essential feature is the metric or pseudometric structure induced on the index set by the covariance... Source:
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This course focuses on Modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic... Topic: probability
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Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with matroids, stochastic domination, negative association, completeness for infinite matroids, tail triviality, and a method for extension of results from orthogonal projections to positive contractions. We also present several new avenues for further... Source:
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We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a certain sense. Examples include statistics such as total edge length and total number of edges of graphs in computational geometry and the total number of particles accepted in random sequential packing models. These rates also apply to the 1-dimensional... Source:
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In this paper, we will consider R-transform theory and R-transform calculus for compatible noncommutative probability space and amagamated noncommutative probability space. By doing this, we can realize the relation between scalar-valued R-transforms and operator-valued moment series, under the compatibility. Also, we can see that there is a big gap between freeness and amalgamated freeness. Source:
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Based on a new analytical approach to the definition of additive free convolution on probability measures on the real line we prove free analogs of limit theorems for sums for non-identically distributed random variables in classical Probability Theory. Source:
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The common structure of the space of pure states $P$ of a classical or a quantum mechanical system is that of a Poisson space with a transition probability. This is a topological space equipped with a Poisson structure, as well as with a function $p:P\times P-> [0,1]$, with certain properties. The Poisson structure is connected with the transition probabilities through unitarity (in a specific formulation intrinsic to the given context). In classical mechanics, where... Source:
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There have been extensive developments recently in modern nonparametric inference and modeling. Nonparametric and semi-parametric methods are especially useful with large amounts of data that are now routinely collected in many areas of science. Probability and stochastic modeling are also playing major new roles in scientific applications. This refereed special volume highlights challenges and developments at this interface of statistics, probability and the sciences, and honors Michael B.... Source: | 677.169 | 1 |
Ants, Bikes and Clocks is a wonderful introduction to applied mathematics via problem solving. Most of the material is calculus free. Students can learn an immense amount about how to approach problems and why they should study math at University.
I use this as a supplement in a 200 level modeling class as well as the main text for a section I teach to math high school teachers. I also leave the book with high school classes I visit.
It is very well written, approachable and filled with great problems and some hints on how to solve them.
Enjoy! | 677.169 | 1 |
Intended for undergraduate and graduate students and all who are interested in computer vision, medical imaging,
and human visual perception, this interactive book presents a tutorial approach to mastering the mathematics of
computer vision and image analysis. One purpose of the book is to bridge the gap between the world of human visual
perception and the world of multi-scale computer vision theory and applications. All chapters are written in
Mathematica, and the text and included code invite readers to explore computer vision on their own. | 677.169 | 1 |
Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject. The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed. MATLAB is used extensively to illustrate the material. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory. This broad coverage, the authors? clear presentation and the fact that the book has been thoroughly class-tested will increase its attraction to undergraduates at each stage of their studies. Contents Preface Part I. Linear Equations: 1. Variable coefficient, second order, linear, ordinary differential equations 2. Legendre functions 3. Bessel functions 4. Boundary value problems, Green`s functions and Sturm-Liouville theory 5. Fourier series and the Fourier transform 6. Laplace transforms 7. Classification, properties and complex variable methods for second order partial differential equations Part II. Nonlinear Equations and Advanced Techniques: 8. Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations 9. Nonlinear ordinary differential equations: phase plane methods 10. Group theoretical methods 11. Asymptotic methods: basic ideas 12. Asymptotic methods: differential equations 13. Stability, instability and bifurcations 14. Time-optimal control in the phase plane 15. An introduction to chaotic systems Appendix 1. Linear algebra Appendix 2. Continuity and differentiability Appendix 3. Power series Appendix 4. Sequences of functions Appendix 5. Ordinary differential equations Appendix 6. Complex variables Appendix 7. A short introduction to MATLAB Bibliography Index. Printed Pages: 552. Bookseller Inventory # 11789 | 677.169 | 1 |
Math 6: Finite Mathematics
Course Information
This course will focus on the mathematics which arises in daily situations for those pursuing careers in Business, Life Sciences, Social Sciences and more. We will begin with solving systems of linear equations and build upon this as we learn markov chains and mathematical finance. If time permits we will study game theory and difference equations. Real world applications will be emphasized and students will have the opportunity to personalize the curriculum to a certain extent. As it is an important skill in the working world, group work will be a large component of the course.
The prerequisites for this course are familiarity with high school algebra (see the instructor if you are worried about meeting this criterion... chances are, you are going to be fine) and a willingness to learn and participate in the class. This class does not assume any background in calculus nor will we be covering any calculus unless the individual student decides to pursue this route.
Textbook
Finite Math and Its Applications (8th edition) by
Goldstein, Schneider, and Siegel Published by Prentice Hall
ISBN: 0-13-010705-0
The textbook will be available at Wheelock
Books. It is likely that there are used copies available both on the internet and here on campus. It may be worth looking around for the best price.
Group Work
Group work will play an important role in this course. In fact, every grade you receive in this class will consist of an individual score and a group score. In the first day of class I will break you into groups of about 3 students each. You will be expected to study with your group, work on projects with your group and work on in-class assignments with your group.
For projects and homework where you are encouraged to work with your group, the group scores will count for more. For exams the group scores will be less. Each assignment, exam and project will outline exactly how the individual and group points will be awarded.
My reason for putting such emphasis on group learning is two-fold. First, employers are looking for graduates who have experience working in teams. Through this group work experience you should gain some skills and experience working on projects and carrying your teammates through the learning process. Second, numerous studies have been done showing that students at all levels perform better when working in group settings. The advanced students gain a higher level of understanding through reviewing the material with the rest of their group. Students who become lost in the material have a support network to turn to for the extra help they need.
If at any time your group is having difficulty working together, make an appointment as a group to meet with me.
The in-class group work will consist of several problems related to the course material. These assignments will not be graded on whether or not your group finishes the assignment, rather on whether or not your group has worked together to make an attempt at the assignment. Solutions to all group assignments will be posted on Blackboard. If you are absent from class, you will not be allowed to make-up points for in-class assignments. There will be more than 5 group assignments but I will only take the top 5 scores for each individual and group grade.
Homework
Homework will be assigned daily and collected every Monday at the
beginning of class. Assignments can be found on the "assignments"
folder in Blackboard. Late assignments will receive no
credit although I will still grade your work if you desire.
Assignments will awarded an individualFor every assignment you turn in, I
expect that:
You use full
sentences with correct punctuation;
Your handwriting is legible or the assignment is
typed up;
Your name appears at the top right corner of the front page; The assignment number is written on the top of the front page; and
The
Examinations
There will be two quizzes and a final in this course.
Quiz 1: Monday, July 17 in
class.
Quiz 2: Monday, August 7 in
class.
Final Exam: Saturday, August 27 at 8am, location
TBA.
Projects
There will be 2 projects in this class. Project descriptions will be posted on Blackboard. You will be expected to do a large portion of the project with your group. The purpose of these projects is to give you real-world context for the class material as well as to give you a chance to display your knowledge in a non-exam setting.
Grades
The grades in this course will be calculated as follows:
individual points
group points
total points
9 Homeworks:
45
9
54
In-class Groupwork:
10
30
40
Project 1:
30
30
60
Project 2:
30
30
60
Quiz 1:
75
5
80
Quiz 2:
75
5
80
Final Exam:
120
6
126
Total Course Points:
385
115
500
I am fond of bonus points. There might be bonus
homework problems, bonus questions on exams, perhaps a bonus
writing assignment, and class participation may serve as a bonus
in the case of borderline final grades.
Honor Principle
Collaboration with your group on homework is highly
encouraged; that is, it's a great idea to talk about the homework problems
with each other and try to solve them together. However, you must
write up homework solutions in your own words.
If you consult any person or source other than the course
textbook, your groupyour group, notes, books, me | 677.169 | 1 |
As a leading global provider of math content, we offer student-oriented geometry textbooks that allow for flexibility in learning structure and teaching style. A full range of learners will be inspired to problem solve with a geometry curriculum that shares proven strategies. Our curriculum guides for geometry educators correlate directly with the class textbooks for streamlined instruction.
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Our high quality resources for the geometry curriculum serve as a partner in student progress, providing clear presentation of material, examples, and homework assistance. We offer geometry teaching guides designed for instructing students in grades 8 through 12. Textbooks and interactive materials can be used to present in-depth concepts for the student who plans to pursue AP classes and STEM studies. Educators can blend print, eText, and interactive online technology into a multidimensional educational experience. Both formal and informal systems will be valuable to educators who are focused on geometry course objectives. Contact us to learn more about how we support lifelong mathematics learning in the dynamic classroom environment | 677.169 | 1 |
Mathematics: AS and A-Level
Course Description
A-Level Mathematics is an excellent foundation for both further study and employment. It remains a particularly impressive qualification that demonstrates core intelligence, a logical mind and excellent problem-solving skills.
•Mechanics - using simple mathematical models to describe a real world situation. Main topics include Kinematics, Dynamics and Statics.
Course Outline
Year 1 (AS Level)
Paper 1 – Pure Mathematics
Paper 2 – Statistics and Mechanics
Year 2 (A Level)
Paper 1 – Pure Mathematics 1
Paper 2 – Pure Mathematics 2
Paper 3 - Statistics and Mechanics
Course Assessment
AS and A level are now separate qualifications but we will recommend that all students sit the AS exam in Year 12 and those that wish to continue in Year 13 will set the three exams for the A level in year 13.
For AS Paper 1 is two hours and worth 67% of the marks and Paper 2 is one hour and worth 33% of the marks.
For the A level each paper is two hours long and each is worth a third of the marks for the whole exam. | 677.169 | 1 |
published:16 May 2017
views:109446 Course4:10
How to prepare for Maths in 4 days - Class 12, 2017
How to prepare for Maths in 4 days - Class 12, 2017published: 13 Aug 2016published: 18 Oct 2016 . theHow to prepare for Maths in 4 days - Class 12, 2017
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Maths Class 12 - 3D Geometry Plane Chapter 11 (ParNEWBURYPORT — While School Committee members examined standardized testing scores at their meeting Tuesday night, Newburyport High School administrators noted that even if students score below average on Advanced Placement tests, they are still better equipped for college-level course work ... The data revealed that students who do take up to five AP courses are handling the coursework well....
The StarterAcademy students first choose one of three, free introductory courses, in science, math or English... Scientific Literacy for Today." Students signing up for one of these courses will be mixed in with paying GCC students who have also signed up for the class. At the same time, students sign up for a second three-credit course the same semester, for up to $727, before student aid....
The blueprint, required by the federal Every Student Succeeds Act, is cited for crediting districts that have high school students in advanced courses. A 200-page New York State education plan that includes steps to discourage student test boycotts and encourage participation in college-level courses in high school has won approval from the U.S....
SAGINAW – Math in the Mail focuses on developing math skills in 3-year-olds by providing the tools needed in the home environment for parents and caregivers ...Math in the Mail is part of a region-wide focus to better prepare students for science, technology, engineering and math (STEM) experiences and STEM careers....
TwizelAreaSchool principalBill Feasey said he has not received much interest in the maths head of department position which has been advertised for two or three months. He believed there was a shortage of secondary maths teachers, as not enough maths graduates were attracted to teaching and could earn "heaps more money" going into other professions....
Under the state's rules for determining county help, those districts, serving several million students, will now face the challenge on their own of narrowing large academic disparities, as indicated by scores on standardized tests in math and English language arts ... Here are the results for math ... In 55 percent of districts with Latino enrollments, Latino students scored in the red or orange range in math....
Some hints at solutions, however, lie in your letters page (same day), where maths and literacy are taught through role play and fascination with numbers. Stem subjects (science, technology, engineering and maths) are innately creative, requiring imagination, speculation, improvisation and rehearsal (experiment) – activities and skills that Rufus Norris will employ every day in his neck of the creative industries woods....
courtesy Fei Fang/CMU]That's why Fei Fang, an assistant professor at CMU's School of Computer Science, designed a new course this semester–one that she sincerely hopes other universities will copy ... "That's the reason why I started this new course." ... But those routes, of course, were driven by vehicles that couldn't pass every environmental obstacle....
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"We still want them to play and enjoy the snow, but we also want them to practice their reading and math skills," she said. As part of the challenge, students were asked to read a book, work for 20-30 minutes on an educational website, conduct a science experiment, write a story or create math problems for family members to solve....
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7 1 Study Guide Intervention Answers 133730
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The mobile phone industry struck a nerve among teachers this month. An industry trade group argued that cell phones should be allowed in the classroom, saying they can be used as a teaching tool to help children with their math skills; in particular, algebra. Well, we're going to avoid that debate this week, but it did make us reflect - what exactly is algebra? Why do so many people find it hard to learn? So we turned to - who else - our math guy, Keith Devlin of Stanford University, to help us out. He joins us from the studios out there in Palo Alto.
Mr. DEVLIN: You know, that actually gets at the nub of why people find it difficult, because they think that's what it is. And it really isn't. To cut straight to the chase, arithmetic is thinking with numbers. It's calculating with numbers. Algebra is reasoning about numbers. So whereas arithmetic, you're actually thinking numerically about the sizes of things and the measures of things, in algebra you're thinking logically and analytically about numbers in general. And that's a very different kind of thinking.
And in fact, the problem is, people spend all of these year learning arithmetic and then they get moderately good or very good at it, and they meet algebra and there's these X's and Y's and Z's that are - at least they're not numbers - so this is just arithmetic. And they keep trying to do it using arithmetic methods. And that isn't the way to do it. You've got to stop doing arithmetic, step back and adopt a whole new way of thinking. It's a very different kind of thinking.
SIMON: Let me bring a question to your attention I don't believe I've asked since I asked it of Karl Geise(ph) at Senn High School in Chicago, one of my math teachers. I said, Mr. Geise, I mean, like, what can you use algebra for anyway? That's exactly how I talked.
(Soundbite of laughter)
DEVLIN: You know, the odd thing is today, in today's society, there's an answer that's staring us all in the face, and that's the computer spreadsheet. It's very hard to do anything these day without a spreadsheet. If you're running a sports competition, you're going to start entering the results on a spreadsheet. If you're keeping track of your finances, if you're running a business, if you're a videogame player and you want to figure out how to equip your warrior character in World of Warcraft and you want to do it correctly and make a good job in the game, you'll start working on a spreadsheet.
And so spreadsheets are ubiquitous. But spreadsheets are all about algebraic thinking. In fact, the thing that the spreadsheet has done is it means we don't need to be good at arithmetic anymore because the spreadsheet does the arithmetic for us. But to put that spreadsheet together so that it does the calculations you want, you have to enter these little instructions, what we call macros, in certain cells that say: Spreadsheet, do the following with these numbers. That's algebraic thinking. You cannot set up a spreadsheet to do anything without doing algebra.
SIMON: And are there different ways of teaching algebra now?
DEVLIN: I think the main thing is the motivation. You know, when I grew up and we met algebra, there were all sorts of weird problems about filling swimming pools with two hoses and the water running out, or putting water in the bath, in the bath. I mean there were all these problems, and you know, I thought to myself, as did all my friends, I will never need to do that. If I need to fill a swimming pool, I'll hire the guy down the road to come and - and run until the water's in, and then he'll turn the tap off.
I mean we all knew that those were fake problems. They were problems designed to provide exercise in the techniques, but they weren't really applicable ones. But with spreadsheets, almost for the first time in history we have an absolutely important self-evident application that's absolutely about algebraic thinking. So the main difference isn't how you teach it now, so much as the motivation.
Kids today, all you've got to do is convince them that spreadsheets are going to be really useful to them in their leisure activities or their professional activities or their home activities, whatever, and then they'll sort of see, oh yeah, I need to learn how to do these things and then they'll put in the effort.
But once you've got the motivation, it's still a matter of - you know, it's the old joke of - how do you get to Carnegie Hall? Well, practice, practice, practice.
SIMON: You know, it occurs to me, a number of years ago when handheld calculators first became well-known, I can remember people saying, well, you know, you can get rid of high school math now, because…
(Soundbite of laughter)
Mr. DEVLIN: Yeah. Yeah, it's like computers led to the paperless office too, yes. So what do we do? We all print off our PDF files all the time. No, it just doesn't work like that. What the computers did, and the calculators, is they changed the mathematics we need to learn and concentrate on. It didn't become important to be good at doing arithmetic. You still need to know about arithmetic. And to understand how to deal with spreadsheets, you need to have some competency in arithmetic, but it's not important to be able to always get the right answers in arithmetic.
What is important now is to be able to tell that computer how to do the work for you. So computers turned us from being at the coal-face, being the mechanics who actually grind at the numbers, to be managers. We're all now managers. We now instruct the computer to do the arithmetic for us. And instructing the computer to do the arithmetic means we need two things. We need a good sense of arithmetic, so we do need to still get people to learn arithmetic up to a point. But what we need in spades is algebraic thinking.
SIMON: Is it true - I have to ask you because I think you probably told this to me once - that there are mathematicians whom you wouldn't trust to figure out the tip on a cup of coffee?
Mr. DEVLIN: I'm one of them, Scott.
(Soundbite of laughter)
Mr. DEVLIN: So I probably did say that. Yeah...
SIMON: I think that's why you made me buy it, if I'm not mistaken.
(Soundbite of laughter)
Mr. DEVLIN: No, in fact, mathematicians are notoriously bad at doing everyday arithmetic, because they never do that. Because if you're a professional mathematician, you're working several levels removed from the levels of numbers in algebra. So you never do basic arithmetic. In fact, not only do mathematicians often make mistakes with arithmetic, we often make mistakes with elementary algebra as well, because our minds are on higher things. At least that's the way I'm going to try to describe it.
SIMON: Keith, wonderful talking to you. Thanks so much.
Mr. DEVLIN: Okay, my pleasure, Scott.
SIMON: Keith Devlin, director of the H-STAR Institute at Stanford University, speaking with us from Palo Alto | 677.169 | 1 |
The purpose of this course is to introduce a set of
numerical algorithms fundamental to scientific computation, ranging from equation
solving, function approximation, integration, difference and differential
equations, to special computer techniques. Emphasis will be placed on efficient
use of computers to optimize speed and accuracy in numerical computation, and extensive
digital computer usage for algorithm verification.
PREREQUISITES:
Prerequisites: CSE1010
(Introduction to Computing for Engineers), CSE1100 (Introduction to Computing),
MATH2110Q (Multivariable Calculus), MATH2410Q (Elementary Differential
Equations) and MATH2210 (Applied Linear Algebra). Those without such prior
backgrounds should contact the instructor and get her permission to register
this course.
The
conceptual and theoretical course contents will be delivered primarily in the
lectures, complemented by readings from the text book. You should review
readings prior to attending a lecture, and review the readings again, along
with any notes you took, after the lecture. Attending the lectures is not a
substitute for reading the text in the book.
You
are expected to attend all lectures. If you are unable to attend a lecture
because of sickness or similar reasons, make sure you get the notes from a
classmate. If you are out of class for an extended period of time because of
sickness, notify your instructor as soon as possible, and see your instructor
immediately upon your return in order to determine how to catch up. If you have
missed a significant portion of the semester due to illness, it is recommended
that you resign from the course.
You
are strongly encouraged to attend the lectures. Attendance will be taken in
class from time to time.
GRADING:
The grade breakdown is as
follows. I reserve the right to make adjustments to the breakdown if I feel it
is necessary.
Assignments (6-7): 30%
Midterm Examinations (2):
40%
Final Examination (1): 30%
Assignments
There
will be a few homeworks which may need some Matlab coding. The purpose of these
is to give you feedback on your understanding of the material, and to reinforce
you concepts discussed in class. The assignment should be handed as a paper
copy in the class the day it is due. Note that assignments handed in late will
not be graded. We reserve the right to ask for your Matlab codes for clearer
grading.
Examinations
There
will be two in-class preliminary examinations, carrying 20% and 20%
respectively, together with a comprehensive final examination (30%) at the end
of the term. Mid-term exams will be held on dates to be announced in lecture.
The final examination will be given on a date to be specified by the
University. Do not make travel plans for times during the examination period
until the final examination schedule has been posted.
If
you miss an examination because of sickness or similar reasons, visit a
physician and obtain a note detailing the period during which you were
medically incapable of taking the exam. Notify your instructor immediately via
email or telephone (voice mail) if you are going to miss an exam before the
exam takes place, unless medically impossible. See your instructor as soon as
you return to class.
All
academic work must be your own. Collaboration, usually evidenced by
unjusti_able similarity in assignments, is never allowed. After an appropriate
informal review, if any students are found in violation of maintaining academic
integrity, sanctions will be imposed, which can be as severe as failing the
course for reasons of academic dishonesty. Especially flagrant violations will
be considered under formal review proceedings, which can call for harsher
sanctions including expulsion from the University. If you ever have any
questions or concerns regarding the policy, particularly as it relates to this
course, please talk to your instructor.
"Academic integrity is the pursuit of
scholarly activity free from fraud and deception and is an educational
objective of this institution. Academic dishonesty includes, but is not limited
to, cheating, plagiarizing, fabricating of information or citations,
facilitating acts of academic dishonesty by others, having unauthorized
possession of examinations, submitting work for another person or work
previously used without informing the instructor, or tampering with the
academic work of other students."
INCOMPLETE GRADES:
We
will follow the University Policy on Incomplete Grades. Take the time to
familiarize yourself with the contents of the related pages.
Generally,
incomplete ("I") grades are not given. However, very rarely, circumstances
truly beyond the student's control prevent him or her from completing work in
the course. In such cases the instructor can give a grade of "I". The
student will be given instructions and a deadline for completing the work,
usually no more than 30 days past the end of the semester. University and department
policy dictate that "I" grades can be given only if the following
conditions are met:
1.An Incomplete will only be given
for missing a small part of the course.
2.An Incomplete will only be given
when the student misses work due to circumstances beyond his/her control.
3.An Incomplete will only be given
when the student is passing the course except for the missed material.
4.An Incomplete is to be made up
with the original course instructor within the time specified by the
appropriate University regulation (see appropriate document above), and usually
within the following semester.
5.An Incomplete will not be given to
allow the student to informally re-take the entire course, and have that grade
count as the grade of the original course.
Incompletes
can not be given as a shelter from poor grades. It is the student's
responsibility to make a timely resignation from the course if he or she is
doing poorly for any reason. The last day to resign the course is Monday,
March 28.
DISABILITIES:
If
you have a diagnosed disability (physical, learning, or psychological) that
will make it di_cult for you to carry out the course work as outlined, or that
requires accommodations such as recruiting note-takers, readers, or extended
time on exams or assignments, please advise the instructor during the _rst two
weeks of the course so that we may review possible arrangements for reasonable
accommodations.
TENTATIVE COURSE OUTLINE:
The
following is a tentative outline of the major topics we will cover in the
course.
·Error analysis
·Roots of equations
·Linear algebraic equations
·Optimization
·Numerical differentiation and
integration
·Ordinary differential equations
·Curve fitting
·Partial differential equations
Additional
or less materials may be discussed in class, subject to schedule and class
feedback, etc. | 677.169 | 1 |
Background
Most college students carry one or more mobile devices with them. This might be a
smart phone, a tablet, or a laptop computer. In addition to fun activities like
sending text messages, checking into Facebook, or watching viral videos, these devices
are reasonably powerful computers. They have the potential to do much more
than an expensive graphing calculator, so why not use them?
List of Web-Apps
Factoring —
Practice algebraic factoring at a variety of different levels.
Simple Derivative Practice —
This app generates progressively more difficult algebraic functions. This is
suitable for a student who knows the derivative rules but has not learned any
transcendental functions.
Derivative Practice —
This app generates progressively more difficult functions and asks you to type
the formula for the derivative, then checks your work. It implements basic powers,
exponential, logarithms, and trigonometric functions, along with products, quotients,
and compositions.
Antiderivative Practice —
This app provides practice in finding antiderivatives of relatively elementary
functions, but does not involve integral notation. Allows practice of antidifferentiation
of powers, polynomials, and exponential functions, as well as practice recognizing
derivatives of trigonometric functions.
Recursive Sequences —
This app implements the computation of a recursive sequence, which you define by
a projection function (the recursive formula) and an initial condition.
Data Explorer —
This app implements a spreadsheet-like view of dependent variables, but so that
entire columns are computed at once using standard mathematical formulas. Special
cases are implemented to generate sequences and accumulations (e.g., Riemann sums).
Linear Algebra Web-Apps
Gaussian Elimination —
This app allows you to enter an arbitrary (moderately small) matrix along with
augmented columns to solve one or more systems of linear equations. Then you can apply
elementary row operations to find row equivalent systems, or you can ask to go straight
to a row-echelon or the reduced row-echelon forms.
Matrix Multiplication —
Drill yourself on matrix multiplication. Recognize when a product is undefined. Compute
the entries of the product matrix.
Matrix Subspaces —
Drill yourself on interpreting the reduced row-echelon form of a matrix and its transpose
to determine bases for the row space, the column space, and the left- and right-null
spaces of the matrix.
Linear Transformation —
Visualize the behavior of a linear transformation and see if you can find eigenvectors and eigenvalues geometrically. | 677.169 | 1 |
About the Department
The Department of mathematics was established in the year 2008. It has highly qualified faculty who actively engaged in teaching, research and continuing education programmes.
Mathematics is the queen of science. Our department aims at developing value-based knowledge at various fields such as Geometrics, Statistics, Algebra and Calculus are utilized throughout the natural sciences. Statistics is the fundemental importance in social sciences, medicine, economics, agriculture, and other disciplines.
Laboratory Facilities
MatLab
Chi Lab
Department Achievements
Students are trained for campus interviews separately.
The student of the department have represented state and university level in many sports events.
The students are permitted to attend seminars in various colleges to explore their knowledge | 677.169 | 1 |
Internationaler Buchtitel. In englischer Sprache. Verlag: GLENCOE SECONDARY, 741 Seiten, L=279mm, B=213mm, H=33mm, Gew.=1860gr, [GR: 12910 - HC/Kinderbücher/Kinderbeschäftigung/Lernen], [SW: - Textbooks], Gebunden, Klappentext: A complete Algebra curriculum by the end of eighth grade!. This exciting new program, developed in cooperation with Education Development Center, Inc., makes mathematics accessible to more of your. middle-school students. They will spend less time reviewing topics from previous grades and more time progressing carefully and successfully toward. the completion of Algebra 1 by the end of grade 8. Informal-to-formal concept development, designed specifically for middle school students, . ensures that students build necessary skills and develop conceptual understanding.. . This Impact Mathematics: Algebra and More for the Middle Grades, Course 2 Arshavsky, Nina / Carter, Ricky / Foster, Sydney!This McGraw-Hill, Books, IMPACT Mathematics: Algebra and More for the Middle Grades, Course 2, Student Edition BooksImpact Mathematics: Algebra and More for the Middle Grades, Course 2 A complete Algebra curriculum by the end of eighth grade!. Bücher / Fremdsprachige Bücher / Englische Bücher / Kinder- & Jugendbücher 978-1-57039-855-1, Glencoe Secondary
(Details of the book - Impact Mathematics: Algebra and More for the Middle Grades, Course 2 | 677.169 | 1 |
Welcome to MAC1105. College Algebra is
a college level course designed to introduce you to a variety of
functions, equations and applications. It combines an algebraic,
graphical, and numerical approach to problem solving, with an
emphasis on utilizing your graphing
calculator to visualize the concepts.
Daily Schedule-
MW ,
TuTh - Outlined is a
and worksheets that you are to work out after
each section is covered in class.
These are the pages that you must print out for
class and homework!
Notes, Handouts &
Homework : Ch 1
& 2 ,
Ch 3 & 4
See Handouts
for more notes, handouts, worksheets, keys to worksheets,
etc.
See Tests
for sample tests, keys to the sample tests & sample final
exam.
See
Notes
during class to follow along in class. | 677.169 | 1 |
Algebraic geometry and geometric modeling either care for curves and surfaces generated by means of polynomial equations. Algebraic geometry investigates the theoretical houses of polynomial curves and surfaces; geometric modeling makes use of polynomial, piecewise polynomial, and rational curves and surfaces to construct laptop types of mechanical parts and assemblies for commercial layout and manufacture.The NSF backed the four-day 'Vilnius Workshop on Algebraic Geometry and Geometric Modeling', which introduced jointly the various best specialists within the learn groups to check a variety of subject matters of curiosity to either fields. This quantity is an outgrowth of that workshop. incorporated are surveys, tutorials, and study papers. additionally, the editors have incorporated a translation of Minding's 1841 paper, 'On the choice of the measure of an equation bought by way of elimination', which foreshadows the trendy software of combined volumes in algebraic geometry. the quantity is appropriate for mathematicians, computing device scientists, and engineers drawn to purposes of algebraic geometry to geometric modeling.
This edited choice of chapters, authored by means of top specialists, offers a whole and basically self-contained building of 3-fold and 4-fold klt flips. a wide a part of the textual content is a digest of Shokurov's paintings within the box and a concise, entire and pedagogical evidence of the lifestyles of 3-fold flips is gifted.
An obtainable textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first ideas. development at the history fabric from algebraic geometry and algebraic teams, the textual content offers an creation to extra complicated and specialized fabric.
Be aware: merchandise do have huge Margins. An advent to summary algebraic geometry, with the single must haves being effects from commutative algebra, that are acknowledged as wanted, and a few straight forward topology. greater than four hundred workouts disbursed through the ebook provide particular examples in addition to extra specialized subject matters now not taken care of mostly textual content, whereas 3 appendices current short bills of a few parts of present examine. | 677.169 | 1 |
I'm getting really tired in my math class. It's harcort math.com , but we're covering higher grade syllabus. The concepts are really complex and that's why I usually doze off in the class. I like the subject and don't want to fail, but I have a big problem understanding it. Can someone help me?
You haven't given any details about the problem that is troubling you. I would like to help you with harcort math.com tried out each one of them myself and that was when I came across Algebra Helper . I found it particularly apt for rational equations, converting fractions and simplifying expressions. It was actually also kid's play to activate this. Once you key in the problem, the program carries you all the way to the solution elucidating every step on its way. That's what makes it terrific. By the time you arrive at the answer, you by now know how to explain the problems. I enjoyed learning to solve the problems with Intermediate algebra, Algebra 1 and Basic Math in math. I am also positive that you too will appreciate this program just as I did. Wouldn't you want to check this out | 677.169 | 1 |
Rhetoric Math
Algebra 2
This is a rigorous course in which the students will be required to derive formulas and explain concepts more than ever. It covers quadratic functions, an in-depth look at real and imaginary numbers, linear and quadratic inequalities, sequences, probability, an introduction to trigonometry, and a thorough investigation of functions in general.
Text:
Elementary Algebra, Harold Jacobs
Algebra and Trigonometry, Paul Foerster
Precalculus
This course requires students to delve deeper than ever before into the fundamental aspects of advanced algebra and will provide a solid preparation for calculus. Students will be comfortable explaining and proving concepts. The bulk of study will be related to logarithmic and trigonometric functions.
Text:
Prelude to Calculus, Sheldon Axler
Math History
This course will entail a broad sweep of mathematical history, through the great theorems of the centuries. Students will study not only the major developments, but also the mathematicians behind them, as well as the impact on our lives today.
At first much of the class is discussion-oriented. The students will then be required to recreate proofs or explain some of the most important theorems of history, such as the infinitude of primes, Archimedes' approximation of pi, and the Pythagorean Theorem. The last semester of the class is dedicated to research of certain aspects of math history. It will conclude with a 10 page research paper on a topic of the student's choice.
Text:
The Mathematical Universe, William Dunham
other various text on the history of math | 677.169 | 1 |
This edition features an even broader array of applications, including all engineering disciplines. The authors' unique approach opens each part of the text with sections called Motivation, Mathematical Background and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References | 677.169 | 1 |
It's an amazing course to take at IMSA if you want to have your mind blown by Fogel's math about once per class period. But, understanding can be quite tough sometimes and will require a very good about of work, so I'd be wary if you're crazy about grades, but the A is definitely possible.
Course highlights:
Everything in the class is a highlight, with Fogel branching off to prove physics and other science topics using the math you learn in class.
Hours per week:
6-8 hours
Advice for students:
Find other people in the class to do the worksheets with. You won't be able to do them alone.
Course Term:Fall 2015
Professor:Micah Fogel
Course Tags:Math-heavyBackground Knowledge ExpectedGo to Office Hours
Jan 15, 2016
| Would not recommend.
This class was tough.
Course Overview:
While the course material is interesting, the teacher's methods are quite flawed.
Course highlights:
The course is beneficial in the sense that it allows for students to think in a multidimensional perspective - which is a useful skill in higher mathematics courses. | 677.169 | 1 |
Fun, friendly coaching and all the practice you need to tackle maths problems with confidence and ease
In his popular Basic Maths For Dummies, professional maths tutor Colin Beveridge proved that he could turn anyone – even the most maths-phobic person – into a natural-born number cruncher. In this book he supplies more of his unique brand of maths-made-easy coaching, plus 2,000 practice problems to help you master what you learn. Whether you're prepping for a numeracy test or an employability exam, thinking of returning to school, or you'd just like to be one of those know-it-alls who says, 'Oh, that's easy!' about any maths problem that comes your way, this book is for you.
Master basic arithmetic, fast – in no time, solving addition, subtraction, multiplication and division problems will seem as easy as tying your shoes
Face down fractions – you'll never again feel shy around fractions, decimals, percentages and ratios
Juggle weights and measures like a pro – whether it's a question of how much it weighs, how long (or far) it is, or how much it costs, you'll never be at a loss for an answer
Product Details
About the Author
Colin Beveridge holds a doctorate in mathematics from the University of St Andrews. He gave up a position as a researcher at Montana State University (working with NASA, among other projects) to become a full–time maths tutor, helping adults, GCSE, A–level and university students overcome their fear of maths – a position he finds far more enjoyable than real work.
Get good guidance on using English well English is a hard language to get right.
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Continuing the work started in the highly successful original edition, this revised and updated major
work explores issues relevant to the culturally different in the United States and cuts across all ethnic/racial minorities. It is divided into three parts coveringPregnancy affects the physiology of women as their bodies adapt to the growing life within
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Midterm 1 Sample Solutions Corrections: In question 2 I added incorrectly
in the last row operation. The correct final answer is (-1,1-2). Also, in
question 1 I should have written "pivot position" rather than "pivot."
Midterm 2 Sample Solutions Correction: In problem 2, the output of the
transformation should have been (a0,a1,a2) rather than (a1,a2,a3). I have
fixed this in the version that is currently posted.
We have a discussion forum on Piazza. This is a
good place to ask questions of each other and the TA's. You
can learn a lot by answering other peoples' questions as
well. It is shared with some of the other sections of Math 18.
There are many words in this class that you will need to
understand, so we have a vocabulary list.
The Supplemental Instruction (SI) program holds study
groups focussed on solving problems, and led by an experienced
undergraduate. Our SI leaders are Lana Andreasyan (landreas)
and Kevin Dam (kqdam). Here
is the meeting schedule.
MyMathLab provides review quizzes for every chapter. They
were compiled by the authors of the textbook, not by me, so they sometimes
cover topics that we will skip in this course. Nonetheless they are good practice. They will
not affect your grade in any way.
The math department provides
drop-in MATLAB tutoring. See here
for the schedule. | 677.169 | 1 |
An in-depth examination of the origins of mathematics, beginning with examples of Babylonian mathematics. Topics may include Pythagorean triples, solution of equations, estimation of pi, duplication of the cube, trisection of an angle, the Fibonacci sequence, the origins of calculus.
[Note: Offered in the spring term of odd years.]
Prereq: MATH 135 or 145, 106/125 or 136 or 146, 138 or 148; Level at least 3A; Not open to General Mathematics students | 677.169 | 1 |
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This is an EDITABLE partner activity worksheet with 6 questions and an enrichment section for faster working students to help explore linear functions.
This is meant as an exploration to introduce linear functions with students having no knowledge on the subject. The students must examine definitions, graphs, and equations using devices to access that internet. Graphing calculators help as well.
Then students work on an application problem to bring this information together. | 677.169 | 1 |
This is 5 points worth activity for MATH 470 students. In this activity
you are asked to present in front of your instructor and class mates one
new section from those listed in the table below.
WHAT DO I
HAVE TO DO?
1)Create a PowerPoint
slides for the section. The 1st slide is to include the
chapter title, section title, your name, ID, etc. Please keep in mind
that you have to learn how to use Equation Editor in PowerPoint.
2)Present for 40
minutes the section in front of class.
3)Expect questions
from your instructor or class mates during the remaining 10 minutes.
4)You may distribute
any handouts if applicable.
5)Toward the end of
the class time you have to present a last slide that lists the main
messages the author wanted to deliver in the section. This is like a
brief summary with emphasis on the key elements of knowledge in the
section.
PLEASE
CONSIDER
1)Understanding a
section is unlike explaining it to others. You need to consider a basic
ground of knowledge in you audience. Build on that basic ground until
you reach the section main points.
2)Try to use graphs to
visualize the math to your audience. Remember a picture is worth a
thousand words.
3)Try to use as much
examples as needed. Number examples ease the understanding.
5)Link your section
with the previous section and briefly introduce your class mates to the
next section.
Sec#
Sec Title
Student Name
Presentation Day
5.2
The Weak Maximum Principle
THAMER AL-SAADI
5.3
Solutions on Bounded Intervals
APALARA TIJANI
5.4
The Heat Equation on the Real Line
5.5
The Heat Equation on the Half Line
5.7
The Nonhomogeneous Heat Equation
Date: 3-10-2009
First Day of Class
MATH 470 Partial Differential
Equations (3-0-3) - Course Description
First order quasilinear equations. Lagrange method and Characteristics.
Classification of linear second order PDEs. Brief review of separation
of variables. The one dimensional wave equation: its solution and
characteristics. Cauchy problem for the wave equation. Laplace's
equation: The maximum principle, uniqueness theorems. Green's function.
Neumann's function. The heat equation in one dimension. | 677.169 | 1 |
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Course Description
Description
CTY's Problem Solving courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards and drawing on software provided by Thinkwell, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging homework, quizzes, and chapter tests. A cumulative midterm and final exam help reinforce concepts and gain mastery. With the guidance of their instructors, students typically select enrichment or supplementary math courses of the appropriate level in between their accelerated courses to ensure a solid foundation and mastery of math concepts at each level.
Problem Solving in Pre-algebra prepares students for a more formal study of mathematics in middle school. It is appropriate for students who have a good understanding of concepts in pre-algebra, but who wish to enrich their skills through interesting word problems and applications. Students continue the study of numbers and their operations. Upon successful completion of this course, students will understand topics in:
algebraic concepts
geometry
radicals and exponents
ratios
proportions
statistics
probability
Students apply what they have learned to solve sets of questions at varying levels of difficulty.
This course provides an excellent foundation for students who will be advancing into Honors Algebra I.
Materials Needed
There are no required materials for this course.
List of Topics
Chapter 1: Essentials of Algebra
Evaluating an Algebraic Expression
Variables and Expressions
Simplifying Algebraic Expressions
Equations and Their Solutions
Simplifying Algebraic Expressions
Solving Simple Equations
Solving Addition Equations
Solving Subtraction Equations
Solving Multiplications Equations
Solving Division Equations
Solving with Variables on Both Sides of the Equation
Solving Literal Equations
Translating Between Words and Math
Chapter 2: Fundamentals of Geometry
Geometry Fundamentals
Angles and Their Relationships
Triangles
Volume and Surface Area
Introduction to Three-Dimensional Figures
Volume of Prisms and Cylinders
Surface Area of Prisms and Cylinders
Chapter 3: Radicals and Exponents
Introduction to Radicals and Pythagorean Theorem
Square Roots and the Pythagorean Theorem
Introduction to Scientific Notation
An Application of Exponents: Scientific Notation
Chapter 4: Ratio and Proportion
Ratio
Ratios and Rates
Applying Rates and Ratios
Proportion
Proportions
Direct and Inverse Variation
Direct Variation
Inverse Variation
Similar Polygons
Similar Figures
Chapter 5: Statistics
Interpreting and Constructing Graphs
Line Graphs
Bar Graphs and Histograms
Reading and Interpreting Circle Graphs
The Mean, Median, and Mode
Mean, Median, Mode, and Range
Frequency Distribution and Histograms
Frequency Tables
Bar Graphs and Histograms
Histograms
Chapter 6: Probability
Simple Probability
Introduction to Probability
Probability of Combined Events
Probability of Independent and Dependent Events
Counting Methods and Sample Spaces
Problem Solving Help Room
Help Room
Each week, all students are invited to a Problem Solving Help Room run by a rotating staff of instructors. Students are encouraged to come with questions or just to meet other online students. Topics reviewed vary each week.
The Problem Solving Help Room meets each Tuesday from 7 – 8 p.m. ET.
Sample Video Lecture
Sample Video | 677.169 | 1 |
Compulsory work
A class list is presented at the start of the session, and
every student has to tick off the exercise he/she is prepared
to present.
For each problem a random student is appointed to present
a solution.
The presenting student has to be able to answer questions about
the solution, both from the class and from the teacher.
The solution does not have to be perfect, but is has to be complete
solution presented in good faith.
In the event that a student is caught bluffing, and clearly is not
able to give an adequate solution when called, all ticks for that
session are cancelled. The class will advice on the decision.
To be admitted to the exam, a student has to have ticked at least
40% of the problems. This is weigted so each tutorial session
counts 1/13 of the total.
The low threshold of 40% is considered to give sufficient slack for
sick leave and special circumstances. Mitigating circumstances
will only be considered in extreme cases.
You may collaborate as much as you please when you prepare for the
tutorial. When you present, however, you are each individually
accountable.
Syllabus
The syllabus is defined by the video lectures and exercise sheets.
The exercise sheets are most important. Students who can answer
all the exercise sheets will have little trouble in the exam.
The exam may contain a few questions which have been covered
only by the video lectures, but such questions will make up
only a minor part of the exam.
Prerequisites
The module assumes that you have learnt a few topics from
the common maths module in the first semester (or elsewhere).
Set theory
You should know what a set is.
You should be familiar with common operations on sets.
Functions - what is a function?
Linear algebra
You should be able to
add and multiply (dot product) matrices as well as vectors.
Rules of the game
Mathematics is no more or less difficult than other subjects, but
it takes time and effort to learn.
It is your responsibility to learn, and you have to put hard work into it.
I am here to help, but it is your responsibility to ask for help.
I assume that you ...
Have a reasonable background in mathematics from college
and the first semester (see above).
Use all of the provided learning aids and activities.
Put in the 16-20h per week assumed by the Bologna documents.
Come to the classroom sessions and ask questions.
I, on my part, will ...
Help as best I can in response to questions.
Amend, change, or extend the learning aids where appropriate.
Note that both videos and exercise sheets may be amended during
the semester. Such changes will be announced in the News section
on the web pages.
You should make sure that you are familiar with
the last version of the material before the exam.
Changes will not be made arbitrarily and hopefully not too often;
they will be made to correct errors and ommissions, or to make
the material easier to understand. | 677.169 | 1 |
Vector Spaces and Subspaces
Transcription
1 Chapter 5 Vector Spaces and Subspaces 5. The Column Space of a Matrix To a newcomer, matrix calculations involve a lot of numbers. To you, they involve vectors. The columns of Av and AB are linear combinations of n vectors the columns of A. This chapter moves from numbers and vectors to a third level of understanding (the highest level). Instead of individual columns, we look at spaces of vectors. Without seeing vector spaces and their subspaces, you haven t understood everything about Av D b. Since this chapter goes a little deeper, it may seem a little harder. That is natural. We are looking inside the calculations, to find the mathematics. The author s job is to make it clear. Section 5.5 will present the Fundamental Theorem of Linear Algebra. We begin with the most important vector spaces. They are denoted by R, R, R 3, R 4, : : :. Each space R n consists of a whole collection of vectors. R 5 contains all column vectors with five components. This is called 5-dimensional space. DEFINITION The space R n consists of all column vectors v with n components. The components of v are real numbers, which is the reason for the letter R. When the n components are complex numbers, v lies in the space C n. The vector space R is represented by the usual xy plane. Each vector v in R has two components. The word space asks us to think of all those vectors the whole plane. Each vector gives the x and y coordinates of a point in the plane : v D.x; y/. Similarly the vectors in R 3 correspond to points.x; y; z/ in three-dimensional space. The one-dimensional space R is a line (like the x axis). As before, we print vectors as a column between brackets, or along a line using commas and parentheses : 4 C i is in R ;.; ; ; ; / is in R 5 ; is in C i : The great thing about linear algebra is that it deals easily with five-dimensional space. We don t draw the vectors, we just need the five numbers (or n numbers).
2 5 Chapter 5. Vector Spaces and Subspaces To multiply v by 7, multiply every component by 7. Here 7 is a scalar. To add vectors in R 5, add them a component at a time : five additions. The two essential vector operations go on inside the vector space, and they produce linear combinations : We can add any vectors in R n, and we can multiply any vector v by any scalar c. Inside the vector space means that the result stays in the space : This is crucial. If v is in R 4 with components ; ; ;, then v is the vector in R 4 with components ; ; ;. (In this case is the scalar.) A whole series of properties can be verified in R n. The commutative law is v C w D w C v; the distributive law is c.v C w/ D cv C cw. Every vector space has a unique zero vector satisfying Cv D v. Those are three of the eight conditions listed in the Chapter 5 Notes. These eight conditions are required of every vector space. There are vectors other than column vectors, and there are vector spaces other than R n. All vector spaces have to obey the eight reasonable rules. A real vector space is a set of vectors together with rules for vector addition and multiplication by real numbers. The addition and the multiplication must produce vectors that are in the space. And the eight conditions must be satisfied (which is usually no problem). You need to see three vector spaces other than R n : M Y Z The vector space of all real by matrices. The vector space of all solutions y.t/ to Ay C By C Cy D. The vector space that consists only of a zero vector. In M the vectors are really matrices. In Y the vectors are functions of t, like y D e st. In Z the only addition is C D. In each space we can add : matrices to matrices, functions to functions, zero vector to zero vector. We can multiply a matrix by 4 or a function by 4 or the zero vector by 4. The result is still in M or Y or Z. The space R 4 is four-dimensional, and so is the space M of by matrices. Vectors in those spaces are determined by four numbers. The solution space Y is two-dimensional, because second order differential equations have two independent solutions. Section 5.4 will pin down those key words, independence of vectors and dimension of a space. The space Z is zero-dimensional (by any reasonable definition of dimension). It is the smallest possible vector space. We hesitate to call it R, which means no components you might think there was no vector. The vector space Z contains exactly one vector. No space can do without that zero vector. Each space has its own zero vector the zero matrix, the zero function, the vector.; ; / in R 3. Subspaces At different times, we will ask you to think of matrices and functions as vectors. But at all times, the vectors that we need most are ordinary column vectors. They are vectors with n components but maybe not all of the vectors with n components. There are important vector spaces inside R n. Those are subspaces of R n.
3 5.. The Column Space of a Matrix 53 z R 3 P.; ; / L y Figure 5.: 4-dimensional matrix space M. 3 subspaces of R 3 : plane P, line L, point Z. x Start with the usual three-dimensional space R 3. Choose a plane through the origin.; ; /. That plane is a vector space in its own right. If we add two vectors in the plane, their sum is in the plane. If we multiply an in-plane vector by or 5, it is still in the plane. A plane in three-dimensional space is not R (even if it looks like R /. The vectors have three components and they belong to R 3. The plane P is a vector space inside R 3. This illustrates one of the most fundamental ideas in linear algebra. The plane going through.; ; / is a subspace of the full vector space R 3. DEFINITION A subspace of a vector space is a set of vectors (including ) that satisfies two requirements : If v and w are vectors in the subspace and c is any scalar, then (i) v C w is in the subspace and (ii) cv is in the subspace. In other words, the set of vectors is closed under addition v C w and multiplication cv (and d w). Those operations leave us in the subspace. We can also subtract, because w is in the subspace and its sum with v is v w. In short, all linear combinations cv C dw stay in the subspace. First fact : Every subspace contains the zero vector. The plane in R 3 has to go through.; ; /. We mention this separately, for extra emphasis, but it follows directly from rule (ii). Choose c D, and the rule requires v to be in the subspace. Planes that don t contain the origin fail those tests. When v is on such a plane, v and v are not on the plane. A plane that misses the origin is not a subspace. Lines through the origin are also subspaces. When we multiply by 5, or add two vectors on the line, we stay on the line. But the line must go through.; ; /. Another subspace is all of R 3. The whole space is a subspace (of itself ). That is a fourth subspace in the figure. Here is a list of all the possible subspaces of R 3 :.L/ Any line through.; ; /.R 3 / The whole space.p/ Any plane through.; ; /.Z/ The single vector.; ; /
4 54 Chapter 5. Vector Spaces and Subspaces If we try to keep only part of a plane or line, the requirements for a subspace don t hold. Look at these examples in R. Example Keep only the vectors.x; y/ whose components are positive or zero (this is a quarter-plane). The vector.; 3/ is included but. ; 3/ is not. So rule (ii) is violated when we try to multiply by c D. The quarter-plane is not a subspace. Example Include also the vectors whose components are both negative. Now we have two quarter-planes. Requirement (ii) is satisfied; we can multiply by any c. But rule (i) now fails. The sum of v D.; 3/ and w D. 3; / is. ; /, which is outside the quarter-planes. Two quarter-planes don t make a subspace. Rules (i) and (ii) involve vector addition v C w and multiplication by scalars like c and d. The rules can be combined into a single requirement the rule for subspaces : A subspace containing v and w must contain all linear combinations cv C dw. Example 3 Inside the vector space M of all by matrices, here are two subspaces : a b a.u/ All upper triangular matrices.d/ All diagonal matrices : d d Add any two matrices in U, and the sum is in U. Add diagonal matrices, and the sum is diagonal. In this case D is also a subspace of U! The zero matrix alone is also a subspace, when a, b, and d all equal zero. For a smaller subspace of diagonal matrices, we could require a D d. The matrices are multiples of the identity matrix I. These ai form a line of matrices in M and U and D. Is the matrix I a subspace by itself? Certainly not. Only the zero matrix is. Your mind will invent more subspaces of by matrices write them down for Problem 6. The Column Space of A The most important subspaces are tied directly to a matrix A. We are trying to solve Av D b. If A is not invertible, the system is solvable for some b and not solvable for other b. We want to describe the good right sides b the vectors that can be written as A times v. Those b s form the column space of A. Remember that Av is a combination of the columns of A. To get every possible b, we use every possible v. Start with the columns of A, and take all their linear combinations. This produces the column space of A. It contains not just the n columns of A! DEFINITION The column space consists of all combinations of the columns: The combinations are all possible vectors Av. They fill the column space C.A/. This column space is crucial to the whole book, and here is why. To solve Av D b is to express b as a combination of the columns. The right side b has to be in the column space produced by A on the left side. If b is not in C.A/, Av D b has no solution.
5 5.. The Column Space of a Matrix 55 The system Av D b is solvable if and only if b is in the column space of A. When b is in the column space, it is a combination of the columns. The coefficients in that combination give us a solution v to the system Av D b. Suppose A is an m by n matrix. Its columns have m components (not n/. So the columns belong to R m. The column space of A is a subspace of R m (not R n ). The set of all column combinations Ax satisfies rules (i) and (ii) for a subspace : When we add linear combinations or multiply by scalars, we still produce combinations of the columns. The word subspace is always justified by taking all linear combinations. Here is a 3 by matrix A, whose column space is a subspace of R 3. The column space of A is a plane in Figure b A D b D v 445 C v Plane D C.A/ D all vectors Av Figure 5.: The column space C.A/ is a plane containing the two columns of A. Av D b is solvable when b is on that plane. Then b is a combination of the columns. We drew one particular b (a combination of the columns). This b D Av lies on the plane. The plane has zero thickness, so most right sides b in R 3 are not in the column space. For most b there is no solution to our 3 equations in unknowns. Of course.; ; / is in the column space. The plane passes through the origin. There is certainly a solution to Av D. That solution, always available, is v D. To repeat, the attainable right sides b are exactly the vectors in the column space. One possibility is the first column itself take v D and v D. Another combination is the second column take v D and v D. The new level of understanding is to see all combinations the whole subspace is generated by those two columns. Notation The column space of A is denoted by C.A/. Start with the columns and take all their linear combinations. We might get the whole R m or only a small subspace.
6 56 Chapter 5. Vector Spaces and Subspaces Important Instead of columns in R m, we could start with any set of vectors in a vector space V. To get a subspace SS of V, we take all combinations of the vectors in that set : S D set of vectors s in V (S is probably not a subspace) SS D all combinations of vectors in S (SS is a subspace) SS D all c s C C c N s N D the subspace of V spanned by S When S is the set of columns, SS is the column space. When there is only one nonzero vector v in S, the subspace SS is the line through v. Always SS is the smallest subspace containing S. This is a fundamental way to create subspaces and we will come back to it. The subspace SS is the span of S, containing all combinations of vectors in S. Example 4 Describe the column spaces (they are subspaces of R ) for these matrices : 3 I D and A D and B D : 4 4 Solution The column space of I is the whole space R. Every vector is a combination of the columns of I. In vector space language, C.I/ equals R. The column space of A is only a line. The second column.; 4/ is a multiple of the first column.; /. Those vectors are different, but our eye is on vector spaces. The column space contains.; / and.; 4/ and all other vectors.c; c/ along that line. The equation Av D b is only solvable when b is on the line. For the third matrix (with three columns) the column space C.B/ is all of R. Every b is attainable. The vector b D.5; 4/ is column plus column 3, so v can be.; ; /. The same vector.5; 4/ is also (column ) C column 3, so another possible v is.; ; /. This matrix has the same column space as I any b is allowed. But now v has extra components and Av D b has more solutions more combinations that give b. The next section creates the nullspace N.A/, to describe all the solutions of Av D. This section created the column space C.A/, to describe all the attainable right sides b. REVIEW OF THE KEY IDEAS. R n contains all column vectors with n real components.. M ( by matrices) and Y (functions) and Z (zero vector alone) are vector spaces. 3. A subspace containing v and w must contain all their combinations cv C d w. 4. The combinations of the columns of A form the column space C.A/. Then the column space is spanned by the columns.
7 5.. The Column Space of a Matrix Av D b has a solution exactly when b is in the column space of A. WORKED EXAMPLES 5. A We are given three different vectors b ; b ; b 3. Construct a matrix so that the equations Av D b and Av D b are solvable, but Av D b 3 is not solvable. How can you decide if this is possible? How could you construct A? Solution We want to have b and b in the column space of A. Then Av D b and Av D b will be solvable. The quickest way is to make b and b the two columns of A. Then the solutions are v D.; / and v D.; /. Also, we don t want Av D b 3 to be solvable. So don t make the column space any larger! Keeping only the columns b and b, the question is : Do we already have b 3? Is Av D b b v D b v 3 solvable? Is b 3 a combination of b and b? If the answer is no, we have the desired matrix A. If b 3 is a combination of b and b, then it is not possible to construct A. The column space C.A/ will have to contain b 3. 5: B Describe a subspace S of each vector space V, and then a subspace SS of S. V 3 D all combinations of.; ; ; / and.; ; ; / and.; ; ; / V D all vectors v perpendicular to u D.; ; /; so u v D V 4 D all solutions y.x/ to the equation d 4 y=dx 4 D Describe each V two ways : () All combinations of.... () All solutions of.... Solution V 3 starts with three vectors. A subspace S comes from all combinations of the first two vectors.; ; ; / and.; ; ; /. A subspace SS of S comes from all multiples.c; c; ; / of the first vector. So many possibilities. A subspace S of V is the line through.; ; /. This line is perpendicular to u. The zero vector z D.; ; / is in S. The smallest subspace SS is Z. V 4 contains all cubic polynomials y D a C bx C cx C dx 3, with d 4 y=dx 4 D. The quadratic polynomials (without an x 3 term) give a subspace S. The linear polynomials are one choice of SS. The constants y D a could be SSS. In all three parts we could take S D V itself, and SS D the zero subspace Z. Each V can be described as all combinations of.... and as all solutions of.... : V 3 D all combinations of the 3 vectors V 3 D all solutions of v v D : V D all combinations of.; ; / and.; ; / V D all solutions of u v D : V 4 D all combinations of ; x; x ; x 3 V 4 D all solutions to d 4 y=dx 4 D :
8 58 Chapter 5. Vector Spaces and Subspaces Problem Set 5. Questions are about the subspace requirements : v C w and cv (and then all linear combinations cv C d w) stay in the subspace. One requirement can be met while the other fails. Show this by finding (a) A set of vectors in R for which v C w stays in the set but v may be outside. (b) A set of vectors in R (other than two quarter-planes) for which every cv stays in the set but v C w may be outside. Which of the following subsets of R 3 are actually subspaces? (a) The plane of vectors.b ; b ; b 3 / with b D b. (b) The plane of vectors with b D. (c) The vectors with b b b 3 D. (d) All linear combinations of v D.; 4; / and w D.; ; /. (e) All vectors that satisfy b C b C b 3 D. (f) All vectors with b b b 3. 3 Describe the smallest subspace of the matrix space M that contains (a) and (b) (c) and 4 Let P be the plane in R 3 with equation x C y z D 4. The origin.; ; / is not in P! Find two vectors in P and check that their sum is not in P. 5 Let P be the plane through.; ; / parallel to the previous plane P. What is the equation for P? Find two vectors in P and check that their sum is in P. 6 The subspaces of R 3 are planes, lines, R 3 itself, or Z containing only.; ; /. (a) Describe the three types of subspaces of R. (b) Describe all subspaces of D, the space of by diagonal matrices. 7 (a) The intersection of two planes through.; ; / is probably a but it could be a. It can t be Z! (b) The intersection of a plane through.; ; / with a line through.; ; / is probably a but it could be a. (c) If S and T are subspaces of R 5, prove that their intersection S \ T is a subspace of R 5. Here S \ T consists of the vectors that lie in both subspaces. Check the requirements on v C w and cv. 8 Suppose P is a plane through.; ; / and L is a line through.; ; /. The smallest vector space P C L containing both P and L is either or..
9 5.. The Column Space of a Matrix 59 9 (a) Show that the set of invertible matrices in M is not a subspace. (b) Show that the set of singular matrices in M is not a subspace. True or false (check addition in each case by an example) : (a) The symmetric matrices in M (with A T D A/ form a subspace. (b) The skew-symmetric matrices in M (with A T D A/ form a subspace. (c) The unsymmetric matrices in M (with A T A/ form a subspace. Questions 9 are about column spaces C.A/ and the equation Av D b. Describe the column spaces (lines or planes) of these particular matrices : A D 4 5 B D 4 5 C D 4 5 : For which right sides (find a condition on b ; b ; b 3 ) are these systems solvable? (a) v 3 v 5 D 4 b 3 b 5 (b) v D 4 b 3 b v v 3 b 3 3 Adding row of A to row produces B. Adding column to column produces C. Which matrices have the same column space? Which have the same row space? A D and B D and C D : For which vectors.b ; b ; b 3 / do these systems have a solution? x 3 x 5 D 4 b 3 b 5 and x 3 x 5 D 4 b 3 b 5 x 3 b 3 x 3 b 3 and x 3 x 5 D 4 b 3 b 5 : x 3 b 3 5 (Recommended) If we add an extra column b to a matrix A, then the column space gets larger unless. Give an example where the column space gets larger and an example where it doesn t. Why is Av D b solvable exactly when the column space doesn t get larger? Then it is the same for A and A b. 6 The columns of AB are combinations of the columns of A. This means : The column space of AB is contained in (possibly equal to) the column space of A. Give an example where the column spaces of A and AB are not equal. b 3
10 6 Chapter 5. Vector Spaces and Subspaces 7 Suppose Av D b and Aw D b are both solvable. Then Az D b C b is solvable. What is z? This translates into : If b and b are in the column space C.A/, then b C b is also in C.A/. 8 If A is any 5 by 5 invertible matrix, then its column space is. Why? 9 True or false (with a counterexample if false) : (a) The vectors b that are not in the column space C.A/ form a subspace. (b) If C.A/ contains only the zero vector, then A is the zero matrix. (c) The column space of A equals the column space of A. (d) The column space of A I equals the column space of A (test this). Construct a 3 by 3 matrix whose column space contains.; ; / and.; ; / but not.; ; /. Construct a 3 by 3 matrix whose column space is only a line. If the 9 by system Av D b is solvable for every b, then C.A/ must be. Challenge Problems Suppose S and T are two subspaces of a vector space V. The sum S C T contains all sums s C t of a vector s in S and a vector t in T. Then S C T is a vector space. If S and T are lines in R m, what is the difference between S C T and S [ T? That union contains all vectors from S and all vectors from T. Explain this statement : The span of S [ T is S C T. 3 If S is the column space of A and T is C.B/, then S C T is the column space of what matrix M? The columns of A and B and M are all in R m. (I don t think A C B is always a correct M.) 4 Show that the matrices A and A AB (this has extra columns) have the same column space. But find a square matrix with C.A / smaller than C.A/. 5 An n by n matrix has C.A/ D R n exactly when A is an matrix.Linear Algebra Notes for Marsden and Tromba Vector Calculus n-dimensional Euclidean Space and Matrices Definition of n space As was learned in Math b, a point in Euclidean three space can be thought of
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Vector Spaces 4.4 and Independence October 18 Goals Discuss two important basic concepts: Define linear combination of vectors. Define Span(S) of a set S of vectors. Define linear Independence of a setMatrix Representations of Linear Transformations and Changes of Coordinates 01 Subspaces and Bases 011 Definitions A subspace V of R n is a subset of R n that contains the zero element and is closed underImages and Kernels in Linear Algebra By Kristi Hoshibata Mathematics 232 In mathematics, there are many different fields of study, including calculus, geometry, algebra and others. Mathematics has been
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How to learn Calculus, and Its tips
Calculus is a branch of mathematics that developed from algebra and geometry. Studying calculus associated with the speed or degree of movement, such as acceleration, and the slope of the curve. The development is supported by Archimides calculus, Leibniz, Newton, Barrow, Descartes, de Fermat, Huygens, and Wallis. The basis of the calculus of derivatives, integrals, and the limit. One of the main objectives for the development of calculus is the tangent line problem-solving.
on the topic of calculus has been implemented in the early period of the 17th. Sir Isaac Newton and Gottfried Wilhelm Leibniz has run a investigation and has provided the largest contribution in the study. Sir Isaac Newton investigation began when the University of Cambridge closed in 1665 which led to his forced return to their places of origin of Lincolnshire.
During 18 months there, he has created 'Method of Fluxions', graviti theory and the theory of light. Furthermore with the creation of these theories, he has written a book entitled 'De Methodist Serierum et Fluxionum' in the year 1671. However, Sir Isaac Newton had failed to publish the book. The book was not published so that John Colson triumphed publish the English version in 1736. While writing the book after Sir Isaac Newton did not have the symbols and formulas.
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Linear Algebra (Chapters 4-7 in Anton-Rorres' book). Euclidean n-Space and n-Vectors, Operations with them. Linear Transformations and their Matrices. Subspaces. Linear Combinations of Vectors. Subspaces spanned by a Set of Vectors. Linear Independence of a Set of Vectors. Basis and Dimension. Standard Basis in n-space. Coordinates of Vectors relative to a Basis. General and Particular Solutions for a Linear System. Row, Column and Nullspace of a Matrix. Finding Bases for them using Elementary Row Operations. Rank and Nullity of a Matrix. Inner Products, Lengths, Distances and Angles relative to them. Orthogonal and Orthonormal Bases relative to an Inner Product. Orthogonal projections to Subspaces. Gram-Schmidt Process (see Example 7 in Chapter 6.3). Eigenvalues and Eigenvectors of Square Matrices.
Fourier Analysis (Chapter 10 in Kreyszig' book). Fourier Series for periodic functions. Euler Formulas for the Fourier Coefficients. Even and Odd Functions. Fourier Cosine and Fourier Sine Series for them. Fourier Integral and Fourier Transform. | 677.169 | 1 |
Nothing like a good criminal investigation to liven up math class!
CSI: Algebra is a collection of nine different algebraically inspired mathematical puzzles with a little international pizazz. The nine puzzles intend to target specific Algebra 1 units and add a little flair to the ordinary challenPre-algebra CSI math activity - King Arthur: Who stole Excalibur? Use math to find out!
King Arthur needs your help! Someone has stolen Excalibur - and without it, his kingdom will fall into ruin.
Five clues have been found throughout the kingdom. Give these clues to your students and each clue (wHere's a real life CSI application of algebra for your students....
Students have to solve a murder investigation using formulae (writing and substituting). They have to gather evidence at three locations: the crime scene, mortuary and forensic laboratory. Once they have collected their evidence,
Here's a real life CSI application of algebra for your students....
There has been a suspicious death. Using their knowledge of formulae and quadratic equations, students have to gather evidence from the crime scene and mortuary to determine (1) who was with the victim moments before death and (2)
Here's a real life crime scene application of algebra and statistics for your students....
Human skeletal remains have been found on a construction site. Most of the bones have been crushed leaving only a pelvis, femur and tooth for students to examine. Students must identify who the remains belong
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Solving Multi-Step Equations 'Math Clues':
This CSI-style game is inspired by the original Clue board game. Students work in small groups as they review solving multi-step equations. Student will solve the equations in order to collect clues. They will then use dedu
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Nothing like a good criminal investigation to liven up math class!
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Calculation of vector components: A tutorial worksheet to help students develop a conceptual framework
Abstract:
When we administered our Test of Understanding of Vectors (TUV) to students who were finishing a physics university remedial course (that covers subjects of a traditional high school physics course), we observed that they have considerable difficulties in calculating the x-component of a vector when the angle given is measured from the y-axis to the vector. As a result of this finding, we decided to design a tutorial worksheet that guides students through the development of a conceptual framework in this subject. The worksheet was implemented with 264 students of the same course in another semester. Upon using the TUV to evaluate the students' understanding, we confirmed that the tutorial worksheet had facilitated their learning. This tutorial worksheet is presented in the appendix and might be used by other physics instructors who teach this material in high schools, colleges or universities. | 677.169 | 1 |
Affine geometry and quadrics are interesting topics by myself, yet also they are vital purposes of linear algebra. they offer a primary glimpse into the realm of algebraic geometry but they're both suitable to quite a lot of disciplines reminiscent of engineering.
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Affinities, Euclidean Motions and Quadrics takes rudimentary, and infrequently taken-for-granted, wisdom and offers it in a brand new, accomplished shape. typical and non-standard examples are validated all through and an appendix offers the reader with a precis of complex linear algebra proof for speedy connection with the textual content. All elements mixed, this can be a self-contained publication perfect for self-study that isn't merely foundational yet distinct in its approach.'
This textual content might be of use to academics in linear algebra and its purposes to geometry in addition to complicated undergraduate and starting graduate scholars.
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Here's a textbook of intuitive calculus. the cloth is gifted in a concrete surroundings with many examples and difficulties selected from the social, actual, behavioural and lifestyles sciences. Chapters comprise center fabric and extra complex non-compulsory sections. The e-book starts with a evaluate of algebra and graphing.
Topology is the mathematical examine of the main simple geometrical constitution of an area. Mathematical physics makes use of topological areas because the formal capability for describing actual house and time. This e-book proposes a totally new mathematical constitution for describing geometrical notions comparable to continuity, connectedness, limitations of units, and so forth, with a purpose to offer a greater mathematical software for knowing space-time.
An−r,1 x1 + · · · + an−r,n xn = bn−r . This is the linear system of n − r equations, n unknowns and rank n − r satisfied by the coordinates x1 , . . , xn of the points of L. The argument proving that this system has rank n − r is the same as that used in the above proof. 6), in the sense that they have the same solutions. The equations given by the linear system AX = B are known as Cartesian equations of the linear variety. Since the systems AX = B and CAX = CB, where C is an invertible matrix, have the same solutions, it is clear that Cartesian equations of a linear variety are not unique.
Moreover, it is the only point satisfying it. To see this let us assume that G satisfies −−−→ −−−→ G P1 + · · · + G Pr = 0. Then −−→ −−→ −−→ −−→ (G G + GP1 ) + · · · + (G G + GPr ) = 0. −−→ Hence, rG G = 0, and so G = G . 28 1. Affine Spaces It is now clear that the role played by P1 in the definition of barycenter can be played by any of the points Pi , i = 1, . . , r. That is, we also have −−→ 1 −−→ G = Pi + (Pi P1 + · · · + Pi Pr ). r The barycenter of two points is called the midpoint between them. | 677.169 | 1 |
Effect of using mathematics teaching aids in teaching mathematics on the achievement of mathematics students
NAME: OGUNSHOLA STEPHEN ADESHINA
MATRIC NO : 081004105
SUPERVISOR: MR OPARA
CHAPTER ONE: INTRODUCTION
1.1 Background to the Study
Mathematics is the foundation of science and technology and the functional role of mathematics to science and technology is multifaceted and multifarious that no area of science, technology and business enterprise escapes its application (Okereke, 2006). Ukeje (1986) described mathematics as the mirror of civilization in all the centuries of painstaking calculation, and the most basic discipline for any person who would be truly educated in any science and in many other endeavours. Despite the importance placed on mathematics, researchers (Odili, 1986; Salau, 1995; Amazigo, 2000; Agwagah, 2001; Betiku, 2001; bioma, 2005; Maduabum and Odili, 2006; Okereke, 2006) had observed that students lack interest in the subject and perform poorly in it. Ukeje (1986) observed that mathematics is one of the most poorly taught, widely hated and abysmally under-stood subject in secondary school, students particularly girls run away from the subject. The West African Examination Council (WAEC) Chief Examiners [2003, 2004, 2005, and 2006] consistently reported candidates' lack of skill in answering almost all the questions asked in general mathematics. WAEC Chief Examiners [2003, 2005] further observed that candidates were weak in Geometry of circles and 3- dimensional problems. According to their reports, most candidates avoided questions on 3-dimensional problem, when they attempt geometry questions; only few of the candidates showed a clear understanding of the problem in their working. WAEC [2004] also reported candidates' weakness in Algebraic expression and word problems among others. Obioma (1985), Obodo (1993) and Okereke (2006) reported gender as a significant factor in mathematics...
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...Teaching is a challenging job, whether you are in charge of a traditional public school classroom or tutoring a single child in a language. Fortunately, there are many aids and accessories available to make the job easier. Though some cost money, others are available for free or easily manufactured from household items or on your computer.
Worksheets
* Worksheets are handouts the students complete to practice their skills. They give the students a chance to get further repetition without taking the teacher's full-time attention. While all students complete their worksheets, the teacher can focus on the individual students who need the most help. Worksheets are also a common form of homework assignment. A student's performance on worksheets can also be used to gauge the student's progress on that particular subject.
Textbooks
* Textbooks are books containing information about a particular subject, organized in a manner calculated to make presenting the information easier. Teachers can read a textbook to confirm or expand their personal knowledge and/or assign readings from a textbook for students to complete. Many textbooks also include quizzes or review questions to help assess how well students have comprehended what they have read. Publishing companies often release matched pairs of textbooks with workbooks (books full of worksheets) on the same subject matter.
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Realia
* Realia are artifacts from the...
...The Impacts of TeachingAids usage on secondary school students' performance in biology: a study of some selected senior secondary school in Yewa South Local government area.
CHAPTER ONE
INTRODUCTION
1. Background to the study
The teaching of Biology to make understanding of the students has been what teachers of the subject find difficult to do. Even as cases may arise when these teachers are not happy about their students' performance in the subject, not many of them have sat down to find out where the problem lies. (Robert, 2009) The few who have endeavored to sleep over the problems in order to proffer solutions have always seen the problems outside themselves despite the fact that there is a lot they can do to make students learn without tears. The teachers have attached the poor performance of students in biology to several factors. Among these factors are:
(a) Students poor knowledge of integrated science
b) The attitude of the students to the subject
c) Lack of good text books
d) Lack of standard laboratory (Taiwo, 1982).
What they have failed to do is trace or tries to view the problems from the perspective of their own performance. It cannot be over stressed that teaching requires a great deal of dedication on the part of the teacher. According to Edun (2003) in his article on "Teaching and Teachers" stressed that "Those who come intoousing followingplayers in the learning process (UNICEF, 2004).Children are the world's most valuable resource as future leaders, they are our future. Nigeria National Policy on education laid emphasis on the quality of education at the primary level and achieving the best educators and curriculum planner, searching for possible ways of making learning more internalizing to students. Teaching has passed from using traditional methods to scientific methods. (Avello 2005)
As policy makers and educational leaders today, we will discuss what we need to change in our education system, though some people see this change as neglecting the core content which is a misconception. The 21st century learning has changed in the way we teach core subjects. The emphasis is on making connections between past experiences and instructions. All these are ideas embedded in 21st century learning without replacing or de-emphasizing the core content. (Becta 2003) In the 25 years since Education 2000 was founded at what might be considered the forerunner of 21st century learning movement, educators have come to place a greater emphasis on basic teaching for students to learn. In the past, classroom focused on content and knowledge while that focus still remains, educators have embraced the idea that teachers should have interactive strategies as such strategies bring new tasks. Children are being given information and communication skills in the classroom. They are being.... | 677.169 | 1 |
69Books a la Carte are unbound, three-hole-punch versions of the textbook. This lower cost option is easy to transport and comes with same access code or media that would be packaged with the bound book.
The Sullivan/Struve/Mazzarella Algebraprogram is designed to motivate students to "do the math"— at home or in the lab—and supports a variety of learning environments. The text is known for its two-column example format that provides annotations to the left of the algebra. These annotations explain what the authors are about to do in each step (instead of what was just done), just as an instructor would do. | 677.169 | 1 |
Hi, I am a freshman in high school and I am having trouble with my homework. One of my problems is dealing with add to word problems; can anyone help me understand what it is all about? I need to complete this asap. Thanks for helping.
Yep May God save us students from the evil of add to word problems. I used to face same problems that you do when I was there. I always used to be confused in Remedial Algebra, Pre Algebra and Basic Math. I was worst in add to word problems until I came to know of Algebra Helper. It is really nice and I would definitely recommend it. The best part of the software is that it will also help you learn algebra and not just give your answers. I found Algebra Helper effective and am sure it will help you too. Enjoy!
Yeah! I agree with you! The money back guarantee that comes with the purchase of Algebra Helper is one of the attractive options. In case you are dissatisfied with the assistance offered to you on any math topic, you can get a refund of the payment you made towards the purchase of Algebra Helper within the number of days specified on the label. Do take a look at before you place the order because that gives a lot of information about the topics on which you can expect to get assisted.
binomials, subtracting fractions and relations were a nightmare for me until I found Algebra Helper, which is truly the best algebra program that I have ever come across. I have used it through several algebra classes – Basic Math, Basic Math and College Algebra. Just typing in the algebra | 677.169 | 1 |
Math Center Level 1 Informations
Publisher's Description:
Math software for students studying precalculus
Math Center Level 1 consists of Graphing calculator 2D, Advanced Calculator, and Simple Calculator called from the Control Panel.
Simple calculator is a general purpose calculator which combines use simplicity and calculation power. It handles simple arithmetic operations and complex formulas.
The Simple Calculator has three windows or boxes: Edit Window, Result Window, and History Window. In the Edit Window you enter formulas using buttons and keyboard. When you use a keyboard, you can use all standard rules of text editing. The most convenient is use of numerical pad on the right of standard keyboard. Buttons also provides full functionality of Simple Calculator. If you mistake in typing formula, like square root of a negative number, you just get a message in the Result Window that the formula is unclear. The Simple Calculator tries to handle all possible ambiguities, following the standard mathematical rules. For example, formula 3/-4 - 5^2 will be treated as 3/(-4) - (5^2) . If you want to be completely sure in the result, use parentheses.
Advanced Calculator is a step farther in complexity comparing to the Simple Calculator. The Advanced Calculator has two editing windows. One is for editing x, and the second is for editing f(x). In the x window you | 677.169 | 1 |
Astronomy For Dummies, 4th Edition by Stephen P. Maran English | September 5th, 2017 | ISBN: 1119374243, 9781119374244 | 395 Pages | True PDF | 21.74 MB Do you know the difference between a red giant and a white dwarf? From asteroids to black holes, this easy-to-understand guide takes you on a grand tour of the universe. Featuring updated star maps, charts, and an insert with gorgeous full-color photographs, Astronomy For Dummies provides an easy-to-follow introduction to exploring the night sky. Plus, this new edition also comes with chapter quizzes online to help your understanding.
Abstract Algebra, Second Edition By Pierre Antoine Grillet English | PDF | 2007 | 684 Pages | ISBN : 0387715673 | 7.66 MB "Abstract Algebra" is a clearly written, self-contained basic algebra text for graduate students, with a generous amount of additional material that suggests the scope of contemporary algebra. The first chapters blend standard contents with a careful introduction to proofs with arrows. The last chapters, on universal algebras and categories, including tripleability, give valuable general views of algebra. There are over 1400 exercises, at varying degrees of difficulty edit the spacing in font sets, and much more.
Provision virtual desktops and applications on a single platform Turn your desktop into a secure digital workspaces are available upon request. Optimize the management of the rights and functions to end users: provides a virtual or remote computers and applications via a single VDI and application virtualization platform. | 677.169 | 1 |
Feedback HOW TO MEMORIZE FORMULAS IN MATHEMATICS: Book-1 Calculus Rajesh Sarswat To learn a large number of formulas in Mathematics is the most tricky part. This book provides easy tricks to learn formulas in Calculus for students. Kindle Edition $
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Editorial Reviews
About the Author
Martha R. Taylor has been teaching biology for more than 35 years. She earned her . in biology from Gettysburg College and her . and . with students in classrooms, in laboratories, and with tutorials has increased her commitment to helping students create their own knowledge of and appreciation for biology. She was the author of the Student Study Guide for ten editions of Campbell Biology. | 677.169 | 1 |
Organized into 12 chapters, this book begins with an overview of stability conditions for numerical methods that can be expressed in the form that some associated function is positive. This text then examines the polynomial approximation theory having applications to finite element Galerkin methods. Other chapters consider the numerical condition of polynomials by examining three particular problem areas, namely, the representation of polynomials, algebraic equations, and the problem of orthogonalization. This book discusses as well a general theory that leads to a systematic way to prepare the initial data. The final chapter deals with the derivation of the Kronecker canonical form.
This book is a valuable resource for applied mathematicians, numerical analysts, physicists, engineers, and research workers.
Table of Contents
Contributors
Preface
Positive Functions and Some Applications to Stability Questions for Numerical Methods
Constructive Polynomial Approximation in Sobolev Spaces
Questions of Numerical Condition Related to Polynomials
Global Homotopies and Newton Methods
Problems with Different Time Scales
Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations
Finite Element Approximations to the One-Dimensional Stefan Problem
The Hodie Method and Its Performance for Solving Elliptic Partial Differential Equations
Solving ODE's with Discrete Data in SPEAKEASY
Perturbation Theory for the Generalized Eigenvalue Problem
Some Remarks on Good, Simple, and Optimal Quadrature Formulas
Linear Differential Equations and Kronecker's Canonical Form
Index | 677.169 | 1 |
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Answers for level up maths homework book
Welcome to Babylon Floral Design, Denver's most unique flower boutique, specializing in cutting edge floral design and unique gift items! Cool Math has free online cool math lessons, cool math games and fun math activities. Ally clear math lessons (pre algebra, algebra, precalculus), cool math. support writing a business plan By Fatih Eroglu Its been a week and boxing fans witnessed a great match between Gennady Golovkin and Daniel Jacobs at Madison Square Garden in New York City. Strive to provide the. Ny people try to study for math in the same way they would study for a history exam : by simply memorizing formulas and equations. How to Study for a Math Exam.
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X and the City , a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through... more...
Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an... more...
Whether discussing habitat placement for the northern spotted owl or black-tailed prairie dog or strategies for controlling exotic pests, this book explains how capturing ecological relationships across a landscape with pragmatic optimization models can be applied to real world problems. Using linear programming, Hof and Bevers show how it is possible... more...
In a straightforward and approachable manner, this book introduces complementarity models, and uses them to carry out an in-depth analysis of energy markets, including formulation issues and solution techniques. more...
The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications... more...
The new edition of Mathematical Modeling , the survey text of choice for mathematical modeling courses, adds ample instructor support and online delivery for solutions manuals and software ancillaries. From genetic engineering to hurricane prediction, mathematical models guide much of the decision making in our society. If the assumptions and... more...
Due to an ever-decreasing supply in raw materials and stringent constraints on conventional energy sources, demand for lightweight, efficient and low-cost structures has become crucially important in modern engineering design. This requires engineers to search for optimal and robust design options to address design problems that are commonly large... more...
The 9th Belgian-French-German Conference on Optimization has been held in Namur (Belgium) on September 7-11, 1998. This volume is a collection of papers presented at this Conference. Originally, this Conference was a French-German Conference but this year, in accordance with the organizers' wishes, a third country, Belgium, has joined the founding... more... | 677.169 | 1 |
MATH-470 History of Mathematics (3)
This course surveys aspects of historical development of mathematics from ancient to modern times and examines the ideological, social, and cultural forces which shaped this development. By providing historical continuity, the course interrelates and unifies the major subject areas such as algebra, calculus and analysis, geometry, number theory, probability, set theory, and the foundation of mathematics. Crosslist:MATH-670. Usually Offered: alternate springs (even years). Prerequisite:MATH-222. | 677.169 | 1 |
The Second Edition of the Pearson Mathematics Student Book offers updated questions, activities, design and full coverage of the Australian Curriculum: Mathematics as well as the 2017 Victorian Curriculum.
It caters for students of all abilities, with improved differentiation of all exercise questions and more questions for students consolidating their skills, in all exercises.
Reader | 677.169 | 1 |
Many years of practical experience in teaching discrete mathematics form the basis of this text book. Part I contains problems on such topics as Boolean algebra, k-valued logics, graphs and networks, elements of coding theory, automata theory, algorithms theory, combinatorics, Boolean minimization and logical design. The exercises are preceded by ample theoretical background material. For further study the reader is referred to the extensive bibliography. Part II follows the same structure as Part I, and gives helpful hints and solutions. Audience:This book will be of great value to undergraduate students of discrete mathematics, whereas the more difficult exercises, which comprise about one-third of the material, will also appeal to postgraduates and researchers | 677.169 | 1 |
Pre-Algebra 1
Getting ready for algebra is a big step. It means making connections between arithmetic and specific mathematical skills. The goal of the Pre-Algebra series is to develop skills in pre-algebra, or the mathematical skills needed to begin solving problems in algebra. This first pre-algebra course introduces working with variables and familiarizes students with mathematical expressions and equations. Prerequisites: successful completion of the course "Practical Math 2," OR instructor's approval based on placement test. Course: MTH-301. Media: B or LP. Lessons: 4 chapters, 11 assignments.
Pre-Algebra 1
Course ID: MTH-301
Audience
Adult Continuing Education and High School Programs
Course Description
Getting ready for algebra is a big step. It means making connections between arithmetic and specific mathematical skills. The goal of this Pre-Algebra series is to develop skills in pre-algebra, or the mathematical skills needed to begin solving problems in algebra. In particular, pre-algebra involves becoming familiar with using mathematical expressions and equations that include numbers in various forms, such as fractions and decimals. This first pre-algebra course introduces working with variables and familiarizes students with mathematical expressions and equations. Working through and reviewing topics in arithmetic will help students develop skills they can use in algebra.
Organization
Four chapters, eleven assignments
Credit
Students who successfully complete both "Pre-Algebra 1" and "Pre-Algebra 2" earn 1 high school credit or Carnegie Unit.
Prerequisites
To enroll in this class, a student needs one of the following prerequisites:
- successful completion of the course "Practical Math 2," OR
- instructor's approval based on placement test
Chapter 2 Number Expressions, Equations, Properties
Objectives: After completing this chapter, the student will be able to
a. recognize and find the value of number expressions
b. simplify number expressions
c. simplify number expressions with parenthesis
d. determine if two number expressions are equivalent
e. write an equation for equivalent number expressions
f. identify and apply addition properties
g. identify and apply multiplication properties
h. identify and apply other properties; distributive property and division property
i. apply concepts of problem solving for numbers and words
j. apply concepts and skills to find area
Chapter 3 Variable Expressions
Objectives: After completing this lesson, the student will be able to
a. identify the variable in a variable expressions
b. identify like terms
c. combine like terms to simplify variable expressions
d. evaluate variable expressions with one operation
e. evaluate variable expressions with more than one operation
f. evaluate variable expressions with more than one variable
g. apply concepts and skills to find volume
Chapter 4 Variable Equations
Objectives: After completing this lesson, the student will be able to
a. identify a variable equation and determine if the given number is a solution
b. tell whether two equations are equivalent
c. identify and apply the properties of equality to make equivalent equations
d. use inverse operations to complete equations
e. solve equations using subtraction
f. solve equations using addition
g. solve equations using multiplication
h. solve equations using division
i. solve equations using more than one operation
j. apply concepts and skills to solve formulas | 677.169 | 1 |
The Essentials of Vedic Mathematics
A handy and useful guide to mastering Vedic mathematics without any help from experts. Vedic mathematics is an ancient technique consisting of sixteen sutras and sixteen sub-sutras. It simplifies not only...Read more
A handy and useful guide to mastering Vedic mathematics without any help from experts. Vedic mathematics is an ancient technique consisting of sixteen sutras and sixteen sub-sutras. It simplifies not only the fundamental arithmetic operations, such as multiplication and division, but also more advanced concepts such as simultaneous equations, quadratic equations, the factorization of cubic equations, and so on. This mathematical technique is rapidly emerging as a tool for students appearing in various competitive examinations, including CAT, MAT, XAT, SAT, engineering and banking examinations, where speed and accuracy play a vital role. As a bonus for students, Rajesh Kumar Thakur has also included in this book chapters for CBSE and ICSE board examinations. Written in simple and lucid language, The Essentials of Vedic Mathematics has been designed to benefit the maximum number of readers. Now you can comprehend the basics of Vedic mathematics without any help from experts. Read less | 677.169 | 1 |
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