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50 high quality printed workbooks cover the basic engineering mathematics and statistics teaching
of both first and second year students in a typical undergraduate engineering degree course.
A significant effort was made to ensure that the workbooks were student focussed and contained
examples of engineering applications of the mathematics. Workbooks 1 - 46 contain mathematics
and statistics material for engineering undergraduates. Workbook 47 contains a miscellany of
Mathematics and Physics related problems and Workbook 48 covers more in depth Engineering Case Studies.
Workbook 49 is a Student's Guide and Workbook 50 is a Tutor's Guide.
The CAL courseware consists of online interactive lessons complementing many of the workbooks.
CAA
resources provide necessary tools for the formative testing of students
by means of large banks of online tests.
If
you would like to use any of these learning resources, you or your institution should become a registered user. If you (or your institution) have not signed up yet, then please read about how to become a registered HELM user.
Additional
resources were developed by our partners during the HELM
project's transferabilty phase. Newcastle University developed video
clips to accompany some workbook sections and Salford University
produced some acoustic examples to complement the existing engineering
examples. HELM also worked with
the RESET project to re-engineer some of the CAL courseware. | 677.169 | 1 |
For questions on Grassmann Calculus and relevant Mathematica packages.
Contact: David Park
Grassmann Calculus is an extended application that incorporates John's Grassmann algebra at its core. It has coordinates, differential forms, various derivative operators and many example notebooks. There is a fuller description and contact at the following link. | 677.169 | 1 |
Provide students with an inclusive, engaged learning experience to gain an understanding
of basic operations.
Students should know at least 70% of the content objectives to proceed to the next course.
Departmental Final Exam
MAT 950
Designed for students requiring basic math and pre-algebra instruction. Covers basic
operations for number systems up to and including real numbers. Includes fractions,
ratios, proportions, decimals, exponents, roots, linear equations, and polynomial
expressions.
Provide students with an inclusive, engaged learning experience to gain an understanding
of basic math and pre-algebra.
Students should know at least 70% of the content objectives to proceed to the next course.
Provide students with an inclusive, engaged learning experience to gain an understanding
of pre- and beginning algebra in an accelerated program.
Students should know at least 70% of the content objectives to proceed to the next course.
Departmental Final Exam
MAT 990
For students who have completed a minimum of one year of high school algebra or who
lack a thorough understanding of basic algebra principles. Teaches integers, solving
equations, polynomial operations, factoring polynomials, systems of equations and
graphs, rational expressions, roots, radicals, complex numbers, quadratic equations
and the quadratic formula. Prepares students for MAT 1010, Intermediate Algebra.
Provide students with an inclusive, engaged learning experience to gain an understanding
of intermediate algebra.
Students should know at least 70% of the content objectives to proceed to the next course.
Departmental Final Exam
MAT 1000
Teaches Beginning and Intermediate Algebra in one semester. Includes linear, quadratic,
and rational expressions, equations, and functions; systems of equations; logarithms;
exponents; graphing; and problem solving. Prepares students for MATH 1030, 1040, and
1050.
Provide students with an inclusive, engaged learning experience to gain an understanding
of beginning and intermediate algebra in an accelerated program to prepare them for
a credit-bearing course.
Students should know at least 73% of the content objectives to proceed to the next course.
Departmental Final Exam
MAT 1010
Expands and covers in more depth basic algebra concepts introduced in Beginning Algebra.
Topics of study include linear and quadratic equations and inequalities, polynomials
and rational expressions, radical and exponential expressions and equations, complex
numbers, systems of linear and nonlinear equations, functions, conic sections, and
real world applications of algebra.
Provide students with an inclusive, engaged learning experience to gain an understanding
of intermediate algebra to prepare them for a credit-bearing course.
Students should know at least 73% of the content objectives to proceed to the next course.
Departmental Final Exam
MAT 1030
How do I tell fact from fiction on the Internet? How will I pay off my student loans?
Should I rent or buy a home? Will I ever be able to retire? These and other real-life
questions are addressed in this course about quantitative reasoning. Upon completion
of this course, students should be able to communicate, interpret, and analyze quantitative
information found in the media and in everyday life to make sound personal, professional,
and civic decisions.
Provide students with an inclusive, engaged learning experience to gain an understanding
of qualitative reasoning.
Upon completion of this course, students should be able to communicate, interpret,
and analyze quantitative information found in the media and in everyday life to make
sound personal, professional, and civic decisions. | 677.169 | 1 |
Algebraic Reasoning High School Textbook
Cosenza & Associates, LLC's,Algebraic Reasoningtextbook addresses the TEKS for the Algebraic Reasoning high school math course. The Texas State Board of Education created this new course to increase the number of rigorous advanced mathematics courses available to students. The Algebraic Reasoning course meets Texas high school graduation requirements to qualify as an advanced mathematics credit on either the Foundation diploma or an Endorsement.
Who wrote Algebraic Reasoning?
Dr. Paul Gray, Jacqueline Weilmuenster, and Jennifer Hylemon led the authoring team. Each of these authors has extensive experience in Texas mathematics education, including as classroom mathematics teachers and district-level mathematics leaders.
Algebraic Reasoning is a textbook written by Texas educators for Texas educators and students!
What does an Algebraic Reasoning lesson look like?
Algebraic Reasoning lessons are inquiry-focused and built around a compacted 5E instructional model. Each lesson begins with a brief Engage activity that teachers can use to launch the lesson. Engage activities help students focus on the content of the lesson and activate prior knowledge that they will need to be successful in the lesson. Hands-on Explore activities allow students to investigate the content and begin to look for patterns and make conjectures. The Explain phase provides students with important formalized content. Stepped-out examples coupled with You-Try-It exercises follow the content summary so students can check their own understanding.
Students and teachers may scan a QR code in the Explain section to view videos. One video summarizes the content from the Explain phase and is ideal for students who want to review what they learned in class that day or for teachers using a flipped-classroom design. Additional videos provide solutions to the You-Try-It problems.
What is contained in the Algebraic Reasoning Student and the Teacher Editions?
The Algebraic Reasoning student edition contains 64 lessons, mid-chapter reviews, and end-of-chapter reviews. Each lesson begins with a Focusing Question to set the stage for student inquiry. Students also see their learning outcomes that are written in student-friendly "I can…" statements. Student editions also contain QR codes in each section that link directly to instructional videos that summarize the Explain section and show students how to work the "You Try It!" problems.
The Algebraic Reasoning Teacher Wraparound Edition (TWE) contains several features to help teachers deliver effective instruction. Instructional hints appear throughout the TWE, offering best-practice based suggestions for use of technology, differentiated instruction, and English language learner support.
Teachers also have online access to ancillary material, including digital versions of the content from the TWE, mid-chapter and end-of-chapter tests and a bank of editable questions that address content from each section within the chapter. | 677.169 | 1 |
This course presents the theory and practice of neural networks with Mathematica and focuses on the Neural Networks package. The features and capabilities of the package are demonstrated, and numerous examples and practical hands-on exercises are included. The material is presented as a sequence of five lectures, each one followed by a problem session to help students understand the material and to provide a focused and practical learning experience. The lectures cover the different kinds of neural networks and the types of problems for which neural networks are used. Basic theoretical concepts, illustrated with graphs, figures, and examples, are covered to support practical neural network training.
The course is designed primarily for people who want and need to estimate relations in data using Mathematica. Students typically have wide-ranging backgrounds and include engineers and professionals who work with all kinds of data, including technical, medical, and economic data.
Syllabus
Introduction: overview of neural network history and types of problems: function approximation, classification, data clustering, time series, and dynamic systems
Theory and Background of Neural Networks: description of the inherited problems when functions are fitted to data, possibilities for handling these problems using neural networks, and practical aspects
Nonlinear Dynamic Black-Box Modeling: modeling of time series and dynamic systems using linear and nonlinear models
Classification and Clustering with Neural Networks: two classes, many classes, neural network classifiers and relations to other classifiers, the perceptron as classifier, nearest-neighbor classification, vector quantization, unsupervised methods, self-organizing maps, and the Hopfield network
All Wolfram Education Group offerings are "hands-on" interactive courses and are taught by certified instructors in a professional computer classroom environment. | 677.169 | 1 |
Nutshell math homework help
CMP offers mathematical help for grade 6, grade 7 and grade 8 for both CMP2 and CMP3.Learning Objective Sums and Differences to 10: Math Terminology for Module 1 New and Recently Introduced Terms View terms and symbols students have used or seen.
Math Question Meme Derp
Get expert advice on reading, homework help, learning activities, and more.The site includes lessons, formulas, online calculators and homework help.
Get homework done by teachers who are experts in high school, college and university homework help.Understand your math homework with help from your friends and the MathChat community.Free printable math. worksheets that are ideal for parents of children in Kindergarten through 8th Grade who want extra homework help in mathematics.NutshellMath is no longer taking new registrations and the service will not be available after October 31, 2013.Online Mathematics Homework WebAssign Login Page for TAMU Students-- You can log in and access materials for your course without payment through September 11, so.Students, teachers, parents, and everyone can find solutions to their math.
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While students can post original homework for help,. said earlier this year that it suspected students were using the service to cheat on their math homework.Best online homework help sites and best online tutoring sites, with summary of key features and benefits.
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We can help you with middle school, high school, or even college algebra, and we have math lessons in.Is helping your child with homework more frustrating and confusing than ever before, thanks to the new Common Core standards.This site is designed for high school and college math students.Hotmath explains math textbook homework problems with step-by-step math answers for algebra, geometry, and calculus.
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The online homework system for the Department of Mathematical Sciences at Indiana University - Purdue University Fort Wayne.
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Correct results and step-by-step solutions for all your math textbook problems.Algebra, math homework solvers, lessons and free tutors online.Pre-algebra, Algebra I, Algebra II, Geometry, Physics.Webmath is a math-help web site that generates answers to specific math questions and problems, as entered by a user, at any particular moment.
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Online Homework videos of EVERY EngageNY lesson all year long.Free math lessons and math homework help from basic math to algebra, geometry and beyond.Math Homework Helper Great math help for elementary and middle school students from Fact Monster.Every student knows how challenging it can be to meet a tight deadline.
This school year, help your child complete his assignments and improve his study skills and grades with new strategies and methods for homework success.Learning Objective Multiplication and Division of Fractions and Decimal Fractions: Math Terminology for Module 4.
Math Blackboard
This online homework help service features math homework help, science homework help, and...Each help options includes worked homework examples and a break down of the math.So-called math-anxious parents who provided frequent help on homework actually hurt their children by passing on their anxiety, a study found. | 677.169 | 1 |
text provides an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry and to the fascinating connections between these fields: the theory of toric varieties (or torus embeddings). The fist part of the book contains an introduction to the theory of polytopes - one of the most important parts of classical geometry in n-dimensional Euclidean space. Since the discussion here is independent of any applications to algebraic geometry, it would also be suitable for a course in geometry. This part also provides large parts of the mathematical background of linear optimization and of the geometrical aspects in Computer Science. The second part introduces toric varieties in an elementary way, building on the concepts of combinatorial geometry introduced in the first part. Many of the general concepts of algebraic geometry arise in this treatment and can be dealt with concretely. This part of the book can thus serve for a one-semester introduction to algebraic geometry, with the first part serving as a reference for combinatorial geometry. | 677.169 | 1 |
Sunday, September 13, 2015
Introductory Complex Analysis by Silverman PDF Download
Introductory Complex Analysis is a scaled-down version of A. I.
Markushevich's masterly three-volume "Theory of Functions of a Complex
Variable." Dr. Richard Silverman, the editor and translator of the
original, has prepared this shorter version expressly to meet the needs
of a one-year graduate or undergraduate course in complex analysis. In
his selection and adaptation of the more elementary topics from the
original larger work, he was guided by a brief course prepared by
Markushevich himself.
The book begins with fundamentals, with a
definition of complex numbers, their geometric representation, their
algebra, powers and roots of complex numbers, set theory as applied to
complex analysis, and complex functions and sequences. The notions of
proper and improper complex numbers and of infinity are fully and
clearly explained, as is stereographic projection. Individual chapters
then cover limits and continuity, differentiation of analytic functions,
polynomials and rational functions, Mobius transformations with their
circle-preserving property, exponentials and logarithms, complex
integrals and the Cauchy theorem , complex series and uniform
convergence, power series, Laurent series and singular points, the
residue theorem and its implications, harmonic functions (a subject too
often slighted in first courses in complex analysis), partial fraction
expansions, conformal mapping, and analytic continuation. | 677.169 | 1 |
Synopsis
Foundation transition practice provides thorough, well graded exercises up to the standard of grade F on the GCSE Mathematics Foundation tier. The booklet follows the structure of the Foundation transition students' book, making it easy to organise extra practice, homework and revision. These booklets are also convenient for use alongside other teaching texts when additional practice is needed: the contents lists are clear and detailed, and matching of all boards' linear and major modular specifications to the section headings of these booklets is downloadable from where answers to the booklets are available in pdf format. | 677.169 | 1 |
Algebra 1 Systems of Equations word problem notes & task cards
Be sure that you have an application to open
this file type before downloading and/or purchasing.
1 MB|18 pages
Product Description
This file includes one page of class notes introducing a strategy for students to use with solving system of equation word problems. Answer Key provided.
30 colorful task cards with easy and more challenging application problems. Can be divided in stations or allow students to work on a set in pairs. Several types of recording sheets are provided: a) five problems per page numbered b) five problems per page blank so students can complete cards in any order they choose c) 10 problems per page numbered. Answer key provided.
Thanks for checking out this product at the miss jude math! shop.
Happy Solving! | 677.169 | 1 |
Wolfram Alpha answers Christmas wishes of world's high school students
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In other news, world's high school math teachers declare Wolfram Alpha, "dead to us."
Have you ever given up working on a math problem because you couldn't figure out the next step? Wolfram|Alpha can guide you step by step through the process of solving many mathematical problems, from solving a simple quadratic equation to taking the integral of a complex function.
[For example] When trying to find the roots of 3x2+x-7=4x, Wolfram|Alpha can break down the steps for you if you click the "Show steps" button in the Result pod | 677.169 | 1 |
Basic Mathematics
Other Titles by Alan Graham
Description
Information
Presents a guide to the basic principles of mathematics with simple explanations of all key areas, including decimals, percentages, measurements, and graphs, and helps apply these principles to everyday | 677.169 | 1 |
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Mathematics
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The study of Mathematics is integral in order to function as a contributing citizen and life-long learner in today's society. Our department's goal is to instill students with an appreciation for Mathematics and prepare them with the necessary mathematical and literacy skills necessary for their selected post-secondary pathway.
Course outlines
Course outlines are intended to provide students with an overall plan for a course to enable them to function efficiently and effectively in the course.
Grade 9 EQAO Assessment of Mathematics
The Grade 9 Assessment of Mathematics tests the math skills students are expected to have learned by the end of Grade 9. Different versions of the test are administered in the academic and the applied math courses. Students in first-semester math courses take the test during a two-week testing window in January; students in second-semester or full-year math courses take the test during a two-week testing window in June. For more information and examples of the assessment and scoring materials, please visit Education Quality and Assessment Office (EQAO).
Math resources
The following math resources are available to help you achieve success. | 677.169 | 1 |
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Related coursesCalculus Two: Sequences and Series is an introduction to sequences, infinite series, convergence tests, and Taylor series. The course emphasizes not just getting answers, but asking the question "why is this true?" | 677.169 | 1 |
Overview Algebra 2 covers all topics that are traditionally covered in second-year algebra as well as a considerable amount of geometry. In fact, students completing Algebra 2 will have studied the equivalent of one semester of informal geometry. Time is spent developing geometric concepts and writing proof outlines. Real-world problems are included along with applications to other subjects such as physics and chemistry.
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I think the Saxon approach is excellent. We used this to home school both our kids and they both now have Doctorates. One in Electrical Engineering. The difference in Saxon's approach is that material is presented in bite size pieces. One concept or even just part of a concept in each lesson. The problems will review this concept to insure it is understood and then --this is the key difference-- in future problem sets there will be problems reviewing past concepts so that what was originally learned is cemented in memory. The end result is very powerful.
Great Investment Nov 18, 2009
I changed from a standard "High School Algebra" textbook to this Algebra 2 textbook. I am seeing better results from using this text and less struggle from my child in mastering the subject. I wished I had used the Saxon program in teaching my older | 677.169 | 1 |
Maths Plus for Victoria: Student Book Bk. 6
Description
Maths Plus for Victoria: VELS Edition is a complete maths program that provides students with the tools to become confident mathematicians. This bestselling primary maths series has been written specifically to cater for the Victorian Essential Learning Standards. Maths Plus for Victoria Student Books have been sequentially developed using clearly explained mathematical concepts in order to develop problem-solving and thinking skills. Student Books: A graded spiralling approach to learning that allows students to revisit and build on concepts. Provides students with opportunities to display the skills and understanding of working mathematically.show more | 677.169 | 1 |
This video introduces students to polynomials and terms.
Part of the AlgebraBasicsSeries:
Learn More at mathantics.com
Visit for more Free math videos and additional subscription based content!
published:23 Oct 2015
views:529261published:16 Feb 2013
views:19516
Do my online quiz:
In this video you learn how to substitute values into variables in equations, and how to simplify algebraic expressions.
For more free lessons, quizzes and full solutions, visit
published:17 Nov 2012
views:47716
This video illustrates the basic rules of Algebra. For exercise and answer sheets, go to:
and the product of two arbitrary elements is thus uniquely determined (because the multiplication in an R-algebra must be R-bilinear). This R-algebra is denoted R⟨X1,...,Xn⟩. This construction can easily be generalized to an arbitrary set X of indeterminates.
with the R-bilinear multiplication that is concatenation on words, where X* denotes the free monoid on X (i.e. words on the letters Xi), denotes the external direct sum, and Rw denotes the free R-module on 1 element, the word w.
Night school
A night school is an adult learning school that holds classes in the evening or at night to accommodate people who work during the day. It can also apply to a community college or university that hold classes for the aforementioned purpose, but also admits undergraduates.
Certain high schools, almost always private or charter do exist in fact, but are usually hard to find.
Algebra
Algebra (from Arabic"al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Middle East, by mathematicians such as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).Algebra Basics: Solving 2-Step Equations - Math AnticsBasic Algebra Skills Part 1published: 23 Oct 2015published: 23 Oct 2015
Basic Algebra Part 1 and 2published: 17 Nov 2012
This video introduces students to polynomials and terms.
Part of the AlgebraBasicsSeries:
Learn More at mathantics.com
Visit for more Free math videos and additional subscription based content!
This video introduces students to polynomials and terms.
Part of the AlgebraBasicsSeries:
Learn More at mathantics.com
Visit for more Free math videos and additional subscription based content!...There was a confusing example in the original video. This is the updated version.
This video ho...
Do my online quiz:
In this video you learn how to substitute values into variables in equations, and how to simplify algebraic expressions.
For more free lessons, quizzes and full solutions, visit
Do my online quiz:
In this video you learn how to substitute values into variables in equations, and how to simplify algebraic expressions.
For more free lessons, quizzes and full solutions, visit There was a confusing example in the original video. This is the updated version.
This vi...This video illustrates the basic rules of Algebra. For exercise and answer sheets, go to:
...
Anyone can do Algebra lesson 2 - substitution, sim...
Basic Algebra Skills PartAnn Marie Awad/CPR hide caption. toggle caption. Ann Marie Awad/CPR ... Ann Marie Awad/CPR ... California community college chancellor calls for dropping algebra. EloyOrtizOakley, chancellor of the California community college system, the nation's largest, told NPR's Robert Siegel this week that he wants to adopt other pathways to a degree that don't require algebra. Algebra is the single most failed college course ... ....
WASHINGTON — Did you know you can use part of a cellphone as a lens to magnify things?. Some local 14-year-olds who were challenged to build a portable, affordable microscope figured that out ... "They didn't have any of this when I was in school," Brumfield chuckled ... The only requirement for students to be considered for the program at Edison is completing algebra I in middle school and filling out an application indicating interest ... .... [HOMICIDE MAP ... 1 ... The judge, Leon Johnson, agreed to transfer the case after hearing testimony that Rushing was getting good grades in school, including algebra... "You've gotten a break....
But something just rang a bell when we saw the DailyWire's piece on algebra being placed on the chopping block because it's "a civil rights issue." ...Algebra Is a 'Civil Rights' Issue ... Algebra is the most failed course at community colleges across the country ... isn't algebra a high school class? ... Tax payer funded J-school morons who don't know algebra is essential to any STEM degree/occupation....
Here are five takeaways from how Gwinnett County students fared. ... Fewer Gwinnett students had below-average scores ...District officials noted that the majority of Gwinnett students now take the Algebra End Of Course exam in place of the eighth grade math End Of Grade test and those results are not included in the calculation. Speaking of Algebra, about 47 percent of Gwinnett test-takers scored proficient or distinguished ... Related ... ....
Dennis Kothmann does algebra for fun—and if you think that makes him strange—consider how he greeted a brain cancer diagnosis last fall. "He exhibited a great deal of joy—it's hard to explain," says his wife, Candace, "but, joy, because he said, 'it's so good to be alive'." ... "It didn't bother me… I have so much faith ... The algebra problems are helping him to regain some cognitive ground lost when surgeons removed his tumor ... Dr ... Pan ... ....
Augustine) has asked the Department of Education (DOE) to fix an unfair grading situation for students who have previously taken Algebra II. The issue stems from the controversial and now eliminated Algebra II end of course exam (EOC) ...Without action, this disparity will carry over not just between Algebra II students this year, but also between those who took it this year and future years....
Atlanta Public Schools showed some gains in test results from the 2017 GeorgiaMilestones, though many students have not yet reached the proficiency level in core areas of learning such as math and science. The tests begin in third grade ... Check back throughout the day ... In high schools, 18.1 percent of students were proficient or distinguished in algebra I, which 82 were beginning or developing learners ... . Related ... ....
>. Ladies and gentlemen, please welcome the host of the Laugh Track column, a man who binge-watches everything ...Mike McIntyre ... Apparently, orange isn't just the new black, it's the new green ... At Hilarities ... The Trenton, New Jersey, native once was a public school algebra teacher and a small business owner in Atlanta before embarking on a comedy career that saw her become the first woman to host BET's "Comic View" in the 1994-95 season.... | 677.169 | 1 |
Course programme
Course in Vedic Mathematics
Today, most of the times mathematics is learnt as a routine process to acquire a degree except for a few instances. But everybody should appreciate the beauty of mathematics and realize the importance of learning the same. A very narrow perspective to know a thing which is very vast and immense itself spoils the joy of learning it.
Vedic Mathematics widens the perspective of viewing at and knowing mathematics. His Holiness Jagadguru Shankaracharya Sri Bharati Krishna Tirtha Swamiji found mathematics in the appendix of Atharva Veda and based on that he formulated sixteen simple aphorisms (Sutras). Swamiji later showed that these Sutras can be applied to solve each and every problem of mathematics easily.
Swamiji said " These 16 sutras apply and cover each and every part of each and every chapter of each and every branch of mathematics - including arithmetic, algebra, geometry, trigonometry, conics, astronomy, calculus etc. In fact there is no part of mathematics - pure or applied - which is beyond their jurisdiction"
Vedic Mathematics can be pursued by students who are above the age of 9 years.
Programme Objective
• To enhance the intelligence by widening the learner's perspective and improving one's logical assessment skill in approaching problems in different ways and arriving at the right solutions quickly. • To simplify and reveal mathematics in a different light • To bypass the customary, complicated steps in solving problems and shows quick methods in solving the same
Programme Highlights 1 There are 16 sutras. These sutras are simple sentences which can be easily understood, remembered and applied 2 A problem can be solved in different methods using different sutras. This gives an option for the student to choose the easiest method 3 The numerals greater than 5 are converted into less than 5, without changing the values. So all the arithmetic computations will become much easier. E.g. If the student knows the multiplication table up to 5 x 5, it is sufficient 4 There are very easy verification techniques in Vedic Mathematics. So, a student can verify the results instantly 5 It saves precious time in solving the problems. Most of the times it looks like magic 6 It can be learnt in a very short span of time
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Do you see something that is not right in this course? Let us know if there are any mistakes and you will help users like yourself. | 677.169 | 1 |
For Teachers
Achievement Standard 2.6 Algebra continues from level 1 with more complex simplifying and solving equations. Several new concepts are introduced: the Quadratic formula, Surds, Logarithms and using logarithms to solve exponential equations. | 677.169 | 1 |
Learn how to apply selected mathematical modelling methods to analyse big data in this free online course. Mathematics is everywhere, and with the rise of big data it becomes a useful tool when extracting information and analysing large datasets.
Use mathematics to create models to solve real-life problems. How do populations grow? How do viruses spread? What is the trajectory of a glider? Many real-life problems can be described and solved by mathematical models. In this course, you will form a team with another student and work in a project to solve a real-life problem | 677.169 | 1 |
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This is an e-textbook for a first course in linear algebra. The topics covered include: Linear Systems, The Vector Space R^n, Matrix Algebra, Determinants, Abstract Vector Spaces, Linear Transformations, Eigenvalues and Eigenvectors, and Orthogonality in R^n. It introduces linear transformations in R^n quite early and uses them to motivate the addition and multiplication of matrices. In addition to the usual theory there are several sections devoted to applications such as Markov chain models, age structured population models, Leontief imput-output models, error-correcting codes, linear recurrence relations, systems of differential equations, and the characterization of real quadratic curves and real quadratic surfaces. We also obtain the canonical forms for real 2 x 2 and 3 x 3 matrices.
The book is rigorous in its treatment of the theory and all important results are proved. What separates this book from print treatments of linear algebra and other e-textbooks is the use of the digital environment to create a pedagogical product that supports student understanding. Specifically, without limitations of length we can regularly spiral back to important concepts and algorithms. Thus, each section begins with a subsection, "What you need to know" reviewing definitions and contains a short quiz with links to solutions. Also to facilitate student understanding, which depends on mastery of over 100 concepts, nearly every instance of a fundamental term is linked back to its definition. Likewise, in proofs, citation of previous results (lemmas, theorems, corollaries) are linked to their original statements and proofs. Also in each section there is a subsection. How to do it, where we describe the specific algorithms students will need to enact when assigned exercises. Further, in addition to a large selection of exercises, each section contains numerous challenge exercises (problems) which require knowledge of the theorems and the application of mathematical reasoning. | 677.169 | 1 |
Algebra 1: Evaluating Expressions
Students discover how to apply the order of operations to evaluating algebraic expressions. In pairs, they solve problems by placing the order of operations steps in correct order. As an exit slip, students write paragraphs about an extensive order of operations problem. | 677.169 | 1 |
Math teachers can make exams with Math-o-mir
Using this version, teachers are able to create math exams and give them to students in electronic form. How can this be done:
Use Math-o-mir in regular way to write down your exam questions
After you finished, go to File->Save As… and in the dialog box choose "MOM exam file" under "Save as type". This way, the document will be saved in exam format.
You will then be asked to provide a password. The password is not needed to open the exam file, but is needed to open exam result files created by students. In addition to password, you need to enter the time-limit for the exam and some math options.
Tell your students to open the file, solve it, and then save results.
Only teacher will be able to open any exam result file by providing the correct password. Nobody else will be able to look into an exam result file.
Anyone willing to test this beta? I am interested to hear your comments and requests. Please write comments here or mail at mathomir(at)gmail.com. Thank you very much. Note that this is beta version and bugs are likely. New ideas are welcome.
Edit on 2011-04-20: There are new features related to hand-drawing in the latest beta3 version:
drawing objects can now be freely rotated by mouse: select one or more objects, right-mouse-click at any sizing handle (red square) and then, holding the right mouse button, move your mouse around.
the SHIFT key can be held while drawing some shapes to achieve special effects: to draw perfect squares or circles, horizontal/vertical lines, equilateral triangles
two new tools for drawing isosceles triangles and right triangles are added
two new tools for drawing circle segments and circle sectors are added
center point to a circle/ellipse can be added: right-click on the circle/ellipse and choose "add center point" from context menu
'close path' option is now available from context menu for open path curves
Any function (even one not found in the toolbox) can now be entered by typing commands in form: \function_name. For example, if you want to enter function called max(), you need to type command \max – after you typed the command you will need to hit the space bar or open parentheses by hiting '(' key.
Some drawings (simple closed path drawings) can now be filled with solid color. To make this, you need to right-click on a closed path drawing and then choose the "Fill" option from the context menu. Functionality of this feature is quite limited.(Note that you can close an open path drawing by right-clicking on it and choosing 'close path' option from the context menu.)
Grid can now be added to coordinate system that was drawn using Cartesian-coordinate-system-drawing-tool. Draw the coordinate system, then right-click onto it and choose "Add grid lines" from the context menu. Resolution of greed lines will be equal to currently selected Math-o-mir grid resolution (see Options->Grid | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
97805213145MP 11-16 Book R3 (School Mathematics Project 11-16)
SMP 11-16 is a mathematics resource for secondary schools which emphasises the relationship between mathematics and the world around us. The course material falls into two parts. Part 1, covering the first two years, consists mainly, but not exclusively, of booklets arranged into strands, which enable pupils to work at their own pace. Part 2, covering Years 9, 10 and 11, consists principally of five series of books, designed to suit pupils of different attainment: Y (yellow), R (red), B (blue), G (green) and A (amber). | 677.169 | 1 |
Be sure that you have an application to open
this file type before downloading and/or purchasing.
5 MB
Product Description
This is a great tool to review the different types of functions students are responsible for recognizing for the common core algebra curriculum.
I have students draw a picture, the general formula and any other important pieces of information. I have attached what I have students write down. We then glue the flip book in their interactive notebook. | 677.169 | 1 |
What is the best way to load a
cross-Channel ferry with cars?
How do SatNav systems or the AA's
Route Planner find the quickest
route from Anglesey to Birkenhead?
How is Maths used to construct
bridges and buildings?
How is Maths used to increase the
efficiency of engines?
Is Maths for you?
You must have achieved at least 5 GCSEs at grade
C or above, including at least a Grade B in GCSE
Maths.
You will need to take an initial assessment to
determine your suitability for this course. The
initial assessment focuses on key algebraic skills
from GCSE that you will need to study the AS
Maths course.
You should have strong algebraic skills.
You are prepared to carry out approximately 3
hours of independent study a week, in addition to
class-based activities.
If you are not ready to start AS Maths upon entry
to college you may be able to take a 1 year course
(Level 3 Algebra and Statistics) which supports
progression onto the AS Maths course the following
year.
A2 Year
Core 3
You will study a number of topics covered in AS
Maths in more depth, including algebra and
functions, trigonometry, exponentials and
logarithms, differentiation, integration and
numerical methods.
Core 4
All assessment for this course is through written examination.
At the end of the academic year you will take three
examinations - one for each module studied. Your progress
towards these examinations is tracked through half term
assessments.
What activities can
I get involved in?
You will have the opportunity to take part in field trips and
workshops as part of the course. Recent visits have included
London, Alton Towers and a Mathematical Mystery Tour of
Liverpool. You may also have the chance to enter many
competitions such as the annual UKMT Maths Challenge and
the Liverpool Mathematical Association 'Pop' quiz, where the
department has scored recent successes.
The College has lots of exciting enrichment and C.V
building opportunities including the chance to earn the
Duke of Edinburgh's Gold Award, learn a new skill, learn a
language, join a club, take up or develop a sport or take on
a new challenge. See the College Prospectus for further
information about what is on offer.
Where does it lead?
You will cover a number of topics in more
detail, including coordinate geometry,
sequences and series, as well as vectors.
Statistics 1
Statistics covers such topics as probability,
correlation and the Normal Distribution.
This module looks into the use of Statistics
for predicting trends, and the reliability of
results.
During AS Maths, you will attend three 90 minute lessons
per week and will be taught by two teachers. One teacher
will teach you the Core 1 and Core 2 modules and the
other will teach you the Decision 1 Module. Students who
progress onto the A2 course and require high grades for
university entry receive four lessons per week during
normal college time.
Expect more from your sixth form
Facebook.com/birkenheadsixthformcollege
How will I be assessed?
@BSFC
A-Level Maths provides the bedrock for getting to
the heart of numbers, shapes, movement, data and
relationships. Advanced Maths is used in many
jobs and has clear and obvious associations with
Physics, Chemistry, Biology, Economics, Business
Studies, Geography and Computing. Perhaps less
apparently it has strong links, both aesthetically
and practically with Art, Design, Music,
Psychology, Law, Sociology and Sports Studies.
Maths A –Level is a very useful, adaptable
qualification. Any Level 3 maths qualification is
considered advantageous by both universities and
employers. Current government advice is for
students to take any level 3 mathematical course
if they are capable of doing so.
A Maths degree can lead to a great variety of
careers including weather forecasting, computer
games programming, in accounting or finance,
scientific research design and developments,
statistics, environmental science, aircraft design
or drugs trial analysis – the list is endless. Maths is
also an essential basis for careers in engineering
and architecture. | 677.169 | 1 |
Conic Sections - Circles in Standard Form
Be sure that you have an application to open
this file type before downloading and/or purchasing.
2 MB|18 pages
Product Description
This is a packet with over 40 problems of circles in standard form. Students are asked to graph each. Questions range from very simple (integer radii and center) to more complex (multiple circles from a single graph, irrational radii, and graphs that don't even graph a circle). All answers are exact and also rounded off when needed. The problems all fit on a single page. The solution span 17 additional pages. All computer made, including graphs. | 677.169 | 1 |
Michael Fischer
Welcome to second year algebra! This course will prepare you for college algebra. We will look at functions of different forms and how we can compare our knowledge of one function to make inferences about other functions. If you would like to earn college credit for this class, follow along with the online class through Education Portal and then register for a CLEP exam. Online resources for our book can be found on ClassZone to support your work in class. We will use the Algebra 2 text book from Macmillan/McGraw-Hill Glencoe. If you struggle with math I highly recommend Barron's painless series, including Painless Algebra.
South Mountain High School • 5401 South 7th Street • Phoenix, AZ 85040 | 677.169 | 1 |
University of Chicago Press: New Titles in Reference and Bibliography
The latest new books in Reference and Bibliographyen-usWed, 26 Jul 2017 05:00:00 GMT1440Everyday Mathematics for Parents
often leaves parents perplexed. Learning is accomplished not through rote memorization, but by actually engaging in real-life math tasks. The curriculum isn't linear, but rather spirals back and forth, weaving concepts in and out of lessons that build overall understanding and long-term retention. It's no wonder that many parents have difficulty navigating this innovative mathematical and pedagogic terrain.Now help is here. Inspired by UCSMP's firsthand experiences with parents and teachers, Everyday Mathematics for Parents will equip parents with an understanding of EM and enable them to help their children with homework—the heart of the great parental adventure of ensuring that children become mathematically proficient. Everyday Mathematics for Parents will become a pocket mentor to parents and teachers new to EM who are ready to step up and help children succeed. With this book in hand, you'll finally understand that while this may not be the way that you learned math, it's actually much better.<div><p><i></i>often leaves parents perplexed. Learning is accomplished not through rote memorization, but by actually engaging in real-life math tasks. The curriculum isn’t linear, but rather spirals back and forth, weaving concepts in and out of lessons that build overall understanding and long-term retention. It’s no wonder that many parents have difficulty navigating this innovative mathematical and pedagogic terrain.</p><p>Now help is here. Inspired by UCSMP’s firsthand experiences with parents and teachers, <i>Everyday Mathematics for Parents</i> will equip parents with an understanding of EM and enable them to help their children with homework—the heart of the great parental adventure of ensuring that children become mathematically proficient.</p> <i>Everyday Mathematics for Parents</i> will become a pocket mentor to parents and teachers new to EM who are ready to step up and help children succeed. With this book in hand, you’ll finally understand that while this may not be the way that you learned math, it’s actually much better.</div>Mathematics and StatisticsReference and BibliographyMon, 10 Jul 2017 05:00:00 GMTThe University of Chicago School Mathematics Project9780226493756Architecture of Frank Lloyd Wright, Fourth Edition
From sprawling houses to compact bungalows and from world-famous museums to a still-working gas station, Frank Lloyd Wright's designs can be found in nearly every corner of the country. While the renowned architect passed away more than fifty years ago, researchers and enthusiasts are still uncovering structures that should be attributed to him. William Allin Storrer is one of the experts leading this charge, and his definitive guide, The Architecture of Frank Lloyd Wright,'s unparalleled architectural style, this new edition is the most comprehensive and authoritative catalog available. Organized chronologically, the catalog includes full-color photos, location information, and historical and architectural background for all of Wright's. Publishing for Wright's sesquicentennial, this new edition will be a trusted companion for anyone embarking on their own journeys through the wonder and genius of Frank Lloyd Wright.<div>From sprawling houses to compact bungalows and from world-famous museums to a still-working gas station, Frank Lloyd Wright’s designs can be found in nearly every corner of the country. While the renowned architect passed away more than fifty years ago, researchers and enthusiasts are still uncovering structures that should be attributed to him.<br /> William Allin Storrer is one of the experts leading this charge, and his definitive guide, <i>The Architecture of Frank Lloyd Wright</i>,’s unparalleled architectural style, this new edition is the most comprehensive and authoritative catalog available.<br /> Organized chronologically, the catalog includes full-color photos, location information, and historical and architectural background for all of Wright’s.<br /> Publishing for Wright’s sesquicentennial, this new edition will be a trusted companion for anyone embarking on their own journeys through the wonder and genius of Frank Lloyd Wright.</div>Architecture: American ArchitectureChicago and IllinoisReference and BibliographySun, 02 Jul 2017 05:00:00 GMTWilliam Allin Storrer9780226435756Protect and Survive
. This booklet will instantly help us remember. Published by the British government in 1980 to educate the public about nuclear war and its aftermath, Protect and Survive Protect and Survive is a uniquely stark reminder of that all-too-recent era.<div>.<br /> <br /> This booklet will instantly help us remember. Published by the British government in 1980 to educate the public about nuclear war and its aftermath, <i>Protect and Survive</i> <i>Protect and Survive</i> is a uniquely stark reminder of that all-too-recent era.</div>History: Military HistoryReference and BibliographyThu, 15 Jun 2017 05:00:00 GMTImperial War Museums9781904897446Bilingual Courtroom
Susan Berk-Seligson's groundbreaking book draws on more than one hundred hours of audio recordings of Spanish/English court proceedings in federal, state, and municipal courts—along with a number of psycholinguistic experiments involving mock juror reactions to interpreted testimony—. This second edition of the The Bilingual Courtroom The Bilingual Courtroom, but also draws attention to the continued need for critical study of interpreting in our ever diversifying society.<div>Susan Berk-Seligson’s groundbreaking book draws on more than one hundred hours of audio recordings of Spanish/English court proceedings in federal, state, and municipal courts—along with a number of psycholinguistic experiments involving mock juror reactions to interpreted testimony—.<br /><br /> This second edition of the <i>The Bilingual Courtroom</i> <i>The Bilingual Courtroom</i>, but also draws attention to the continued need for critical study of interpreting in our ever diversifying society.</div>Law and Legal Studies: General Legal StudiesLaw and Legal Studies: The Constitution and the CourtsReference and BibliographyTue, 23 May 2017 05:00:00 GMTSusan Berk-Seligson9780226329338Write No Matter What
With growing academic responsibilities, family commitments, and inboxes, scholars are struggling to fulfill their writing goals. A finished book—or even steady journal articles—may seem like an impossible dream. But, as Joli Jensen proves, it really is possible to write happily and productively in academe..Write No Matter What draws on popular and scholarly insights into the writing process and stems from Jensen's experience designing and directing a faculty writing program. With more than three decades as an academic writer, Jensen knows what really helps and hinders the scholarly writing process for scholars in the humanities, social sciences,and sciences. Cut down the academic sword of Damocles, Jensen advises. Learn how to write often and effectively, without pressure or shame. With her encouragement, writers of all levels will find ways to create the writing support they need and deserve.<div>With growing academic responsibilities, family commitments, and inboxes, scholars are struggling to fulfill their writing goals. A finished book—or even steady journal articles—may seem like an impossible dream. But, as Joli Jensen proves, it really is possible to write happily and productively in academe.<br /><br />.<br /><br /><i>Write No Matter What</i> draws on popular and scholarly insights into the writing process and stems from Jensen’s experience designing and directing a faculty writing program. With more than three decades as an academic writer, Jensen knows what really helps and hinders the scholarly writing process for scholars in the humanities, social sciences,and sciences.<br /><br /> Cut down the academic sword of Damocles, Jensen advises. Learn how to write often and effectively, without pressure or shame. With her encouragement, writers of all levels will find ways to create the writing support they need and deserve.</div>Library Science and Publishing: PublishingReference and BibliographyFri, 28 Apr 2017 05:00:00 GMTJoli Jensen9780226461700 | 677.169 | 1 |
Review info & popularity
Brief course description
This course is a prep course for the GRE Subject exam in Mathematics. If you wish to apply for a grad program in math, statistics and such, this exam is required.
This is the eighth module and includes advanced methods and examples needed in order to excel in the more challenging problems of the exam. More importantly, the course teaches techniques for solving problems FAST (since in the exam you will have 2.5 min per question – very little time).
We will go over the following topics:
(Read more about this course on the official course page.)
Gilad Pagi bio
Gilad Pagi graduated 1st in class during his B.S in Math and B.S+M.S in Engineering. Pagi has more than 10 years of experience in teaching, including teaching positions in calculus and linear algebra university courses, private and group tutoring. Pagi achieved a top score in the subject math exam (900). He currently serves as a calculus instructor at the University of Michigan, Ann Arbor, where he is pursuing his PhD in Mathematics. | 677.169 | 1 |
PM is a non-profit organization that has developed curriculum and provided its users with professional development support for 18 years. Our textbooks are written mainly by middle school and high school classroom teachers in collaboration with university professors in math and education. The Algebra Connections course was written with the California standards in hand. Based on a review the released items from the 2003-2006 CST Algebra exam, a student who successfully completes this course should be able to correctly answer any of the questions on this test.
The CPM curriculum is based on contemporary research. We have monitored the progress of teachers and students using CPM materials. Our primary goal is the long-term retention of mathematical knowledge . The research supports three fundamental principles: Social interaction increases the ability of students to learn ideas and integrate them into existing cognitive structures. Hence, CPM lessons use study teams. The integration of knowledge is best supported by engaging in a wide array of problems around a single idea. Hence, CPM lessons are problem-based. Long-term retention and transfer of knowledge are best-supported by spaced practice. Hence, CPM spreads practice with ideas over days, weeks, and months.
Studies of Results Since the standards were adopted, CPM schools have outperformed the state average on the STAR tests. CPM high schools scored 6-10% higher than the state average on the SAT-9, 9-11th grade tests from 1998-2002. The CST scores for 2002-2007 have shown similar results. 8th grade scores in CPM schools are 59% higher than the state average and 31.5% higher in 9th grade. Other studies show that students at both ends of the ability of spectrum have also been well served by CPM materials. Students in both low-performing and high-performing schools score higher than matched groups of comparison schools. These reports are available on this CD. The same reports and others are available at the CPM website,
Briefly, the components of the California Edition of the Algebra Connections Program are the student text, the teacher binder, an Extra Practice workbook, a Parent Guide, and free homework help through Hotmath.com. CPM has created a California Edition of the Algebra Connections Program. Several problems in various homework sets have been replaced to add practice with some of the content standards. Four additional lessons have been added to extend the development of a few concepts. The Teacher Edition contains most of the resources needed--lesson plans, resource pages, and assessments--to use the program. Extra practice and parent support are offered in booklets and as free downloads at the CPM web site. Hotmath.com provides an "electronic copy" of the textbook along with tutorial solutions to all homework problems.
To highlight the features of this program, we will examine a typical lesson which helps to develop the content for California Content Standard 9.0: Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables to sketch the solution sets.
The lesson we will examine is lesson 6.2.3, which is in the third lesson of the second section of Chapter 6 . It is one of several lessons that develop the skill of solving systems of linear equations. This lesson is a good example of a typical Algebra Connections lesson. A copy f this lesson is on the CD and in the PDF copy of the Teacher Edition. Note that this slide shows part of the extensive discussion of the lesson for the teacher.
The Lesson Objective clearly states the content objectives for the lesson. For example, the lesson objectives for this lesson is "Students will develop the Elimination Method for solving systems of equations." Then the length of the lesson, core problems, ways of thinking, and materials are listed. Core problems are the minimum work required to meet the objectives of the lesson. Their designation is especially helpful when the pace of the course needs to be adjusted for individual students or the class.
A key part of the teacher materials is the "Suggested Lesson Activity" portion of the teacher notes. These notes are descriptive so that teachers understand how the problems are intended to support students' development of the skill or concept. These suggestions outline how the lesson should unfold. Some of the common suggestions found in these notes are: • Advice on how to use any manipulatives, models, or technology, • Questions to ask students during classwork, • Discussions of the mathematical content for the teacher. * Possible strategies for implementing the lesson, like that highlighted on the slide.
Finally, there are suggestions for how to bring closure to the lesson. These notes will often recommend questions to use during a whole-class discussion, or will require students to summarize their understanding of a new concept in their Learning Logs (a structured note-taking tool). Following the teacher notes are the elements from the student text. As you can see here, a header states the math content of the lesson (Solving Systems Using Elimination) and offers a broad mathematical question that is answered with this lesson (Can I solve without substituting?). The puzzle-piece icon contains a design that links it to the other lessons of this section, both to give a visual clue and to represent the connections between mathematical content of the lesson. Each lesson contains a brief lesson introduction which motivates the content and makes connections to previously-learned content. This is followed by the problems that develop the content. In this lesson, students are given a challenging system of equations and asked to use the substitution method. However, converting an equation so that it is solved for a variable creates messy fractions which makes solving more complicated. This problem not only requires students to review the previous method they learned, but also motivates them to seek another method to solve complicated systems of equations.
The next problem introduces the main content of this lesson: The Elimination Method. Algebra tiles are used to help students understand why two sides of two different equations can be added together. This builds on work with algebra tiles and Equation Mats from Chapters 2, 3, and 5 previously. Notice that this lesson is not a free-form or unguided exploration, but instead A STRUCTURED, PROBLEM-BASED LEARNING APPROACH, WITH A CLEAR, EXPECTED MATHEMATICAL OUTCOME.
The structured developmental problems provide contexts and questions that require students to be actively involved in learning the content of the lesson. They are essentially a Socratic outline of the lesson. Note that the student text contains questions that teachers can use to guide a whole-class discussion. The teacher text also includes these questions. In addition, each part of the student problems is followed by the answer in bold.
After the core content is developed, the remainder of the lesson regularly provides problems for students to further develop as well as practice the idea. In this lesson, problem 6-58 offers a context which can be solved by the Elimination Method. Problem 6-59 presents a situation where adding the equations does not immediately eliminate a variable. It asks students to consider what else they could do with the equations to eliminate the x-terms. Then problem 6-90 provides additional practice for students to solve in class.
Once the students have been introduced to an idea and worked on the developmental problems toward the expected outcome in the structured lesson, the idea is formalized in a "Math Notes" box. These resources use accepted mathematical language to state definitions, properties, and theorems, as well as provide examples and explanations.
Study teams foster the learning of mathematics. They have additional benefits, but we use the research-based team learning as a major part of how students learn mathematics. Students develop skills and concepts using structured problems with clear objectives. Study teams create vibrant classrooms where students are engaged in doing and talking about mathematics.
Homework assignments are designed to: Offer practice with the day's topic, Include spaced practice to reinforce and deepen the knowledge of previous topics, Provide extensions and enrichments of some topics, and Occasionally contain a pre-problem that anticipates an upcoming topic.
Students have free access to tutorial help from any computer with internet access. All of the problems and math notes boxes are available at which provides everyone with an electronic textbook. All of the "Review and Preview" problems have step-by-step solutions there. Students may ask for a hint to get started or the first step of a solution. They use this resource as necessary until they can complete the problem themselves or use the solution as a learning aid for the skill or concept in the problem.
The structure of the lessons offers teachers several ways to interact with students. During the lesson, they circulate among the study teams. When they notice that several or most of the students need assistance with a specific skill or idea, they pull the class together for a targeted lecture*. As students work on problems, teacher check for understanding by asking questions, oftentimes those that are provided in the teacher materials. Teachers test student results , requiring students to form logical arguments to support their reasoning. These observations allow teachers to catch and correct student errors , as well as decide what action is necessary for the lesson closure. Teachers can also question the processes used by the students in their solutions, requiring them to reflect on the best strategies to use for different types of problems. Finally, teachers conduct closure activities for the lessons as well as the chapters as a whole. *Targeted lectures means that a teacher addresses the entire class when the observation of student work indicates a need to do so, in contrast to assuming that everyone needs to hear the same thing and giving a general lecture without reference to student need.
The assessment sections of the Teacher Edition provide comprehensive resources for various types of formal assessment. The Assessment Handbook discusses several formats for assessing the progress of students as listed on the slide. There is an assessment plan for each chapter. Each plan suggests where the five strategies can be used during the chapter as well as the content to include on the individual test. The test bank contains some pre-made tests and numerous problems for teachers to use to construct their own tests. In addition, teachers are able to monitor student progress on an informal, daily basis while interacting with the study teams. They gather information about student understanding, their difficulties, and issues that they may need to address with the class as a whole.
In short, the lessons are a blend of student engagement with rich developmental problems that allow thinking and talking about mathematics, targeted lectures based on observed students needs, teacher interaction with students in their study teams on a regular basis, class discussions, and student presentations. The course teaches the required standards. The lesson plans suggest and their structure allows various paths through the lessons so that the objectives are accessible to a broad range of students. There are several forms of intervention available for the teacher. Much of this is addressed in the "Universal Access" tab of the teacher edition and in the lesson notes. One resource for intervention is the Extra Practice booklet, which contains straight-forward, direct instruction of most topics, along with solved examples. It offers an alternative explanation of a topic after students have some experience with it by doing the developmental lesson.
The Extra Practice booklet contains many additional problems on the specific skill for use in class or at home. Teachers may use a section of this resource with the entire class, give it to one or a few students who need additional work with part or all of the topic, or use it for tutorial sessions outside of the regular class period. This can be done with the booklet, a copy of the topic, or online. Answers are provided so that the student receives immediate feedback on whether he or she is correctly solving the problems.
Likewise, the Parent Guide presents the ideas for each chapter in the same direct instruction mode as the Extra Practice booklet so that parents can quickly review topics to help their child. Both of these resources are available in print form or as a free download from the CPM website. We want to stress that our field-testing and subsequent usage show that students who complete the lessons as intended, including homework, have adequate practice and master the material. However, should students need additional practice or an alternative explanation of the topic, teachers can integrate these resources to differentiate instruction for students. If teachers need help with the mathematics of the lesson, the Extra Practice and Parent Guide booklets augment the support found in the lesson plan notes.
CPM writers are careful to write so that students can read the textbook. Our Algebra Connections text has a reading level of 7.4 and a score of 64.0 on the reading ease scale. The latter number indicates "easy reading." This means that its language is targeted for a student enrolled in the first half of the seventh grade. Anecdotally, teachers in some CPM schools have told us that their English departments have attributed improved reading scores to the use of CPM in the math classes.
The features of the Algebra Connections course are listed on the slide.
Requires students to formulate logical arguments (Standards 24 and 25) Making Connections--page 64 of the Teacher Edition (end of Chapter 1) Justifying--pages 166-67 of the Teacher Edition (end of Chapter 2) Generalizing--pages 255-56 of the Teacher Edition (end of Chapter 3) Reversing thinking -- pages 350-51 of the Teacher Edition (end of Chapter4) Applying and Extending--pages 426-27 of the Teacher Edition (end of Chapter 5)
See the section after the last lesson in each chapter of the Teacher Edition.
Algebra Connections uses an advanced type of algebra tile. In addition to 1, x and x^2 tiles, thee tiles include y, xy, and y^2 so that the representation of algebraic expressions and equations can be extended to more complex polynomials.
The larger activities in the developmental lessons usually offer teachers and students the option to read the problem statement devise a solution strategy, and then solve the problem or to use the next few problems for a structured, guided approach to solving the problem that still requires mathematical thinking and dialogue among the students.
CPM Algebra Overview
2.
Background of CPM <ul><li>Supported by research in methodology and studies of student results, available at </li></ul><ul><li> </li></ul><ul><li>CPM has developed curriculum for 18 years </li></ul><ul><li>Written with the help of California classroom teachers based on their experience of what effectively develops both procedural skills and conceptual understanding. </li></ul>Rigorous • Aligned • Balanced • Accessible
3.
Research Base Rigorous • Aligned • Balanced • Accessible <ul><li>Research Support: </li></ul><ul><li>Social interaction increases the ability of students to learn ideas </li></ul><ul><li>The integration of knowledge is best supported by engaging in a wide array of problems around a single idea. </li></ul><ul><li>Long-term retention and transfer of knowledge are best-supported by spaced learning. </li></ul>
6.
Examining a Lesson The Structure of the Teacher Materials We will examine a lesson developing the content for Standard 9.0: Rigorous • Aligned • Balanced • Accessible 9.0: Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables to sketch the solution sets.
27.
Use of Algebra Tiles <ul><li>" Legend" reminds students and teachers which tiles are positive and negative </li></ul><ul><li>" Minus" region negates the tiles in that region, helping students represent the opposite of a negative. </li></ul>Rigorous • Aligned • Balanced • Accessible Symbolic manipulation is developed through use of concrete tools
28.
Further Guidance Rigorous • Aligned • Balanced • Accessible For big activities and key challenging problems, Further Guidance is available for students who need additional assistance. | 677.169 | 1 |
How to Prepare for the Sat II: Mathematics Level IC
Paperback
Item is available through our marketplace sellers.
Overview inequalities,
ratio, proportion and similarity, counting problems, the binomial theorem,
probability, and an introduction to statistics. The new eighth edition contains
many new practice questions--a total of 900 multiple-choice questions in all-
with answers, and extensive revision of review material.
Customer Reviews
Most Helpful Customer Reviews
How to Prepare for the Sat II: Mathematics Level IC 4.5 out of 5based on
0 ratings.
2 reviews.
Guest
More than 1 year ago
I have used this book and previous editions to supplement my classroom teaching for almost 30 years, and I strongly recommend it to other teachers. The test-taking advice, alone, is worth the price of the book, which has a chapter on problem-solving strategies, test-taking tips distributed throughout the book, and test-taking techniques summarized at the end of each chapter. It is loaded with multiple-choice questions, carefully explained. There are enough to assign 25 a week for every week of the school year as a math review and continuous practice in problem-solving. The information is reliable, dependable and accurate. My students find the back of the book summaries of facts, formulas and procedures to be a handy reference to jog foggy memories. The layout is clear, easy to read and follow, and duplicates the style and structure of actual test materials, all of which help make students just a bit more comfortable with the test, itself. The author provides lots of useful advice both as an experienced math teacher and a college counselor. The advice would be especially valuable for new teachers who may be unfamiliar with the test and need authoritative help in guiding and preparing students.
Guest
More than 1 year ago
This book was ok in reviewing for the Math IC exam, but if you only have a short amount of time to review, this book it not for you; I would suggest the Princeton Review book instead. It goes in depth with EVERYTHING, and functions more like a mini-textbook than a review book. However, this book does have alot of practice examinations to use, unlike the Princeton Review book. | 677.169 | 1 |
Be sure that you have an application to open
this file type before downloading and/or purchasing.
50 MB|143 pages
Product Description
In these functions activities, students will practice defining, comparing, evaluating, and analyzing linear functions. Students will understand that for each input there is exactly one output, what makes a function linear versus nonlinear, the meaning of rate of change and initial values given real scenarios, the correlation between a verbal scenario and its graph, and so much more. This bundle includes resources aligned to 8.F.A.1, 8.F.A.2, 8.F.A.3, 8.F.B.4, and 8.F.B.5. For each standard there is a discovery-based worksheet and an activity designed to facilitate practice with functions. A Review BINGO is also included.
This bundle contains products that are part of the Discovery-Based Worksheet Series. Discovery-Based Worksheets have been specially designed to engage students in learning that moves beyond traditional skills practice. Students will develop a deeper understanding of the big idea and will make connections between concepts. These worksheets make a great introduction to a new topic or summary at the end of a lesson or unit.
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Friday, September 11, 2015
Elementary Number Theory: Second Edition by Underwood Dudley PDF Download
Ideal for a first course in number theory, this lively, engaging text
requires only a familiarity with elementary algebra and the properties
of real numbers. Author Underwood Dudley, who has written a series of
popular mathematics books, maintains that the best way to learn
mathematics is by solving problems. In keeping with this philosophy, the
text includes nearly 1,000 exercises and problems—some computational
and some classical, many original, and some with complete solutions.
The
opening chapters offer sound explanations of the basics of elementary
number theory and develop the fundamental properties of integers and
congruences. Subsequent chapters present proofs of Fermat's and Wilson's
theorems, introduce number theoretic functions, and explore the
quadratic reciprocity theorem. Three independent sections follow, with
examinations of the representation of numbers, diophantine equations,
and primes. The text concludes with 260 additional problems, three
helpful appendixes, and answers to selected exercises and problems. | 677.169 | 1 |
Book Description:
Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages the reader to use computer-aided algebra to solve problems in mathematical physics. To request a copy of the Solutions Manual, visit:
Download Link:
Related Books:
Jun 30 2016 For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained....
Jun 30 2016 The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fiber bundles and their applications to di... | 677.169 | 1 |
Week 14
4.5, 4.7 Eigenspaces, Diagonalization
Fall 2015
Consider a system
Ax = x
where A is an n n matrix, is an eigenvalue of A. Then
a. (a basis of) eigenspace, E , is found by solving ( A I )x =
b. the dimension of the eigenspace is called the geometr
Week 3
14.7 Maximum and Minimum Values
Q: What is a critical point?
A: For a function of two variables z = f ( x, y ) , a critical point can be
Q: How to find a critical point?
A: (a, b ) is a critical point of f ( x, y ) , if
i)
Both f x (a, b ) = 0 and
Week 13
3.6, 3.8 Gram-Schmidt Process, Least Square Method
Fall 2015
Q:
Is it possible to construct an orthogonal basis? How?
A:
Yes! If we have a basis, we can generate an orthogonal basis by using Gram-Schmidt
process.
Gram-Schmidt Process
Let W be a p-
Multivariable Calculus Advice
Showing 1 to 1 of 1
I would definitely recommend this course, for me it was a requirement to take, however, it was actually a very fun course, I know that is weird to say about a calculus course, but it was. I learned a lot and the course definitely helped me with some of my more advanced engineering courses.
Course highlights:
So many things to highlight, but the major parts were pretty obvious, its in the name, multi variable calculus. Matrix calculus was a huge topic, and a pretty tough one if you didn't know what you were doing or were a little rusty on matrix algebra, but the professor made sure to catch the students up before moving on to quickly.
Hours per week:
6-8 hours
Advice for students:
Make sure you attend class! I cannot stress that enough. I missed a few classes thinking I could teach some of the information to myself from the book, but I was very wrong. Attending class and picking the professors brain with any questions is pretty key to passing this class. | 677.169 | 1 |
By "See the Concept" features, where students make important connections through detailed visualizations that deepen understanding.
RocksAbout the Author:Dr. Gary Rockswold has taught mathematics for 25 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate and graduate students, and adult education classes. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy, and computer science. Outside of mathematics, he enjoys spending time with his wife and two children.
Description du livre Pearson. État : Good. 0321900448 May have signs of use, may be ex library copy. Book Only. Used items do not include access codes, cd's or other accessories, regardless of what is stated in item title. N° de réf. du libraire Z0321900448Z3
Description du livre Pearson Education (US), United States, 2013. Mixed media product. État : New. 5th BTE9780321900449 | 677.169 | 1 |
Paperback | June 5, 2012
Pricing and Purchase Info
about
A no-nonsense, practical guide to help you improve your algebra II skills with solid instruction and plenty of practice, practice, practice
Practice Makes Perfect: Algebra II presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations, as well as an introducing you to probability and trigonometry. Inside you will find the help you need for boosting your skills, preparing for an exam or re-introducing yourself to the subject. More than 500 exercises and answers covering all aspects of algebra will get you on your way to mastering algebra!
About The Author
Christopher Monahan is a retired teacher of math with more than 30 years of classroom experience at the college and high school level. As a member of the Association of Mathematics Teachers of New York State, Monahan served as president (2009-2010) and vice president (2006-2007). He served on a number of committees for the New York Sta... | 677.169 | 1 |
Introduction to MathCAD
For Freshman or Introductory courses in Engineering and Computer Science. ESource-Prentice Hall's Engineering Source-provides a complete, flexible introductory engineering and computing program. Featuring over 15 modules and growing, ESource allows professors to fully customize their textbooks through the ESource website. Professors are not only able to pick and choose modules, but also sections of modules, incorporate their own materials, and re-paginate and re-index the complete project. or
"synopsis" may belong to another edition of this title.
From the Back Cover:
prenhall/esource
Features * Introduces Mathcad's basic mathematical and data analysis functions (e.g., trigonometric, regression, and interpolation functions) using easy-to-follow examples, then applies the functions to examples drawn from emerging or rapidly developing fields in engineering. * Teaches users how to make use of Mathcad's special features, such as solve blocks for iterative solutions, QuickPlots to visualize functions, and working problems with units. * Exercise problems that have been designed to cover a variety of engineering disciplines. * Themes of Chapter openers are often integrated with application examples, and exercise problems to sustain student interest and involvement. | 677.169 | 1 |
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Secondary algebraic manipulationThis worksheet has 36 algebraic expressions, which need to be factorised. The questions are not organised by type and therefore students are expected to identify how to factorise the expressions using an appropriate method: taking out the highest common factor, difference of two squares, product-sum method, by pairing or a combination of these methods, which trains students to double-check if they have fully factorised expressions. The worksheet includes worked answers.
The worksheet is targeted at the most able GCSE students who are aiming for grade 9. Fluency in factorising algebraic expression is essential at the start of the AS-level course and this worksheet is very useful for students who need to revise this skill after a long summer holiday.
The worked answers accompanying this worksheet allow the teaching and learning to continue beyond the classroom and it is therefore an ideal resource on a school's VLE as a revision tool for independent study at home.
For your convenience, the Word file is included and can be edited to meet the needs of your students.
This is a detailed checklist with examples, for the edexcel c1 exam. Sorted by topic. 4pages.
Checklists are great for the teacher and student as you can track what topics have been covered, what topics have been learnt and topics that need to be revisited.
As a tutor, I normally get the student to fill out the checklist so I can see what they have done in class also. :) | 677.169 | 1 |
Two sisters, life, books, family, fun & giveaways
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UnLock Math's Pre-Algebra ~ A TOS Review
Recently, Jackson and I received a full year's subscription to UnLock Math's excellent UnLock Pre-Algebra to review, via the Schoolhouse Review Crew. We've really benefited from this online pre-algebra course. I'd love to share our experiences with you!
What is UnLock Pre-Algebra?
Creators Matthew and Alesia Blackwood (who were not only homeschooled themselves, but are currently teaching their own children at home) have created a most unusual, and excellent math program. UnLock Pre-Algebra is a complete online pre-algebra course for students in grades 7-8. It covers a full scope and sequence of pre-algebra. (Just scroll to the bottom of that link to view everything this course covers.) Lessons are clearly taught (by a human teacher, not just an automated voice!) and students have immediate opportunities not only to put their new knowledge into practice, but to review recent facts and lessons. And all of this is accomplished in a calm and enjoyable manner and environment.
UnLock Pre-Algebra Dashboard
How does this course work?
This online course itself is well-organized and easy to use. Once the parent has set up a student account, the student logs into his dashboard. The dashboard enables the student to access everything from the lessons themselves, to his cumulative score, to his overall progress in the course. It also allows the student (or parent) to access his gradebook and progress reports, which break down his scores on each type of problem, lesson, or test. UnLock Math records the lessons (and their scores) that the students complete, and each day when they log into the dashboard, the column on the left side will show them which lessons they've completed and which one they should work on next.
Alesia teaching a lesson
The online lessons are taught by Alesia Blackwood, a competent and enjoyable high school math instructor. She is very experienced in taking math concepts and teaching them in such a way that students who've disliked math or even feared it, can understand and excel at it.
The lessons are organized so that each day, students: practice what they've already learned; watch a new online lesson; work problems on the new concepts; and even attempt an extra credit problem. Here's the format each lesson follows:
Warmup: 5 questions for the student to "get into" math mode
Video Lesson: Alesia Blackwood presents the lesson/concept of the day. These lessons tend to range anywhere from 5-15 minutes long, depending on what's being taught.
Practice Problems: Here, the student puts into practice what he's just learned from the video lesson. There are usually around 20 questions and they are scored.
Stay Sharp: This section includes problems from previous lessons. This practice helps students to solidify prior concepts and continue to build good problem-solving skills.
Challenge: Each lesson contains one Challenge problem for extra credit. These are, as the name implies, challenging math questions which really make the student think. (If the question is missed, however, the student doesn't lose any points.)
Tests and quizzes are also part of this curriculum, as are midterm and final exams.
A sample problem
How we used it:
This summer, we used UnLock Pre-Algebra as our main and only math curriculum. We did about three lessons per week (except for the week we were on vacation). Actually, since it was summer and Jackson (who's going into 8th grade) wanted to get his homeschool lessons done as quickly as he could, he did all three lessons on one day most weeks. This actually worked well for us, although during the fall/spring school year we'd spread them out to one lesson per day (or 5 per week), just so that Jackson's math muscles get used every day. It generally took him about 15-35 minutes to complete a lesson. I would sit nearby and watch the lessons so that I knew what he was learning and how Alesia was teaching each concept.
The gradebook and progress reports are perhaps the best I've ever seen in a math curriculum! I love being able to see how well Jackson did on every area (they both show how much time he spent on each type of problem, and the scores he made on them all), and knowing at a glance which areas we need to spend more time on. UnLock Pre-Algebra can even give your student more practice in different areas, as needed!
Our impressions and conclusions:
I really liked Alesia's methods and manner of teaching. She is so interesting and so clear. She also uses some amazing graphics and a touch screen board (to write on, display problems and work problems on) as she teaches the lesson, which I think will appeal to today's teens. I found this curriculum to be more challenging than the one we used last year, but it wasn't too difficult for Jackson. I think it just made him work a bit smarter and harder.
One issue that I sometimes have with online math curricula was completely set aside by UnLock Pre-Algebra. Often, when we've done online math in the past, I have missed having a paper textbook that Jackson could use for review and just have alongside him when the lessons were taught. I've felt that the lack of an actual textbook impaired the learning of new topics from time to time. However, UnLock Math has instructional notes for each lesson, so you can print them out, keep them in a notebook and use them for reference. That is great for review and further study, and he found it so useful.
And I will also tell you that we're so impressed with this that we plan to continue with it throughout the year! I love its format, the challenge it provides to Jackson, and how thorough each lesson is. I give high marks to UnLock Pre-Algebra!
You may purchase UnLock Pre-Algebra from UnLock Math for $299 annually, or $49 monthly. And, the Blackwoods are offering a $50 coupon for any of our readers who purchase the annual course of either UnLock Pre-Algebra or UnLock Algebra 1. Check out UnLock Math's pre-algebra course. I think you'll be impressed…and your students will really learn!
Enjoy! –Wren
DISCLOSURE: Finch and Wren have affiliate relationships with a number of excellent companies. If you purchase an item through our affiliate links, finchnwren will earn a commission. However, you will never pay more for the item when you purchase it through our links. And, we only recommend products that we truly believe in. Thank you! | 677.169 | 1 |
Welcome to MGF1107.
This course consists of the following topics: financial
mathematics, linear and exponential growth, numbers and number
systems, history of mathematics, elementary number theory,
voting techniques, graph theory and society.
Daily Schedule-
TuTh
- A | 677.169 | 1 |
Inside this Revision Guide you'll find everything you need to succeed in the new GCSE 9-1 Maths Higher. It is packed full of tips and tasks to make sure you really know and understand the key revision points. Written by Maths experts and combined with cutting edge technology to help you revise on-the-go.
Synopsis:
Revision is serious business...and we're serious about revision. Inside this Revision Guide you'll find everything you need to succeed in the new GCSE 9-1 Maths Higher examinations. It is packed full of tips and tasks to make sure you really know and understand the key revision points. Written by Maths experts and combined with cutting edge technology to help you revise on-the-go, you can: * Use the free, personalised digital revision planner and get stuck into the quick tests to check your understanding * Download our free revision cards which you can save to your phone to help you revise on the go * Implement 'active' revision techniques - giving you lots of tips and tricks to help the knowledge sink in Snap it! Read it, snap it on your phone, revise it...helpsyou retain key facts Nail it! Examiner tips to help you get better grades Stretch it! Support for the really tough stuff that will get you higher grades The perfect companion...GCSE 9-1 Maths Higher Practice Book * 100s of practice questions * Exam techniques explained * Matches 9-1 specification | 677.169 | 1 |
High School Math Word Wall IdeasCircuit Training - Algebra / Geometry REVIEW for Algebra II
This 42-question circuit will help your students who are entering algebra 2 to review their algebra I and geometry skills. It will generate a lot of good discussion during those first few days of classes before you launch into the first chapter. Here are the student directions: Begin in cell #1. | 677.169 | 1 |
Quiz On Basic Integration Formulas
Students participate in a formal assessment of knowledge concerning the basic Integration Formulas. They apply the review practices given in the resource links to problems found in the assessment. The teacher should use these as review before taking the quiz. | 677.169 | 1 |
Showing 1 to 3 of 3
Alejandra Martinez
Math 2413-Calculus I
Writing assignment #3
Explain when you must use the product rule and when you might multiply and then use the basic
derivative rules. Do the same for the quotient rule.
When given a F(x) x G(x) type of equation, the
Math 2413-Calculus I
Alejandra Martinez
Writing assignment #4
Sec. 3.5
Explain the steps for implicit differentiation and when it is best to use this method.
When given an equation like x2+y2=25 you must first take the derivative of each term
when you tak
Alejandra Martinez
Math 2413-Calculus I
Writing assignment #2
Sec. 2.6
Explain the process of finding the vertical and horizontal asymptotes and what you have to be
careful about using this process in naming the vertical asymptotes.
The method to finding
Calculus I Advice
Showing 1 to 2 of 2
He would never move to a new lesson unless everyone understood the material
Hours per week:
6-8 hours
Advice for students:
Go to class. Always be there on time and don't miss out on the exams and reviews.
Course Term:Fall 2016
Professor:Charles Whitfield
Course Required?Yes
Course Tags:Great Intro to the SubjectMany Small AssignmentsGreat Discussions
Mar 13, 2016
| Would highly recommend.
Pretty easy, overall.
Course Overview:
I would highly recommend it because Professor Whitfield is so understanding and teaches with great detail. If you have a question about something; he will most likely explain it and go through the process again.
Course highlights:
I have an advantage in this course because I had a calculus class during high school; therefore, I am familiar with the lessons he taught. | 677.169 | 1 |
A Physicist's Guide to Mathematica
A Physicists Guide to Mathematica(r) teaches students and professional physicists how to master Mathematica using examples and approaches that will appeal to them. The book illustrates the usefulness of Mathematica in learning, teaching, and carrying out research in physics. Part One gives a practical, physics-oriented, and self-contained introduction to the program. Part Two covers the application of Mathematica to mechanics, electricityand magnetism, and quantum physics. Mathematica enables the user to solve a wide range of physics problems, from the most important to those that are just for fun, and provides an environment that allows the user to develop a greater intuitive understanding of physics. This book aids the reader in using Mathematica for numerical, symbolic, and graphical calculations, and also demonstrates the programs capability to animate two- and three-dimensional graphics. Tams treatment of the subject is greatly detailed, and makes this book an essential reference for anyone needing an introduction to Mathematicas application to physics. This book teaches upper-division and graduate physics students as well as professional physicists how to master Mathematic(r), using examples and approaches that are motivating to them. It also shows that this computer algebra system can be a powerful and wonderful tool for learning, teaching, and doing physics. Part I gives a practical, physics-oriented, and self-contained introduction to Mathematica. Part II considers the application of Mathematica to mechanics, electricity and magnetism, and quantum physics.
* Requires no prior knowledge of Mathematica or computer programming * Includes a disk containing all Mathematica input used in the text for practical application, which can be used by both Macintosh and Windows users
"synopsis" may belong to another edition of this title.
Book Description:
Compatible with Mathematica version 3.0!
From the Back Cover:
Mathematica enables the user to solve a wide range of physics problems and provides an environment that allows the user to develop a greater intuitive understanding of physics. This book will aid the reader in using Mathematica for numerical, symoblic, and graphical calculations, and also will demonstrate the program's capability to animate two- and three-dimensional graphics. Tam's treatment of the subject is greatly detailed, and makes A Physicist's Guide to Mathematica an essential reference for anyone needing an introduction to Mathematica's applications to physics. | 677.169 | 1 |
HSC Study Tips
Tag: maths extension 2
Mathematics is one of the most rewarding subjects for your HSC, especially at the extension levels, where it's one of the highest scaling subjects you can choose. Each year, the majority of students that score a 99+ ATAR did very well for Maths Extension 1 and 2. For maths extension 2 especially, each year the majority of the 21 or 22 students that score the perfect ATAR of 99.95 get 97+ for maths extension 2 as their HSC mark.
Even if you're not aiming for such a high ATAR, doing well in any level of mathematics will get you closer to your goal in no small amount.
With every subject, there's the content, then there's technique. This fact is especially significant in maths extension 2 – things like knowing shortcuts / quick methods to verify the correctness of answers, how well you know your way around your Board-approved calculator, how well you understand the marking process and how to get partial marks, etc.
We all know the commonly told tips that your teachers at school have no doubt told you many times by now (e.g. writing partial answers for partial marks). Here's a few lesser known tips ourmaths tuition classes give our students as part of our Extension 2 maths course:
Volumes – easy way to check answer for volumes
Here's a useful tip for the Volumes topic in Maths Extension 2 – Pappus' Centroid Theorem. This theorem states that the volume of a solid of revolution generated by rotating a plane figure about an external axis is equal to the product of the cross-sectional area and the distance travelled by the cross section's centroid.
Using this theorem, we can calculate all questions involving rotating a shape around an axis (e.g. circle around an axis to produce a torus) simply by finding the area of the cross section, then multiplying this with the distance travelled by the centroid of the cross section. It's much quicker and reliable (because it's simpler – less can go wrong) than using any of the prescribed methods, e.g. cylindrical shells or adding slices.
For example, what's the volume of a circle, centre origin, radius 4, rotated about the line x=6? The answer is simply: the area of the circle – 16π multiplied by the distance travelled by the centre of the circle, which is 12π. The volume is therefore 192π^2 or 1894.96 cubic units. You can verify this with the cylindrical shells method.
Of course, in answering an exam question, you need to use the cylindrical shells method. The Pappus' Centroid Theorem is just a useful tool to quickly check the correctness of your final answer. If there's disagreement, you know you need to check your answer, and this would have easily saved you some lost marks!
Volumes, integration and other applications – the area of an ellipse and the volume of an ellipsoid
Here's another tip to make you quicker at checking your integration results. It's also helpful for other topics (e.g. volumes).
It's a good idea to memorise the area of an ellipse:
And the volume of an ellipsoid:
These are not too hard to remember because in the special case of the circle and sphere, r=a=b and r=a=b=c respectively, which causes both equations to reduce to the equations of the area and volume of a sphere respectively.
There are occasionally situations where you have a definite integral you need to evaluate, where the expression to be integrated is in the form of an ellipse. For volume questions, solids of rotation would often form ellipsoids and knowing the simple formula could give you a quick tool to check the correctness of your answer.
Don't be afraid to include explanations as part of your solution
Here's a tip our extension 2 maths tutors love to give our students. In many situations in mathematics, especially in maths extension 2, some explanation saves you a lot of calculation.
For example, if you're doing an integration and the form is that of a circle, instead of going through the x=sinα substitution, it's easier to just write "This represents the area of a semi circle with radius r" – that's all you need, then you can write the answer. Or if you need to evaluate a definite integral of an odd function with symmetrical limits, then the answer is always 0.
Sometimes you need to take cases – explain why some cases are impossible and this will save you time because you don't need to cover them. Sometimes a graphical solution will show why one graph will never intersect another graph (hence no real roots to a related equation). The point I'm making is explanation goes a long way. The entire Mathematical Induction topic in 3 unit is based on explaining rather than using purely numbers, symbols and algebra.
Another situation would be proof questions (and we get many of these in Extension 2) that require you to prove LHS = RHS. Instead of starting somewhere random, you can start with what you're trying to prove and write "If the above is true (what we're required to prove), then:" and you can proceed to manipulate what you're trying to prove. Just write 'Then' at the beginning of each line to signify you haven't proven it yet, but if the original LHS = RHS, THEN so far these lines of working must all be true. Eventually, when you reach a situation that is in fact true (e.g. 1=1) then you're finished, just write "And since the final line is true, the original LHS = RHS).
Integration by parts – LIATE
We all should know how to do integration by parts by now – but sometimes choosing which one should be u and which should be v can get tricky. A reminder, here is the definition of integration by parts:
OR
Choosing which one should be u (or f(x) if you prefer the first line) is an important decision – choose the wrong one and you'll waste precious exam time going down a path that may lead to an impossible integral.
The general rule of thumb is to remember LIATE. LIATE stands for:
Logarithm
Inverse trigonometric functions
Algebra (general polynomials)
Trigonometric functions
Exponential
You should give preference to the left-most function to be set as u. The reason for this is as you move from the left to the right in LIATE, functions become easier to integrate, so you should prefer to integrate the easy ones (e.g. trigonometric functions and exponentials are easy to integrate) and differentiate the hard ones (e.g. logarithms can't easily be integrated).
L'Hopital's rule
In the Graphs topic, there are many compound graphs that give rise to situations where you have infinite multiplied by 0. When this limit occurs, 3 possibilities arise:
Graph turns to 0
Graph turns to infinite
Graph turns to a constant
To find out how, we suggest to students to learn how to use L'Hopital's rule to discover the relative speed of curves. This rule only applies when the limit below turns to infinite or negative infinite, or 0.
For example, lets see what happens to the graph at y=xlnx close to x=0. We set f(x) = lnx and g(x) = 1/x so that f(x)/g(x) = xlnx. When we evaluate the limit for f'(x)/g'(x) we find it equals (1/x)/(-1/x^2) which equals –x. This would turn to 0 as x approaches 0 so this shows the graph y=xlnx turns to 0 instead of negative infinite at x near 0. Incidentally, this is also one of our HR manager's favourite questions to ask potential candidates for maths tutors, even if they tutor lower levels of maths (you'd be surprised how many people apply to be a mathematics tutor but can't even graph y=xlnx).
Use your calculator memory effectively
Become proficient in the use of your Board-approved calculator that you can take with you to the exam room. If you're swift with using your calculator's memory slots, this makes rechecking over your answers so much faster and accurate (if you happen to finish your exam with 20 minutes to spare, you can literally go through the entire exam once or even twice! If you're good with your calculator, that is). And this helps even more in subjects like HSC Physics and HSC Chemistry where there's lots of calculator work that requires a final definite numerical answer.
Another reason is exact values. Your calculator's memory actually stores something to the order of 100 digits (much more than what's only shown on screen when you press '='). Sometimes when you're supposed to get an exact value, if you put in your written down answer (that's only rounded to 3-4 digits at most) you will get some answer like 1.99837734 but if you subbed in your memory-stored calculator, you will get an exact value of 2. In complex questions, even simple clues like knowing something is an exact value could be the difference between doing the question and skipping it altogether.
Multipart questions (attempt part 2)
We should all know to be able to attempt the next subpart of an exam question by now. E.g. if you can't do part a, which required you to prove a result to be used for part b, you should use the result to do part b so that you can still score partial marks for the question.
Sometimes even within a single part worth multiple marks, there are two parts to the question (e.g. "Show that LHS = RHS and hence derive an expression for acceleration of the particle.") In these examples, if you can't do the question as they intended, just use the result you're given and finish the second part of the question for partial marks. If the question was worth 3 marks, you should at least get a mark for your efforts.
Maths tutoring helps
Sometimes if you're stuck with a teacher at school that's not very knowledgeable, it would be wise to seek outside help. This situation is particularly common in disadvantaged schools – not all schools even offer extension 2, and for schools that do, not all their teachers assigned to the course are actually capable of teaching all parts of the course effectively. Getting outside help also gives you an important advantage over your peers when it comes to internal assessments (where you're up against your peers for the top assessment ranks).
HSC scaling is a popular topic to HSC students and parents, and is often an area that is commonly misunderstood. Scaling is important as it affects all students aspiring to get into university after the HSC.
Scaled marks versus HSC marks
A commonly misunderstood concept is the relationship between HSC marks and scaled marks. HSC marks are the marks the Board of Studies awards you, and appear on your Record of Achievement. These marks determine which performance band you fall in (e.g. Band 6 or E4) for each of your HSC subjects. These marks measure how well you did according to the subject's requirements. E.g. if you received a Band 6 in English Advanced, it means your performance satisfied all the criteria required by the HSC English syllabus to achieve a Band 6. However, in any year, any amount of HSC students can get a Band 6. For example, in a particularly smart year, a higher proportion of students may receive Band 6 in English Advanced. It is not how well you do in your subject, but rather, how well you do relative to other students which determine your UAI. Here's where your scaled marks come into play.
Your scaled marks will NOT be shown to you at the end of your HSC, as you will only be shown your HSC marks (aligned marks, to be precise). Ironically, it is your scaled marks which are the most important determinant to your UAI. Scaled marks are calculated by the UAC (not the BOS) under a totally different process. Basically, these marks measure your performance relative to other students. (For a more technically accurate discussion on scaled marks and what they mean, as well as the mathematics behind UAI calculation, please read our article on the mechanics of HSC scaling) Remember, your HSC marks are a measure of how well you did in your subject, but your scaled marks measure how well you did relative to other students. It is your scaled marks which are used to calculate your UAI, not your HSC marks.
Through the process of scaling, the UAC converts your raw examination marks (the actual marks you received in your external and moderated internal assessment) into scaled marks. These scaled marks are then added up to arrive at your aggregate mark (students refer to this as your 'aggregate') out of 500. The UAI is simply a percentile rank of your aggregate, which is the total of your scaled marks in your top 10 units.
How can knowledge of HSC scaling help me?
Understanding the process allows you to plan your HSC, to an extent, in such a way as to make scaling work to your advantage. For example, if you enjoy maths, you should choose Maths Extension 2 in order to take advantage of its enormous scaling effect. Similarly, if you enjoy science, you should take Chemistry and Physics, as they scale relatively well.
In other words, comparing subjects in terms of their scaling effect can assist you with your decision as to which subjects to take for your HSC. In order to quantitatively compare the scaling effect of different courses, you will need to get familiar with reading statistics published by UAC. The rest of this article will highlight the important things to note.
Reading 'scaled means'
Firstly, what are 'scaled means'? The scaled mean for each subject is the average scaled mark received by all students who took that subject for that year. For example, in 2008, the scaled mean for Maths Extension 2 was 43 out of 50. This means that among the Maths Extension 2 students in 2008, the average of their scaled marks was 43 out of 50. This subject has traditionally been one of the highest scaled subjects available for the HSC. In terms of reading these scaling statistics, generally the higher the scaled mean, the higher the scaling effect.
Each year, the UAC publishes a scaling report which contains important scaling statistics for all HSC subjects eligible to contribute to a UAI. For more information, read about UAC scaling statistics. In the report, there is an important section called Table A3, which is a table setting out the scaled means of all subjects.
To illustrate the effect of scaling, in 2008, a Maths Extension 2 student only needs to be in the top 46% out of all Maths Extension 2 students to get a scaled mark of 45 out of 50 (or 90/100). A Maths (2 unit) student would need to be in the top 3% out of all Maths (2 unit) students in order to achieve the same result. These facts are read off the UAC scaling report. In the 99th percentile, a Maths (2 unit) student receives a scaled mark of 46.1 out of 50. In the 75th percentile, a Maths Extension 2 student receives a scaled makr of 46.2 out of 50. Arguably it is easier to be above average in Maths Extension 2 than to be near the top of the state in Maths (2 unit). This is the main benefit derived from choosing high scaling subjects.
Effect on UAI calculation
Simply put, the higher the total of your scaled marks, the higher your UAI will be. Sometimes when students choose subjects with lower scaled means, do spectacularly in their HSC (e.g. receive Band 6 for all of their units) but receive a UAI that is lower than what they had expected.
For example, if you did English Standard, IPT, Legal Studies and Biology, and scored 90 in all of your subjects, your UAI would be around 94 in 2008. While this is in no way a poor UAI, if you received the same HSC (aligned) marks for English advanced, Maths Extension 1 & 2, Chemistry and Physics, your UAI would be in the vicinity of 99. Again this is because of the scaling effect across different subjects. While all subjects are different and some will be more difficult than others, the best approach to dealing with HSC scaling is to choose the subjects you are interested in, while giving consideration to the scaling effect of your choices. (For more information, read our article on HSC subject selection) | 677.169 | 1 |
Elementary and Intermediate Al best-selling author Pat McKeague, this text presents the topic using the same features that have successfully helped so many students learn algebra in his other titles. Approximately half of the book's 91 sections are in the first six chapters on beginning algebra. The material on intermediate algebra follows Chapter 7. | 677.169 | 1 |
The Tobey/Slater series builds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical "building block" organization makes it easy for readers to understand each topic and gain confidence as they move through each section. The authors provide a "How am I Doing?" guide to give readers constant reinforcement and to ensure that they understand each concept before moving on to the next. With Tobey/Slater, readers have a tutor and study companion with them every step of the way. Whole Numbers, Fractions, Decimals, Ratio and Proportion, Percent, Measurement, Geometry, Statistics, Signed Numbers, Introduction to Algebra, Consumer Finance Applications, Tables, Scientific Calculators. For all readers interested in basic college mathematics.
"synopsis" may belong to another edition of this title.
From the Publisher:
This clear, accessible treatment of basic college mathematics features an enhanced problem-solving strand highlighted by A Mathematics Blueprint for Problem Solving that helps students determine where to begin the problem-solving process, as well as how to plan subsequent problem-solving steps. Also includes Step-by-Step Procedure, realistic Applications, and Cooperative Learning Activities in Putting Your Skills to Work.
From the Back Cover:
This clear, accessible treatment of basic college mathematics features an enhanced problem-solving strand highlighted by A Mathematics Blueprint for Problem Solving that helps determine where to begin the problem-solving process, as well as how to plan subsequent problem-solving steps. The book includes Step-by-Step Procedure, realistic Applications, and Cooperative Learning Activities in Putting Your Skills to Work. Also includes an updated 4-color design that incorporates many graphs and charts to help students learn to read, analyze and interpret the types of data they see presented in many newspapers and magazines. Suitable for Basic College Mathematics courses including lecture-based classes, discussion oriented classes, self-paced classes, mathematics labs, and computer or audio-visual supported learning centers. | 677.169 | 1 |
Math Lit
ISBN-10: 0321818458
ISBN-13: 9780321818454 Math Lit, by Kathleen Almy and Heather Foes, provides a one-semester alternative to the traditional two-semester developmental algebra sequence for non-STEM (Science, Technology, Engineering, and Math) students. This new approach offers an accelerated pathway to college readiness through developmental math, allowing non-STEM students to move directly into liberal arts math or introductory statistics, while also preparing STEM students for intermediate algebra. Through its emphasis on contextual problem-solving, the Almy/Foes worktext and its accompanying MyMathLab® course help students understand and practice the major themes of numeracy, proportional reasoning, algebraic reasoning, and functions | 677.169 | 1 |
In the Eighth Edition of CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Eighth Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, International Metric Sixth
Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition.
The goal of this text is to help students leam to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students. With few exceptions we adhere to the following policies. • The section exercises are graded into three consecutive groups: (a) The first exercises are routine, modelIed almost exactly on the exam pIes; these are intended to give students confidence. (b) Next come exercises that are still based directly on the examples and text but which may have variations of wording or which combine different ideas; these are intended to train students to think for themselves. (c) The last exercises in each set are difficult. These are marked with a star (*) and some will challenge even the best students. Difficult does not necessarily mean theoretical; often a starred problem is an interesting application that requires insight into what calculus is really about. • The exercises come in groups of two and often four similar ones.
Calculus: The Language of Change is an innovative new introductory text that blends traditional and reform approaches, and focuses on understanding calculus as its own language. With accessible writing and presentation, the text allows students to gradually understand the language – first by reviewing vocabulary, and then by quickly moving to present calculus conceptually, computationally, and theoretically. Within this framework, derivatives and integrals are developed side by side, coverage of theory is offered at various levels, and computing devices are incorporated generically. A full range of student and instructor resources make Calculus: The Language of Change an outstanding course package. | 677.169 | 1 |
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The objective for this lesson is How to graph vertical and horizontal shifts and reflections of the graphs of the sine and cosine functions.
These lessons are done in Smart Notebook. Each lesson contains an Opening Activity (bell ringer);an objectives slide, which includes the common core standards the lesson is tied to; a definition slide; example slides; 'try' slides for the students; and a recap slide. Feel free to edit, change, add, or subtract from the lessons as you like. Make them your own. | 677.169 | 1 |
New York Algebra 2 and Trigonometry, Student Edition
New York Algebra 2 and Trigonometry is the third of three books in Glencoe's New York High School Mathematics Series. This series offers complete coverage of New York's Mathematics standards, strands, and performance indicators. As students learn to integrate a comprehensive array of tools and strategies, they become proficient in mastering concepts and skills, solving problems, and communicating mathematically.
This series of books helps your students identify and justify mathematical relationships; acquire and demonstrate mathematical reasoning ability when solving problems; use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes; and succeed on the Regents Examinations.
"synopsis" may belong to another edition of this title.
About the Author:
John A. Carter, PhD, is the principal of Adlai E. Stevenson High School in Lincolnshire, Illinois. He previously served as the director of mathematics and the assistant principal for teaching and learning at Adlai E. Stevenson. He taught mathematics for nineteen years at Community High School in West Chicago and at Stevenson High School.
As a teacher and professional developer, Dr. Carter's work has focused on teaching mathematics for understanding, stu dent engaged learning, and developing student reasoning. As a presenter and lesson-study facilitator, he regularly works with teachers to examine their instructional practices, further their content knowledge, and improve student achievement.
Dr. Carter has served on the Board of Directors for the National Council of Teachers of Mathematics as well as been a member of National Council of Teachers of Mathematics committees, task forces, and writing groups. He received the Presidential Award for Excellence in Mathematics Teaching in 1993 and was awarded the T. E. Rine Secondary Mathematics Teaching Award from the Illinois Council of Teachers of Mathematics in 2000.
Dr. Carter earned a bachelor's degree in mathematics, a master's degree in education, and a master's degree in educational administration from the University of Illinois at Urbana-Champaign. He earned his doctorate in mathematics education from Illinois State University and completed postdoctoral work in educational administration at Loyola University Chicago.
Book Description Glencoe/McGraw-Hill. Hardcover. Book Condition: New. 0078885000 These are new condition books, no student wear at all. May have school inventory markings. The NY edition is identical to the national edition with the addition of NY material at the front. Multiple copies. Bookseller Inventory # Z0078885000ZN | 677.169 | 1 |
Mandelstep - Karl J. Runge
The idea behind "mandelstep" is that by letting you select starting positions and looking at a handful of iteration "trajectories" or "orbits," you can begin to understand more about the different regions of the Mandelbrot set - not just whether a point
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Mark's Maths and Excel Homepage
- Mark Dabbs
Teacher's Friend Markbook and Gradebook: two Excel spreadsheet files that are custom built to record pupil marks and then weight, average, and grade them automatically. One file does the above for a single class; a second file can import all of the information
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Math4U2 - University of Applied Science in Augsburg
In German: 2D interactive Java function plotter with animations. Download to run on most computers. It has rich functionality for linear algebra and infinitesimal calculus. Control function parameters and animations. Lessons can be written using XML files
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Mathansw: Math Software by Solveware - Solveware, Inc.
Math tools for people at work who need the answers to problems they encounter on the job: surveyors, navigators, managers, engineers, architects, supervisors, estimators, programmers, machinists, mold makers, teachers, college students, apprentices, home
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MathBits.com - Frederick and Donna Roberts
Devoted to offering fun, yet challenging, lessons and activities in high school/college level mathematics and computer programming to students and teachers. Includes Teacher Resources for Algebra, Geometry, Algebra 2, and Statistics; Finding Your Way
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Math Education for the 21st Century - Sarah Inkpen
"Technology is an essential part of our future, but technology alone will not educate us. Interactive software, information retrieval systems, multimedia presentations and virtual reality enhance understanding and facilitate knowledge building if and
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Mathematical Software - ZIB/Math-Net
A collection of references to research software available in the public domain from the fields of Computational Geometry, Visualization; Mathematical Optimization; Mathematical Statistics; Numerical Analysis; Object Oriented Libraries, and Symbolic Computation.
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Mathematics - Centre for Educational Technology (CET)
A research and development center for math education. Read descriptions of CET's programs and workbooks, including One, Two and Three (Aahat, Shtayim, Ve Shalosh), for grades K-6; and Visualizing Mathematics, for grades 7-12. Learn about and download
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Math Engine - MathEngine plc
MathEngine is a provider of natural behavior technology for 3D applications and simulations. MathEngine's core product is a software toolset for modeling and adding physics-based behavior into interactive 3D graphics applications. Products include the
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Math Facts NOW! - Thomas Furtado
Software for the PC intended to develop weak areas in children's knowledge of the basic facts of addition, subtraction, multiplication, and division. Testimonials available on the site, and a trial version (just for division) is downloadable.
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MathGrapher
A graphing tool for 2D and 3D functions and data, shaded surfaces, contour plots. It does linear and non-linear curve fitting, and you may integrate and analyse systems of up to 20 coupled differential equations. Analysis tools include power spectrum
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MATHPLOTTER - Miguel Bayona
A tool for graphing functions and mathematical equations, intended for teachers of mathematics. It will enhance the quality of printed mathematical documents such as tests, handouts, and quizzes. The programs can also be used for educational purposes.
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Mathstar
Software packages for mathematics, science, finance and engineering, based around the Mathstar core, covering approximately all the mathematics used through high school to first-year university. Power Calculator = Mathstar + Electrical routines for technicians
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Matrix Calculator
Key in a matrix of any size, cell by cell, then click the buttons for worked derivations of its determinant, inverse, eigenvalues, diagonal matrix, or lower upper (LU) decomposition. Input the cells of a second matrix to multiply, add, or subtract it
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Matroid Theory - Sandra Kingan
Matroids are an abstraction of several combinatorial objects, among them graphs and matrices. The word matroid was coined by Whitney in 1935 in his landmark paper "On the abstract properties of linear dependence." In defining a matroid Whitney tried to
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Meaningful Learning Research Group - Dr. Joseph Novak
The group works with a number of common beliefs, primary among them the idea that the best way to teach is to determine what the student already knows, and then to teach from there. They believe that teaching and learning grounded in a coherent theory
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PRE-ALGEBRA--Hatz
CC3 Pre-ALG--Minowitz
ALGEBRA I--France
ALGEBRA I--Rasmussen
CCA Algebra--MinowitzCCA ALGEBRA--France
Mon - Lsn 7.1.1 (day 1) = What do exponential graphs look like?
I can...
investigate the family of functionsGEOMETRY--Kocmound
CW = 9-41 through 9-42
HW = 9-45 through 9-52
Fri - Lsn 9.1.5 = Chapter 8 Individual Test
GEOMETRY--France | 677.169 | 1 |
ISBN-10: 0321501071
ISBN-13: 9780321501073
Edition: 8 text balances solid mathematical coverage with a comprehensive overview of mathematical concepts as they relate to varied disciplines. The text provides an appreciation of mathematics, highlighting mathematical history, and applications of math to the arts and sciences. It is an ideal book for students who require a general overview of mathematics, especially those majoring in liberal arts, the social sciences, business, nursing and allied health fields. Let us introduce you to the practical, interesting, accessible, and powerful world of mathematics today-the world ofA Survey of Mathematics with Applications,8e | 677.169 | 1 |
Quantities
Reason Quantitatively And Use Units To Solve Problems.
Standard
Description
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HSN.Q .1
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
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HSN.Q .2
Define appropriate quantities for the purpose of descriptive modeling.
10
HSN.Q .3
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
11
The Complex Number System
Perform Arithmetic Operations With Complex Numbers.
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HSN.CN.1
Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.
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HSN.CN.2
Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
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HSN.CN.3
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
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Represent Complex Numbers And Their Operations On The Complex Plane.
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HSN.CN.4
(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
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The Real Number System
Extend The Properties Of Exponents To Rational Exponents.
Standard
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HSN.RN.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
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HSN.RN.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
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Use Properties Of Rational And Irrational Numbers.
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HSN.RN.3
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
11
Vector And Matrix Quantities
Perform Operations On Matrices And Use Matrices In Applications.
Standard
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HSN.VM.10
(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
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HSN.VM.11
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
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HSN.VM.12
(+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
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HSN.VM.6
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
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HSN.VM.7
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
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HSN.VM.8
(+) Add, subtract, and multiply matrices of appropriate dimensions.
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HSN.VM.9
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
8
Perform Operations On Vectors.
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HSN.VM.4
(+) Add and subtract vectors.
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HSN.VM.4.a
Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
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HSN.VM.4.b
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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HSN.VM.4.c
Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
5
Represent And Model With Vector Quantities.
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HSN.VM.1
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
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HSN.VM.2
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
6
HSN.VM.3
(+) Solve problems involving velocity and other quantities that can be represented by vectors. | 677.169 | 1 |
CPM Educational Program
CPM Teacher Guidebook
How Do I Get Precalculus and/or Calculus Assessments?
Precalculus and Calculus assessments are only available as downloadable files. These files can be modified by cutting and pasting items from the file to create your tests and quizzes. Both Precalculus and Calculus files contain sample Chapter tests and quizzes. The assessment files are only available through the assessment portal requiring a teacher login.
1. Log in to the CPM Assessment Site. Click on either Precalculus or Calculus on the top bar.
Choose Assessment.
2. The link takes you to the site where each of the chapter files are located.
3. Download the chapter files to your computer.
4. Assessments include quizzes for various sections.
5. Assessments include Chapter Tests.
6. Assessments include a Team Test for Precalculus and a Review for Calculus. | 677.169 | 1 |
Introduction to General Relativity, Black Holes, and Cosmology
General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on.
This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics.
Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordstrom and interior Schwarzchild solutions.
The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory. | 677.169 | 1 |
...AS Further Mathematics Why study AS Further Mathematics? Some students decide during their first year at College that they are interested... Learn about: Engineering Mathematics, Mathematics Series Financial Mathematics, Engineering Mathematics, Mathematical Economics Basic Mathematics, Engineering Mathematics, Actuarial Mathematics...
...AS/A2 Further Mathematics Why study Further Mathematics? Some students know that they plan to apply for a Mathematics or related course at University... Learn about: Financial Mathematics, Engineering Mathematics, Mathematical Economics... | 677.169 | 1 |
Pages
Monday, January 25, 2016
This semester I gave my Grade 12s a term project to practice function transformations. I began by sourcing the #MTBoS to see who had ventured down this road before. Luckily, several had and they had great advice regarding how to structure the task. I use Desmos regularly in class, so it was not a huge stretch for them to pick up the tool. I did show them how to restrict domain and range (although most of them stuck exclusively to domain). I gave them the project as we began to talk about function transformations, and they had 3.5 months to complete it. They complained, but the results were fantastic. (...bunch of drama queens). Couple of important points, and then I'll let you peruse/steal the handouts and view the samples of student work (of which I am extremely proud). Pointer #1: It was important that students copied a piece of art (this was typically a cartoon of sorts). Making them copy a pre-existing piece meant they must think about how the parameters shift to match. No lines are arbitrarily chosen.
Pointer #2: Illustrate how a variety of functions could model the same segment of line. When I do it again, I may even have weekly challenges as they are introduced to more and more function variety. Something small. I may project a simple image and ask, "What functions would you use to draw this?"
With all that out of the way, here are the materials I used:
Here is the handout I gave them. (It stresses the pre-drawing as well as the replication of a piece of art)
I was skeptical throughout the process because they resisted giving me updates on their progress. On the whole, they were fantastically done. I can also say that they did very well with function transformations on exams. Now that I (and you) have samples of work, it will go all the smoother the next time. NatBanting | 677.169 | 1 |
aim of this book is to describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra. | 677.169 | 1 |
Advanced Algebra Factoring Video Tutorials
Many students learning advanced algebra find factoring difficult. They feel overwhelmed with factoring homework, tests and projects. And it is not always easy to find factoring tutor who is both good and affordable. Now finding factoring help is easy. For your factoring homework, factoring tests, factoring projects, and factoring tutoring needs, TuLyn is a one-stop solution. You can master hundreds of math topics by using TuLyn.
At TuLyn, we have hundreds of video tutorial clips including factoring videos.
Our factoring videos replace text-based tutorials and give you better step-by-step explanations of factoring. Watch each video repeatedly until you understand how to approach factoring problems and how to solve them.
Hundreds of video tutorials on factoring make it easy for you to better understand the concept.
This math video tutorial gives a step by step explanation to "Method For Factoring A Trinomial With Leading Coefficient Other Than One".
The video tutorial is recommended for Advanced Algebra students.
This math video tutorial gives a step by step explanation to "Method For Factoring A Trinomial With Leading Coefficient Other Than One 2".
The video tutorial is recommended for Advanced Algebra students.
This math video tutorial gives a step by step explanation to "Method For Factoring A Trinomial With Leading Coefficient Other Than One 3".
The video tutorial is recommended for Advanced Algebra students.
This math video tutorial gives a step by step explanation to "Method For Factoring A Trinomial With Leading Coefficient Other Than One 4".
The video tutorial is recommended for Advanced Algebra students.
This math video tutorial gives a step by step explanation to "Method For Factoring A Trinomial With Leading Coefficient Other Than One 5".
The video tutorial is recommended for Advanced Algebra students. | 677.169 | 1 |
651083
ISBN: 0078651085
Publication Date: 2005
Publisher: Glencoe/McGraw-Hill School Pub Co
AUTHOR
Glencoe McGraw-Hill Staff
SUMMARY
"Glencoe Pre-Algebra" is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation.Glencoe McGraw-Hill Staff is the author of 'Pre-Algebra', published 2005 under ISBN 9780078651083 and ISBN 00786510 | 677.169 | 1 |
Congruence and similarity year 9Download our congruence and similarity year 9 eBooks for free and learn more about congruence and similarity year 9. These books contain exercises and tutorials to improve your practical skills, at all levels!
To find more books about congruence and similarity year 9, you can use related keywords : Hydrological Similarity, Goat Similarity Download, Goat Similarity Download, What Is The Similarity Between Bhabhi And Aunty.pdf, Icse Std 10th Maths Similarity, Manorama Year Pdf, Manorama Year Pdf, Manufacturing.pdf For 2nd Year, Achieve Anything In Just One Year Pdf, Chudachudi 16 Year
You can download PDF versions of the user's guide, manuals and ebooks about congruence and similarity year 9, you can also find and download for free A free online manual (notices) with beginner and intermediate, Downloads Documentation, You can download PDF files (or DOC and PPT) about congruence and similarity year 9 | 677.169 | 1 |
Description - A Computational Introduction to Number Theory and Algebra by Victor Shoup
Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This This edition now includes over 150 new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
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4 Topic 4: The Circle 1 Find the circumference of circles 2 Find the area of circles 3 Solve area problems involving circles Topic 5: Volume 1 Find the volumes of cylinders and spheres 2 Find the volume of cones 3 Find the volume of pyramids Topic 6: Similar Geometric Figures 1 Find the corresponding parts of similar triangles 2 Find the corresponding parts of similar figures Module 8: Introduction to Polynomials Topic 1: Adding and Subtracting Polynomials 1 Identify the terms of a polynomial 2 Add polynomials 3 Find the opposite of a polynomial 4 Subtract polynomials Topic 2: Multiplying Polynomials 1 Multiply a monomial times a polynomial 2 Multiply a binomial times a trinomial 3 Multiply binomials using FOIL Topic 3: Translate from English to Algebra 1 Translate from English to Algebra 2 Write algebraic to compare quantities Topic 4: Factoring Using the Greatest Common Factor 1 Find the greatest common factor (GCF) 2 Factor out the GCF from a polynomial Module 9:, Inequalities, and Applications Topic 1: Addition and Multiplication Principles of Equality 1 Use the addition principle of equality 2 Use the multiplication principle of equality 3 Use the division principle of equality Topic 2: Using Both Principles of Equality Together 1 Solve equations using both principles 2 Solve equations when the variable is on both sides 3 Solve equations with parentheses Topic 3: Solving with Fractions 1 Solve equations with fractions Topic 4: Formulas 1 Solve a formula for a specified variable Topic 5: Using to Solve Word Problems 1 Solve number problems 2 Apply the Mathematics Blueprint of Problem Solving Topic 6: Solving Word Problems Involving Money and Percents 1 Solve problems involving periodic rate charges 2 Solve percent problems 3 Solve investment problems 4 Solve coin problems Topic 7: Solving Inequalities in One Variable 1 Interpret inequality statements 2 Graph an inequality on a number line 3 Translate from English to Algebra 4 Solve and graph an inequality Module 10: Graphing and Functions Topic 1: The Rectangular Coordinate System 1 Plot a point, given the coordinates 2 Determine the coordinates of a plotted point 3 Find ordered pairs for a given linear equation Topic 2: Graphing Linear 1 Graph a linear equation by plotting three points 2 Graph a straight line by plotting its intercepts 3 Graph horizontal and vertical lines Topic 3: The Slope of a Line 1 Find the slope of a line given two points 2 Find the slope and y-intercept of a line 3 Write the equation given the slope and y- intercept 4 Graph a line using the slope and y-intercept 5 Find slopes of parallel and perpendicular lines
5 Topic 4: Writing the Equation of a Line 1 Write an equation given a point and the slope 2 Write an equation of a line given two points 3 Write an equation of a line given its graph Topic 5: Graphing Linear Inequalities 1 Graph linear inequalities in two variables Topic 6: Functions 1 Understand the concepts of relation and function 2 Graph simple nonlinear equations 3 Determine whether a graph represents a function 4 Use function notation Module 11: Systems of Linear and Inequalities Topic 1: Systems of Linear in Two Variables 1 Identify ordered pair solutions to a system 2 Solve a system of two equations by graphing 3 Solve a system of two equations by substitution 4 Solve a system of two equations by addition 5 Identify systems with no unique solution 6 Choose a method for solving systems Topic 2: Systems of Linear in Three Variables 1 Identify ordered triple solutions to a system 2 Solve systems with non-zero coefficients 3 Solve systems with zero coefficients Topic 3: Applications of Systems of Linear 1 Solve applications with systems in two variables 2 Solve applications with systems in three variables Topic 4: Systems of Linear Inequalities 1 Graph a system of linear inequalities Module 12: Exponents and Polynomials Topic 1: The Rules of Exponents 1 Use the product rule with exponential 2 Use the quotient rule with exponential 3 Raise exponential to a power Topic 2: Negative Exponents and Scientific Notation 1 Use negative exponents 2 Use scientific notation Topic 3: Fundamental Polynomial Operations 1 Recognize polynomials and determine their degrees 2 Add polynomials 3 Subtract polynomials 4 Evaluate polynomials to predict a value Topic 4: Multiplying Polynomials 1 Multiply a monomial by a polynomial 2 Multiply two binomials Topic 5: Multiplication Special Cases 1 Multiply the sum and difference of two terms 2 Square binomials 3 Multiply polynomials with more than two terms Topic 6: Dividing Polynomials 1 Divide a polynomial by a monomial 2 Divide a polynomial by a binomial Module 13: Factoring Topic 1: Removing a Common Factor 1 Factor polynomials with a common factor Topic 2: Factoring by Grouping 1 Factor with four terms by grouping Topic 3: Factoring Trinomials When a = 1 1 Factor trinomials when a = 1 2 Factor trinomials with a = 1 and a common factor Topic 4: Factoring Trinomials When a 1 1 Factor trinomials by the trial-and-error method 2 Factor trinomials with a 1 by grouping 3 Factor trinomials with a 1 and a common factor Topic 5: Special Cases of Factoring 1 Factor the difference of two squares 2 Factor perfect square trinomials 3 Factor the sum and difference of two cubes 4 Factor out a common factor first
MAT 0950 Course Objectives 5/15/20134/27/2009 A student should be able to R1. Do long division. R2. Divide by multiples of 10. R3. Use multiplication to check quotients. 1. Identify whole numbers. 2. IdentifyChapter 3 Vocabulary equivalent - Equations with the same solutions as the original equation are called. formula - An algebraic equation that relates two or more real-life quantities. unit rate - A rate
2012-2013 Math Content PATHWAY TO ALGEBRA I Unit Lesson Section Number and Operations in Base Ten Place Value with Whole Numbers Place Value and Rounding Addition and Subtraction Concepts Regrouping ConceptsSCOPE This course is divided into two semesters of study (A & B) comprised of five units each. Each unit teaches concepts and strategies recommended for intermediate algebra students. The first half of
Course Objectives The Duke TIP course corresponds to a high school course and is designed for gifted students in grades seven through nine who want to build their algebra skills before taking algebra inDevelopmental Math Course Outcomes and Objectives I. Math 0910 Basic Arithmetic/Pre-Algebra Upon satisfactory completion of this course, the student should be able to perform the following outcomes and
High School Mathematics Algebra This course is designed to give students the foundation of understanding algebra at a moderate pace. Essential material will be covered to prepare the students for Geometry.
REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts which are taught in the specified math course. The sheetsCore Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readinessTo the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requiresFirst Nine Weeks SOL Topic Blocks.4 Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole and natural. 7. Recognize that the
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
Introduction to the Instructor TERM 1 This calendar of lessons was prepared as a textbook independent sequence of lessons and the order of topics can be modified based on the textbook selection. The columns
I The Real and Complex Number Systems 1. Identify subsets of complex numbers, and compare their structural characteristics. 2. Compare and contrast the properties of real numbers with the properties of
Moore Catholic High School Math Department COLLEGE PREP AND MATH CONCEPTS The following is a list of terms and properties which are necessary for success in Math Concepts and College Prep math. You will
1 Algebra Scope and Sequence of Instruction Instructional Suggestions: Instructional strategies at this level should include connections back to prior learning activities from K-7. Students must demonstrateMATH Activities ver3 This content summary list is for the 2011-12 school year. Detailed Content Alignment Documents to State & Common Core Standards are posted on NOTE: Penda continues
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS The intermediate algebra skills illustrated here will be used extensively and regularly throughout the semester Thus, mastering these skills is anIntroduction to the Practice Eams The math placement eam determines what math course you will start with at North Hennepin Community College. The placement eam starts with a 1 question elementary algebra
Nativity Catholic School Rising 7th grade IXL Language Arts and Math Summer Homework Please work on the following skills listed in the 6th Grade Math and Language Arts IXL Program for a minimum of 60 minutes | 677.169 | 1 |
How is calculus used in the real world?
A:
Quick Answer
In the real world, calculus is used to build search engines and weather models, to study epidemiology and to construct buildings and bridges. Algorithms derived from calculus also allow searches to be conducted on social media sites like Facebook and Twitter.
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Major search engines like Google and Yahoo use calculus every day to create algorithms that make it easy to search for specific data. These algorithms combine geographic information, Web history and webpage reviews to find precise facts. Companies such as Facebook use these formulas to help users search for people or pages on their sites.
Weather models are built by computers that use calculus-derived algorithms to predict future weather. The computers are capable of sorting through factors like wind speed, temperature and region to depict an accurate picture of the weather. Calculus also provides the foundation for the equations meteorologists use to calculate the impact of changes in temperature and atmospheric pressure.
Public health is impacted by calculus via epidemiology, which is the study of the spread of infectious disease. The number of people already infected by a disease and the number of people not infected are put into equations that predict infection rates and speeds, origination points and the most effective modes of treatment.
Calculus is a significant factor in the architecture of buildings and bridges. Algorithms take into account factors such as supporting weight needed, distance and local weather patterns to create the safest and most attractive designs possible. | 677.169 | 1 |
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Year 10
- General Mathematics (Semester 2)The aim of this course is to develop students' understanding of practical areas of Mathematics in the context of everyday life, in order to improve and extend problem solving skills and strategies.
Throughout the semester students will develop knowledge based around the following key foci:
Statistics: including collection, display and interpretation and analysis of data.
Business Mathematics: including revisiting percentages in the context of shopping mark ups and discounts. Simple interest and compound interest calculations including: savings accounts, loans and investments.
Linear Graphs and Modelling: including sketching and interpreting line graphs that represent real life situations.
Students will use the CAS (Computer Algebra Systems) calculator as a learning tool to enhance their understanding of the above concepts. General Mathematics curriculum is built around the strands of Number and Algebra and Statistics and Probability.
Main Assessment Tasks
Skills based tasks, for example, tests, homework sheets
Problem solving and Modelling activities
Equipment
Text book – see the booklist for the correct title and edition
CAS calculator – TI-nspire CX CAS
Folder or exercise books
Digital device
Ruler
Pathways
Year 10 General Mathematics leads directly to Units 1 & 2 General Mathematics followed by Units 3 & 4 Further Mathematics. | 677.169 | 1 |
PACE Mathematical Foundations MOOC is an online program designed to enhance your mathematics skills in the areas of Number Theory, Algebra, Geometry, Probability and Statistics. This MOOC is designed to help develop the skills needed to be successful in college-level mathematics | 677.169 | 1 |
can we solve the national debt crisis? Should you or your child take on a student loan? Is it safe to talk on a cell phone while driving? Are there viable energy alternatives to fossil fuels? What could you do with a billion dollars? Could simple policy changes reduce political polarization? These questions may all seem very different, but they share two things in common. First, they are all questions with important implications for either personal success or our success as a nation. Second, they all concern topics that we can fully understand only with the aid of clear quantitative or mathematical thinking. In other words, they are topics for which we need math for life—a kind of math that looks quite different from most of the math that we learn in school, but that is just as (and often more) important. In Math for Life, award-winning author Jeffrey Bennett simply and clearly explains the key ideas of quantitative reasoning and applies them to all the above questions and many more. He also uses these questions to analyze our current education system, identifying both shortfalls in the teaching of mathematics and solutions for our educational future. No matter what your own level of mathematical ability, and no matter whether you approach the book as an educator, student, or interested adult, you are sure to find something new and thought-provoking in Math for Life.
Editorial Reviews
Review
"An insightful look at the crucial role mathematics plays in understanding the complexities of today's society. . . . The author's pleasant, conversational style shows that such insight can be developed without obscure or high-level computation. . . . Any reader, but especially parents, politicians, and professional educators, would benefit from reading this book. Summing up: Highly recommended. All levels/libraries." —Choice Magazine
"Full marks to Jeffrey Bennett for delivering exactly what his title promises. This is not the math your teacher (probably) said you would need in adult life but never did; it's the math you know you need—but likely don't have." —Keith Devlin, PhD, author, The Math Gene, and the Math Guy on National Public Radio
"Should be required reading for every American. There's no more powerful way to equip yourself for our increasingly complex and quantitative world than to read Math for Life." —K. Shane Goodwin, professor of mathematics, Brigham Young University–Idaho
"Brilliantly illustrates the importance of numeracy in all aspects of life." —David Taylor, assistant professor of mathematics, Roanoke College
About the Author
Jeffrey Bennett is an astrophysicist and educator who proposed the idea for and helped develop the Voyage Scale Model Solar System—the first science-oriented exhibit approved for permanent installation on the National Mall in Washington, DC. He is the lead author of college textbooks in four subjects—astronomy, astrobiology, mathematics, and statistics—and has written critically acclaimed books for the general public including Beyond UFOs and On the Cosmic Horizon. He is also the author of children's books, including those in the Science Adventures with Max the Dog series and The Wizard Who Saved the World. He lives in Boulder, Colorado.
Top customer reviews
This is a tough book to rate. The topic (getting folks comfortable with real-world, everyday-useful math and some of its implications) is important, and Bennett's general approach is both sensible and potentially effective. I really wanted to like this book. Unfortunately, while some sections are excellent, there are just too many (easily avoidable) problems: too much carelessness, too many opportunities for insight missed, too much that misleads. I wavered between 2 and 3 stars, but finally went with 3: while there are serious flaws, some of the discussions are very good.
My slightly sour take on this book began with the discussion of the bubble in median housing prices on page 4. The term "median" was not even defined; it was simply equated with "average", which tends to reinforce the mistaken notion that when someone says "average" they always mean "typical." This would have been a great place to start untangling the differences between the common-language meaning of "average" (which always means typical) and the various math-language meanings of "average" (mean, median, mode, which may or may not correspond to "typical"). The difference between median and mean are clarified much later (p. 44-46), but I was very grumpy 'til I got there.
The sloppy accuracy/precision discussion on p.21 didn't help. That discussion involves two scales that measure weight, an analog scale that reads weight to the nearest pound, and a digital scale that reads out to the nearest 0.01 lb. Bennett goes on to say "This means that the digital scale is more precise." That isn't correct; in the scale context precision refers to the repeatability of measurements of the same weight, not how many digits there are in the readout. He knows that; he was just careless.
Obviously, a book of this type must simplify many things. But there is a line between simple and simplistic, and too often this book veers into simplistic and outright misleading. An example of the latter: in his discussion of the impending financial problems with Social Security, he says (p117) that ".. during the 20th century, life expectancies in the US rose an average of 3 years per decade. If that trend continues…" The 3 years/decade is more or less true, but it refers to the life expectancy at birth (with much of that gain due to a reduction in infant mortality early in the century). What matters to SS is life expectancy at retirement age. That has not grown at anything like 3 years/decade (if it had been, we would all expect to live well past 100).
His discussion of the US debt/deficit problem is also simplistic and misleading. For example, a bar chart on p108 shows the annual federal gov't deficit and debt (not inflation-adjusted; a terrible choice) from 1970 to 2013, and in absolute terms rather than as a % of GDP (the standard and much more informative way to display that data). Clearly, his purpose was to create a maximally-scary plot rather than a more informative plot (which would have been scary enough).
In general, as Bennett's discussion topics move away from the scientific/technical (his sweet spot) and wander into "softer" areas (such as economics), the discussions become increasingly simplistic, sloppy, misleading, and error-prone. Based on just this book, the answer to the question "Does Bennett have any clear sense of what he knows and what he doesn't know?" would have to be a resounding "No."
One of the better examples of that (one of many) is found on p145: "The bottom line is that global warming is real and poses a great threat to our future, and anyone who claims otherwise is either very bad at math or deliberately distorting the facts." That last part is simply absurd. Bennett evidently has no understanding of the psychology/sociology of belief formation; he needs to read "Don't Even Think About It" by Marshall. Climate change denial isn't primarily about math and data, it's about the ways the brain works and the social/political/ideological influences that conspire to produce particular beliefs.
There is a much to admire in this book, but it is very sloppy and misleading in spots; it could have benefitted from better pre-pub readers. His attempts to teach everyday math and its connection to real-world problems are laudable and often instructive. Bennett's hopefully more rigorous textbooks (dealing with real-world math, statistics) might well be interesting and informative reads. But like all textbooks these days, they are too darn expensive.
So, a reluctant 3-star rating. I am sorry I have to rate such an error-filled and often misleading book so high, and sorry I have to rate a book with both great intentions and some excellent discussions so low. But there it is.
This book is a great primer into the absolute necessity for everyone to understand basic mathematics. The ideas are explained simply and eloquently. The topics are related to everyday finance, loans, realestate, interested and retirement - who doesn't need to know about these? There is a lot of attention to politics and energy issues as well. Finally, he ends with concrete suggestions on how to improve your own understanding and how we might change our educational systems for the better. A first rate book!
There are some important concepts, such as compound interest the basics of taxation,and a good introduction to the science of clmate change.However, Math for Life is really useful only for readers with almost no background in math.
Bennett also makes some very questionable economic assumptions, overstating the danger of the country's debt crisis. He talks primarily about the dangers of absolute debt; most economists would consider Debt to GDP to be a far more important number. he never considers any option other than massive cuts to Social Security and Medicare, never considering the possibility of an economic growth. Also, his repetition of the argument that "the government should balance their books like a family," is wrong.
This is really a must-read for, well... everyone. It is so common for people to feel that many of the issues being debated in our society are simply too technical for them to understand. Or worse, not really understanding an issue, to simply take the word of politicians they want to believe, who sadly seem not to really understand the issues themselves. I wish every politician were REQUIRED to read this book before taking office! Each of us has the responsibility to be an informed citizen, and this book gives you the mathematical foundation to understand so many important issues, and to feel confident in your grasp of the salient mathematical underpinnings. Moreover, the book manages to teach these ideas in a way that anyone can understand and enjoy. It also gives you necessary tools to manage your own life! It is truly satisfying to feel your grasp of these important concepts. There is seldom a book that has so much to offer to so many, especially in such a delightfully satisfying way! | 677.169 | 1 |
This Maths Revision and Practice range contains clear and accessible explanations of all the GCSE content, with lots of practice opportunities for each topic throughout the book. Based on new research that proves repeated practice is more effective than repeated study, this book is guaranteed to help you achieve the best results. There are clear and concise revision notes for every topic covered in the curriculum, plus seven practice opportunities to ensure the best results.
Includes: · quick tests to check understanding · end-of-topic practice questions · topic review questions later in the book · mixed practice questions at the end of the book · free Q&A flashcards to download online · an ebook version of the revision guide · more topic-by-topic practice and a complete exam-style paper in the added workbook UK. Book Condition: New. Based on new research that proves repeated practice is more effective than repeated study, this Maths all-in-one revision and practice book is guaranteed to help you achieve the best results. Containing clear and accessible explanations of all the GCSE content, there are lots of practice opportunities for each topic throughout the book. Series: Collins GCSE Revision and Practice - New 2015 Curriculum. Num Pages: 216 pages. BIC Classification: 4KHT; 4Y; YQM; YQZ. Category: (E) Primary & Secondary Education; (J) Children / Juvenile. Dimension: 213 x 298 x 16. Weight in Grams: 612. . 2015. Paperback. . . . . Books ship from the US and Ireland. Bookseller Inventory # V9780008112523 | 677.169 | 1 |
Topics included:
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- Variations
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College intermediate algebra help free
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Also included are the solutions with full explanations. Algebra is a technique of writing a college intermediate algebra help free problem in terms of equations and formulae and solve them to get the answer. Elementary algebra has its use in day to day life. It can help you in solving games and puzzles. Algebra finds its use in maths, engineering, statistics, science.Learning Algebra is achievable for all, you just need to take things one step at a time and learn the basic rules before getting to the complex problems.
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This 32-question circuit begins with an addition problem and ends with a definite integral which requires substitution. This circuit could be used for placement or diagnosis, especially for those students whose transcripts are hard to decipher (home-schooled students, non-traditional age college students, international students).
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One of the most valuable tools acquired in a university education, college algebra is essential for courses from the sciences to computing, engineering to mathematics. It can help you do better on placement exams, even before college, and it's useful in solving the computations of daily life. Now anyone with an interest in college algebra can master it. In College Algebra Demystified, entertaining author and experienced teacher Rhonda Huettenmueller breaks college algebra down into manageable bites with practical examples, real data, and a new approach that banishes algebra's mystery.
With College Algebra Demystified, you master the subject one simple step at a time—at your own speed. Unlike most books on college algebra, general concepts are presented first—and the details follow. In order to make the process as clear and simple as possible, long computations are presented in a logical, layered progression with just one execution per step.
This fast and easy self-teaching course will help you:
Perform better on placement exams
Avoid confusion with detailed examples and solutions that help you every step of the way
Get comfortable with functions, graphs of functions, logarithms, exponents, and more
Master aspects of algebra that will help you with calculus, geometry, trigonometry, physics, chemistry, computing, and engineering
Reinforce learning and pinpoint weaknesses with questions at the end of every chapter, and a final at the end of the book
"synopsis" may belong to another edition of this title.
About the Author:
Rhonda Huettenmueller (Sanger, TX) has taught mathematics at the college level for over 14 years. Popular with students for her ability to make higher math understandable and even enjoyable, she incorporates many of her teaching techniques in this book. She received her Ph.D. in mathematics from the University of North Texas.
Book Description 2004. Paperback. Book Condition: New. 1st. Paperback. A BETTER WAY TO COLLEGE ALGEBRA X-PERTISEOne of the most valuable tools acquired in a university education, college algebra is essential for courses from the sciences to compu.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 446 pages. 0.644. Bookseller Inventory # 9780071439282 | 677.169 | 1 |
Description
The only High School Math app on Number & Quantity designed for students, parents, and teachers! Now with common core curriculum builder and a powerful lesson designer.
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In high school, students will be exposed to an extension of number, when the real numbers are augmented by the imaginary numbers to form the complex numbers. With each extension of number, the meanings of addition, subtraction, multiplication, and division are extended. In each new number system—integers, rational numbers, real numbers, and complex numbers—the four operations stay the same in two important ways: They have the commutative, associative, and distributive properties and their new meanings are consistent with their previous meanings. Extending the properties of whole-number exponents leads to new and productive notation. Calculators, spreadsheets, and computer algebra systems can provide ways for students to become better acquainted with these new number systems and their notation. They can be used to generate data for numerical experiments, to help understand the workings of matrix, vector, and complex number algebra, and to experiment with non-integer exponents.
In high school, students encounter a wider variety of units in modeling, e.g., acceleration, currency conversions, derived quantities such as person-hours and heating degree days, social science rates such as per-capita income, and rates in everyday life such as points scored per game or batting averages. They also encounter novel situations in which they themselves must conceive the attributes of interest. Such a conceptual process is sometimes called quantification.
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How to Solve Tensor Algebra Problems
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Tensor algebra is a branch of mathematics, related in part to one dimensional vector analysis, which has become increasingly used in recent years. You will encounter it in the latter years of your school syllabus and certainly as part of any applied or engineering maths type courses you can take at college. It is used extensively in physics, fluid mechanics, stress analysis and other areas. It is still evolving and increasing computer processing power has and will continue to play a role in that. Some concepts and methods for their use make this type of work difficult and many people have to go online to get tensors explained properly. Many have been choosing us over our 5+ years of service because they know we have the highly qualified staff who can help them.
The Skills You Need to Evaluate Tensor Quantities
In many ways tensor algebra and analysis is an extension of vector analysis. Vectors can be used to describe a point in space, a line or surface in multi dimensions.
Vectors can use a distance + direction type approach, or a system of co-ordinates.
Tensors allow geometric shapes to be modeled and processes taking place along their surfaces and within them to be evaluated. This is why fluid dynamics in various conduits, finite element stress analysis, and rock mechanics are all recent applications.
Tensors can also be represented using a co-ordinate approach which leads to the production of 3 dimensional matrices, or arrays. As with vectors, the proper handling of a matrix or array can lead to solutions for tensor algebra problems.
You should be familiar not just with differentiation and integration to evaluate tensor quantities. You will require familiarity with different co-ordinate systems, cartesian or polar, plus know how to get dot or scalar products.
Matrix skills are essential so learn how to multiply, transform and invert them properly. Advances in computer handling of arrays has accelerated this field of mathematics.
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Exponents
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These are lesson notes for Exponents that include a warm-up (equations & inequalities and integers), "I/We/You Do" Practice, Summary, Extra Practice/Ticket Out the Door Problems, Cornell Notes, Graphic Organizer (Flow Map). This is in Word format so that you may be able to adjust the notes to fit your textbooks and class. (For the extra practice, and for purpose of downloading the file without it being skewed, you will need to insert a few exponents before copying). | 677.169 | 1 |
This course is the first half of a standard one-year course in elementary algebra. Topics to be covered include: the concept of a variable, evaluation of expressions, and simple algebraic modeling. Students will solve and graph linear equations and inequalities. | 677.169 | 1 |
Mathematics
Course Descriptions
MTH010 Fundamentals of Math 3-0-3 Fundamentals of Math is designed to review and/or establish basic arithmetic skills with integers, fractions, decimals, ratios, and percents. Students are introduced to variables, basic linear equations, proportions, and geometry formulas. Degree- and certificate-seeking students required to complete developmental coursework must enroll in the required developmental course(s) prior to or immediately following their first six credit hours of enrollment at MACC. (FA, SP, SU)
MTH011 Fundamentals of Algebra 3-0-3 Fundamentals of Algebra is designed for the student who lacks the necessary algebraic skills to undertake collegelevel courses. It includes the study of the real number system, basic linear equations and inequalities, as well as their applications. Linear equations in two variables are covered with graphing, writing equations of lines, and solving systems of linear equations. Exponents are studied along with the operations of addition, subtraction, multiplication, and division of polynomials. Degree- and certificate-seeking students required to complete developmental coursework must enroll in the required developmental course(s) prior to or immediately following their first six credit hours of enrollment at MACC. Prerequisite: Eligible placement score, grade of "C" or higher in MTH010 or successful completion of appropriate module in the Computer Assisted Pre-Algebra sequence.
MTH015 Fundamentals of Technical Mathematics 3-0-3 This course is designed to provide an introduction and/or review of mathematics concepts and skills for students entering technical programs. The emphasis will be on direct technical applications rather than theoretical mathematics. Topics include integers, decimals, fractions, measurement (U.S. and metric), angles area, perimeter, volume, linear equations, polynomials, and graphs. Degree- and certificate-seeking students required to complete developmental coursework must enroll in the required developmental course(s) prior to or immediately following their first six credit hours of enrollment at MACC. (FA)
MTH016 Computer Assisted Pre-Algebra I 3-0-3 This course is designed for students who lack the necessary arithmetic and/or algebraic skills to undertake courses in mathematics and science. This course emphasizes individualized instruction and computer-assisted learning. Concepts are divided into modules which students must master to progress in the course. Students who pass module 12 have met the prerequisite for MTH100. Students who pass module 6 have met the prerequisites for any class for which MTH010 is a prerequisite. Degree- and certificate seeking students required to complete developmental coursework must enroll in the required developmental course(s) prior to or immediately following their first six credit hours of enrollment at MACC.
MTH017 Computer Assisted Pre-Algebra II 3-0-3 A continuation of MTH016. Students who pass module 12 have met the prerequisite for MTH100. Students who pass module 6 have met the prerequisites for any class for which MTH010 is a prerequisite. Prerequisite: A grade of "C" or higher in MTH016. Degree- and certificate-seeking students required to complete developmental coursework must enroll in the required developmental course(s) prior to or immediately following their first six credit hours of enrollment at MACC.
MTH018 Computer Assisted Pre-Algebra III 3-0-3 This course is a continuation of MTH017. Students who pass module 12 have met the prerequisite for MTH100. Students who pass module 6 have met the prerequisite for any class for which MTH010 is a prerequisite. Prerequisite: A grade of "C" or higher in MTH017. Degree- and certificate seeking students required to complete developmental coursework must enroll in the required developmental course(s) prior to or immediately following their first six credit hours of enrollment at MACC.
MTH019 Computer Assisted Pre-Algebra Supplement 3-0-3 Students who need two or fewer modules to satisfy the prerequisite for a subsequent math class may enroll in this class to complete those modules. Instructor approval is required. Students who pass module 12 have met the prerequisite for MTH100. Students who pass module 8 have met the prerequisites for any class for which MTH010 is a prerequisite. Degree- and certificate-seeking students required to complete developmental coursework must enroll in the required developmental course(s) prior to or immediately following their first six credit hours of enrollment at MACC.
MTH 020 Transition to College Algebra 1-0-1 This course is intended as an alternative for students who can demonstrate skills they already possess and, therefore, accelerate the math sequence path into MTH140 College Algebra. The course is only a quick review of topics usually covered in MTH100 Intermediate Algebra, with special attention to rational expressions, radicals, and factoring. Degree- and certificate-seeking students required to complete developmental coursework must enroll in the required developmental course(s) prior to or immediately following their first six credit hours of enrollment at MACC. Prerequisite: Successful completion of MTH011 with a "B" or higher, successful completion of module 12 the first time enrolled in MTH016, instructor recommendation, or placement scores for MTH100. (SU)
MTH080: Support for Technical Mathematics (1-0-1) This course provides co-requisite support and supplemental instruction for students who are co-enrolled in the appropriate section of MTH130 Technical Mathematics, with emphasis placed on experiences that enhance the materials presented in the accompanying class. Topics include integers, decimals, fractions, measurement (US and metric), angles area, perimeter, volume, linear equations, polynomials, and graphs. Prerequisite: Placement will be determined by Compass/ACT Scores. Eligible placement score: ACT: 18 or higher; Compass (pre-Algebra): 60 or higher; Compass (Algebra): 26 or higher. Corequisite: The accompanying section of MTH130 Technical Mathematics. (FA, SP)
MTH 090: Support for College Algebra 3-0-3 This course provides co-requisite support and supplemental instruction for students who have met the prerequisites to enroll in MTH100 Intermediate Algebra. Emphasis is placed on experiences that enhance the materials presented in the accompanying MTH140 College Algebra class. Upon completion, students should be able to solve problems, apply critical thinking, work in teams, and communicate effectively. Degree- and certificate-seeking students required to complete developmental coursework must enroll in the required developmental course(es) within their first six credit hours at MACC. Prerequisite: Eligible placement score for MTH100, grade of "C" or higher in MTH011, or successful completion of the appropriate module in the Computer Assisted Pre- Algebra sequence. Corequisite: The accompanying section of MTH140.
MTH130: Technical Math 3-0-3 Technical Mathematics includes topics in right triangle trigonometry; quadratic equations; trig. identities, functions and graphing; vectors; and analytic geometry necessary for students in technical programs. Prerequisite: Eligible placement score or grade of "C" or higher in MTH011 or MTH015 or successful completion of the appropriate module in the Computer Assisted Pre-Algebra sequence.
MTH135: Advanced Technical Math 2-0-2 Advanced Technical Mathematics is designed for students in technical programs needing additional mathematics topics including exponents and logarithms, matrices, progressions and the binomial theorem, and statistics for process control. The emphasis is on technical applications. Prerequisite: A grade of "C" or higher in MTH 130.
MTH140: College Algebra 3-0-3 Topics include a review of basic algebra; various functions and their graphs, including polynomial and rational functions and exponential and logarithmic functions; and an introduction to analytic geometry. The course includes systems of equations and inequalities. Prerequisite: Eligible placement score, grade of "C" or higher in MTH020, MTH100, or co-requisite of MTH090. (FA, SP, SU)
MTH 141: Contemporary College Mathematics 3-0-3 This course contains selected topics from number theories, algebra, geometry, probability, and statistics with emphasis on applications of mathematics. (IN)
MTH145: College Trigonometry 3-0-3 This course includes angle-based trigonometric functions and their inverses, multiple angle formulas, identities, trigonometric equations, radian measure, arc length, angular velocity, graphs of trigonometric functions, and solution of right triangles. This course does not meet the math requirement for the AA degree. Prerequisite: Eligible placement score or a grade of "C" or higher in MTH140.
MTH150: Precalculus 5-0-5 This course is a unified study of College Algebra and Trigonometry designed to prepare students for Calculus. The course will focus on algebraic, trigonometric, logarithmic and exponential functions. Prerequisite: Eligible placement score, grade of "C" or higher in MTH020 or MTH100. (FA, SP, SU)
MTH 201: Analytic Geometry and Calculus I 5-0-5 Students are introduced to plane analytic geometry, including limits, continuity, derivative for functions of a single variable, differentials, indefinite and definite integrals, and applications of the derivative and integral. (FA, SP)
MTH202: Analytic Geometry and Calculus II 5-0-5 This course is a continuation of MTH201. Topics include logarithmic and exponential derivatives and integrals, integration techniques, sequences and series, and parametric and polar curves. Prerequisite: MTH201 with a grade of "C" or better.
MTH203: Analytic Geometry and Calculus III 5-0-5 This course is a continuation of MTH202. An introduction to multi-variable calculus. Topics include vector-valued functions, partial derivatives, multiple integration, and vector calculus. Prerequisite: MTH202 with a grade of "C" or better.
MTH215: Introduction to Probability and Statistics 3-0-3 This course is designed primarily for students seeking a degree in business. Probability theory, random variables, expectations, continuous and discrete probability distributions, descriptive statistics, sampling distributions, estimation, and hypothesis testing are covered. (IN)
MTH 250: Differential Equations 3-0-3 This is an advanced course for pre-engineering students. Topics include differential equations of first order and first degree, applications of first order, first degree differential equations, homogeneous linear differential equations with constant coefficients, Laplace transforms, power series, series solutions, and numerical solutions of differential equations.(SP)
*Students planning to transfer to the University of Missouri-Columbia will not be able to use MTH160 – Elementary Statistics as a pathway course. These students will need to take MTH140 – College Algebra for fall 2017. See your advisor for additional information. | 677.169 | 1 |
Curriculum
Maths
Welcome to the Walton High Maths Curriculum Page
Mathematics is a creative and highly inter-connected discipline that is essential to everyday life. It is critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. The study of mathematics provides a foundation for understanding the world and making a positive contribution to society.
At Walton High we want our students to be functionally numerate, to reason mathematically and to apply mathematical techniques to solve problems in a variety of contexts. Through exciting and challenging learning opportunities we hope to instil in our students an appreciation of the power and beauty of mathematics and a sense of curiosity and enjoyment about the subject.
Key Stage 3
At Walton High Key Stage 3 Mathematics is a two year programme whose aim is to provide students with numerical and basic algebraic fluency together with a foundation in solving problems in mathematical and non-mathematical contexts. For further information about the transition from Key Stage 2 to Key Stage 3 mathematics, the essential knowledge that we expect students to have at this level and the changes in the 2014 curriculum please see the presentation from the Year 7 information evening.
Key Stage 4
At Walton High we follow a 3-year Key Stage 4 programme using AQA's new Mathematics GCSE. Each student follows either a 'Foundation' or 'Higher' pathway, depending upon which one will allow the best level of progress for that student.
The content of the course is organised into broad topic areas, the weightings of which are set out in the table below | 677.169 | 1 |
3 Pages: Detailed Handout (Lesson) / Worksheet / Key
Equation editor software within MS Word is used for a clear, professional look.
Word is needed to print. MathType is needed to edit equations.
Page 1 is a handout that clearly and concisely describes what is meant by factoring by grouping, when it applies, and how to apply it accurately and completely. Included are detailed step-by-step instructions, along with several examples. | 677.169 | 1 |
The
Mathematics Department at
the University of Michigan
has made a commitment to
making these introductory
courses a vital part of our
undergraduate students' education. We
have changed both the content
of the courses and the ways
we teach them by drawing
ideas simultaneously from
calculus reform nationwide
and from the cooperative
learning movement. Our
texts, with their fresh approach
to calculus, give us the
opportunity to strengthen
students' grasp of the underlying
concepts. Students
are taught to read the textbook
and write full essay answers
to many of the interesting
problems. In our classes
students work together actively,
and outside the class they
meet frequently to solve
their team homework problems.
We
have included some materials
that you may find useful
in learning more about our
program: | 677.169 | 1 |
Calculus of variations
Background to the schools Wikipedia
This Schools selection was originally chosen by SOS Children for schools in the developing world without internet access. It is available as a intranet download. See to find out about child sponsorship.
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown functions and their derivatives. The interest is in extremal functions that make the functional attain a maximum or minimum value – or stationary functions – those where the rate of change of the functional is precisely zero.
Perhaps the simplest example of such a problem is to find the curve of shortest length, or geodesic, connecting two points. If there are no constraints, the solution is obviously a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as geodesics. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, where the optical length depends upon the material of the medium. One corresponding concept in mechanics is the principle of least action.
Many important problems involve functions of several variables. Solutions of boundary value problems for the Laplace equation satisfy the Dirichlet principle. Plateau's problem requires finding a surface of minimal area that spans a given contour in space: the solution or solutions can often be found by dipping a wire frame in a solution of soap suds. Although such experiments are relatively easy to perform, their mathematical interpretation is far from simple: there may be more than one locally minimizing surface, and they may have non-trivial topology.
History
The calculus of variations may be said to begin with a problem of Johann Bernoulli's (1696). It immediately occupied the attention of Jakob Bernoulli and the Marquis de l'Hôpital, but Euler first elaborated the subject. His contributions began in 1733, and his Elementa Calculi Variationum gave to the science its name. Lagrange contributed extensively to the theory, and Legendre (1786) laid down a method, not entirely satisfactory, for the discrimination of maxima and minima. Newton and Leibnitz also gave some early attention to the subject. To this discrimination Brunacci (1810), Gauss (1829), Poisson (1831), Ostrogradsky (1834), and Jacobi (1837) have been among the contributors. An important general work is that of Sarrus (1842) which was condensed and improved by Cauchy (1844). Other valuable treatises and memoirs have been written by Strauch (1849), Jellett (1850), Hesse (1857), Clebsch (1858), and Carll (1885), but perhaps the most important work of the century is that of Weierstrass. His celebrated course on the theory is epoch-making, and it may be asserted that he was the first to place it on a firm and unquestionable foundation. The 20th and the 23rd Hilbert problems published in 1900 enticed further development. In the 20th century Hilbert, Noether, Tonelli, Lebesgue and Hadamard among others made significant contributions. Marston Morse applied calculus of variations in what is now called Morse theory. Pontryagin, Rockafellar and Clarke developed new mathematical tools for optimal control theory, a generalisation of calculus of variations.
Weak and strong extrema
The supremum norm (also called infinity norm) for real, continuous, bounded functions on a topological space is defined as
.
A functional defined on some appropriate space of functions with norm is said to have a weak minimum at the function if there exists some such that, for all functions y with ,
.
Weakmaxima are defined similarly, with the inequality in the last equation reversed. In most problems, is the space of r-times continuously differentiable functions on a compact subset of the real line, with its norm given by
.
This norm is just the sum of the supremum norms of and its derivatives.
A functional is said to have a strong minimum at if there exists some such that, for all functions y with , . Strong maximum is defined similarly, but with the inequality in the last equation reversed.
The difference between strong and weak extrema is that, for a strong extremum, is a local extremum relative to the set of -close functions with respect to the supremum norm. In general this (supremum) norm is different from the norm that V has been endowed with. If is a strong extremum for then it is also a weak extremum, but the converse may not hold. Finding strong extrema is more difficult than finding weak extrema and in what follows it will be assumed that we are looking for weak extrema.
The Euler–Lagrange equation
Under ideal conditions, the maxima and minima of a given function may be located by finding the points where its derivative vanishes. By analogy, solutions of smooth variational problems may be obtained by solving the associated Euler–Lagrange equation.
Consider the functional:
The function should have at least one derivative in order to satisfy the requirements for valid application of the function; further, if the functional attains its local minimum at and is an arbitrary function that has at least one derivative and vanishes at the endpoints and , then we must have
for any number ε close to 0. Therefore, the derivative of with respect to ε (the first variation of A) must vanish at ε = 0.
where we have used the chain rule in the second line and integration by parts in the third. The last term in the third line vanishes because at the end points. Finally, according to the fundamental lemma of calculus of variations, we find that will satisfy the Euler–Lagrange equation
In general this gives a second-order ordinary differential equation which can be solved to obtain the extremal . The Euler–Lagrange equation is a necessary, but not sufficient, condition for an extremal. Sufficient conditions for an extremal are discussed in the references.
In order to illustrate this process, consider the problem of finding the shortest curve in the plane that connects two points and . The arc length is given by
with
and where , , and .
for any choice of the function . We may interpret this condition as the vanishing of all directional derivatives of in the space of differentiable functions, and this is formalized by requiring the Fréchet derivative of to vanish at . If we assume that has two continuous derivatives (or if we consider weak derivatives), then we may use integration by parts:
with the substitution
then we have
but the first term is zero since was chosen to vanish at and where the evaluation is taken. Therefore,
for any twice differentiable function that vanishes at the endpoints of the interval.
We can now apply the fundamental lemma of calculus of variations: If
for any sufficiently differentiable function within the integration range that vanishes at the endpoints of the interval, then it follows that is identically zero on its domain.
Therefore,
It follows from this equation that
and hence the extremals are straight lines.
The Beltrami Identity
Frequently in physical problems, it turns out that . In that case, the Euler-Lagrange equation can be simplified using the Beltrami identity:
where is a constant. The left hand side is the Legendre transformation of L with respect to f '.
du Bois Reymond's theorem
The discussion thus far has assumed that extremal functions possess two continuous derivatives, although the existence of the integral A requires only first derivatives of trial functions. The condition that the first variation vanish at an extremal may be regarded as a weak form of the Euler-Lagrange equation. The theorem of du Bois Reymond asserts that this weak form implies the strong form. If L has continuous first and second derivatives with respect to all of its arguments, and if
then has two continuous derivatives, and it satisfies the Euler-Lagrange equation.
Functions of several variables
Variational problems that involve multiple integrals arise in numerous applications. For example, if φ(x,y) denotes the displacement of a membrane above the domain D in the x,y plane, then its potential energy is proportional to its surface area:
Plateau's problem consists of finding a function that minimizes the surface area while assuming prescribed values on the boundary of D; the solutions are called minimal surfaces. The Euler-Lagrange equation for this problem is nonlinear:
See Courant (1950) for details.
Dirichlet's principle
It is often sufficient to consider only small displacements of the membrane, whose energy difference from no displacement is approximated by
The functional V is to be minimized among all trial functions φ that assume prescribed values on the boundary of D. If u is the minimizing function and v is an arbitrary smooth function that vanishes on the boundary of D, then the first variation of must vanish:
Provided that u has two derivatives, we may apply the divergence theorem to obtain
where C is the boundary of D, s is arclength along C and is the normal derivative of u on C. Since v vanishes on C and the first variation vanishes, the result is
for all smooth functions v that vanish on the boundary of D. The proof for the case of one dimensional integrals may be adapted to this case to show that
in D.
The difficulty with this reasoning is the assumption that the minimizing function u must have two derivatives. Riemann argued that the existence of a smooth minimizing function was assured by the connection with the physical problem: membranes do indeed assume configurations with minimal potential energy. Riemann named this idea Dirichlet's principle in honour of his teacher Dirichlet. However Weierstrass gave an example of a variational problem with no solution: minimize
among all functions φ that satisfy and W can be made arbitrarily small by choosing piecewise linear functions that make a transition between -1 and 1 in a small neighbourhood of the origin. However, there is no function that makes W=0. The resulting controversy over the validity of Dirichlet's principle is explained in . Eventually it was shown that Dirichlet's principle is valid, but it requires a sophisticated application of the regularity theory for elliptic partial differential equations; see Jost and Li-Jost (1998).
Generalization to other boundary value problems
A more general expression for the potential energy of a membrane is
This corresponds to an external force density in D, an external force on the boundary C, and elastic forces with modulus acting on C. The function that minimizes the potential energy with no restriction on its boundary values will be denoted by u. Provided that f and g are continuous, regularity theory implies that the minimizing function u will have two derivatives. In taking the first variation, no boundary condition need be imposed on the increment v. The first variation of is given by
If we apply the divergence theorem, the result is
If we first set v=0 on C, the boundary integral vanishes, and we conclude as before that
in D. Then if we allow v to assume arbitrary boundary values, this implies that u must satisfy the boundary condition
on C. Note that this boundary condition is a consequence of the minimizing property of u: it is not imposed beforehand. Such conditions are called natural boundary conditions.
The preceding reasoning is not valid if vanishes identically on C. In such a case, we could allow a trial function , where c is a constant. For such a trial function,
By appropriate choice of c, V can assume any value unless the quantity inside the brackets vanishes. Therefore the variational problem is meaningless unless
This condition implies that net external forces on the system are in equilibrium. If these forces are in equilibrium, then the variational problem has a solution, but it is not unique, since an arbitrary constant may be added. Further details and examples are in Courant and Hilbert (1953).
Eigenvalue problems
Both one-dimensional and multi-dimensional eigenvalue problems can be formulated as variational problems.
Sturm-Liouville problems
The Sturm-Liouville eigenvalue problem involves a general quadratic form
where φ is restricted to functions that satisfy the boundary conditions
Let R be a normalization integral
The functions and are required to be everywhere positive and bounded away from zero. The primary variational problem is to minimize the ratio Q/R among all φ satisfying the endpoint conditions. It is shown below that the Euler-Lagrange equation for the minimizing u is
where λ is the quotient
It can be shown (see Gelfand and Fomin 1963) that the minimizing u has two derivatives and satisfies the Euler-Lagrange equation. The associated λ will be denoted by ; it is the lowest eigenvalue for this equation and boundary conditions. The associated minimizing function will be denoted by . This variational characterization of eigenvalues leads to the Rayleigh-Ritz method: choose an approximating u as a linear combination of basis functions (for example trigonometric functions) and carry out a finite-dimensional minimization among such linear combinations. This method is often surprisingly accurate.
The next smallest eigenvalue and eigenfunction can be obtained by minimizing Q under the additional constraint
This procedure can be extended to obtain the complete sequence of eigenvalues and eigenfunctions for the problem.
The variational problem also applies to more general boundary conditions. Instead of requiring that φ vanish at the endpoints, we may not impose any condition at the endpoints, and set
where and are arbitrary. If we set the first variation for the ratio is
where λ is given by the ratio as previously. After integration by parts,
If we first require that v vanish at the endpoints, the first variation will vanish for all such v only if
If u satisfies this condition, then the first variation will vanish for arbitrary v only if
These latter conditions are the natural boundary conditions for this problem, since they are not imposed on trial functions for the minimization, but are instead a consequence of the minimization.
Eigenvalue problems in several dimensions
Eigenvalue problems in higher dimensions are defined in analogy with the one-dimensional case. For example, given a domain D with boundary B in three dimensions we may define
and
Let u be the function that minimizes the quotient with no condition prescribed on the boundary B. The Euler-Lagrange equation satisfied by u is
where
The minimizing u must also satisfy the natural boundary condition
on the boundary B. This result depends upon the regularity theory for elliptic partial differential equations; see Jost and Li-Jost (1998) for details. Many extensions, including completeness results, asymptotic properties of the eigenvalues and results concerning the nodes of the eigenfunctions are in Courant and Hilbert (1953).
Applications
Some applications of the Calculus of variations include:
The derivation of the Catenary shape
The Brachistochrone problem
Isoperimetric problems
Geodesics on surfaces
Minimal surfaces and Plateau's problem
Optimal Control
Fermat's principle
Fermat's principle states that light takes a path that (locally) minimizes the optical length between its endpoints. If the x-coordinate is chosen as the parameter along the path, and along the path, then the optical length is given by
where the refractive index depends upon the material. If we try then the first variation of A (the derivative of A with respect to ε) is
After integration by parts of the first term within brackets, we obtain the Euler-Lagrange equation
The light rays may be determined by integrating this equation.
Snell's law
There is a discontinuity of the refractive index when light enters or leaves a lens. Let
where and are constants. Then the Euler-Lagrange equation holds as before in the region where x<0 or x>0, and in fact the path is a straight line there, since the refractive index is constant. At the x=0, f must be continuous, but f' may be discontinuous. After integration by parts in the separate regions and using the Euler-Lagrange equations, the first variation takes the form
The factor multiplying is the sine of angle of the incident ray with the x axis, and the factor multiplying is the sine of angle of the refracted ray with the x axis. Snell's law for refraction requires that these terms be equal. As this calculation demonstrates, Snell's law is equivalent to vanishing of the first variation of the optical path length.
Fermat's principle in three dimensions
It is expedient to use vector notation: let let t be a parameter, let be the parametric representation of a curve C, and let be its tangent vector. The optical length of the curve is given by
Note that this integral is invariant with respect to changes in the parametric representation of C. The Euler-Lagrange equations for a minimizing curve have the symmetric form
where
It follows from the definition that P satisfies
Therefore the integral may also be written as
This form suggests that if we can find a function ψ whose gradient is given by P, then the integral A is given by the difference of ψ at the endpoints of the interval of integration. Thus the problem of studying the curves that make the integral stationary can be related to the study of the level surfaces of ψ. In order to find such a function, we turn to the wave equation, which governs the propagation of light.
Connection with the wave equation
The wave equation for an inhomogeneous medium is
where c is the velocity, which generally depends upon X. Wave fronts for light are characteristic surfaces for this partial differential equation: they satisfy
We may look for solutions in the form
In that case, ψ satisfies
where According to the theory of first-order partial differential equations, if then P satisfies
along a system of curves (the light rays) that are given by
These equations for solution of a first-order partial differential equation are identical to the Euler-Lagrange equations if we make the identification
We conclude that the function ψ is the value of the minimizing integral A as a function of the upper end point. That is, when a family of minimizing curves is constructed, the values of the optical length satisfy the characteristic equation corresponding the wave equation. Hence, solving the associated partial differential equation of first order is equivalent to finding families of solutions of the variational problem. This is the essential content of the Hamilton-Jacobi theory, which applies to more general variational problems.
The action principle
The action was defined by Hamilton to be the time integral of the Lagrangian, L, which is defined as a difference of energies:
where T is the kinetic energy of a mechanical system and U is the potential energy. Hamilton's principle (or the action principle) states that the motion of a conservative holonomic (integrable constraints) mechanical system is such that the action integral
is stationary with respect to variations in the path x(t). The Euler-Lagrange equations for this system are known as Lagrange's equations:
and they are equivalent to Newton's equations of motion (for such systems).
The conjugate momenta P are defined by
For example, if
then
Hamiltonian mechanics results if the conjugate momenta are introduced in place of , and the Lagrangian L is replaced by the Hamiltonian H defined by
The Hamiltonian is the total energy of the system: H = T + U. Analogy with Fermat's principle suggests that solutions of Lagrange's equations (the particle trajectories) may be described in terms of level surfaces of some function of X. This function is a solution of the Hamilton-Jacobi equation: | 677.169 | 1 |
This Contains Discrete Mathematics And Its Applications (Seventh Edition) by Professor of Kenneth H. Rosen. Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic. This also contains Summing Consecutive Integers, Bijection Principle, Binomial Coefficients, Pascal's Triangle, Cryptography and Modular Arithmetic, Induction and Recursion & Recurrences | 677.169 | 1 |
The Mathematics Bible
"The First GAMSAT-Specific Mathematics Study Guide Ever!"
Name: Matthew Re: Students need a mathematics resource for GAMSAT preparation that targets all mathematics topics in the exam.
This is the first mathematics-specific study guide that covers all the topics that can arise in section 3. Our team has put together the ultimate study guide that you can use to help you confidently tackle questions in Section 3 that require calculations.
While there is not an actual Mathematics section in the GAMSAT exam, it is crucial that you understand the basic concepts required for success in Section 3. In particular, basic mathematical skills are required in most GAMSAT physics and chemistry questions, as well as some biology-related questions.
Are You Lacking The Mathematics Skills Required To Answer Questions In
Section 3 Of The GAMSAT?
Does the thought of exponentials, logarithms, algebra, factorisation, surds, indices, and scientific notation leave you feeling overwhelmed for the GAMSAT?
If the answer is yes, you are in the same boat as many other students!
Many students have not honed their mathematics skills for the last few years and this is a major problem. As you may already know, the chemistry and physics questions in the GAMSAT contain many calculations and mathematical problems. Punnet-square probability calculations for biology arise in almost every GAMSAT exam. By not revising and practicing your mathematics skills you are putting yourself at a great disadvantage.
Many students email our team and ask –
"Can I study Mathematics from my year 11 and 12 textbooks?"
Well technically, the answer is YES, but is this the most efficient way?
How will you know what topics to study and how in-depth your study should be?
And how much will it actually help you since no calculators are allowed in the GAMSAT, yet most year 11 and 12 books require students' to have a calculator to solve many of the problems.
Well…
We Have A Solution! The AceGAMSAT Team Have Created The Mathematics Bible!
Our team have dedicated months of hard work to create the ultimate study guide that covers all the relevant topics for GAMSAT Mathematics to the required depth.
So What Does The
Mathematics Bible Cover?
The Mathematics Bible is split into two sections.
Section 1: GAMSAT Mathematic Topics The following topics will be covered in the required depth for the GAMSAT exam:
Properties of Integers
Orders of Operations
Algebra
Factorisation
Surds
Logarithms and Exponents
Scientific Notation
Basic Geometry
Graphs
Probability
Section 2: Estimation Techniques for the GAMSAT Estimation techniques are crucial as calculators are banned and time is very limited in the GAMSAT exam. Estimation techniques will be covered for a range of topics that commonly arise in the GAMSAT.
I Don't Know How Long We Are Going To Offer This!
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The next move is up to you. I've shown you that The Mathematics Bible is as risk-free as an offer can come. You and I both know that if you've read this far in the letter, you're seriously interested in smashing the GAMSAT on your first attempt. All that's left to do now is take action. | 677.169 | 1 |
ATTENTION, Please: MathBits.com is being moved to a new server which will enhance interactive access. This move may cause interruptions in availability over the next 7 to 10 days. We apologize for any inconvenience this may cause. Thank you for your patience.
JavaMathBits.com Beginning JAVA Programming Course with a mathematical flair!
Also the free JavaBitsNotebook web site for lessons using Eclipse.
Mathematics Resources
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fun, yet challenging, lessons and activities in
secondary (and college level) mathematics and computer programming
for students and teachers.
Created by two mathematics teachers. Please read the Terms of Use.
"Mathematics seems to endow
one with something like a new sense."Charles Darwin
"MathCaching Topic Series" (for specific topic areas) can be found in all subscription areas.
FREE!MathBitsNotebook.com devoted to Common Core!
Algebra 1 - OPEN; Geometry - OPEN; Algebra 2 - OPEN
All standards from the Common Core are addressed, with special considerations to the PARCC MCF and SBAC. Material is presented in a lesson format with follow-up interactive practice problems. | 677.169 | 1 |
Systems in Three Variables
Students are introduced to systems of three equations with three variables. The goal of the lesson plan is developing strategies for solving such systems, such as making choices about when to use substitution or elimination, or when using matrices and technology is beneficial. | 677.169 | 1 |
This tried-and-true text from Allyn Washington preserves the author's highly regarded approach to technical math, while enhancing the integration of technology. Appropriate for a two- to three- semester course, BASIC TECHNICAL MATHEMATICS WITH CALCULUS shows how algebra, trigonometry, and basic calculus are used on the job. It addresses a vast number of technical and pre-engineering fields, including computer design, electronics, solar energy, lasers fiber optics, and the environment. Known for its exceptional problem sets and applied material, the book offers practice exercises, writing exercises, word problems, and practice tests. This edition features more technical applications, over 2300 new exercises, and additional graphing calculator screens | 677.169 | 1 |
References & Citations
Bookmark
Mathematics > Algebraic Geometry
Title:
How to Compute a Puiseux Expansion
Abstract: In this paper, an explanation of the Newton-Peiseux algorithm is given. This
explanation is supplemented with well-worked and explained examples of how to
use the algorithm to find fractional power series expansions for all branches
of a polynomial at the origin. | 677.169 | 1 |
Showing 1 to 5 of 5
D. Levy
5
Numerical Dierentiation
5.1
Basic Concepts
This chapter deals with numerical approximations of derivatives. The rst questions
that comes up to mind is: why do we need to approximate derivatives at all? After
all, we do know how to analytically d
D. Levy
6
6.1
Numerical Integration
Basic Concepts
In this chapter we are going to explore various ways for approximating the integral of a
function over a given domain. There are various reasons as of why such approximations
can be useful. First, not eve
D. Levy
2
2.1
Methods for Solving Nonlinear Problems
Preliminary Discussion
In this chapter we will learn methods for approximating solutions of nonlinear algebraic
equations. We will limit our attention to the case of nding roots of a single equation
of
D. Levy
4
Approximations
4.1
Background
In this chapter we are interested in approximation problems. Generally speaking, starting from a function f (x) we would like to nd a dierent function g(x) that belongs
to a given class of functions and is close to | 677.169 | 1 |
Pricing and Purchase Info
about
Difference equations are models of the world around us. From clocks to computers to chromosomes, processing discrete objects in discrete steps is a common theme. Difference equations arise naturally from such discrete descriptions and allow us to pose and answer such questions as: How much? How many? How long? Difference equations are a necessary part of the mathematical repertoire of all modern scientists and engineers.In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron-Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly. The book contains many worked examples and over 250 exercises. While these exercises are accessible to students and have been class-tested, they also suggest further problems and possible research topics.
From the reviews:"The book under review is written for advanced undergraduate majors. . This book is well written and easy to read, with a large number of exercises . . Difference equations: from rabbits to chaos is a good text for those who want to teach an introductory course in recurrences from a collection of various classical points of view. . anyone interested in difference equations . will want Cull, Flahive, and Robson as a reference because of its interesting and unique collection of topics." (Shandelle M. Henson, Mathematical Reviews, Issue 2006 j)"This book is a nice addition to an already nice group of books on difference equations . . would be especially appealing to students who like to compute. . This book contains many interesting examples . . There are over 250 exercises. This book could be used for an upper level undergraduate course or for a beginning graduate level course. . it would be nice to have in one's personal library." (Allan Peterson, SIAM Review, Vol. 48 (1), 2006)"Recognizing the increasing importance of difference equation models . the authors aimed to write a book that provides a solid foundation in the field and is accessible to undergraduates. . this text is written in an informal style and with an 'algorithmic spirit'. . There are many worked examples and the exercise sets are good . . it provides an accessible introduction to the material and a firm foundation for applications in various scientific fields." (Henry Ricardo, MathDL, September, 2005)"As the authors point out in their introduction this is a textbook for undergraduate students taking introductory courses on discrete mathematics. The text is quite elementary, written for an audience with a preference for computational aspects of mathematics and modelling real world phenomena. This is also reflected by the exercises at the end of each chapter. Starting with simple examples . the reader is lead to basic notions and theorems of basic linear algebra and analysis. Proofs are worked out accurately . ." (Stefan Hilger, Zentralblatt MATH, Vol. 1085, 2006)"This book is specifically designed for American undergraduate students studying mathematics or computer science; it is part of Springer's undergraduate texts in mathematics. . It will be useful to have on the bookshelf, and when there is a specific difference equation in front of me it will be my first port of call." (Tony Crilly, The Mathematical Gazette, Vol. 91 (521), 2007) | 677.169 | 1 |
Chapter 1
How big can a cell be?
(The power of functions)
The shapes of living cells are designed to be uniquely suited to their functions. Few cells are
really spherical. Many have long appendages, cylindrical parts, or branch-like structures.
But here,
Chapter 9
Exponential Growth and Decay:
Dierential Equations
9.1
A dierential equation is an equation in which some function is related to its own derivative(s). For
each of the following functions, calculate the appropriate derivative, and show that the
Chapter 1
Review of Straight Lines
We start with a brief review of properties of straight lines, since these properties are fundamentally
important to our understanding of more advanced concepts (tangents, slopes, derivatives). Skills
described in this in
Chapter 5
Tangent lines, linear
approximation, and
Newtons method
A straight line has the property that its slope is the same at every point on its graph. Thus,
given a known point (x1 , y1 ) on the line and the slope m, the equation of the line is found
Chapter 2
Average rates of change,
average velocity and the
secant line
In this chapter, we introduce the idea of an average rate of change. To motivate ideas, we
examine data for two common processes, changes in temperature, and motion of a falling
objec
Applications of Derivatives Review #3
(1) A particle moves along the x-axis so that its position at time t ,
0 t 5
, is given by
s(t) = 3t(t 1)(t 3).
(a)
Find the minimum velocity of the particle.
(b)
Find the average velocity of the particle over the int
Applications of Derivatives Test Review #2
(1) The position of a particle is given by the equation
s(t ) t 3 6t 2 9t
where t is measured in
seconds and s in meters.
(a) Find the velocity at time t.
(b) What is the velocity after 2 sec? After 4 sec?
(c) WhDifferential Calculus: Mathematics 102
The University of British Columbia
Notes by Leah Edelstein-Keshet1: All rights reserved
September 8, 2015
1
This disclaimer is inserted in view of UBC Policy 81. Copyright Leah Edelstein-Keshet. Not to
be copied, use | 677.169 | 1 |
Precalculus: Real Mathematics, Real People
ISBN-10: 1305071700
ISBN-13: 9781305071704 courses that require the use of a graphing calculator, PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, 7th Edition, features quality exercises, interesting applications, and innovative resources to help you succeed. True to the book's focus on student support, selected examples include notations directing you to previous sections where you can review concepts and skills needed to master the material at hand. The book's careful writing and detailed solutions that begin and end on the same page, make it accessible and easy-to-read. Side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles, and examples throughout feature real-life scenarios show you the relevance of mathematics in your life and future | 677.169 | 1 |
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