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Mathematics
Mathematics should be studied for its fascinating sophistication and its inherent elegance as a way of viewing the world around us. Over two years, you will study and investigate a wide range of mathematical concepts. If you enjoyed the challenge of problem solving in your Maths GCSE, you will definitely find A Level Mathematics an appealing choice.
Subject content
The content of A Level Mathematics splits broadly into the two strands of Pure Maths and Applied Maths (Mechanics and Statistics).
Pure Maths extends work covered at GCSE on algebra, trigonometry and graphs, as well as introducing brand new topics such as logarithms, calculus and vectors.
Applied Maths helps us to understand how modelling can turn a complicated real-world problem into a simpler one that can be analysed and solved using mathematical methods.
Mechanics describes the motion of objects and how they respond to forces, from cars in the street to satellites revolving around a planet. Statistics allows us to investigate real-world data. From this we are able to make predictions and assess the validity of certain statistical models used to analyse the ever-changing world around us.
You can view EDEXCEL course specifications by clicking on the link below;
Specific entry requirements
GCSE Grade 5 preferable 6 or above in Mathematics. Students will also need to pass an entry excam at the beginning of the course ( made up of GCSE questions) Pass mark is 60%.
Equipment
Students will need to purchase a specific calculator for the course: Casio FX991ex.
Learning methods
You will discover and explore maths by discussion and group work as well as independent research and practical work.
Assessment
The course will be linear with all exams at the end of the two years of study. At A Level there are three exams: two Pure papers and one Applied (Mechanics and Statistics). The content from both years of study are examined in these three papers.
Progression opportunities
Maths is a versatile A Level choice and is highly regarded by Higher Education establishments. Maths is a key component of many degree courses, including computer science, engineering, natural sciences, economics, medicine, geography, architecture and of course, mathematics itself. Graduates go on to have a wide range of careers in any job where logical thought and problem solving are required such as business, accountancy or computing.
Silvia Kablanova
Achieved an A* in Mathematics, A* in Biology and A in Chemistry. Silvia moved to Barnsley from Bulgaria two years ago.
"I would absolutely recommend Barnsley Sixth Form College; the tutors are so supportive and I wouldn't have got the results I did without their help. I'm now going on to study Medicine at the University of Sheffield." | 677.169 | 1 |
Mathematics Companion Essential and Advanced Mathematics for Scientists and Engineers
ISBN-10: 0750310200
ISBN-13: 9780750310208 style of The Physics Companion and The Electronics Companion, this book is a revision aid and study guide for undergraduate students in physics and engineering. It consists of a series of one-page-per-topic descriptions of the key concepts covered in a typical first-year "mathematics for physics" course. The emphasis is placed on relating the mathematical principles being introduced to real-life physical problems. In common with the other companions, there is strong use of figures throughout to help in understanding of the concepts under consideration. The book will be an essential reference and revision guide, particularly for those students who do not have a strong background in mathematics when beginning their degree | 677.169 | 1 |
Courses & Units
Teaching the 7-12 Mathematics Curriculum EMT525
A minimum enrolment number of 12 applies to this offering. Should enrolments not reach the minimum number required for on-campus study, students may be transferred to the on-line offering and advised of this change before semester commences.
Students enrolling in this unit with six units of tertiary mathematics study, at least two of which are at third year level are deemed to have mathematics as their first teaching method qualification. Students enrolling in this unit with four units of tertiary mathematics study, at most two of which are at first year level are deemed to have mathematics as their second teaching method qualification.
Enrolment in this unit requires at least four 12.5% units of tertiary maths, with no more than two at first year level
Introduction
This unit is the first of a pair of
units that present the theory, methods and practice of teaching mathematics
(and teaching for numeracy) in the secondary years. EMT525 addresses the Year
7-12 curriculum and its implementation, with a particular focus on teaching and
learning issues on key topic areas of Years 7-10, with some coverage of years
11 and 12 as appropriate. Curriculum documents will be a major focus (including
the Australian Curriculum, local and international curricula), alongside
implementation strategies, related resources and expected learning outcomes.
Significant topics include the teaching and learning of rational and irrational
numbers, and integer arithmetic; proportional reasoning; early algebra
learning; probability; statistics; geometry; and principles of lesson planning.
Teaching and learning experiences
involve participation in practical activities as well as an analysis of the
issues related to mathematics education.
The broad aims for this unit are to:
Develop personal competence, understanding and confidence with the mathematical concepts, knowledge and skills that are essential for the curriculum at the level of teaching anticipated.
Acquire knowledge and develop skills relating to the progression and development of the topics in the Mathematics curriculum from Year 7 to Year 12.
Engage in discussions and develop opinions about current issues in Mathematics and numeracy education and the secondary years of schooling.
Build understanding of variations in students' progression through the curriculum
Summary
Unit name
Teaching the 7-12 Mathematics Curriculum
Unit code
EMT525
Credit points
12.5
Faculty/School
College of Arts, Law and Education School of Education
Discipline
School of Education
Coordinator
Associate Professor Helen Chick | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
A comprehensive study guide with age- and grade-appropriate content designed to familiarize students with new Common Core State Standards
With content developed by a team of teachers and curriculum specialists and reviewed by assessment experts with a minimum of five years of classroom teaching experience, SOLARO mathematics study guides are wholly curriculum aligned and serve as an excellent source of material for review and practice. Each guide breaks down the Common Core State Standards into teachable units, making it simple for educators and students to identify key learning concepts and how they align with the accompanying exercises and assessments. The practice questions and sample tests have detailed solutions that show problem-solving methods, highlight concepts that are likely to be tested, and point out potential sources of errors. The multiplatform SOLARO study solution also features additional learning tools in the complementary online version, and is designed to be used by students throughout the school year for reviewing and understanding course content, preparing for assessments, and, ultimately, achieving success.
Developed and designed for seventh grade students, this study guide is aligned to Common Cores prescribed curriculum for students who aim to have completed High School Algebra I by the end of eighth grade. The guide includes sections such as Rational Numbers, Irrational Numbers, Radical and Integer Exponents, Equivalent Relationships, Linear Relationships, Random Sampling, and Congruence and Similarity.
About the Author
Castle Rock Research Corp. is an educational resource development company that serves individual learners, schools and jurisdictions, education ministries, colleges, universities, and corporate clients with an array of print products and online services. It is based in Edmonton, Alberta. | 677.169 | 1 |
When you have the right math teacher, learning math can be painless and even fun! Let Basic Math and Pre-Algebra Workbook For Dummies teach you how to overcome your fear of math and approach the subject correctly and directly. A lot of the topics that probably inspired fear before will seem simple when you realize that you can solve math problems, from basic addition to algebraic equations. Lots of students feel they got lost somewhere between learning to count to ten and their first day in an algebra class, but help is here! | 677.169 | 1 |
With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.
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This book provides guidance for elementary teachers who are looking to learn the basics of the varying levels of elementary math. Sonnabend provides an active, engaging approach to get students into the underlying concepts of elementary education mathematics. The book includes coverage of problem-solving, reasoning, sets, arithmetic, geometry, measurements, algebra, computers, statistics, and probability. Sonnabend's well-organized lesson format encourages students to participate in the development and explanation of concepts, establishing a solid understanding of mathematics. | 677.169 | 1 |
Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical...
A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deepThe essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with...
Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete...
This volume addresses a number of topological themes of direct relevance to chemists. Topological concepts are now regularly applied in wide areas of chemistry including molecular engineering and design, chemical toxicology, the study of molecular...
Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970 edition.
Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the...
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Elementary Topology: A Combinatorial and Algebraic Approach focuses on the application of algebraic methods to topological concepts and theorems.The publication first elaborates on some examples of surfaces and their classifications. Discussions...
Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate...
Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental...
Following their introduction in the early 1980s o-minimal structures were found to provide an elegant and surprisingly efficient generalization of semialgebraic and subanalytic geometry. These notes give a self-contained treatment of the theory of...
The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology...
Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers...
A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep...
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated...
This updated and revised edition of a widely acclaimed and successful text for undergraduates examines topology of recent compact surfaces through the development of simple ideas in plane geometry. Containing over 171 diagrams, the approach allows...
Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students'apos; intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. 1968 edition.
Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at...
Students must prove all of the theorems in this undergraduate-level text, which focuses on point-set topology and emphasizes continuity. The final chapter explores homotopy and the fundamental group. 1975 edition.
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometricalTopology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who 'quot;gave topology wings'quot; in a classicThe first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric...
This classic work has been fundamentally revised to take account of recent developments in general topology. The first three chapters remain unchanged except for numerous minor corrections and additional exercises, but chapters IV-VII and the new...
Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Explorations in Topology gives students a rich experience with low-dimensional topology, enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that would help...
Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving... | 677.169 | 1 |
How can using Aleks™ daily help you?
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Presentation on theme: "How can using Aleks™ daily help you?"— Presentation transcript:
1 How can using Aleks™ daily help you? Aleks PresentationHow can using Aleks™ daily help you?
2 Aleks PresentationYou have probably heard about the Algebra 1 Math requirement, but may not know what it is, or why it is so important to you.
3 Aleks PresentationThe Los Angeles Unified School District has raised the requirements for high school graduation.You need to pass Algebra 1 to graduate high school.
4 Aleks PresentationA-G Requirements for most colleges require the passing of Algebra 1 with a grade of "C" or better.
5 Aleks Presentation What is Algebra? Why do I need to take it? Why do schools make such a big deal about getting ready for it? Why do my parents care if I pass, or get a high grade? Isn't it just another Math class?
6 Aleks Presentation What is Algebra? Algebra, for most students, can be thought of as a system of brain puzzles that are common to all students around the world. Solving the problems involves using rules that you need to learn, memorize, and put to use when you take quizzes and tests.
7 Aleks Presentation Why do I need to take it? Taking and passing Algebra 1 with a "C" or better, along with other Math classes, is a graduation requirement for all LAUSD high schools.It is also a requirement for admission to California State Universities.
8 Aleks PresentationWhy do schools make such a big deal about getting ready for it?The reason your teachers make such a big deal about learning your math skills in earlier grades, and then passing Algebra 1, is this:Students who pass Algebra in Middle School or High School almost always go to college, but students who don't almost never get to college.
9 Aleks PresentationWhy do my parents care if I pass, or get a high grade?Your parents want you to be successful in school. Parents want their children to someday be smarter in school, and possibly more successful in careers, than they were.Your parents want to be proud of you.You want to be proud of yourself.
10 Aleks Presentation Isn't Algebra just another Math class? No. Passing Algebra 1, more than almost anything else you do in school, is an indicator of the choices you'll have in your future. In The United States of America, you can decide what future you'll have, but you have to work hard to get to college where you'll have the chance to make your choices.
11 Aleks PresentationWhat if I don't pass Algebra 1 the first time I take it?You can re-take Algebra 1 if you get less than a C the first time. Many students don't pass Algebra 1 the first time. Ideally, you'll pass the first time. It doesn't matter as much when you pass it, but that you ultimately do pass.
12 Aleks Presentation Algebra is like a mountain to climb…. Using Aleks, along with carefully doing your classwork and homework, will help you get to the top.
13 Mt. Algebra You may be asking yourself, Can I get to the top? You can, but it will take a lot of hard work on your part. Teachers can teach you how to climb, but you have to do the climbing!
14 Aleks PresentationYou can teach yourself how to climb the Algebra mountain by using Aleks….
15 You can log in to Aleks™ from anywhere you can access the Internet, including at home, or the library.
16 The first time you log in, you are given a short test The first time you log in, you are given a short test. This helps Aleks find out what you already know, and what you need to learn.
17 You will need to use paper and pencil to answer most of the questions.
18 When you enter your answer and click Next, you will not be told if you are right or wrong.
19 If you don't know how to answer a question, click "I haven't learned this yet."
64 Many students are able to complete more than one pie, or one year's growth in a school year.
65 The teacher is notified when a student has completed an Aleks course (pie).
66 Hard Work in Math Class + Hard Work in Aleks A student could begin the year as a D student who hates Math, but finish the year as an A or B student who gets it.Hard Work in Math Class Hard Work in Aleks
67 A student could begin the year as BB (Below Basic) and finish the year as a P (Proficient) student. There are direct connections between Aleks and your State Tests you'll take at the end of the year. | 677.169 | 1 |
Summary module description:
This module continues the study of functions of one complex variable.
Aims:
To continue the study of functions of one complex variable, and in particular of analyticity and its consequences
Assessable learning outcomes:
By the end of the module, students are expected to be able to:
• Identify different type of singularities of complex functions;
• Use residue calculus to study zeros and poles of given functions;
• Use residues to compute complex and real integrals;
• Use Rouche's Theorem to estimate the number of zeros of complex functions in regions of the complex plane.
Additional outcomes:
The use of complex analytic arguments to derive basic results in algebra and real analysis
Outline content:
Starting from Cauchy's theorem and its consequences, discussed in the prerequisite complex analysis module, the module will present further properties of sequences and series of complex functions, and singularities of complex functions, leading to the concept of analytic continuation. More advanced consequences of residue calculus, such as the maximum modulus, argument principle and Rouche's theorem, will be presented | 677.169 | 1 |
8th Grade Common Core Math Pre-Assessment
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This pre-assessment is compromised of 14 questions that map to the most common 6th and 7th grade pre-requisite skills needed for 8th grade math. The standards assessed are 6.EE.B.5, 6.EE.B.7, 6.G.A.3, 7.NS.A.2, 7.NS.A.3, 7.EE.A.1, 7.EE.A.2, 7.EE.B.3, 7.EE.B.4, 7.G.A.1, 7.G.A.2, 7.G.B.5, 7.G.B.6, and 7.RP.A.2. These are all mapped to the pre-requisite skills needed for 8.NS.A.1, 8.EE.A.2, 8.EE.A.4, 8.EE.B.5, 8.EE.B.6, 8.EE.C.7, 8.EE.C.8, 8.F.A.1, 8.F.A.2, 8.F.A.4, 8.G.A.1, 8.G.A.3, 8.G.B.6, 8.G.B.8, and 8.SP.A.1. The pre-assessment is a 5 page document. This pre-assessment can be used as an individual assignment at the beginning of the year or each question can be used for a pre-requisite assessment as the 8th grade standard it maps to is introduced. An answer key is included that gives the standard addressed and what 8th grade standards each question is a pre-requisite for. | 677.169 | 1 |
NCERT Solutions For Class 11
Our experts at Byju's have analysed and reviewed comprehensive chapter-wise NCERT solutions for all subjects of class 11. The Class 11 NCERT solutions for all the subjects such as Maths, Physics and Chemistry are provided in a chapter-wise manner for every question of exercise in the NCERT textbook.
The question papers set for CBSE class 11 exams are mainly based on the exercise questions published in NCERT books. So our aim is to help every student to compare their answers and math solutions along with solved examples for class 11 syllabus and other subjects to perform well in CBSE board examination. Students can clarify their doubts regarding subjects by connecting to our expert mentors at 09243500460. | 677.169 | 1 |
"There may be those on earth who dress better or eat better, but those who enjoy the peace of God sleep better"
No-Nonsense Algebra {Math Essentials Review}
My oldest son said to me the other day, "I don't really need to know all of this stuff!" We were talking about math. And I had to admit that some of what he was learning, I wasn't sure was really something he needed. At least not yet. He is soon to be twelve; very advanced in many ways yet in others, not so much. Needless to say, given the opportunity, I was happy to try out Mastering Essentials Math Skills No-Nonsense Algebra fromMath Essentials. This is a complete algebra high school program that includes free access to online video tutorials. Although my son is a bit young for this program, he certainly was eager to get ahold of a program that only teaches "what you need to know."
I think I still have nightmares about high school math! Since I do not want my children to "suffer" through years of math as I did when I was young, the concept of Math Essentials really excited me! Their lessons are short and simple; where my son gets distracted easily (which then turns into frustration and discouragement, this program is so concise in every lesson that he isn't given the chance to get lost. 🙂
Some of the topics taught within this program are:
Necessary Tools
Graphing and Analysing Linear Equations
Polynomials
Rational Expressions (Algebraic Fractions)
Radical Expressions and Geometry
Algebra Word Problems
It begins with pre-algebra and goes all the way through to quadratic equations.
This program really is no nonsense! Isn't that a relief for anyone that is struggling with math?
Throughout the pages of this book there arehelpful hints. These offer some great shortcuts and tips.
There are examples that show every step you will take, all the way to the solution.
And of course there is a review at the end of each section to ensure that what has been taught has also been caught.
In all honesty I had a feeling this would be pretty challenging for my oldest son BUT I reminded him when we started with the very fist lesson that this is meant to be taught in short and simple lessons, only what he needs to know. The goal being to master those things that are essential in math.
In the very first video, he makes sure the kids know how important it is for them to copy the work that is being done as they watch in the video. And as he goes along he often says, "copy this along with me." I know my son needs those reminders.
As my son begins each lesson, he makes sure to keep his notebook and pencil nearby. Each lesson begins with an introduction which defines important mathematical words. There are also examples that walk you through each step and then exercises to complete (do these in your notebook because this is really more of a text than a work book). He recommends that you also keep handy graph paper and a ruler. We begin each lesson watching the video; often we will watch it a second (maybe even third) time as my son works through the exercises.
There are also a couple handy resources in the back of this book:
multiplication tables
fraction/decimal equivalents
important symbols and formulas
square roots table
common prime numbers
We really liked the way this program is put together. My younger son (who is only seven but loves math) even watched the videos here and there with us. At times he would even work some problems himself along with his brother. For my oldest son this was a perfect program to use. With simple yet direct lessons and instruction, he was able to see, and do, right along with the instructor. Between the hands on method, and the audio and visual provided, this really helped him to learn and grow a greater understanding of the value that math has in life. This is a very simple program; no frills and no thrills. Just straightforward math, the simplest way possible. And they have many more programs to choose from so be sure and check this one out! | 677.169 | 1 |
The perfect solution for physics students and teachers everywhere, Physics 101 SE is the premier physics calculation tool, allowing you to focus on physics and not mathematical busywork by working with over 150+ equations and other features.
Physics 101 SE Description
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The perfect solution for physics students and teachers everywhere, Physics 101 SE is the premier physics calculation tool, allowing you to focus on physics and not mathematical busywork by working with over 150+ equations and other features such as: 1) 150 Physics Equations organized in twenty three sections 2) Free Body Diagram Simulator 3) Projectile Simulator 4) Circuit Simulator 5) Unit Converter6) and much, much more
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Relief valve sizing calculator mainly carries out calculations based on equations specified by American petroleum institute. The equations allow engineers to size relieve devices that can be used for different industrial applications Downloads: 0 - Demo - Download Now | 677.169 | 1 |
Get mathtastic and practice your ALGEBRA SKILLS by playing this uber-fun game and reviewing the basics of algebra such as: variables, terms, math expressions, equations and more! We got graphics, animation, and loud noises to help make you a PRO at solving equations and getting ready for calculus and college math courses!! Aligned with UK GCSE, US Common Core, SAT and other standard math tests, this brain training app will get you ready for any math course you choose… with a vengeance!!
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This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.
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The purpose is to share public content about the different topics studied in math for 7th graders. The content will have the form of images, videos or links to web sites that can be helpfull for a better understanding of topics.
The purpose is to share public content about the different topics studied in math for 7th graders. The content will have the form of images, videos or links to web sites that can be helpfull for a better understanding of topics. | 677.169 | 1 |
Introduction to Calculus and Study Guides
I have to admit; I was one of those in high school and even college who never really "got" calculus. I could go through the motions of doing really hard problems, but most of the time, never really understood why I was doing them.
Calculus can be that way; and sometimes it's all right! I hope to be able to help you know what you need to understand and what you just need to be able to do, when going through your Calculus classes. Honestly, there are some parts that I still don't really understand.
This first section of Calculus will cover the Advanced Placement (AP) AB course, since that's what I typically tutor. I hope to eventually cover the more advanced BC course, and I will indicate it as so.
To simplify, typically your first calculus class has to do with rates of things (Differentiation) and area of things (Integration). What calculus adds to what you've been doing in Algebra and Geometry is that the concepts are extended to finding rates and areas of curvy things (lines and 3-D objects); it was first invented in the 1700's (possibly earlier!) to be used in many concepts in Physics (not my favorite subject!) J
In fact, calculus grew from some problems that European mathematicians were working on during the seventeenth century: general slope, or tangent line problems, velocity and acceleration problems, minimum and maximum problems, and area problems.
Calculus usually starts out with the study of limits, which can be quite frightening and confusing. This is because we need limits to "understand" the foundation of Differential Calculus; we need to "appreciate" the math before we plug away at doing it much easier. Let's plug through limits as well as we can! | 677.169 | 1 |
This page lists the key features of the GMAT Problem Solving format — one of two basic formats for GMAT Quantitative (math) questions. It also provides the directions for answering questions in this format.
Directions for Answering Problem Solving Questions
The following directions will appear on your screen just before your first Problem Solving question (and you can access them while tackling any Problem Solving question by clicking on the HELP button):
Directions: Solve each problem and indicate the best of the answer choices given.
Numbers: All numbers used are real numbers.
Figures: A figure accompanying a Problem Solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie on a plane unless otherwise indicated.
To review these directions for subsequent questions of this type, click on HELP.
Note that in the Problem Solving format figures (visuals) are drawn to scale unless the question at hand indicates otherwise. | 677.169 | 1 |
Polynomials I
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Practice with the basics of polynomials: listing terms, and identifying degree, name, and coefficient; identifying like terms; adding and subtracting terms, collecting like terms and distributing and simplifying. Also available as part of a combo set. | 677.169 | 1 |
9780130412140
0130412147114.00
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Summary
The Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Counting and Probability; A Preview of Calculus; and more. For individuals with an interest in learning Precalculus as it applies to their everyday lives.
Table of Contents
(All chapters end with a Chapter Review and a Project at Motorola). Preface. List of Applications. 1. Graphs.
The Viewing Rectangle. Using a Graphing Utility to Graph Equations. Using a Graphing Utility to Locate Intercepts and Check for Symmetry. Using a Graphing Utility to Solve Equations. Square Screens. Using a Graphing Utility to Graph Inequalities. Using a Graphing Utility to Solve Systems of Linear Equations. Using a Graphing Utility to Graph a Polar Equation. Using a Graphing Utility to Graph Parametric Equations. | 677.169 | 1 |
and aerospace engineers involves the theory of beams. A fundamental
concept in beam theory is the idea of a centroid, or more
generally, the center of gravity. Given a strangely-shaped region cut
out of stiff cardboard, students can readily understand the idea of
center of mass: it's the point where the region would exactly balance
on the tip of a pencil. A more difficult problem is how to compute
the location of that point, especially if the material is not
symmetric and is not of uniform density.
As soon as the multivariable calculus students are introduced to
double integrals, they are immediately asked to think about the
geometric ideas associated with numerically approximating the area of
a planar region. They use Maple to help them explore the idea of
superimposing a grid on a region and adding up the area of all
squares that are "inside" the region. The region we give them is a
model of the state of Minnesota
(see Figure 1); the
location of the state boundary was derived from a cartographic
database. We call this the
"state of Minnesota lab".
Figure 1:(Left) A model of the state of Minnesota with a superimposed 10 x 10 grid. If you know that scale factors of the model, can you
bound the area of the state? (Right) A model of a population distribution
for the state of Minnesota. Students are asked to find the demographic
center of the state.
The students quickly ask a fundamental question: "if a
square is only partially contained in a region, do we include its area
in the final sum?" This leads to a discussion of upper bounds, lower
bounds, and error estimates. It is not long before a second
fundamental question is proposed: "If we want to know the area
better, can't we just use a finer grid?" This leads to discussions
of convergence, Riemann sums, and numerical methods for approximating
double integrals. Furthermore, the students recognize these somewhat
abstract mathematical ideas as being useful and natural, rather than
thinking of them as artificial constructs that are unrelated to
engineering.
Eventually each group agrees on a number to assign
"the" area of the model. For homework they are asked to look up the
true area of the state and to compare their estimate with the official
value; most estimates are within 5%.
Once the students have learned and extended some of these ideas, they
are asked to compute the centroid of the state, and then to consider
what happens to the "center" of Minnesota if we do not assume a
uniform density distribution. Specifically, we create a model that
takes into account a real geological feature: the Great Iron Range of
northern Minnesota. The model represents the Iron Range by assuming a
density distribution which is highest in a roughly east-west swath
across the upper portion of the state. The students discover that if
we assume such a density distribution, then the state's "geological"
center of mass is further north-east than if we assume a uniform
distribution. The students then look at a model of a population
distribution in which the bulk of the state's population lies in the
eastern portion of the state, and in which the state's population
decreases from south to north. They conclude that the demographic
center of this model is just northwest of the Twin Cities.
The students are now equipped to take a density function for
any distribution of objects (people, soybeans, income, voters,
etc.) and find the center of mass for that distribution, but they
also learn more from this lab than just how to find a center
of mass.
They learn to question the accuracy of a model and to
interpret a model's predictions. They learn that some problems have
no closed-form analytic solutions. They learn both theoretical
and numerical techniques of integration, and why each is important.
Finally, they learn these concepts better with by using technological
tools, because of the rich exploration that technology permits. | 677.169 | 1 |
Quantitative Literacy
Drake students will learn to reason with the symbols and components of mathematical languages as well as effectively use the principles that underlie these operations. Courses that satisfy this requirement will have mathematical reasoning as their principal focus. They may also address questions that engage learners with the world around them and help them to analyze quantitative claims that arise from the study of civic, political, scientific, or social issues. Quantitative literacy courses may be focused on the mathematical needs of a specific discipline or on a specific interdisciplinary issue or problem. These courses will engage students to achieve these student learning outcomes. Students will be able to:
Analyze and present solutions to problems using symbols and components from mathematical languages and their underlying principles.
Identify and execute appropriate mathematical operations for a given question | 677.169 | 1 |
Monday, November 18, 2013
Algebra 1 INB Pages - Polynomials and Factoring
(I promise there are graphic organizers and downloads at the bottom of this post. But, I'm so behind on blogging that I have a rather long back story that I must tell you in order for these pictures to make any sense. Feel free to scroll to the bottom to get to the good stuff. But, you'll likely end up scrolling back to the top to understand what you're looking at.)
This year, I am taking a big risk with my Algebra 1 kiddos. I taught them to factor quadratic trinomials with a leading coefficient greater than one before we ever discussed solving equations. Last year, I crammed in factoring quadratics at the very end of the school year. I was feeling rushed, and I needed to cover factoring quadratics and simplifying radicals before the end-of-instruction exam. I didn't feel like I really did either topic justice because I was so rushed.
This year is different. Really different. My Algebra 1 students came in at a much lower level than my students last year. After spending weeks on integer operations and the order of operations and all that fun stuff that students should already know from middle school, I still had a lot of kids who were just not getting it. That was nothing new. Last year, my students struggled with these topics, too. And, last year, I moved on to solving equations and HOPED that the rules for dealing with integers and all that good stuff would "click" when they started seeing it in equations. That worked to a certain extent.
This year, I could tell I was more frustrated and my students were more frustrated than normal. The kids who understood integer operations were bored out of their minds. They wanted to move onto something new. The kids who didn't understand integer operations still didn't quite know that they didn't understand them. So, my constant review as futile. My students had solved equations in middle school, so that wouldn't be something new and exciting. After teaching them the distributive property, I had an epiphany.
Okay. I need to pause the story. Yes, I know you're wanting to know what my epiphany was. But, you're just going to have to wait. If you're protesting with me in your mind right now, I'll tell you what I tell my kids a lot. You'll live. Is that a little harsh? I probably say that more in my classroom than I should. Anyway... I made a commitment to myself last year that I would stop teaching students to FOIL. I learned to multiply binomials by FOILing. But, I'm learning that some of the tricks that I was taught in Algebra are just that. They are tricks that work, but students don't quite know why they work. If my students can see a problem as an extension of the distributive property, they can solve a myriad of problems in different forms. If students only know how to FOIL, they are going to be stuck and not know what to do when they are asked to multiply a trinomial and a binomial. Last year, instead of teaching students to FOIL, I taught students what I called "The Double Distributive Property." This could be extended to the triple distributive property as well. And, it worked out pretty well.
Back to my epiphany. What if didn't teaching the double distributive property as a separate property? What if just told my students that when they see two polynomials being multiplied together that it is a distributive property problem? So, I did just that. Day one of the distributive property featured monomials times binomials. Day two of the distributive property featured polynomials times polynomials. I made no distinction between the two. When my students see two polynomials being multiplied, they automatically think distributive property. And, that makes me insanely happy.
After teaching students to distribute, the natural thing to teach students is to undistribute, or factor. When my students were first reviewing integer operations, I gave them a sheet of diamond puzzles or X-puzzles to complete. I taught my students to factor quadratics with a leading coefficient of 1 using the X-puzzle.
Then, we moved onto factoring quadratics with a leading coefficient greater than 1. Again, I changed my teaching approach from last year. Last year, I taught my students to do the Airplane Method. This worked. But, I still had a few students who never caught on. This summer, at the Common Core conference I went to, I was introduced to the Slide and Divide method of factoring. Another teacher mentioned that she called it the Bottoms Up Method. I combined these two ideas to create the "Slide, Divide, Bottoms Up!" Method. My students LOVE it.
Yes, this is a trick. But, I haven't figured out a better way to teach it. When I took Algebra 1, I learned the guess and check method. And, I found that method to be torturous. But, I didn't know there was a better, faster, easier way. Now that I do know there is a better way, I would never go back.
So, without further ado, I think I've given you enough back story to help you understand the context behind these foldables and interactive notebook pages for Algebra 1.
Last year, I had a conversation with a student that changed my outlook on vocabulary. This was not my own student but the child of a coworker. Before tutoring him one day, he was sitting in his mom's office, discussing why he was having so much trouble in algebra. He said, "My teacher just keeps going on and on and on. And, he keeps saying this word that nobody knows what it means. And, the whole class is lost." Naturally, I wanted to know what the word was. "I don't know. I think it starts with a b." Since they were working on polynomials and factoring, I took an educated guess: "binomial." Yes, that was the word. Once I described to this student what a binomial was, he began to realize that maybe this wasn't as hard as he had made it out to be.
This year, I am emphasizing vocabulary more. I don't want students to think that I use words without ever telling them what they mean. At the very least, they should know that the vocabulary word should be in their interactive notebook somewhere.
Polynomial Frayer Model
Rules for Naming Polynomials
We spent an entire 50-minute period on the definition of a polynomial and how to name polynomials. Is this on the EOI? No. But should I still teach it? Yes! When my students see one of these words, I want them to feel confident, not confused or frustrated. These are words they will encounter for the rest of their mathematical careers. I'm hoping that by putting emphasis on them now, I will save my students a lot of grief later on.
I told my students that when polynomial parents have children, they don't get to choose their names like human parents do. Instead, polynomial parents must follow strict naming rules. I lamented about how sad this was. I mean, what if the parents wanted to be creative? What if the parents wanted their child to have the same last name as them? The first name of any polynomial child is determined by its degree. The last name of any polynomial child is determined by its number of terms.
One of my students asked me if I was going to use these rules to name my own children. Apparently, I seem like the type of person who would name my child "Cubic Trinomial." I guess I should take that as a compliment...
Introduction to Polynomials Interactive Notebook Pages
Factoring Quadratic Trinomials with a Leading Coefficient of 1
Examples of Factoring Quadratic Trinomials with a Leading Coefficient of 1
Basic Factoring Interactive Notebook Pages
Factoring Quadratic Trinomials with a Leading Coefficient Greater than One
(More Affectionately Known as: Slide, Divide, Bottoms Up!)
Examples of Factoring Quadratic Trinomials with a Leading Coefficient Greater than One
Just saw this post -- I have always taught by grouping. I teach grouping before doing this and then it is so easy for them. Also I have NEVER in 25+ years used FOIL -- it just seemed silly. I have always used the double distributive method since they already understand distributive. Also, I make them draw arrows from the 1st set of parentheses to the 2nd -- 1st term, arrows above; 2nd term, arrows below. We call them "rainbows". So now I say "Use your rainbows" and they remember!
I love the box method because it is so much more organized than the table method. I also don't use FOIL (though I do show them because I've been "told" I "have to" teach it because "everyone" uses FOIL. I also call it double distribution! I am going to look into grouping more (I do teach it but for specific quadratics).
After I show my kids the box method, I sometimes show them FOIL if someone asks about it. I love when they see right off the bat that it's the EXACT same thing. They usually remark that the box method is so much more organized than all the arrows. Make this teacher's heart happy. <3
As I'm preparing to teach factoring to my 9th grade Algebra students, I stumbled on this post. It sounds like you use the box method for multiplying binomials...have you tried it for factoring as well? It's a nice visual set up of the grouping method. I've tried slide and divide in the past (though I like the "bottoms up" name better!) but I don't actually have them "slide" the a over. I just ALWAYS have them multiply a and c to get the top of the diamond (even if it's a 1). That way, when they look back at the original problem, they don't mistakenly look at the "slide" version and forget to divide. Also, I've found it helpful to have students do the "divide" part with the numbers still in the diamond. They seem less likely to forget that step when we set it up that way.
I've seen on several of your posts comments about factoring by grouping. Do you have any ISNB pages for factoring by grouping? Or a blog post about teaching it? I am getting ready to teach our polynomial unit which includes factoring. Thanks!
I've used a hybrid of factoring by grouping. I'll see if I can find the handout I have for my class and email it to you. Factoring by grouping is great because it really reflects the "undoing" of the double distributive property. It's more work, but they can SEE it happening.
Me too! I've taught factoring differently every single time I've ever taught it. Next year, I'm thinking of doing factoring by grouping. Slide, Divide, Bottoms Up worked great. My kids just can't seem to remember the steps now that it's been a few months. I'm still on the lookout for the perfect way to teach factoring...
Love the emphasis on vocabulary! I taught Algebra 1 to struggling students and noticed how important it was for them to be able to put words with the math steps. P.S. I don't think telling the kids "you'll live" is harsh - I'm always telling my own children "if that's the worst thing that happens to you today, you're having a pretty good day" when they complain about small things. :)
I teach grouping, the xbox (which is the x but with the grouping part done in a box), and the method but with just the x but with a slight variation. You may like it because it's a little less confusing. Instead of rewriting the equation because they have to divide the coefficient, just have them only divide the factors INSIDE the x, simplify/reduce those factors, and then set up their parenthesis with the whole numbers but do "bottoms up", as you call it, when writing the binomials, if a one of the factors is not divisible. I hpe you understand this. It's a tiny bit less confusing and less work :)
This post is awesome. You clearly have very high standards for your students and that is so good to know! To factor trinomials with a leading factor greater than 1, I use the "magic number" method. 1: Find AC (magic number) 2: find what 2 numbers add to get AC. 3: replace B with these 2 factors. 4: group 5: factor each parenthesis. 6: rewrite as (inside stuff once)(outside stuff). The only weird part is needing to change the sign in the 2nd parenthesis sometimes. I made a silly video that I posted on my blog about it. Excuse the music, I used tho think I had skillz:
Great post! I love the "slide, divide, bottoms up" method. I did a similar method, but named it after another teacher from whom I learned it! At least your naming gives the kids clues about the steps! I love your interactive notebook ideas, too. I'm excited to have found you! Keep it up!
Great post! I used the Sum Product puzzles for the first time this year. Digging around in my Math Coach's closet I found this X Factoring book by Michael L. Flowers that I think the puzzles on the internet may be borrowed from him. What I found interesting about the book was that the puzzles were organized "upside down" from the ones online and scaffolded. By Upside Down, I mean the sum is at the top and the product is at the bottom. I first saw the puzzles maybe 5 years ago, but I was turned off by the product at the top. When transitioning to trinomials, the sum is generally in the middle and the product last. So with the puzzles from the book - I was able to wrap my mind around that idea a little easier. Also, the book modifies the puzzles where the side numbers are given and the product section is shaded out. So those pages give students practice with just adding the side numbers. I wish I had opened the book before I used some of the puzzles I found online.
From the puzzle, students can make the puzzle template by putting b on top and c on the bottom and solving the puzzles that have already been practiced!!!
Also, in the book, he addresses when a is not equal to 1. The students - CREATE their own puzzle with ac at the bottom and b at the top. Once they find the side numbers - the author suggests the AC split (of the middle term and factor by grouping). Which is what I teach. I have taught the Slide and Divide method, but felt a little uncomfortable explaining how the "trick" work. There is a method called "Chunking" I believe that I have read about in an NCTM publication on High School Mathematical Reasoning. I have also seen it in some of the Common Core and PAARC materials. Chunking puts me in mind of U-substitution when dealing with quadratics that are reducible to quadratic form. I like the chunking method, but I have only taught it to Algebra 1 students once. Unfortunately, it was 2 or 3 days after a my co-worker taught the Lizzie method which the students seemed to like more.
Thanks for sharing about the book. I'm going to have to check that out!
A friend showed me the chunking method again the other day, and I'm a convert. I've decided this is the way I'm going to teach it next year! In two years of teaching, I've taught factoring 4 different ways. I'm finally glad to find a way I love that doesn't rely on a trick. Thanks for sharing!
One thing you might want to change is saying that the difference of squares is only for quadratics (or degree 2 polynomials). Sometimes the difference of squares shows up in situations with logarithms, imaginary numbers, and higher degree polynomials.
I love your blog, and you create a lot of great materials! I have found that factoring by grouping is really helpful for students that struggle to remember the algorithm. For example, the Algebra 1 and Algebra 2 teachers teach the Divide/slide method. However, by the time the students get to me in Pre-Calculus, they have forgotten how to do it. I found the factoring by grouping tends to stick with them a little longer. I would love to see how you would teach factoring by grouping, or how you would set up a graphic organizer for that.
Great point about the difference of squares! I need to think about how to word that for next year. Hmmm...
And, thanks for your kind words about my blog. They mean a lot to me! A few months ago, I had a friend show me how to factor by grouping, and I fell in LOVE with the method. I've decided that I can never go back to sliding and dividing after learning the other way. In 2 years of teaching, I have now taught factoring 4 different ways. I've decided that factoring by grouping will be the way I teach from here on out.
I'm going to have to spend some time thinking about a graphic organizer for factoring by grouping, though.
I have been teaching factoring to Algebra students for many years, and nothing has worked better than factoring by grouping. They understand it and retain it! Many of my students last year wanted to use this method to factor trinomials even when a was 1. I actually enjoy teaching factoring now because of this approach! Good luck!
Gosh, I have probably taught factoring by grouping for over 15 years. I believe the students retain it with this method because they can actually see the process of a reverse distributive property. By the time we reach factoring, they fully understand the distributive property and now with factoring, can see how it actually can be worked backwards.
Hi all, I feel your pain in trying to teach factoring. I teach college level math in a HS dual enrollment program on a college campus. I am not sure you appreciate how very important the skills you teach are in higher math. In all the calculus courses, 1, 2, and 3,and Differential Equations, factoring is an important skill. How many times I have been in the middle of a 3 page problem, and factoring comes up? By this time, most can do it, but even after 11 years of math, at least half of it algebra, some of the brightest kids in the county still can't factor, so they can finish the problem. They understand the calculus, but hang up an algebra skills. This slide divide is interesting, but IMHO it is a "wrote" method, meaning they have to memorize the steps and it does not give them an understanding of the concept. I love the AC method, also called grouping. To me, it is not whether they can get the answer today, it is whether they can understand the process for the long term. After finding you on Pinterest, and going to your blog, I have learned a lot. Cool method, but not sure it has staying power. Thank you for the insight. I will most likely post a handout on the AC method in the next few days. And to tell the truth, when some are stuck, they just go back to trial and error, so they can move on and finish the bigger problem. Visit my TpT store, lots of innovative material for all levels of Algebra and up. If anyone emails me and mentions this blog, I will send for free. joan@distancemath.com. No blog yet, just an old-fashioed website, Sorry this was so long, but so is my career :)
Thanks for the comment Joan! I'm still definitely learning when it comes to teaching factoring. A few months ago, a friend show me how to split the middle term and factor by grouping. Once I saw this I fell in LOVE. It works every single time and it's not a silly trick for students to remember. I liked Slide and Divide, but it always seemed a bit gimmicky. Still, it was better than the torture of guess and check. But, I'm definitely going to teach splitting the middle term and factoring by grouping next year. In 2 years of teaching, I've taught factoring 4 different ways. Hopefully this fourth way will do the trick!
I'm not sure what part of factoring out the GCF from polynomials you're working with, but if your students already know how to get the GCF and they just have a problem taking it out, I saw a video online that says to tell the students: 1) Write the GCF on the outside. 2) Think: (always a good thing :) ) "What can I multiply the GCF by to get each term that I started out with?" This tends to work with the way students think and doesn't get them mixed up by starting with dividing, etc...
I teach guess and check, factor by grouping, and the box method to factor. I let my students decide which method they prefer. The grouping and box method I teach for trinomials just reinforce those methods when they have to use those to factor higher order polynomials.
In classes past Algebra, I show the slide/divide as a shortcut. Slide and divide is not a trick. It works because (ax + b)(cx + d) = acx^2 + (ad+bc)x + bd = ac(x + b/a)(x+d/c).
Like others have mentioned in the above comments, I also teach factoring by grouping for factoring trinomials. I think I saw I later blog post where you mentioned that you would be trying it. :) Good luck!
Also, I agree wholeheartedly about the FOIL method. I never teach it. I like teaching them that it's the distributive property because then it's an algorithm easily extended to other situations.
I'm about to start factoring, and I will definitely be using the Halloween Candy Tax story along with these INB pages for factoring notes (what to use when and the steps). I'm curious, would you be willing to share the editable doc of the factoring when a > 1 page so that I can easily add more rows to fit my method?
Thanks for blogging. You are inspiring me, and I'm in year 8 of teaching!
I LOVE YOUR BLOG!!! I'm a first-year teacher and your blog has been so wonderful and inspirational and just SUCH a HUGE help! I love it! Thank you for spending so much time to inform everyone else that is using your blog as resource! I read some about factoring and the 'slide, divide, bottoms up' method... I saw in your Trig post that you were trying to find a different game plan for teaching factoring... I was just wondering how you decided to teach that! We are working on factoring now... and running out of time before EOCs... and my students will definitely struggle in memorizing the steps.
Does the slide, divide, bottoms up work for leading coefficients that are not prime numbers? I am having trouble with one where 6x^2 is the first term (and there is no greatest monomial factor). Thanks, Kristina
I used the mistake method for factoring this year because that is what my department uses but I believe that I will switch back to factoring using the box next year. It is basically factoring with grouping but organizes it a little differently. The students can retain this easier, in my experience, especially if you teaching multiplying using boxes as well. I've decided that there is truly no great way to teach factoring that works for everyone.
My Algebra I students tend to struggle with polynomials in general. It seems to be even more of a struggle this year. I have found that using the foldables for guided notes help. I do show my students distributive, the box method, and foil when multiplying. I have students who find each of them easier than the others.
I have never used the box method for factoring. It is a good idea to have the students multiply a and c when a is 1 to have them form a habit. I waited this year and told them "Now we are going to add another step." I wish I would have done this from the beginning.
is there any way you could email me some tips on teaching factoring by grouping? it sounds like that is the most popular method to teach factoring trinomials. i've taught factoring by grouping with four terms, but not with 3. any tips or examples?
I have read your post on teaching factoring using slide, divide, bottoms up and am intrigued. I've always used the AC method using factoring by grouping. Now that you've taught factoring using several methods, which do you prefer or do you teach them all? | 677.169 | 1 |
The Love Affair of Romeo & Juliet
A System of Discrete-Time Equations
1. Home
The goal of this website is to introduce the idea of mathematical modeling using a system of linear discrete-time equations. It intends to familiarize readers with the behaviour of a linear system, and introduce the reader to the idea of fixed points for systems and elementary Linear Stability Analysis.
To understand the content, a reader should possess knowledge of discrete-time equations in one-dimension, linear algebra, and of partial derivatives.
This module was written by Gerda de Vries and Cole Zmurchok for CRYSTAL-Alberta.
Content adapted from A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Tools, by G. de Vries et al, SIAM 2006, with permission and Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, by Steven H. Strogatz, Perseus Books, 1994. | 677.169 | 1 |
MA1006: ALGEBRA (2017-2018)
Course Overview
This course introduces the concepts of complex numbers, matrices and other basic notions of linear algebra over the real and complex numbers. This provides the necessary mathematical background for further study in mathematics, physics, computing science, chemistry and engineering.
What other courses must be taken with this course?
What courses cannot be taken with this course?
Are there a limited number of places available?
No
Course Description
The basic course includes a discussion of the following topics: complex numbers and the theory of polynomial equations, vector algebra in two and three dimensions, systems of linear equations and their solution, matrices and determinants.
Syllabus
Solving equations.
Polynomial equations and their roots, polynomial long division, the Rational root theorem.
Introduction to complex numbers. The addition, subtraction, multiplication and division of
Complex numbers. Modulus and Argument and the representation of such numbers on an Argand diagram. Loci and regions in the Argand diagram. De Moivre's theorem and applications. Complex exponential, logarithm, sine and cosine.
Assessment
Formative Assessment
In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination.
Feedback
In-course assessment will be marked and feedback provided to the students.
Support tutorials to be arranged by the Course Coordinator, as need arises. | 677.169 | 1 |
Boiled-down essentials of the top-selling Schaum's Outline series for the student with limited time
What
Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials.
Designed to appeal to underprepared students and readers turned off by dense text
Cartoons, sidebars, icons, and other graphic pointers get the material across fast
Concise text focuses on the essence of the subject
Delivers expert help from teachers who are authorities in their fields
Perfect for last-minute test preparation
So small and light that they fit in a backpack!
"synopsis" may belong to another edition of this title.
About the Author:
Robert E. Moyer, Ph.D., is Associate Professor of Mathematics at Southwest Minnesota State University in Marshall, MN.
McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide | 677.169 | 1 |
Introduction to the History of Mathematics by Howard Eves
By Howard Eves
This vintage best-seller via a widely known writer introduces arithmetic background to math and math schooling majors. prompt essay issues and challenge stories problem scholars. CULTURAL CONNECTIONS sections clarify the time and tradition within which arithmetic built and advanced. pix of mathematicians and fabric on ladies in arithmetic are of designated curiosity.
This publication isn't a handbook within the ordinary feel, yet a compilation of evidence referring to Lie algebras that continually look in actual difficulties. the cloth lined is the results of a number of seminars given by way of the writer in the course of a long time, and synthetize the most proof that are supposed to be identified to any physicist.
This can be a revision of an past capacity and Their Inequalities through the current writer and Professors Mitrinovic and Vasic. not just does this e-book deliver the sooner model brand new yet enlarges the scope significantly to provide an entire and in-depth therapy of all facets of the sector. whereas the point out of capability happens in lots of books this is often the single complete therapy of the topic.
Is there something extra appealing than an "A" in Algebra? to not the Lial workforce! Marge Lial, John Hornsby, and Terry McGinnis write their textbooks and accompanying assets with one aim in brain: giving scholars the entire instruments they should be successful. With this revision, the Lial crew has extra subtle the presentation and workouts in the course of the textual content.
Note that we could have written 0' ∈ s instead of [0', [0, 0']] ∈ s, since [1, [0, 1]] = (1+ ((0+1)2+0))2 + 1 = 5. e. ) The above definition of y = x! is an example of a definition by primitive recursion; we have a base clause 0! = 1 in which the function's value at zero is specified, and an induction clause (n+1)! ) in which the value at n+1 is specified in terms of its value at n. x. Here, the induction is carried out on the variable y; however the value of the function also depends on x, which is kept fixed while y varies.
Tarski's definition appeared when some logical positivists had expressed doubts about the possibility of a scientifically acceptable definition or theory of truth. Tarski showed that this way of defining satisfaction and hence truth existed, and that it had important uses in logic and mathematics. The second disjunct will be a formula true of two numbers a,s if a is an atomic formula of the form P13t1t2t3, where t1, t2 and t3 are terms of RE, and s is sufficient for and satisfies a: D2(a,s)=df.
N ≤ y)(∃p ≤ y)(y = [n, p] ∧ Digp (x, n, p)). x ∈ y is true of two numbers a,b if b codes a finite set S and a is a member of S. Note that Digp(m,n,p) and x ∈ y are formulae of Lim+. We could have carried out the construction in Lim, but it would have been more tedious, and would not have had any particular advantage for the purposes of this course. There are two special cases we should check to make sure our coding scheme works: namely, we should make sure that the sets {0} and Ø have codes. If y is not in the range of our pairing function, then x ∈ y will be false for all x; so y will code Ø. | 677.169 | 1 |
Gerard Venema on Exploring Advanced Euclidean Geometry with GeoGebra
This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincaré disk model for hyperbolic geometry | 677.169 | 1 |
Introduction to the Matrix
A matrix (plural matrices) is sort of like a "box" of information where you are keeping track of things both right and left (columns), and up and down (rows). Usually a matrix contains numbers or algebraic expressions. You may have heard matrices called arrays, especially in computer science.
As an example, if you had three sisters, and you wanted an easy way to store their age and number of pairs of shoes, you could store this information in a matrix. The actual matrix is inside and includes the brackets:
Matrices are called multi-dimensional since we have data being stored in different directions in a grid. The dimensions of this matrix are "2 x 3" or "2 by 3", since we have 2 rows and 3 columns. (You always go down first, and then over to get the dimensions of the matrix).
Again, matrices are great for storing numbers and variables – and also great for solving systems of equations, which we'll see later. Each number or variable inside the matrix is called an entry or element, and can be identified by subscripts. For example, for the matrix above, "Ashley's number of pairs of shoes (5)" would be identified as , since it's on the 2nd row and it's the 1st entry.
Adding and Subtracting Matrices
Let's look at a matrix that contains numbers and see how we can add and subtract matrices.
Let's say you're in avid reader, and in June, July, and August you read fiction and non-fiction books, and magazines, both in paper copies and online. You want to keep track of how many different types of books and magazines you read, and store that information in matrices. Here is that information, and how it would look in matrix form:
We can add matrices if the dimensions are the same; since the three matrices are all "3 by 2", we can add them. For example, if we wanted to know the total number of each type of book/magazine we read, we could add each of the elements to get the sum:
We could also subtract matrices this same way.
If we wanted to see how many book and magazines we would have read in August if we had doubled what we actually read, we could multiply the August matrix by the number 2. This is called matrix scalar multiplication; a scalar is just a single number that we multiply with every entry. Note that this is not the same as multiplying 2 matrices together (which we'll get to next):
Multiplying Matrices
Multiplying matrices is a little trickier. First of all, you can only multiply matrices if the dimensions "match"; the second dimension (columns) of the first matrix has to match the first dimension (rows) of the second matrix, or you can't multiply them. Think of it like the inner dimensions have to match, and the resulting dimensions of the new matrix are the outer dimensions.
Here's an example of matrices with dimensions that would work:
Notice how the "middle" or "inner" dimensions of the first matrices have to be the same (in this case, "2"), and the new matrix has the "outside" or "outer" dimensions of the first two matrices ("3 by 5").
Now, let's do a real-life example to see how the multiplication works.Let's say we want to find the final grades for 3 girls, and we know what their averages are for tests, projects, homework, and quizzes. We also know that tests are 40% of the grade, projects 15%, homework 25%, and quizzes 20%.
Here's the data we have:
Let's organize the following data into two matrices, and perform matrix multiplication to find the final grades for Alexandra, Megan, and Brittney. To do this, you have to multiply in the following way:
Just remember when you put matrices together with matrix multiplication, the columns (what you see across) on the first matrix have to correspond to the rows down on the second matrix. You should end up with entries that correspond with the entries of each row in the first matrix.
For example, with the problem above, the columns of the first matrix each had something to do with Tests, Projects, Homework, and Quizzes (grades). The row down on the second matrix each had something to do with the same four items (weights of grades). But then we ended up with information on the three girls (rows down on the first matrix).
So Alexandra has a 90, Megan has a 77, and Brittney has an 87. See how cool this is? Matrices are really useful for a lot of applications in "real life"!
Now let's do another example; let's multiply the following matrices:
Don't worry; probably most of the time you'll be doing matrix multiplication will be in the calculator!
Oh, one more thing! Remember that multiplying matrices is not commutative (order makes a difference), but is associative (you can change grouping of matrices when you multiply them). Multiplying matrices is also distributive (you can "push through" a matrix through parentheses), as long as the matrices have the correct dimensions to be multiplied.
Matrices in the Graphing Calculator
The TI graphing calculator is great for matrix operations! Here are some basic steps for storing, multiplying, adding, and subtracting matrices:
(Note that you can also enter matrices using ALPHA ZOOM and the arrow keys in the newer graphing calculators.)
We'll learn other ways to use the calculator with matrices a little later.
Determinants, the Matrix Inverse, and the Identity Matrix
Soon we will be solving Systems of Equations using matrices, but we need to learn a few mechanics first!
Most square matrices (same dimension down and across) have what we call a determinant, which we'll need to get the multiplicative inverse of that matrix. The inverse of a matrix is what we multiply that square matrix by to get the identity matrix. We'll use the inverses of matrices to solve Systems of Equations; the inverses will allow us to get variables by themselves on one side (like "regular" algebra). You'll solve these mainly by using your calculator, but you'll also have to learn how to get them "by hand".
Note that the determinant of a matrix can be designated by \(\det \left[ \text{A} \right]\) or \(\left| \text{A} \right|\), and the inverse of a matrix by \({{\text{A}}^{{-1}}}\).
Let's do some examples and first get the determinant of matrices (which we can get easily on a calculator!). The determinant is always just a scalar (number), and you'll see it with two lines around the matrix:
Now let's use the determinant to get the inverse of a matrix. We'll only work with 2 by 2 matrices, since you'll probably be able to use the calculator for larger matrices. Note again that only square matrices have inverses, but there are square matrices that don't have one (when the determinant is 0):
Note that a matrix, multiplied by its inverse, if it's defined, will always result in what we call an Identity Matrix: . An identity matrix has 1's along the diagonal starting with the upper left, and 0's everywhere else.
When you multiply a square matrix with an identity matrix, you just get that matrix back: . Think of an identity matrix like "1" in regular multiplication (the multiplicative identity), and the inverse matrix like a reciprocal (the multiplicative inverse).
Solving Systems with Matrices
Why are we doing all this crazy math? Because we can solve systems with the inverse of a matrix, since the inverse is sort of like dividing to get the variables all by themselves on one side.
To solve systems with matrices, we use . Here is why, if you're interested in the "theory" (the column on the right provides an example with "regular" multiplication). (I is the identity matrix.)
Let's take the system of equations that we worked with earlier and show that it can be solved using matrices:
Oh, and there's another way to solve these in your calculator, but your teacher may not tell you. I'm not going to go into the details, but it's using a method called reduced row echelon form, where we can put everything in one matrix (called an augmented matrix). Let's try this for the following matrix:
A little easier, right?
Solving Word Problems With Matrices
Now that we know how to solve systems using matrices, we can solve them so much faster! Let's do a couple of pure matrices problems, and then more systems problems :).
Matrix Multiplication Problem
Solutions:
(a) When we multiply a matrix by a scalar (number), we just multiply all elements in the matrix by that number. So 2P =
(b) When we square P, we just multiply it by itself. Let's do this "by hand":
(c) Since , we have . Let's use our calculator to put P in [A] and in [B]. Then .
Matrix Equation Problem:
This one's a little trickier, since it doesn't really look like a systems problem, but you solve it the same way:
Solve the matrix equation for X (X will be a matrix):
Solution:
Let's add the second matrix to both sides, to get X and it's coefficient matrix alone by themselves. Then we'll "divide" by the matrix in front of X. Watch the order when we multiply by the inverse (matrix multiplication is not commutative), and thank goodness for the calculator!
We can check it back: . It works!
Matrix Multiplication Word Problem:
The following matrix consists of a shoe store's inventory of flip flops, clogs, and Mary Janes in sizes small, medium, and large:
The store wants to know how much their inventory is worth for all the shoes. How should we set up the matrix multiplication to determine this the best way?
Solution:
The trick for these types of problems is to line up what matches (flip flops, clogs, and Mary Janes), and that will be "in the middle" when we multiply. This way our dimension will line up. Another way to look at it is we need to line up what goes across the first matrix with what goes down the second matrix, and we'll end up with what goes down the first matrix for these types of problems.
So our matrix multiplication will look like this, even though our tables look a little different (I did this on a calculator):
So we'll have $1050 worth of small shoes, $2315 worth of medium shoes, and $1255 worth of large shoes for a total of $4620.
Another Matrix Multiplication Word Problem:
A nut distributor wants to know the nutritional content of various mixtures of almonds, cashews, and pecans. Her supplier has provided the following nutrition information:
Her first mixture, a protein blend, consists of 6 cups of almonds, 3 cups of cashews, and 1 cup of pecans. Her second mixture, a low fat mix, consists of 3 cups of almonds, 6 cups of cashews, and 1 cup of pecans. Her third mixture, a low carb mix consists of 3 cups of almonds, 1 cup of cashews, and 6 cups of pecans. Determine the amount of protein, carbs, and fats in a 1 cup serving of each of the mixtures.
Solution:
Sometimes we can just put the information we have into matrices to sort of see what we are going to do from there. It makes sense to put the first group of data into a matrix with Almonds, Cashews, and Pecans as columns, and then put the second group of data into a matrix with information about Almonds, Cashews, and Pecans as rows. This way the columns of the first matrix lines up with the rows of the second matrix, and we can perform matrix multiplication. This way we get rid of the number of cups of Almonds, Cashews, and Pecans, which we don't need. So here is the information we have in table/matrix form:
Then we can multiply the matrices (we can use a graphing calculator) since we want to end up with the amount of Protein, Carbs, and Fat in each of the mixtures. The product of the matrices consists of rows of Protein, Carbs, and Fat, and columns of the Protein, Low Fat, and Low Carb mixtures:
But we have to be careful, since these amounts are for 10 cups (add down to see we'll get 10 cups for each mixture in the second matrix above). Also, notice how the cups unit "canceled out" when we did the matrix multiplication (grams/cup time cups = grams).
So to get the answers, we have to divide each answer by 10 to get grams per cup. So the numbers in bold are our answers:
Matrix Word Problem when Tables are not Given:
Sometimes you'll get a matrix word problem where just numbers are given; these are pretty tricky. Here is one:
An outbreak of Chicken Pox hit the local public schools. Approximately 15% of the male and female juniors and 25% of the male and female seniors are currently healthy, 35% of the male and female juniors and 30% of the male and female seniors are currently sick, and 50% of the male and female juniors and 45% of the male and female seniors are carriers of Chicken Pox.
Using two matrices and one matrix equation, find out how many males and how many females (don't need to divide by class) are healthy, sick, and carriers.
Solution:
The best way to approach these types of problems is to set up a few manual calculations and see what we're doing. For example, to find out how many healthy males we would have, we'd set up the following equation and do the calculation: .15(100) + .25(80) = 35. Likewise, to find out how many females are carriers, we can calculate: .50(120) + .45(100) = 105.
We can tell that this looks like matrix multiplication. And since we want to end up with a matrix that has males and females by healthy, sick and carriers, we know it will be either a 2 x 3 or a 3 x 2. But since we know that we have both juniors and seniors with males and females, the first matrix will probably be a 2 x 2. That means, in order to do matrix multiplication, the second matrix that holds the %'s of students will have to be a 2 x 3, since there are 3 types of students, healthy (H), sick (S), and carriers (C). Notice how the percentages in the rows in the second matrix add up to 100%. Also notice that if we add up the number of students in the first matrix and the last matrix, we come up with 400.
Matrix Multiplication when Diagonals are Answers:
The first table below show the points awarded by judges at a state fair for a crafts contest for Brielle, Brynn, and Briana. The second table shows the multiplier used for the degree of difficulty for each of the pieces the girls created. Find the total score for each of the girls in this contest.
Solution:
This one's a little trickier since it looks like we have two 3 x 2 matrices (tables), but we only want to end up with three answers: the total score for each of the girls.
If we were to do the matrix multiplication using the two tables above, we would get:
Hmm….this is interesting; we end up with a matrix with the girls's names as both rows and columns. It turns out that we have extraneous information in this matrix; we only need the information where the girls' names line up. So we only look at the diagonal of the matrix to get our answers: Brielle had 86.8 points, Brynn 79.2 points, and Briana 110 points.
What we really should have done with this problem is to use matrix multiplication separately for each girl; for example, for Brielle, we should have multiplied and so on. Oh well, no harm done; and now you'll know what to do if you see these types of matrices problems.
Using Matrices to Solve Systems
Solve these word problems with a system of equations. Write the system, the matrix equations, and solve:
Finding the Numbers Word Problem:
The sum of three numbers is 26. The third number is twice the second, and is also 1 less than 3 times the first. What are the three numbers?
Let x = the first number, y = the second number, and z= the third number. So here are the three equations:
Note that, in the last equation, "one less than" means put the –1 at the end (do this with real numbers to see why).
We need to turn these equations into a matrix form that looks like this:
So we need to move things around so that all the variables (with coefficients in front of them) are on the left, and the numbers are on the right. (It doesn't matter which side; just watch for negatives). If we just have the variable in the equation, we put a 1 in the matrix; if we don't have a variable or a constant (number), we put a 0 in the matrix. So we get: and in matrix form:
Putting the matrices in the calculator, and using the methods from above, we get:
So the numbers are 5, 7, and 14. Much easier than figuring it out by hand!
A Florist Must Make 5 Identical Bridesmaid Bouquets Systems Problem
A florist is making 5 identical bridesmaid bouquets for a wedding. She has $610 to spend (including tax) and wants 24 flowers for each bouquet. Roses cost $6 each, tulips cost $4 each, and lilies cost $3 each. She wants to have twice as many roses as the other 2 flowers combined in each bouquet. How many roses, tulips, and lilies are in each bouquet?
Solution:
Let's look at the question that is being asked and define our variables: Let r = the number of roses,t = the number of tulips, and l = the number of lilies. So let's put the money terms together, and also the counting terms together:
Now let's put the system in matrices (let's just use one matrix!) and on the calculator:
So for all the bouquets, we'll have 80 roses, 10 tulips, and 30 lilies.
So for one bouquet, we'll have of the flowers, so we'll have 16 roses, 2 tulips, and 6 lilies.
An Input Output Problem
Input-output problems are seen in Economics, where we might have industries that produce for consumers, but also consume for themselves. An application of matrices is used in this input-output analysis, which was first proposed by Wassily Leontief; in fact he won the Nobel Prize in economics in 1973 for this work.
We can express the amounts (proportions) the industries consume in matrices, such as in the following problem:
The following coefficient matrix, or input-output matrix, shows the values of energy and manufacturing consumed internally needed to produce $1 of energy and manufacturing, respectively. In other words, of the value of energy produced (x for energy, y for manufacturing), 40 percent of it, or .40x pays to produce internal energy, and 25 percent of it, or .25x pays for internal manufacturing. Of the value of the manufacturing produced, .25y pays for its internal energy and .10y pays for manufacturing consumed internally. The inputs are the amount used in production, and the outputs are the amounts produced.
(a) If the capacity of energy production is $15 million and the capacity of manufacturing production is $20 million, how much of each is consumed internally for capacity production?
(b) How much energy and manufacturing must be produced to have $8 million worth of energy and $5 million worth of manufacturing available for consumer use?
Solution:
(a) If production capacities are $15 million for energy and $20 million for manufacturing, the amount consumed internally is . So $11 million of energy is consumed internally and $5.75 million of manufacturing is consumed internally.
This makes sense, for example, since we're multiplying the proportion of energy consumed internally (.4) by the production capacity for energy ($15 million) and adding that to the proportion of energy needed for internal manufacturing (.25) by the production capacity of manufacturing ($20 million) to get the total dollar amount of energy needed or consumed internally ($11 million). Then we do the same for manufacturing.
(b) The amount of energy and manufacturing to be produced to have $8 million worth of energy and $5 million worth of manufacturing available for consumer (non-internal) use is solved using the following equation (we want what's "left over" after the internal consumption, so it makes sense): . To get , we can use the formula . So the two industries must produce $17.7 million worth of energy and $10.5 million worth of manufacturing, respectively.
Cramer's Rule
Sometimes you'll have to learn Cramer's Rule, which is another way to solve systems with matrices. Cramer's Rule was named after the Swiss mathematician Gabriel Cramer, who also did a lot of other neat stuff with math.
Cramer's rule is all about getting determinants of the square matrices that are used to solve systems. It's really not too difficult; it can just be a lot of work, so again, I'll take the liberty of using the calculator to do most of the work 🙂
Let's just show an example; let's solve the following system using Cramer's rule:
To solve for x, y, andz, we need to get the determinants of four matrices, the first one being the 3 by 3 matrix that holds the coefficients of x, y, and z. Let's call this first determinant D;
Now we'll get a matrix called , which is obtained by "throwing away" the first (x) column, and replacing the numbers with the "answer" or constant column. So
You can probably guess what the next determinant we need is: , which we get by "throwing away" the second column (y) of the original matrix and replacing the numbers with the constant column like we did earlier for the x. So Similarly,
OK, now for the fun and easy part! To get the x, y, and z answers to the system, you simply divide the determinants So Now we know that x = 5, y = 1, and z = –2.
Note that, like the other systems, we can do this for any system where we have the same numbers of equations as unknowns.
Number of Solutions when Solving Systems with Matrices
Most systems problems that you'll deal with will just have one solution. (These equations are called independent or consistent).But, like we learned in the Systems of Linear Equations and Word ProblemsSection here, sometimes we have systems where we either have no solutions or an infinite number of solutions.
Without going too much into Geometry, let's look at what it looks like when three systems (each system looks like a "plane" or a piece of paper) have an infinite number of solutions, no solutions, and one solution, respectively:
Systems that have an infinite number of solutions (called dependent or coincident) will have two equations that are basically the same. One row of the coefficient matrix (and the corresponding constant matrix) is a multiple of another row. Then it's like you're trying to solve a system with only two equations, but three unknowns.
A system that has an infinite number of solutions may look like this:
Systems with no solutions (called inconsistent) will have one row of the coefficient matrix a multiple of another, but the coefficient matrix will not have this. So a system that has no solutions may look like this:
When you try to these types of systems in your calculator (using matrices), you'll get an error since the determinant of the coefficient matrix will be 0. This is called a singular matrix and the calculator will tell you so:
Also, if you put these systems in a 3 by 4 matrix and use RREF, you'll be able to see what is happening. For the systems with infinite solutions, you can see you won't get an identity matrix, and that 0 always equals 0. You can actually define the set of solutions by just allowing z to be anything, and then, from the other rows, solve for x and y in terms of z: This would look like so the solution set for {x, y, z} is {5 – .375z, 3 + .875z, z}. (This may be a little advanced for high school 🙂 )
For the system with no solutions, you'll get this, where you can see that you still don't have an identity matrix, and 0 can never equal 1 from the last row:
Learn these rules, and practice, practice, practice!
For Practice: Use the Mathway widget below to try a Matrix Multiplication problem. Click on Submit (the blue arrow to the right of the problem) and click on Multiply the Matrices
2 thoughts on "The Matrix and Solving Systems with Matrices"
On the first example above, you must have updated it because you mention an entry "Brett" but that is not currently included.
Thank so much for a great website! I recommend it to my students when they are absent or need extra clarity on a topic. You explain things very well and have (so far) all the topics I need! | 677.169 | 1 |
Math Placement ACT-SAT
The data shows the math placement cuttoffs for different colleges as of Spring 2016. The data was collected from university web pages. Placement levels were Calculus I, One Step below Calculus (typically trig), or Two Steps below Calculus (typically college algebra).
edit#gid=0
As part of the Math Leadership Corp (MLC) collaborative process, Teachers continually use student formative and summative data to improve their instructional practice and influence their colleagues through research informed coaching, co-planning, classroom observations, demonstrations and critical reflection of practice. Being part of the MLC program, Ms. Garcia's has researched the role that questioning plays in the classroom from a students' perspective. Using research she read from Make One Change, teach students to ask questions, she has decided to teach "students, rather than teachers, assume responsibility for posing questions". She will gather categorical data to see if 80% of 8th grade students feel that asking questions in a math classroom is helpful and whether their is a relationship between asking questions and higher performance on math assessments.
The first and second column:
I found that posing and asking questions is helpful
Helpful (1)
just another thing to do (2)
not helpful (0)
I found that taking notes after discussing the questions with my peers was...
Helpful (1)
just another thing to do (2)
not helpful (0)
Third column are Interim scores
Fourth column Interim scale
Fifth column-- students who asked questions on Interim
Sixth column-- students grades on in class assessment
Seventh column -- students who asked questions on class assessment
Is it Real or Fake?
Results of a coin flipping activity in MATH 2450 at Bowling Green State University.
X = number of heads
Y = length of longest run (of H or T)
Z = number of switches (H to T or T to H) | 677.169 | 1 |
MathPapa - Algebra Calculator & Equation Solver991 characters
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Version 1.1 released on September 30, 2015 - Fixed a UI issue for iOS 9
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Mathematical Connections: A Modeling Approach To Finite Mathematics, Vol. Ii Preliminary Edition Using technology as a tool for solving problems, this unique book presents the practical, day-to-day applications of mathematical concepts by connecting them to real-world examples and reader's actual problems. The focus is on the entire process of problem-solving, including the formulation and validation of mathematical models.Approaches the problem-solving process from beginning to end, using actual situations readers' need to solve. Helps readers understand mathematical functions and models: identifying and validating assumptions of models, making ballpark estimates, verifying calculations, performing sensitivity analysis, and identifying an appropriate level of precision to reflect a reasonable margin of error.
Free Webs Library 2017 is in no way intended to support illegal activity. We uses Search API to find the overview of Mathematical Connections: A Modeling Approach To Finite Mathematics, Vol. Ii Preliminary Edition | 677.169 | 1 |
Mathematics
The course covers pure mathematics which extends algebra, trigonometry and transformations covered at GCSE. New topics such as logarithms, differentiation and integration are included. Applications of mathematics to model situations and to solve problems in a variety of contexts are learnt in the statistics and mechanics part of the course.
Specific requirements
A minimum of five GCSEs, two 6 grades, and three 4 grades.
GCSE English at grade 4.
Grade 7 in Maths preferred. Students with grade 6 may be considered according to their GCSE profile.
If a grade 6 in Maths is achieved a G-Score of 6 will also be required.
Please click here to see grades conversions in line with the new grading system.
Where does it lead?
Mathematics is a subject which can be studied in order to develop high levels of numeric and problem solving skills. Studying mathematics opens up a wide range of career paths. Students with a mathematics A level often go to work in areas such as engineering, architecture, accounting, business, pharmacy, statistics, medicine and dentistry.
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Amusingly, it seems like the course is marketed towards a nonexistent demographic. It's made so that someone without calculus training can understand it, but realistically nobody without calculus training can understand it. | 677.169 | 1 |
Edexcel A levelMathematics (2008)
Here, you'll find everything you need to study for or to teach the Edexcel GCE AS and A level in Mathematics, including key documents and the latest news.
Students of our Edexcel A level in Maths will develop an understanding of mathematics and mathematical processes, develop the ability to reason logically and construct mathematical proofs, and understand coherence and progression in mathematics and how different areas of mathematics can be connected.
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Our Edexcel A level Mathematics specification enables students to follow a flexible course in maths (including Pure Mathematics, Further Mathematics and Additional Further Mathematics) to suit their individual needs and goals.
You will encourage students to take increasing responsibility for their own learning and the evaluation of their own mathematical development. They'll learn to reason logically and understand mathematical processes in a way that promotes confidence and fosters enjoyment.
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Our Edexcel A level Mathematics specification enables you to follow a flexible course in maths to suit your individual needs and goals.
You can choose to study between 3 and 18 units in a range of disciplines (Pure, Mechanics, Statistics and Decision maths) to give up to a maximum of 3 A levels in Mathematics, Further Mathematics and Further Mathematics Additional.
Alternatively, you can complete a single AS or A level specialising in Pure Mathematics. | 677.169 | 1 |
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I am very pleased to present "Equations and Inequalities in Algebra" for your teaching enjoyment! In this power point, students learn the difference between an equation and an inequality. They also learn the various translations, in words, for the inequality symbols and how to recognize solutions to both equations and inequalities. They learn to check for possible solutions, use mental math to solve equations, solve real-life situations that correspond to common-core standard, write equations and inequalities as they apply to real-life situations, and check to determine whether or not a solution is correct. There are multiple practice problems with solutions provided. Thank you! . | 677.169 | 1 |
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Class 8 – Relations
Online Tests
Study Material
Introduction: In our daily life, we come across many relations such as father-son, brother-sister, teacher-student and many more. In mathematics too, we come across relation such as A is a subset of B, Line l is parallel to line m. Number m is less than number n
In all these situations, we notice that a relation involves pairs of objects in certain order. This synopsis deals with the study of relations in mathematics.
Ordered pair:
In mathematics, an ordered pair is a combination of two objects.
Two elements a and b listed in a specific order, form an ordered pair, denoted by (a, b).
In an ordered pair (a, b), we call a as first component or first coordinate and b as second component or second coordinate. By changing the position of the components, the ordered pair is changed.
Thus, (a, b) ¹ (b, a)
Equality of ordered pairs:
Two ordered pairs (a, b) and (c, d) are said to be equal if and only if a = c and b = d.
i.e., (a, b) = (c, d)
Example:Given Find a and b ?
Solution:
Cartesian product of two sets: For the given two sets A and B, the set containing all the ordered pairs where the first element is taken from A and second element is taken from B is called the Cartesian product of two sets A and B.
Example: If A = {2, 4, 6}, B = {1, 3, 5} thenfind A × B using tree diagram.
To represent A × B using tree diagram, write all the elements of A vertically and then for each element of A, write all the elements of B as shown and arrows as shown in the figure below.
Relation: Let A and B be two non-empty sets. Then a relation R from A to B is the set of all ordered pairs such that and a is associated with b according to a definite rule. If we say that a is related to b and we write .
Clearly, every relation R from A to B is a subset of A × B. i.e., .
A"relation" is just a relationship between any two sets of information. Consider a relationship between all the people in a class and their heights. The pairing of names and heights is a relation. This pairing is done so that either if a person's name is known we can give that person's height, or else a height is given, the names of all the people who are that tall can be known. We also come across various relations in real life like 'is mother of ', is son of','is teacher of '. Let us now define the mathematical relation.
Definition:Let A and B be two non-empty sets and R is called a relation from the set A to B. (Any subset of is called a relation from A to B).
∴ A relation contains ordered pairs as elements. Hence "A relation is a set of ordered pairs".
Example:
1.Let A= {1, 3, 4}, B = {1, 2}
Then,A × B = {(1,1), (1,2), (3,1), (3,2), (4,1), (4,2)}
Let R1= {(3, 1), (3, 2), (4, 1), (4, 2)}
We can observe that and also that forevery ordered pair (a, b) ∈ R1, a>b.
Hence R1 is the relation "is greater than" from A to B.
2. In the previous example, let Here also, and we also notice that for every ordered pair .
Hence, R2 is the relation "is less than or equal to" from A to B.
i) If then the number of possible relations from A to B is 2mn. [Since every relation from A to B is a subset of A × B, the number of relations is equal to number of subsets of A × B].
ii) A relation R is said to be defined on a set A if .
iii) If n(A) = m the number of relations defined on A, i.e.,
Example: Let A = {1, 2, ………10} then there are relations on A.
Domain and Range of a Relation:Let A and B be two non-empty sets and R be a relation from A to B, we note that
i) The set of first co-ordinates of all ordered pairs in R is called the domain of R.
ii) The set of second co-ordinates of all ordered pairs in R is called the range of R.
i) Roster-method (or) List method: In this method we list all the ordered pairs that satisfy the rule or property given in the relation.
Example: Let A = {1, 3, 5}, B = {3, 4, 6}
If R is a relation from A to B having property "is less than" then the roster form of R is
R = {(1, 3), (1, 4), (1, 6), (3, 4), (3, 6), (5, 6)}
ii) Set-builder method: In this method, a relation is described by using a representation and stating the property or properties, which the first and second co-ordinates of every ordered pair of the relation satisfy through the representation. Example: Let A = {1, 2, 4}
If R is a relation on A defined as "is greater than or equal to", the set builder form of R is .
iii) Arrow diagram: In this method, a relation is described by drawing arrows between the elements which satisfy the property or properties given in the relation.
Example:Let A = {2, 3, 4} B = {1, 3, 4}
Let R be a relation from A to B with property "is equal to".
The arrow diagram of R is
Let A and B be two non-empty sets. The Cartesian product of A and B, denoted by A · B is the set of all ordered pairs (a, b), such that a A and b B.
i.e., A · B = {(a, b)/a A,b B}
1. A · B ≠ B · A, unless A = B
2. For any two sets A and B. n(A · B) = n(B · A)
3. If n(A) = p and n(B) = q, then n(A · B) = pq
If A = {1, 2, 3} and B = {3, 4, 5}, then find A · B.
Consider the elements of A on the X-axis and the elements of B on the Y-axis and mark the points | 677.169 | 1 |
Algebra 1 EOC STAAR Review BINGO Game
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Fun and interactive Bingo game is the perfect activity for the days leading up to the Algebra 1 EOC or as cumulative review throughout the year. This game is designed for scholars to solve questions by graphing on calculators as review before their EOC exam however answers can be found a variety of ways. The game includes the following topics:
1. Finding Vertex of Quadratic Parabolas
2. Finding the Roots/Solutions of Quadratic Functions
3. Finding the Solution to a System of Equations
4. Finding the Zero of a Linear Function
Some equations require students to first convert into Standard/Slope Intercept Form for practice. Most BINGO cards give an equation requiring students to find a characteristic.
Product is Powerpoint- can be edited to suit your needs!!
The Texas TEKS covered are as follows:
Category 2:
Readiness Standard A.3(C) graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems
Supporting Standard A.3(F) graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist
Category 4:
Readiness Standard A.7(A) Graph | 677.169 | 1 |
Do my algebra
A digital library containing Java applets and activities for K-12 mathematics. Math-U-See is math you'll love. Math-U-See is a complete K-12 math curriculum focused on homeschool and small group learning environments that uses. The producers of Mathematica, one of the common software packages for advanced mathematics. Maxima, a Computer Algebra System. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor. ClassZone Book Finder. Follow these simple steps to find online resources for your book. PatrickJMT: making FREE and hopefully useful math videos for the world. Teacher Login / Registration : Teachers: If your school or district has purchased print student editions, register now to access the full online version of the book.
GeorgiaStandards.Org (GSO) is a free, public website providing information and resources necessary to help meet the educational needs of students. Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples. Algebraic thinking with a function machine. What's the rule? Enter your own values or let the computer decide for you. Bellevue College (formerly Bellevue Community College, BCC) is a leading institution of higher education in the Pacific Northwest, located in Bellevue Washington. A digital library containing Java applets and activities for K-12 mathematics. Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons (pre-algebra, algebra, precalculus), cool math. If you're seeing this message, it means we're having trouble loading external resources for Khan Academy. If you're behind a web filter, please make sure that the.
USATestprep offers test prep resources to support teachers and administrators. Request your free trial of state-aligned practice tests. We would like to show you a description here but the site won't allow us. Pearson Prentice Hall and our other respected imprints provide educational materials, technologies, assessments and related services across the secondary curriculum. Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples. Welcome! InterAct Math is designed to help you succeed in your math course! The tutorial exercises accompany the end-of-section exercises in your Pearson textbooks. Pearson Prentice Hall and our other respected imprints provide educational materials, technologies, assessments and related services across the secondary curriculum. Welcome! InterAct Math is designed to help you succeed in your math course! The tutorial exercises accompany the end-of-section exercises in your Pearson textbooks.
HotBot.com Search Engine – Famous Original Search Engine from 1996. Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math. Covers the basic materials for algebra, calculus, and differential equations. Includes examples, review questions, common errors, study tips and formula tables(PDF. The producers of Mathematica, one of the common software packages for advanced mathematics. GeorgiaStandards.Org (GSO) is a free, public website providing information and resources necessary to help meet the educational needs of students. Bellevue College (formerly Bellevue Community College, BCC) is a leading institution of higher education in the Pacific Northwest, located in Bellevue Washington.
Math-U-See is math you'll love. Math-U-See is a complete K-12 math curriculum focused on homeschool and small group learning environments that uses. Algebraic Reasoning Find the value of each object in the puzzle by looking for mathematical relationships. The best multimedia instruction on the web to help you with your homework and study. Algebraic thinking with a function machine. What's the rule? Enter your own values or let the computer decide for you. Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons (pre-algebra, algebra, precalculus), cool math. Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.
Maxima, a Computer Algebra System. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor. Covers the basic materials for algebra, calculus, and differential equations. Includes examples, review questions, common errors, study tips and formula tables(PDF. West Texas A&M University (WTAMU), rich in history that dates to 1910, is the northernmost senior institution of higher learning in Texas. As the only bachelor's and. Teacher Login / Registration : Teachers: If your school or district has purchased print student editions, register now to access the full online version of the book. ClassZone Book Finder. Follow these simple steps to find online resources for your book. | 677.169 | 1 |
Pre-Calculus Lesson 11 Polynomial Theorems
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This lesson plan includes theorems related to finding the zeros of polynomial functions including the remainder theorem, the factor theorem, and the rational zeros theorem, among others. Teachers should use the instruction to prepare for guided practice where students will practice how to use the information provided. | 677.169 | 1 |
Mathematics
MATHEMATICS DEPARTMENT
Staff Profile:
Mr. Vikas Ware : M.Sc. (Head of the Department)
Email: vikas.ware@ves.ac.in
Area of Interest: Mathematics and Computer Programming.
As member of the examination committee he has developed a software to be used for the purpose of result analysis.
The objective of the 'Solver Competition' is to enhance thinking ability of the students. The competition is open to all college students with an objective to popularize mathematics and problem solving. For a week, everydaya new problem is displayed on the notice board. Students who solves the maximum problems correctly are declared as the winners.
Mathamaze :
It is an intra-collegiate paper presentation competition. The FY, SY and TYBSc students give presentations about ideas in mathematics that AMAZE them. The selected students are further assigned a teacher mentor to prepare for the intercollegiate competitions.
Diverse teaching methods adopted.
Department caters to Science students as well as Commerce students. Therefore diverse teaching methods are adopted depending on the need and size of the class.
Regular tutorial classes held in smaller batches for Science as well as Commerce students
During these tutorial sessions students are encouraged to make presentations on various topics. Problem solving sessions are held.Remedial sessions are held with students who find it difficult to cope with the subject
M³ Contest
Mathemight
Special 'Introductory Statistics' module run for students opting for the Additional Credit Programme
The department encourages students to participate in intercollegiate competitions | 677.169 | 1 |
This is a near-final draft made available due to high demand by the Algebra in Words readership, so students and instructors can begin using its helpful content immediately. The finalized publication is due out soonTopics in Algebra II primarily extend concepts learned in Algebra I and also include functions, complex numbers, exponential and logarithmic functions, use of the graphing calculator, matrices, conics, sequences and series. Algebra II follows either Algebra I or Geometry in the sequence of math courses and is often used as a developmental course at the college level under the name Intermediate Algebra.
This text bridges the gap between traditional and reform approaches to algebra encouraging students to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, | 677.169 | 1 |
.Sc Mathematics
Broad purpose and intentions of the Programme
Aims
Science and technology plays an important role in the economic development of any country. The economy of a country by and large depends on sscience and technological knowledge its citizens have. Mathematics, being the Queen of all sciences, gives an advantage over the other subjects to understand and develop modern technologies. So it becomes important for any country to offer courses in pure and applied mathematics for the aspiring citizens. Further, industries such as Education, Telecommunications, Finance, Banking, Hydropower, Information Technology, Government and private agencies using demographic data etc. require people who are trained with basic knowledge and skills in Mathematics.
In this regard, Sherubtse College has been playing a vital role in producing graduates with above mentioned skills since 1983. After the college came out of the tutelage of the University of Delhi in 2003, it started offering B.Sc. in Maths-Physics and B.Sc. in Maths-Chemistry programmes. So far five cohorts have passed out and most of them are absorbed into various agencies of the country and the feedbacks received from the stakeholders are very encouraging.
However, with the changing needs of the potential employing agencies, the college has come of a time whereby specialised skills in individual subjects are to be imparted for the future requirements of the agencies. Further the graduates of the current programme opined that they did not possess sufficient knowledge and skills in any of the two subjects they have taken. So the college decided to offer degree programmes in individual science subjects. With these broad intentions, B.Sc. Mathematics programme is proposed to be offered from July 2016. This programme is aimed at producing graduates in Mathematics who have strong knowledge and skills in the field of Mathematics encompassing coherent theoretical and practical knowledge of the subject. It is developed and proposed with the intention to increase the number of qualified Mathematics graduates in the country required by different agencies.
Objectives
The aims and objectives of the programme are the following:
1. Equip students with knowledge of the axiomatic nature of mathematics, and enable them to work creatively within this framework
2. Provide students with a thorough knowledge of fundamental mathematical facts, and solve problems which can be analyzed mathematically
3. Provide high quality and relevant education in the field of Mathematics
4. Expose the students to the applications of physical and mathematical principles.
5. Offer a stimulating and supportive environment, which would encourage students to be receptive of new ideas and help them attain their full academic potential.
6. Provide grounding in a coherent body of knowledge, a broad coverage of related academic skills, personal development and social skills. | 677.169 | 1 |
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The study guide is meant to be used right before a mid-chapter test in Algebra 2 or perhaps a chapter test in Algebra I.
Instead of having students work on practicing more problems, (which in my classroom they practiced a lot already) This type of story telling has worked well, it helps my students remember concepts that they may not think about all the time.
I also have a short video as they work in the computer room, which I hope to include in this product very soon. If you are interested in the video from Educreations, please email me and I can send you the link.
The topics included are:
1- Writing a quadratic function in Vertex Form
2- Writing a quadratic function in Standard Form
3- Writing a quadratic function in Factored Form
4- Finding the vertex in standard form
5- Finding the axis of symmetry in standard form
6- Finding the y-intercept
7- Writing domain and range of a quadratic function
8- Finding maximum or minimum values in a parabola
9- 4-examples of graphing a quadratic function
I hope this study guide is helpful to you and your students; I would love to hear back from you and see how it helped you. | 677.169 | 1 |
Linear Algebra
In this linear algebra instructional activity, students solve 3 different sets of problems that include rank, dimension, nullspace and range of linear algebra. They determine the relation between the rank of a matrix and the dimension of its range. Then, students determine the relation between the dimension of a domain of a matrix transformation. | 677.169 | 1 |
Mathematics
The Math Department at JFK Middle College is determined to enable all of our students to be successful and prepared for the next level in their Math education. Math is a sequential curriculum where skills and concepts build and expand from a basic set of fundamentals to more abstract thinking and problem solving. In order for students to be able to think more critically and at higher levels, they must know the basics and be able to apply them on a consistent and proficient level.
JFK Middle College Math Department offers the following courses:
Integrated Math 2
Integrated Math 3
Probability and Statistics
Pre-Calculus
Calculus
In addition to the above courses, many JFK Middle College students take Mathematics Courses at Norco College to fulfill additional graduation and A-G requirements.
In order to take Math classes at Norco College, JFK Middle College students must either provide them a prerequisite verification form, or take the Accuplacer Exam. For those students who have finished JFK Integrated Math 3 or JFK Pre-Calculus both semesters with an A or B, please follow the steps outlined here to register for a College Math Course: How to Register for a College Math Course. To determine which College Math Course to take, please see your JFK Math teacher or the Math Department Chair, Mrs. Reynolds. | 677.169 | 1 |
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Developmental Math
Dev Math Student Resources
Requirements
Students who scored below 34 on the ELM (given after March 2003) start in Developmental Mathematics I, Math 092. Math 092 is a Basic Math/Pre-algebra course. Math 092 is a 3-unit course.
Students who scored 34 or above but below 50 on the ELM, or those who successfully complete Math 092, take Developmental Mathematics II, Math 093 or Math 097. Math 093 is a 5-unit Elementary Algebra course. Math 097 is a 5-unit Elementary Algebra and Pre-statistics course. (Please see your advisor before enrolling in Math 097.)
Students who scored 50 or above on the ELM or are ELM exempt can enroll in Math 102, Math 103/L, Math 131, Math 140, and/or Math 210.
Successful completion of Math 093 allows students to enroll in Math 102, Math 131, Math 103/L, Math 140, and/or Math 210. Always consult with your adviser about the right mathematics class for your program of study. Successful completion of Math 097 allows students to enroll in Math 140, and/or Math 210. Always consult with your adviser about the right mathematics class for your program of study.
Walk in tutoring lab is located at BH 400 open Monday-Thursday 8:30 a.m.- 5:00 p.m., Friday 8:30 a.m. to 2:00 p.m. Tutoring in Building 21 available Monday-Thursday evenings from 6:00 p.m.-11:00 p.m. | 677.169 | 1 |
Mathematics & Accounting
Overview
The Mathematics and Accounting Faculty at Horowhenua College has the objective of providing all students the opportunity to grow in confidence and to enable them to increase in knowledge and competency in Mathematics and Accounting. We employ eight highly qualified teaching staff that include specialists in Statistics, Accounting and Calculus. We have designed several courses aimed at maximising the potential of all our students and adopt industry leading best practice processes.
Facilities
Horowhenua College has seven classrooms dedicated to Mathematics and Accounting teaching spread across two teaching blocks. The Mathematics and Accounting Faculty also has use of a bookable pod of 25 computers and a number of tablets.
Courses on offer
Year 13: Mathematics, Calculus, Statistics and Modelling, Accounting and Services Academy
Year 12: Mathematics, Maths Applied, Trades Academies and Accounting
Year 11: Mathematics A and B, Pre-Trades Academy and Accounting
Year 10: All of our Year 10 Mathematics classes are streamed into core classes so that pupils work in a challenging environment with students of a similar ability.
Year 9: All of our Year 9 Mathematics classes are streamed into core classes so that pupils work in a challenging environment with students of a similar ability.
Course Structure
Extra-Curricular Activities
The Horowhenua College Mathematics and Accounting Faculty have a number of extra-curricular activities on offer:
Love Horowhenua
Sophie Woods - Denmark, July to November 2013
Horowhenua College has been a good experience for me. There are a lot of different subjects and you can choose the subjects you want. The subjects are fun and enjoyable.
When you are an exchange or international student you get really close to the other international students. You hang out a lot with them in the breaks and afterschool. The school has a trip around the north island for all the new international students as well. It was really fun.
I had drama, art, photography, English, Math and Outdoor education. In drama I was in a group where we made our own play. In Art we painted a mural on a board which also included collage and mixed medium on a theme we chose. My teacher was very helpful and patient. I learned a lot and the other students were very talented.
In photography you learnt how to use Photoshop and how to make a folio board again on our own theme.
Outdoor education was my must enjoyable subject. I had an awesome teacher that was always smiling and helpful. He was really into his work and wanted to be a really good teacher for the students and made a questionnaire at the end of the year.
Horowhenua College has been a good experience for me and I have made a lot of new international friends.
» View all testimonials | 677.169 | 1 |
"Elementary Statistics: A Step By Step Approach" is for general beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. This edition places more emphasis on conceptual understanding and understanding results. This edition also features increased emphasis
Book Description Book Condition: New. New. International edition. Different ISBN and Cover image but contents are same as US edition. Perfect condition. Customer satisfaction our priority. Bookseller Inventory # ABE-BOOK-12336 | 677.169 | 1 |
Description:
About this title:
Synopsis: This edition of Swokowski's text is truly as its name implies: a classic. Groundbreaking in every way when first published, this book is a simple, straightforward, direct calculus text. It's popularity is directly due to its broad use of applications, the easy-to-understand writing style, and the wealth of examples and exercises which reinforce conceptualization of the subject matter. The author wrote this text with three objectives in mind. The first was to make the book more student-oriented by expanding discussions and providing more examples and figures to help clarify concepts. To further aid students, guidelines for solving problems were added in many sections of the text. The second objective was to stress the usefulness of calculus by means of modern applications of derivatives and integrals. The third objective, to make the text as accurate and error-free as possible, was accomplished by a careful examination of the exposition, combined with a thorough checking of each example and exercise.
About the Author:
Earl Swokowski authored multiple editions of numerous successful textbooks, including CALCULUS; CALCULUS OF A SINGLE VARIABLE; FUNDAMENTALS OF COLLEGE ALGEBRA; and PRECALCULUS: FUNCTIONS AND GRAPHS, all published by Cengage Learning Brooks/Cole.212659
Book Description PWS-Kent Publishing Company. Hardcover. Book Condition: Fair. 0534924921 0534924921-4932559CS70000OE46W | 677.169 | 1 |
Algebra 2B
How would you un-bake a cookie? Could you un-burn a candle? Unless you have a time machine, some things in life can't be reversed. However, if you can represent a relationship with an equation, then it becomes relatively easy flip the mathematical model around and do all sorts of otherwise impossible things, like control time …
Have you ever watched a jet fly across the sky? Have you ever gone swimming or watched a swim meet? Have you ever tried to count the oranges stacked in a pyramid at the grocery store? If you have, then polynomials are already a part of your life more than you might realize. Aerospace engineers …
Transcript: Rational Expressions and Functions Pineapples make great snacks, but have you ever seen a pineapple plant? They start out as little blossoms in a tropical field, before traveling across the world to your supermarket. When you cut a pineapple in half, it's pretty obvious how many pieces you have. But if you're having friends …
What happens when you or a loved one gets sick? What might have caused the illness, and what might you have to do to get well again? Imagine getting together with all of your friends. And all of their friends. And all of their friends' friends. And all of their friends' friends' friends. Like putting … | 677.169 | 1 |
Wednesday, August 9, 2017
Math Essentials ~ No-Nonsense Algebra Reveiw
Math is the most stressful subject in our household. I have one child who is good at math but hates it and another who struggles with math and feels very unsure about his abilities. When I was asked to review No-Nonsense Algebra from Math Essentials, I was pleased, but my kids were devastated. They were ready for a break from math and were not at all happy about testing out this new product over the summer.
What is it?
This is a two part program. It is a workbook and textbook in one paperback and there is a code inside the book which gives you free access to online lessons. As the title of the program states, there are no distractions or nonsense in this program. Each lesson is broken into five parts.
The online video ~ a short lesson that takes about 10 minutes to watch and helps the student work through the corresponding problems in the lesson he or she is working on.
Introduction ~ This is at the beginning of each lesson and is written directly to the student.
Examples ~ There are two to four examples with each lesson.
Exercises ~ There are 15 to 20 problems to work out in each lesson.
Review ~ There are a few problems to go over in order to review what you have learned at the end of each lesson.
How we used it ~
I decided to use the program with my youngest who is entering 8th grade this fall. She is comfortable in math but doesn't care for it. She likes the workbook style and is always telling me to find curriculum that will get her through her school work in the most efficient way possible so that she can get back to her first love, DANCE. She has been working in a pre-algebra workbook for a few months prior to this program. We worked on the first section, Necessary Tools for Algebra, which is essentially pre-algebra. As it turned out, she decided that the course "wasn't so bad after all". She thought the videos were nicely presented and explained the material well. The problems are worked out on a whiteboard, while the teacher talks in the background. She also liked the workbook layout. She liked that there wasn't a lot of problems. She liked that this program promotes independence and that she did not need to wait for instructions from me to get her work done. She could even check her solutions in the back of the book (as long as she showed her work on paper for me).
I like this program for her as well. It is just the right fit for Anne. I do think it wouldn't work for my son, because he needs tons of repetition. There are only about 15 problems for each lesson. I realize that the concept is that, if you understand it, you only need to do it a few times. However, with a learning disabled person, repetition is the key to success. That said, I think this program is great for many neurotypical ("normal") kids.
I also appreciate that the book is non-consumable, so it could be used for multiple children. The student does need to write the problems out on a separate sheet of paper. My daughter decided to finish the workbooks that she has been using for pre-algebra and then return to this program to complete pre-algebra for this coming school year. She really likes that it is very efficient.
1 comment:
You should try khanacademy.org for your son. They have free, online math courses for K-Calculus. After you've started the "mission" in his grade level, the practice problems will repeat themselves as needed. They also have videos introducing each new topic, and as a bonus they also have a number of other subjects. | 677.169 | 1 |
Read Mathematics - ronhe.herokuapp.com
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Restrictions
Overview
Recently some quite novel applications have been found for "Discrete Mathematics", as opposed to the "Continuous Mathematics" based on the Differential and Integral Calculus. Thus methods for the encoding of information in order to safeguard against eavesdropping or distortion by noise, for example in online banking and digital television, have involved using some basic results from abstract algebra. This module will provide a self-contained introduction to this general area and will cover most of the following topics: (a) Modular arithmetic, polynomials and finite fields: Applications to orthogonal Latin squares, cryptography, "coin-tossing over a telephone", linear feedback shift registers and m-sequences. (b) Error correcting codes: Binary block, linear and cyclic codes including repetition, parity-check, Hamming, simplex, Reed-Muller, BCH, Golay codes; channel capacity; Maximum likelihood, nearest neighbour, syndrome and algebraic decoding.
Details
This module appears in:
Maths Stage 2/3
Postgraduate
Short-Term Study
STMS Undergradute Stage 2 & 3
Contact hours
48 hours - 36 hours of lectures of formal exposition of the subject and 12 hours of examples classes.
Learning outcomes
The Intended Subject Specific Learning Outcomes. On successful completion of the module students will have:
a. improved their precision in logical argument and enhanced their skills in symbolic calculation with more complex discrete structures;
b. a reasonable knowledge of the definitions of terms used in the module and a reasonable understanding of the statements, proofs and implications of the basic theorems given in the course (sufficiently well to be able to construct simple proofs of related results);
c. revised modular arithmetic and polynomial algebra and obtained a reasonable understanding of the theory of finite fields (and related finite rings);
d. developed a critical appreciation as to how this material can be applied to concrete problems in a number of different areas relating to electronic communication systems (cryptography and, primarily, in the study of error correcting codes);
The Intended Generic Learning Outcomes. On successful completion of the Module, students will have:
(i) developed a logical, mathematical approach to solving problems and will be able to solve
problems and present solutions relevant to discrete structures and their applications to IT
communications;
(ii) furthered their ability to work with relatively little guidance on the subject matter and
exercises associated with the course;
(iii) obtained the basic mathematical background necessary to follow the rapidly changing developments in IT communications.
(iv) improved their key skills in written communication, numeracy and problem solving.
University of Kent makes every effort to ensure that module information is accurate for the relevant academic session and to provide educational services as described. However, courses, services and other matters may be subject to change. Please read our full disclaimer. | 677.169 | 1 |
This book teaches students the basics of differentiation, which is a large part of first-year calculus. The student is first instructed on how to compute derivatives of most elementary functions. Next, the student is taught basic rules for differenti... READ MORE » ... READ MORE » | 677.169 | 1 |
all about mathematics ebook you can browse and download here
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Learn to Know Complex Numbers Complex Number, same with Real Number, is a part of numbers family in math. Actually, The Real Numbers are one special matter of Complex Numbers System. Oh yeah, I can' write more, because I just have learned it. I haven't also understood it. So, for more lesson, search it on… | 677.169 | 1 |
Course description
This is an introductory course to sieve methods. We will start with a study of the so-called combinatorial sieve, which will include Brun's pure sieve and the beta-sieve, leading to the fundamental lemma of sieve methods. Several applications will be given, such as the Brun-Titchmarsh inequality and bounds for the number of primes that are values of a given polynomial. Then we will introduce Selberg's approach to sieving. We shall also discuss the optimality of Selberg's sieve and the parity problem of sieve methods. Next, we will study prime solutions to linear equations and Cramer's model of the integers and, subsequently, the revolutionary work of Goldston, Pintz and Yildirim on small gaps among primes. The course will then shift to the study of bilinear sums and the large sieve, as well as one of its main applications: the Bombieri-Vinogradov theorem. We will conclude with three additional topics, provided that time permits: smooth numbers and large gaps between primes, the linear sieve and Maier's matrix method, and the affine sieve.
Grades and homework
Your grade will be based entirely on the number of points you accumulate on the following assignments: | 677.169 | 1 |
> What makes this most amazing for me is the real time feedback students get to help them adjust their ability to interpret functions.
Since you are impressed by this, tell us what this means. For example, tell us...
1. What does the author mean by ?their ability to interpret functions?? 2. How is this important in the students' ability to mathematically analyze functions? 3. Why isn?t there ANYTHING in these lessons to increase the students' ability to mathematically analyze functions? 4. Why isn?t there ANY real time feedback in these lessons to help students adjust their ability to mathematically analyze functions? | 677.169 | 1 |
Experiments with MATLAB
By Cleve Moler, MathWorks
Experiments with MATLABis a free, online book for educators and high school students looking for material that goes beyond their standard courses. College students early in their careers will also find value in the materials and exercises.
Now a full-fledged technical computing language, MATLAB started in the late 1970s as a simple "Matrix Laboratory." Experiments with MATLAB builds on this laboratory tradition by describing experiments involving applied mathematics and technical computing. MATLAB programming is introduced with code snippets and small programs, many of which use interactive graphics.
To make the most of the book's experiments, readers need a high-school-level knowledge of geometry, algebra, and trigonometry. Experiments with MATLAB introduces topics involving calculus, matrices, and differential equations, but it does not assume that students have completed courses in these subjects.
In this Cleve's Corner, I've included edited excerpts from Experiments with MATLAB to give you some idea of the level and tone of the book. I encourage you not only to read about the experiments but also to modify and improve them.
Iteration
The first chapter asks you to pick a number—any number. Enter it into MATLAB with
x = your number
Now enter the statement
x = sqrt(1+x)
Use the up-arrow and enter keys to repeatedly execute the statement until the displayed values stop changing.
Here are the first and last few lines that you will see if you choose x = 3 as your starting value.
No matter what value you start with, you always converge to the same final value, 1.6180339… . Do you recognize this number?
This experiment motivates a discussion of the two meanings of the equals sign: as the assignment operator in programming languages and as the symbol for equality in equations.
How would you solve the following equation?
\[ x = \sqrt{1 + x} \]
Don't use a computer! Do it in your head or on paper. Square both sides and move everything to one side of the equals sign to get a quadratic equation.
\[ x^2 - x - 1 = 0 \]
Then use the quadratic formula to find the positive root,
\[ \phi = \frac{1 + \sqrt{5}}{2} = 1.6180339 … \]
This is our old friend, the golden ratio.
Calendars and Clocks
Friday the 13th is sometimes considered unlucky, but is it unlikely? What is the probability that the 13th day of any month will fall on a Friday? The quick answer is 1/7, but that is not quite right. The rules for leap years ensure that our Gregorian calendar repeats itself every 400 years, or 4800 months. A simple experiment using the MATLAB datenum and weekday functions can count how often the 13th day of each month falls on a Friday, producing the graph in Figure 1. It turns out that the 13th is more likely to fall on a Friday than on any other day of the week. The probability is 688/4800 = .143333, which is slightly larger than 1/7 = .142857.
Figure 1. MATLAB plot showing that the 13th day of a month is more likely to be a Friday than any other day of the week. Click on image to see enlarged view.
The Exponential Function
Too many students who have recently taken a beginning calculus course think the derivative of \(e^x\) is \(x e^{x-1}\). How can we better understand the number \(e\) and the function \(e^x\)? MATLAB can compute powers, \(y = a^x\), for a scalar \(a\) and a vector \(x\).
a = 2
x = 0:0.01:2
y = a.^x
We can also compute an approximate slope or approximate derivative, without any formal rules of differentiation, using
h = 0.0001
yp = (a.^(x+h) – a.^x)/h
Then the statement
plot(x,[y; yp])
produces the first plot shown in Figure 2. The blue curve is the graph of \(2^x\). The green curve is its approximate derivative. The graph of the approximate derivative has the same shape as the graph of the original function but is below it. In fact, the ratio yp./y is a constant independent of \(x\).
Figure 2. Varying the base in a plot of ax and its approximate derivative to discover e. Click on image to see enlarged view.
The M-file expgui lets you move the blue line with the mouse and slowly vary the base of \(a^x\). The second shows the graph of \(3^x\) and its approximate derivative. The green curve is now above the blue curve. As you move from \(a=2\) to \(a=3\), you pass the situation shown in the third plot, where the green curve is on top of the blue curve. For this value of \(a\), the function is its own derivative. The value displayed for \(a\) is \(e\) and the function is \(e^x\), one of the most important functions in mathematics.
We've skipped an important but subtle mathematical and computational question: How does MATLAB compute \(a^x\) without knowing about \(e\)? Well, actually, it can't, so our whole argument is circular. But if anybody asks that question, we have a terrific topic for discussion.
Solving the Amazing T Puzzle
I first saw the wooden puzzle shown in Figure 3 at Puzzling World in Wanaka, New Zealand. Now their most popular puzzle, it was a well-known toy in the 1800s and an advertising tool in the early 1900s.
Figure 4 shows the MATLAB electronic version of the four pieces. They all have the same width, but different heights. One has an unshapely chunk cut out of it, resulting in an irregular pentagon. Using MATLAB and the GUI for the book's sample T Puzzle M-file, you could move the pieces around with the mouse. It turns out that the four pieces can be arranged to form the capital "T" shape shown in Figure 5. What happened to all those 45° angles—and to that chunk?
Figure 4. This electronic puzzle is manipulated by complex arithmetic.
Figure 5. Make this T.
Our program for manipulating the T puzzle uses complex arithmetic. For example, the coordinates of the largest puzzle piece are given by the complex vector
z = [0 1 1+2i 3i]
where the horizontal and vertical dimensions are represented by the real and imaginary components, respectively. Translating the piece in response to mouse motion is easily done by a complex vector subtraction
z = z - w
We rotate the piece about its center by an angle \(\theta\) using the following statements:
mu = mean(z)
omega = exp(i*theta)
z = omega*(z – mu) + mu
Where do you learn that complex multiplication by \(e^{i\theta}\)is a rotation?
The Game of Life
John Horton Conway's "Game of Life" made its debut on the cover of Scientific American in October 1970 and has had a small but loyal following ever since. It is an example of the complexities that can be generated by apparently simple cellular automata.
In "Life", the universe is an infinite, two-dimensional rectangular grid. The population is a collection of grid cells marked as alive. The population evolves at discrete time steps known as generations. At each step, the fate of each cell is determined by the vitality of its eight nearest neighbors and by this rule: A live cell with two live neighbors, or any cell with three live neighbors, is alive at the next step.
This deceptively simple rule leads to an incredible variety of patterns, puzzles, and unsolved mathematical problems.
The "Game of Life" MATLAB program discussed in Experiments with MATLAB is a beautiful example of the use of the sparse matrix data structure. The universe is a sparse matrix X with a finite number of 1s marking the live cells. The size of X grows to accommodate any expanding population.
generate another sparse matrix Y with elements between 0 and 8 that count the number of live neighbors. The rule of "Life" is then implemented in a single MATLAB statement:
X = (X & (Y == 2)) | (Y == 3);
Because all populations follow this rule, the initial population configuration determines how the game of life plays out. In Bill Gosper's initial population, known as the glider gun (Figure 6), the central portion of the gun oscillates, emitting an infinite stream of gliders that pass out of view and into the void. Gosper's configuration was the first to create an unbounded population.
Further Experimentation
Reading about the exercises in Experiments with MATLAB is not nearly as fun—or as educational—as running them yourself. So if you find them interesting, or if you know students who would be interested, please take a look at Experiments with MATLAB. Then run, discuss, and improve the experiments together. Programs, especially MATLAB programs, are vehicles of discourse with people, and not simply ways to send commands to a machine. | 677.169 | 1 |
Integral Calculus with Applications to Physical Sciences and Engineering
MAT 101
-
Winter 2014
MATH 101 Lab 2
1
In this lab we will look at volumes of rotation. The introduction to the lab sets
up graphs of two surfaces of revolution around the x-axis. Question 2 repeats the
revolution around the y-axis.
Hand in a commented worksheet in lab class.
Integral Calculus with Applications to Physical Sciences and Engineering
MAT 101
-
Winter 2014
1
MATH 101 Lab 1
For two curves = ( ) and = ( ) with ( )
between the curves is given by
y
f x
y
g x
Z a
b
( ) on an interval
g x
f x
( ) ; ( )dx
f x
g x
], the area
a b
:
In this lab we will look at Maple's commands for integration and what happens for
ge
Integral Calculus with Applications to Physical Sciences and Engineering
MAT 101
-
Winter 2014
1
MATH 101 Lab 4
In this lab we will draw curves de ned by parametric equations and polar coordinates
and nd areas and arc lengths. The length of an arc of a curve given by parametric
equations x = f (t), y = g(t), where
t
traces the curve once, is given
Integral Calculus with Applications to Physical Sciences and Engineering
MAT 101
-
Winter 2014
Math 101
Intermediate Algebra
Order of Operations
Chapter 1, Section 4
Exponents
An exponential expression is bn.
b is called the base and n is called the exponent.
bn means multiply b by itself n times.
Roots and Radicals
A radical expression is
.
is the
Integral Calculus with Applications to Physical Sciences and Engineering
MAT 101
-
Winter 2014
TERM TEST TWO
MATH 101, Winter 2000
Friday, March 3, 2000
NAME AND STUDENT NUMBER:
1. Write down all necessary work. Use the back side of the sheets, if needed.
2. Calculators are allowed, but not needed (and not recommended).
3. Maximum Possible Score =
Integral Calculus with Applications to Physical Sciences and Engineering
MAT 101
-
Winter 2014
MATH 101 Lab 5
In this lab we look at some of the tools that can be used for solving problems on sequences and series. We
know that a huge set of functions can be created by using the elementary functions xr , where r is a real
constant, all of the polyno | 677.169 | 1 |
Linear Algebra And Its Applications 4th Edition - reyot.herokuapp.com
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Derek Bridge
Past Teaching
Maths for Information Processing
Context
This course was taught to two types of student in the University of York's
Computer Science Department. There were students studying for a taught
M.Sc. in Information Processing and the Human-Computer Interface.
This was a conversion course, giving IT skills to students whose first
degree was not Computer Science. And there were undergraduates studying
for a
B.A. in Information Technology, Business Management and a modern foreign
Language (ITBML). In neither case was it possible to assume anything other
than the most rudimentary mathematical knowledge. Fear of maths was also
prevalent. I taught the course in 1995 and 1996.
Workload
Lectures: 18 * 1 hr lectures
Practicals: 9 * 2 hr practicals
Private study: 52.5 hrs (including revision)
Assessment: 1.5 hrs (excluding revision)
Prerequisites
A willingness to learn some maths.
Assessment
An unseen 90-minute paper, worth 50 marks.
All questions to be answered.
Description
The course introduces students to some of the branches of discrete
mathematics that are most important to information processing.
Aims
Students should acquire the ability to formulate and evaluate
mathematical expressions in a range of mathematical models that are used
in information processing.
Students should master mathematical material that is co-requisite
and pre-requisite for other courses.
Content
(L1) The role of maths in information processing.
(L2-L3) Expressions and evaluation.
(L4-L6) Set theory.
(L7-L8) Relations.
(L9) Functions.
(L10-L12) Syntax and semantics of propositional logic.
(L13-L14) A proof theory for propositional logic.
(L15-L18) An introduction to the syntax and semantics of
first-order predicate logic. | 677.169 | 1 |
Maths Problems
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Among all academic assignments, math problems are considered to be the most difficult tasks that students have to deal with during their academic career. A student having incomplete knowledge of math concepts, equations, and expressions can not complete math problems with correct answers. Students have to regularly practice math problems to be successful. Moreover, math problems are quite similar to financial problems, and accounting problems.
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Trigonometry the Easy Way Third Edition
This (Anderson) is a great introduction for the undergraduate math major. There are six functions of an angle commonly used in trigonometry. Descartes' rule of signs: Approximate solutions of roots of polynomials by Newton-Raphson method - Homer's method; Cardan's method of solution of a cubic polynomial. Prerequisite(s): STAT 25100 or STAT 25150, or STAT 24400, or MATH 20500/MATH 20900 and permission of the instructor This course focuses on the interplay between abstract algebra (group theory, linear algebra, and the like) and geometry.
Pages: 0
Publisher: Barrons (2001)
ISBN: B0019APJAG
KEY TO MR LOCK'S TRIGONOMETRY FOR BEGINNERS: ADAPTED FROM THE KEY TO THE ELEMENTARY TRIGONOMETRY.
For more on the history of trigonometry: History of trig Trigonometric functions are defined using the unit circle. The Unit Circle is centered at (0,0) and has a radius of 1 unit. Let Θ (theta) be an angle measured counterclockwise from the x-axis along an arc of the circle College Mathematics Basic Course in Essentials of Algebra, Trigonometry, Analytic Geometry, Calculus With Exercises, Examinatio. The direction you must follow the great circle (also known as bearing) can be computed by the great_circle_direction() function: use Math::Trig 'great_circle_direction'; $direction = great_circle_direction($theta0, $phi0, $theta1, $phi1); Alias 'great_circle_bearing' for 'great_circle_direction' is also available. use Math::Trig 'great_circle_bearing'; $direction = great_circle_bearing($theta0, $phi0, $theta1, $phi1); The result of great_circle_direction is in radians, zero indicating straight north, pi or -pi straight south, pi/2 straight west, and -pi/2 straight east Plane Trigonometry Made Plain With Logarithmic and Trigonometric Tables.
Trigonometry
Elementary trigonometry [microform]
Forth grade graghing equations, matcad software free download, aptitude book download, solve 3 variable system with ti-83, hyperbola graph. +teaching permutation, 6th grade math solving addition equations games, what we do with the least common denominator, how to convert mixed numbers to dicimals, log simplify base 2 An Elementary Treatise on Plane & Spherical Trigonometry... That makes sense, until you stop and actually count the school subjects you used recently Mathematical Tables Consisting of Logarithms of Numbers 1 to 108000: Trigonometrical, Nautical, and Other Tables. When Yukari from Azumanga Daioh gets tired of being just a language teacher, she decided to teach math instead... for about five seconds; then she realizes she's not up to the task and switches to P. Even Minamo (generally the more competent of the two) is shown to be less than proficient in mathematics. InuYasha: In one episode, Kagome actually had a nightmare about geometry download Trigonometry the Easy Way Third Edition pdf. Students will learn to work with various types of functions in symbolic, graphical, numerical and verbal form." The University of California at Irvine awards the certificate of completion. 10-12 (graph above: absolute value of the gamma function in the complex plane, source: Wikimedia Commons) Here is an unordered list of online mathematics books, textbooks, monographs, lecture notes, and other mathematics related documents freely available on the web Algebra and Trigonometry (2006 4th Edition) (Enhanced with Graphing Utilities). A Treatise On Trigonometry.
I've attached a PowerPoint slide show I created to illustrate the chance of winning a lottery - the last page is a worksheet the students would have in order to follow along with the slide show. At the senior level I've created a variety of assignments ( I changed the lotteries I used from year to year ) primarily based on calculating the expected value of a set of lotteries Principes D'Astronomie Spherique; Ou, Traite Complet de Trigonometrie Spherique: Dans Lequel on a Reuni Les Solutions Numeriques, Gemetriques & Analyt. Softschools.com provides free math worksheets and games and phonics worksheets and phonics games which includes counting, addition, subtraction, multiplication Student Solutions Manual with Study Guide, Volume 1 for Serway/Vuille's College Physics, 10th. Mathematics is like a kin of science which lays the foundation for Physics and Chemistry. Various topics like calculus, differential equations and quadratic equations are used in almost all the questions of physics and chemistry. As a matter of fact, Science progresses only with the aid of Mathematics. It is aptly remarked that The syllabus of IIT JEE Mathematics is a perfect blend of easy and difficult topics College Algebra & Trigonometry by Ratti,J. S.; McWaters,Marcus S.. [2010,2nd Edition.] Hardcover. In fact, it's not too hard to integrate this now, because of the work that we've done Trigonometry the Easy Way Third Edition online. His work is seen as significant in passing on knowledge to Europe. Jabir ibn Aflah was considered a vigorous critic of Ptolemy's astronomy. His treatise helped to spread trigonometry in Europe in the 13th century, and his theorems were used by the astronomers who compiled the influential Libro del Cuadrante Sennero (Book of the Sine Quadrant) under the patronage of King Alfonso X the Wise of Castille (1221-1284) New Trigonometry for Schools. Hipparchus may have taken the idea of this division from Hypsicles who had earlier divided the day into 360 parts, a division of the day that may have been suggested by Babylonian astronomy. [13] In ancient astronomy, the zodiac had been divided into twelve "signs" or thirty-six "decans" MIDDLE GRADES MATH 2010 PROGRESS MONITORING ASSESSMENTS ALGEBRA READINESS. Learn trigonometry online and find a trigonometry tutor. Any trigonometric function (f), therefore, always satisfies either of the following equations: f(q) = a / b OR f(a / b) = q, where q is the measure of a certain angle in the triangle, and a and b are the lengths of two specific sides. If the former equation holds, we can choose any right triangle, then take the measurement of one of the non-right angles, and when we evaluate the trigonometric function at that angle, the result will be the ratio of the lengths of two of the triangle's sides Elementary Trigonometry. Trigonometry, which studies the measure of triangles, takes algebra to the next level. Its most well-known features include the Pythagorean Theorem and the sine, cosine, and tangent ratios. Our trig calculator can help you check problems that involve these relationships as well as many others ALGEBRA AND TRIGONOMETRY W/O CD. Online tutoring can be done from the comfort of home and is a great supplemental or remedial help Mechanics (Teach Yourself Books). Click the 'Apply' button at the bottom of the edit box. The calculated values will display on the options box. Click the 'OK' button to close the options box. The calculations and triangle diagram will be displayed on your screen. If the triangle diagram is too big to display properly on your computer screen, briefly press the F10 key to reduce its size Plane Trigonometry - Parts 1-2: Trigonometric Tables. | 677.169 | 1 |
Download and read online Linear Algebra and Its Applications Books a la Carte Edition in PDF and EPUB NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value-- courses in linear algebra. With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand. Also available with MyMathLab MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. MyMathLab includes assignable algorithmic exercises, the complete eBook, interactive figures, tools to personalize learning, and more.
Download and read online Linear Algebra and Its Applications in PDF and EPUB Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on the proofs. Strang's emphasis is on providing understanding.
Download and read online Linear algebra with applications in PDF and EPUB Offering the most geometric presentation available, Linear Algebra with Applications, Fourth Edition ExtDownload and read online Student Study Guide for Linear Algebra and Its Applications in PDF and EPUB Line algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts are not easily understood, and require time to assimilate.
Download and read online Introduction to Linear Algebra in PDF and EPUB Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: • A new chapter on singular values and singular vectors, including ways to analyze a matrix of data • A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages • A new section on linear algebra and cryptography • A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.
Download and read online Lay Linear Algebra and Its Applications in PDF and EPUB This package includes Linear Algebra and Its Applications by Lay and the accompanying Student Study Guide. Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. David Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible. An integral part of this text, the Study Guide incorporates detailed solutions to every third odd-numbered exercise, as well as solutions to every odd-numbered writing exercise for which the main text only provides a hint.
Download and read online Elementary Linear Algebra in PDF and EPUB Elementary Linear Algebra, 5th edition, by Stephen Andrilli and David Hecker, is a textbook for a beginning course in linear algebra for sophomore or junior mathematics majors. This text provides a solid introduction to both the computational and theoretical aspects of linear algebra. The textbook covers many important real-world applications of linear algebra, including graph theory, circuit theory, Markov chains, elementary coding theory, least-squares polynomials and least-squares solutions for inconsistent systems, differential equations, computer graphics and quadratic forms. Also, many computational techniques in linear algebra are presented, including iterative methods for solving linear systems, LDU Decomposition, the Power Method for finding eigenvalues, QR Decomposition, and Singular Value Decomposition and its usefulness in digital imaging. The most unique feature of the text is that students are nurtured in the art of creating mathematical proofs using linear algebra as the underlying context. The text contains a large number of worked out examples, as well as more than 970 exercises (with over 2600 total questions) to give students practice in both the computational aspects of the course and in developing their proof-writing abilities. Every section of the text ends with a series of true/false questions carefully designed to test the students' understanding of the material. In addition, each of the first seven chapters concludes with a thorough set of review exercises and additional true/false questions. Supplements to the text include an Instructor's Manual with answers to all of the exercises in the text, and a Student Solutions Manual with detailed answers to the starred exercises in the text. Finally, there are seven additional web sections available on the book's website to instructors who adopt the text. Builds a foundation for math majors in reading and writing elementary mathematical proofs as part of their intellectual/professional development to assist in later math courses Presents each chapter as a self-contained and thoroughly explained modular unit. Provides clearly written and concisely explained ancillary materials, including four appendices expanding on the core concepts of elementary linear algebra Prepares students for future math courses by focusing on the conceptual and practical basics of proofs
Download and read online Linear Algebra Done Right in PDF and EPUB This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
Download and read online Handbook of Linear Algebra in PDF and EPUB The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts. Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical problems.
Download and read online Linear Algebra with Applications in PDF and EPUB UpdatedDownload and read online Linear Algebra For Dummies in PDF and EPUB Learn to: Solve linear algebra equations in several ways Put data in order with matrices Determine values with determinants Work with eigenvalues and eigenvectors Your hands-on guide to real-world applications of linear algebra Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systems Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices Open the book and find: Theoretical and practical ways of solving linear algebra problems Definitions of terms throughout and in the glossary New ways of looking at operations How linear algebra ties together vectors, matrices, determinants, and linear transformations Ten common mathematical representations of Greek letters Real-world applications of matrices and determinants
Download and read online Linear Algebra A Modern Introduction in PDF and EPUB David maturity
Download and read online Linear Algebra in PDF and EPUB Holt's Linear Algebra with Applications blends computational and conceptual topics throughout. Early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. This organization also makes it possible to treat eigenvalues and eigenvectors earlier than in most texts. Abstract vector spaces are introduced later, once students have developed a solid conceptual foundation. Concepts and topics are frequently accompanied by applications to provide context and motivation. Because many students learn by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce topics. The text also has over 2500 exercises, covering computational and conceptual topics over a range of difficulty levels.
Download and read online Linear Algebra with Applications Alternate Edition in PDF and EPUB Building upon the sequence of topics of the popular 5th Edition, Linear Algebra with Applications, Alternate Seventh Edition provides instructors with an alternative presentation of course material. In this edition earlier chapters cover systems of linear equations, matrices, and determinates. The vector space Rn is introduced in chapter 4, leading directly into general vector spaces and linear transformations. This order of topics is ideal for those preparing to use linear equations and matrices in their own fields. New exercises and modern, real-world applications allow students to test themselves on relevant key material and a MATLAB manual, included as an appendix, provides 29 sections of computational problems. | 677.169 | 1 |
Statistics math answers
Statistics Homework Help and Answers. Popular Statistics Textbooks See all Statistics textbooks up to: 850 gold Probability and Statistics Index. Graphs Index. What is Data? What is Data? Discrete and Continuous Data
Problems on statistics and probability are presented. The answers to these problems are at the bottom of the page. When a die is rolled and a coin (with Heads and.
Statistics math answers
Math Mammoth Statistics & Probability is a worktext covering statistics and probability topics for 6th-7th grades. Being a worktext, the book contains BOTH the.
Free math worksheets of statistics for high school teachers and students. Statistics and probability. Printables. Amazon.com: Plane Answers to Complex Questions: The Theory of Linear Models (Springer Texts in Statistics) (9781441998156): Ronald Christensen: Books Learn about arithmetic, algebra, geometry, statistics, and trigonometry. See how to use math formulas and equations.
Statistics tutorials, lessons, activities and guides to assist with all assignments.
Learning Math: Data Analysis, Statistics, and Probability is one of five video- and Web-based mathematics courses for elementary and middle school teachers. Problems on statistics and probability are presented. The answers to these problems are at the bottom of the page. Given the data set 4 , 10 , 7 , 7 , 6 , 9 , 3 , 8 , 9 Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math … | 677.169 | 1 |
printable worksheet makes it easy to introduce the route inspection algorithm and will help your students understand how to apply the algorithm.
The first page reminds students about Eulerian and semi-Eulerian graphs, how these are the types of graphs we require to solve the route inspection problem, and then has an example where you can introduce the idea of adding/repeating arcs to create the type of graph you need.
The next page summarises the steps of the general algorithm and then the set of example questions begins. There are 14 questions in total, all with diagrams, with some requiring a closed route and some that do not. Fully worked solutions for all examples are provided.
Full lesson on investigating graph theory and networks which is extremely derivative -- very largely based on the stupendous lesson and worksheet uploaded by @Owen134866. I have added some more scaffolding in terms of discussing vocabulary and created a support sheet so that this topic can be accessed at KS3 and above.
I have delivered this lesson successfully to mixed ability Year 7s and high ability Year 9s to date, and always really enjoy it. It's generally something I pull out towards the end of term as a treat with a view to improving students' problem-solving skills.
Extension worksheet is adapted from the Konigsberg problem entry on Wikipedia although I have not yet used it -- it might prove to be a good extension to the main lesson for A Level students.
Please do rate and review this resource -- I appreciate feedback! the Decision Mathematics module for A level powerpoint covering all areas of Decision 1 (I realise they are only putting it in further maths from 2017). It contains brief notes by way of an explanation, model answers to questions and a question or two for the students to do; all of the questions come with answers that you can display when ready. The slide show comes with a progress grid (regularly referred to in the presentation) so that students can mark their progress from start to finish and pinpoint any areas that may need extra work with a "red/amber/green" system that they fill in. It's what I use in my lessons before setting tasks from worksheets or text books to practice.
Powerpoints and Notebook presentations that show learners how to complete the minimum connector problems using Prims and Kruskals algorithm. A presentation of how to use Travelling salesperson algorithm to find a complete cycle.
Powerpoint and Notebook presentations that show students how to complete the Chinese postman algorithm. Smartboard presentation covers basic graph theory such as Eulerian graphs and other terminology | 677.169 | 1 |
MAT1101 Discrete Mathematics for Computing (FOSCI)
Synopsis
This course introduces the basic elements of discrete mathematics which provide a foundation for an understanding of algorithms and data structures used in computing. Topics covered include number systems, logic, relations, functions, induction, recursion, Boolean algebra and graph theory. | 677.169 | 1 |
CHOVANEC, MEGAN
Pre-AP and regular classes will learn the same content throughout the year, however pre-ap students may dive into a topic in more depth due to the faster speeds of the classes. Regular algebra 1 classes may spend more time reviewing the core concept of a topic. Pre-AP students will also have higher level thinking questions on tests and quizzes and will be expected to write their thoughts and ideas in a more precise and exact manner. Pre-AP students will have much less access to a calculator.
If you are having trouble viewing the document, click here to download it. | 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. A Brief Review of Arithmetic Skills; Real Numbers and Variables; Equations and Inequalities; Solving Applied Problems; Exponents and Polynomials; Factoring; Rational Expressions and Equations; Graphing and Functions; Systems of Equations; Radicals; Quadratic Equations. For all readers interested in basic college mathematics.
"synopsis" may belong to another edition of this title.
About the Author:
John Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and has served as the mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.
Jeffrey Slater has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Mass. with his wife Shelley and his yellow lab Gracie.
Jamie Blair has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the Center, and as a result of this effort has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007 Jamie was appointed to the Team of Basic Skills Specialist by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California.
Book Description Pearson Education (US), United States, 2008. Paperback. Book Condition: New. 7th edition. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible.
Book Description Pearson Education (US), United States, 2008. Paperback. Book Condition: New. 7th edition. Language: English . | 677.169 | 1 |
algebra 1 Archives - ItsMyAcademy.com
In this 3rd lesson of Language of Algebra we will learn new term called – Algebraic Expression with variables. You will understand what are called expression and how they are formed by using variables in mathematics. It is very helpful for pre algebra learning students. If you have any doubt or question regarding this algebra 1 […]
Let's learn uses of Algebraic variables in common rules of arithmetic mathematics and geometry. You will learn how algebraic variables helps other branch of mathematics to denote various aspects .1. Rules from Geometry & 2. Rules from Arithmetic. First we will discuss rules from Geometry then 2nd one for Arithmetic we will learn in next […]
"Algebra 1 " course is designed for the students who are learning either pre algebra or algebra 1 in their school. They can use our Algebra 1 lessons online for free for their reference. Any doubt or question regarding the lessons, you are free to ask below the lesson in question answer section. I will […] | 677.169 | 1 |
Math 1110 Algebra II
Math 1110 in the Developmental Math Program in the Department of Mathematics at Western Michigan University is designed to sharpen algebraic skills and concepts in a function-based setting. Topics include linear functions, quadratic functions, composing and decomposing functions, inverse functions, logarithmic and exponential functions. The course emphasizes both the manipulation of symbols and an understanding of when manipulations are effective and appropriate.
This course serves as a prerequisite course and does not satisfy the Proficiency 3 general education requirement. | 677.169 | 1 |
inductive intro to logs & exponents
Inductive intro to exponents and logs:
The following is a condensation of my understanding for our inductive intro to exponentials. I am inventing notation here.
First: teach some properties of composition for linears – the concept here is the generalization of multiplication from multiple addition to scaling: that students will immediately understand but never realized:
Using a concrete example (draw graph), argue that If L is linear, then: | 677.169 | 1 |
IXL skills are aligned to the Georgia Standardsof Excellence Standards and provide comprehensive coverage of math concepts and applications. With IXL, you can easily find unlimited practice problems specifically tailored to each required standard. | 677.169 | 1 |
Measurement benchmarks : estimating and measuring by Cornelia C Tierney(
Book
) 2
editions published
between
1998
and
2004
in
English
and held by
34 WorldCat member
libraries
worldwide
Emphasis on mathematical thinking and teaching strategies on metric system and U.S. standard measures of length, distance,
weight, volume, and time
Building on numbers you know by Marlene Kliman(
Book
) 4
editions published
between
1998
and
2006
in
English
and held by
33 WorldCat member
libraries
worldwide
Emphasis on mathematical thinking and teaching strategies on exploring strategies for computation and estimation, especially
with multiplication and division
Programming Icons by Marlene Kliman(
Book
) 4
editions published
in
1984
in
English and Undetermined
and held by
19 WorldCat member
libraries
worldwide
Metaphors for understanding graphs : what you see is what you see by E. Paul Goldenberg(
Book
) 3
editions published
between
1988
and
1989
in
English
and held by
12 WorldCat member
libraries
worldwide
Computer graphing makes it easier for students and teachers to create and manipulate graphs. Scale issues are nearly unavoidable
in the computer context. In interviews and protocol analysis with six students from grade 8, and 12 students from grades 11
and 12, it became apparent that some aspects of scale are clearly understood very early while other aspects remain confusing
to even some of the most successful students in pre-calculus and calculus, and that there is a consistency and meaning in
metaphors which students invoked in explaining their ideas to themselves and teachers. Three metaphors inferred from students'
words and one metaphor supplied by the authors are discussed. These are: (1) the computer as automatic paper and pencil; (2)
scaling is like using a magnifying glass; (3) scaling as a rubber sheet (supplied by the authors); and (4) the mathematical
curve as a bead necklace. Some implications concerning the curriculum are discussed. (Yp)
Investigations in number, data, and space(
Book
) 1
edition published
in
2006
in
English
and held by
8 WorldCat member
libraries
worldwide
Part of a K-5 mathematics curriculum, with curriculum units for classroom use and resources for teachers; the Investigations
curriculum was developed at TERC, formerly Technical Education Research Centers | 677.169 | 1 |
Paperback | December 18, 2012
Pricing and Purchase Info
about 20to help them succeed in the classroom and on exams.SchaumFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!
Schaum's Outlines--Problem Solved.
About The Author
Frank Ayres Jr., PhD, was formerly professor and head of the Department of Mathematics at Dickinson College, Carlisle, Pennsylvania. He is the author of eight Schaum's Outlines.
Robert E. Moyer taught mathematics at Southwest Minnesota State University. He received his Doctor of Philosophy in Mathematics Education from the Univ... | 677.169 | 1 |
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This introduction to modern or abstract algebra addresses the conventional topics of groups, rings, and fields with symmetry as a unifying theme, while it introduces readers to the active practice of mathematics. Its accessible presentation is designed to teach users to think things through for themselves and change their view of mathematics from a system of rules and procedures, to an arena of inquiry. The volume provides plentiful exercises that give users the opportunity to participate and investigate algebraic and geometric ideas which are interesting, important, and worth thinking about. The volume addresses algebraic themes, basic theory of groups and products of groups, symmetries of polyhedra, actions of groups, rings, field extensions, and solvability and isometry groups. For those interested in a concrete presentation of abstract algebra.
This text is an introduction to "modern" or "abstract" algebra for undergraduate students. The book addresses the conventional topics; groups, rings, and fields, with symmetry as a unifying theme. This subject matter is central and ubiquitous in modern mathematics and in applications ranging from quantum physics to digital communications.
The most important goal of this book is to engage students in the active practice of mathematics. Students are given the opportunity to participate and investigate, starting on the first page. Exercises are plentiful, and working exercises should be the heart of the course.
This text provides a thorough introduction to abstract algebra at a level suitable for upper-level undergraduates. The text would also be useful for an undergraduate topics course (for example, on geometric aspects of group theory or on Galois theory).
The required background for using this text is a standard first course in linear algebra. I have included a brief summary of linear algebra in an appendix to help students review. I have also provided appendices on sets, logic, mathematical induction, and complex numbers. The instructor may wish to go through this "corequisite" material systematically, or to dip into it from time to time as needed. It might also be useful to recommend a short supplementary text on set theory, logic, and proofs to be used as a reference and aid; several such texts are currently available.
The text is adaptable to different teaching styles. My own preference is increasingly to lecture little, and to use class time for discussing problems. But those who wish to present the material in systematic lectures will find the subject matter cleanly organized and presented in the text. I offer one piece of pedagogical advice both to instructors and students: This stuff takes time, give it the time it needs. Students have an enormous amount to learn "between the lines" of the text. They not only have to learn the mathematics, but they need to learn how mathematics is done, how to read and write mathematics, and how to approach solving problems. They need to learn to tinker, to try examples, to formulate and solve a simpler problem, to try a special case, to think about analogies, to guess at intermediate results, and so on. It is important for the instructor to slow the pace of the course in order to encourage exploration, and it is important for the student to devote the (many) hours which are actually needed to absorb the material and to solve the problems.
The subject treated in this text is usually called abstract algebra. In common language, abstract means both "difficult" and "impractical," and it is a little unfortunate to start out by labeling the subject as hard but useless! It won't be out of place here to make some (encouraging) remarks about abstraction. It tikes some effort to remember that even the counting numbers were once (and in principle still are) an enormous abstraction. But they are familiar, they no longer seem difficult, and no one would doubt their usefulness. Abstractions with which we have become familiar eventually lose their aura of abstractness, but those with which we are not yet familiar seem abstract indeed. So it is with the ideas of this course. They may seem abstract today, but as they become familiar they will seem more concrete.
Mathematics involves a continual interplay between the abstract and the concrete: Abstraction is necessary in order to understand concrete phenomena, and concrete phenomena are necessary in order to understand the abstractions. Meanwhile, as one continues to study mathematics the perceived boundary between the abstract and concrete inevitably shifts.
Organization.
The text has been substantially revised for this second edition. The most important innovation is the long introductory chapter, entitled "Algebraic Themes," which treats many of the more elementary topics—symmetries, the integers, modular arithmetic, polynomials, and permutations—and introduces the important algebraic objects—groups, rings and fields—that are the subject of the rest of the book. The chapter also contains new sections on counting and cryptography. Chapter 6, on rings has been expanded, with a more complete discussion of Euclidean, principal ideal, and unique factorization domains. The classification of finite abelian groups has been moved to Chapter 3, on products of groups, and a section on vector spaces and bases has, appropriately, been added to this chapter. There is a new appendix containing a review of linear algebra (Appendix E). | 677.169 | 1 |
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I created this document by compiling a list of the standards for CCSS Traditional Secondary Math Pathway using Appendix A. I color coding them based on CCSS Algebra 1, CCSS Geometry, and CCSS Algebra 2. Then I created a list for CCSS Course 1, CCSS Course 2, and CCSS Course 3 that shows where the standards from the traditional pathway fall for the international pathway.
This document is really helpful when teachers, administrators and parents are having conversation about the two pathways. | 677.169 | 1 |
A Gentle Introduction to the Art of Mathematics
Publisher: Southern Connecticut State University 2009 Number of pages: 428
Description: The point of this book is to help you with the transition from doing math at an elementary level (which is concerned mostly with solving problems) to doing math at an advanced level (which is much more concerned with axiomatic systems and proving statements within those systems). | 677.169 | 1 |
g(Math) for Forms
g(Math) is an Add-on for Forms that makes Forms math friendly by allowing users to create graphs, statistical displays, and other complex math all in the sidebar where it can be inserted into a Form. Also, responders completing a Form may use g(Math) to create graphs, statistical displays, and other math in their responses. For all grade levels. | 677.169 | 1 |
System requirements:
Our users: Julie Simons, GA
I love it. It is much easier to move around and the colors are easier on the eyes. James Grinols, MN
The software has been a great help learning radical equations, now I don't have to spend so much time doing my algebra homework. Monica, TX
Be it Step by Step explanation for an equation or graphical representation, you get it all. I just love to use this due to the flexibility it provides while studying. Kevin Woods, WI27:
how to find the answer for x in a fraction/algebra
what is the difference between evaluation and simplification of an expression
math worksheets with variables
simplify multiplying integers
simplify fractions square roots
steps on how to balance equations
how to solving differential equation with matlab
algebra 2 teacher's edition book with workbook answer key and quizzes and tests with answers by larson, boswell, kanold, and stiff | 677.169 | 1 |
Math 319: Math Modeling
Prof. Andrew Ross
Fall 2016
Basic Information
Note: this syllabus is temporary, and may change up to the first day of class.
This version posted on: 2016-09-02
General Description
Math Modeling is the art of taking a real-world problem and stating it
in mathematical terms. It often involves making simplifying assumptions.
In our class, we get in the habit of doing all the parts of the
math modeling cycle: modeling, solving, checking, and guessing.
Often, a large part of the problem is even deciding which problem to solve.
For example, should you find the best schedule for your staff at one
location, or consider opening new locations? Should you
start with a theoretical model then match it to data, or just model
the data directly? We will also consider a lot of common
mathematical models, and explore their properties.
The U of M has two related courses: Math 462, "Mathematical
Modeling", and Math 463, "Mathematical Modeling in Biology". However,
these
focus on differential equation models, while this class focuses on
regression, operations research, and dynamical systems.
Many assignments in this course will be in the form of papers, which I
want to be well written. Please consult with
The Writing Center
for help in tuning up your writing.
Teaching philosophy, interests
I am a very applied mathematician. Applied, applied, applied. Not pure. Impure.
I try to focus on real-world problems, rather than artificial drill problems (though
I do recognize the need for some drill). My classes spend much more time on formulating
problems (going from the real world to math notation and back) than on proving theorems.
If you want the theoretical basis for anything we are discussing, please ask!.
(not-absolutely-)Required materials
Most students do well in this course without a textbook. For those who
feel the need to have one just in case, I suggest finding
"A First Course in Mathematical Modeling", any edition, by
Giordano, Weir, and Fox, in a library or the Math Den (PH 501).
A lot of our work will be done on computers, specifically in Excel or other spreadsheet software (except Apple Numbers). If you
had been waiting for a good reason to buy a laptop, this is it.
Spreadsheets other than Excel (such as OpenOffice/LibreOffice, Google Docs, etc.) work reasonably well for most things in the class, but some things really don't work well without name-brand Excel. Fortunately, it's available free to EMU students (as of Fall 2016). Email me to ask for details.
Course Web Pages
I will post data files, homework assignment files, etc. on
my home page.
We will use an on-line gradebook (via
EMU Canvas) to keep track of grades.
You are expected to keep an eye
on your scores using the system, and get extra help if your scores
indicate the need.
Nearly everything will be submitted via the various dropboxes inside EMU Canvas. The rule is: if it's not in a dropbox, it doesn't exist (for grading purposes).Microsoft Excel, or other spreadsheet software like Gnumeric or OpenOffice or Google Docs
Python or R
is used for only a few people's projects--most people don't use them.
Mathematica, Maple, or Matlab/Octave/Scilab
are even more rarely used in this class.
Course Content
Course Goals
Our primary goal is to teach you to be a good (or great!) January 19 - 23, 2017.
I participated in this
3 times as an undergrad and had a lot of fun. Recent EMU teams have done well!Teach you how to communicate your math models by writing math papers and giving math presentations.
Student Outcomes
By the end of the course, students will be able to:
(General modeling skills):
categorize problems into operational/tactical/strategic categories,
identify nearby problems in the oper./tact./strat. hierarchy,
evaluate models by constructing simple test cases,
conduct cross-validation when needed,
select the most important variables to start modeling with,
(Empirical modeling skills):
use ordinary, semilog, and loglog plots to evaluate relationships in data sets,
Outline/schedule
This course was originally organized around the Giordano modeling textbook, though it is not required for the course.
Here we show which chapters from that book we cover,
in roughly the order we will cover them. A star (*)
denotes full coverage, a plus (+) denotes partial coverage, and no
symbol denotes no coverage. For example, DTMCs (as cool as they are)
will be covered in Math 419 rather than 319.
Grading Policies
Attendance
Regular attendance is strongly recommended. Since there
is no formal textbook, missing class means you will miss a lot!
If you must miss a class,
arrange to get a copy of the notes from someone, and arrange for
someone to ask your questions for you.
My lectures and discussions mostly use the document camera, along with
demonstrations in Excel and other mathematical software. I do not
usually have PowerPoint-like presentations, and thus cannot hand
out copies of slides.
Homework
Homework will be assigned about once per class meeting, though some assignments are short. It will
sometimes be a small problem set designed to help you
understand the behavior of math models. Other times, it will involve
writing up a little paper on an assigned topic. All homework should
be typed unless noted.
Homework papers should be submitted on-line, where they might be
checked by TurnItIn something like this:
10 pct: proposal
80 pct: work and written report
10 pct: presentation
The final presentations will be made during the
time slot reserved for the final exam.
On average, students should spend a total of about 30 minutes in office hours
discussing the project. Plan for this in advance!
Overall Grades
In the unfortunate event of a need, the appropriate grade or
grades might be dropped entirely, rather than giving a make-up, at the instructor's discretion.
You are highly encouraged to still complete the relevant assignments
and consult with me during office hours to ensure you know the
material.
Your final score will be computed as follows:
50 percent for all the homework together,
20 percent for the mid-term project, and
30 percent for the final project.
Final percentage scores will be given letter grades as follows:
92.0 and above : A
88.0 to 92.0: A-
84.0 to 88.0: B+
80.0 to 84.0: B
76.0 to 80.0: B-
72.0 to 76.0: C+, etc Other Math Modeling Students
In the last two semesters, I've asked my math modeling students to give
advice to you, future math modeling students, based on their experiences
in my course. Here are some of the highlights:
* work in groups * start the first day assignment is given *
don't take too many credits w/ this class * ask a lot of questions *
utilize
the class. You will learn a lot in the end, but be ready to work.
[prof ross:] add a note to the syllabus stating something
to the effect of, "This class will not be like other math classes.
Instead of straight-up problems or proofs, the biggest amount of work
will be setting up the models, exercises, etc. and in analysing what
your results mean. It will not be the mathematical work done to obtain
the
about and interested in even if they're harder. It will make this math
class the best one you've ever taken.
Don't drop the class! It sounds impossible in the beginning, but stick with it.
Don't procrastinate.
Take differential equations close to this class, it will make more sense!
Start projects ASAP.
Ask questions!!! The professor will guide you along the way like Yoda.
Talking to anyone about your projects or the homework, be it Prof. Ross or other students, is a really, really good idea.
Never be afraid to ask for help.
If project falls through, have backups.
Standard University Policies
In addition to the articulated course specific policies and expectations, students are responsible for understanding all applicable University guidelines, policies, and procedures. The EMU Student Handbook is the primary resource provided to students to ensure that they have access to all university policies, support resources, and student's rights and responsibilities. Changes may be made to the EMU Student Handbook whenever necessary, and shall be effective immediately, and/or as of the date on which a policy is formally adopted, and/or on the date specified in the amendment. Please note: Electing not to access the link provided below does not absolve a student of responsibility. For questions about any university policy, procedure, practice, or resource, please contact the Office of the Ombuds: 248 Student Center, 734.487.0074,
emu_ombuds@emich.edu, or visit the website:
HERE to access the University Course Policies | 677.169 | 1 |
Introduction to Algebra Instructor: Eric Anderson 10 cr. A course for students that need to review the essential skills and concepts required in order to succeed in Algebra I. This class does not apply towards an Honor diploma.
Algebra IInstructor: David Pennock10 cr. A step-by-step development of the basic concepts and skills of algebra; including a study of functions, set theory, positive and negative numbers, equations and inequalities, factoring, graphing, radicals, and quadratics. Problem solving techniques and applications are emphasized throughout the course. Prerequisite: Satisfactory score on Algebra Aptitude Test.
Algebra II Instructor: David Pennock10 cr. An advanced course, continuing the study of functional relations and quadratics. Rational and irrational expressions, complex numbers, conic sections, systems of equations and inequalities, matrices, basic concepts of trigonometry and its functions are presented. Prerequisite: Algebra I and Geometry, with a minimum of "C" for each semester.
Calculus Instructor: David Pennock 10 cr. A preparatory course for those students planning to study calculus in college. Analytic geometry, algebra, and trigonometry are integrated along with other important mathematics topics. Special emphasis is placed on the study of polynomial, rational, and exponential functions. Limits, derivatives, integrals, and their applications are studied. Open to those students with advanced standing and desiring a fourth year of mathematics. GeometryInstructor: Amy Miller10 cr. A thorough study of the basic concepts of geometry, with special emphasis on individual reasoning. Brief introduction to trigonometry and coordinate geometry is included. | 677.169 | 1 |
Pre -cal Advice
Showing 1 to 3 of 5
Unit circle and parabolas were key concepts during the course. Also, the quadratic equation was interesting to memorize.
Hours per week:
3-5 hours
Advice for students:
Always listen to the teacher, and come into tutorials for help. Also, your class serves as a useful resource when the teacher isn't available.
Course Term:Fall 2015
Professor:murack
Course Tags:Math-heavyParticipation CountsCompetitive Classmates
Mar 05, 2017
| Would recommend.
Not too easy. Not too difficult.
Course Overview:
I recommend this class, because the teacher is super strategic, she'll always have an easier way of teaching you, but there's homework every single day. Which for some people it can be helpful and for some painful.
Course highlights:
I learned all the algebra 2 and geometry stuff more deeply and apply the same formula to a different situations.
Hours per week:
6-8 hours
Advice for students:
Do your homework everyday and make sure to take note on a flip book, especially the formulas! Super helpful! | 677.169 | 1 |
Beginning and Intermediate Algebra, 2nd Edition by Sherri Messersmith
By Sherri Messersmith
Starting and Intermediate Algebra, 2e, through Messersmith is the 1st textual content in a chain of destiny choices in developmental arithmetic. the writer offers the content material in bite-size items, focusing not just on studying mathematical innovations, but additionally explaining the why in the back of these thoughts. for college kids, studying arithmetic isn't just in regards to the memorization of ideas and formulation, however it is usually concerning the trip of studying how one can challenge clear up. by way of breaking the sections down into potential chunks, the writer has pointed out the center areas the place scholars usually fight, after which assists them in realizing that fabric to achieve success relocating ahead. confirmed pedagogical gains, like you attempt difficulties after each one instance, make stronger a student?s mastery of an idea. whereas educating within the school room, Messersmith has created worksheets for every part that fall into 3 different types: evaluate worksheets/basic talents, worksheets to educate new content material, and worksheets to reinforce/pull jointly various recommendations. those worksheets are a good way to either improve guideline and to offer the scholars extra instruments to achieve success in learning a given subject. the writer is usually a really renowned lecturer, and unearths it vital to be within the video sequence that accompany her texts. eventually, the writer reveals it vital not to basically offer caliber, but additionally an plentiful volume of routines and purposes. The publication is followed via a variety of worthy supplementations, together with McGraw-Hill?s on-line homework administration method, MathZone. Messersmith ? mapping the adventure to mathematical success!.
Contents: having a look ahead; Case Histories; the nice Pyramid; the traditional Cambodians; the child Prodigy; The Treaty of Croton; Paralyzed and Petrified; throughout the Tunnel; Bogged; get away; Heathen Gods; technology and Religiosity; outdated Clo'; the good Emancipator; The Fourth size; The final Idol; Retrospect; and The Priesthood of technology.
ALGEBRA AND TRIGONOMETRY: actual arithmetic, actual humans, seventh version, is a perfect scholar and teacher source for classes that require using a graphing calculator. the standard and volume of the routines, mixed with attention-grabbing functions and leading edge assets, make instructing more uncomplicated and aid scholars prevail.
Angle measures opposite sides of equal length are the same. mЄB ϭ 38° 38° ϩ mЄB ϭ 38° ϩ 38° ϭ 76°. We have found that the sum of two of the angles is 76Њ. Since all of the angle measures add up to 180Њ, mЄA ϭ 180° Ϫ 76° ϭ 104° mЄA ϭ 104° mes47759_ch01_026-039 10/20/2007 04:37 Page 28 pinnacle 201:MHIA038:mhmes2:mes2ch01: 28 Chapter 1 The Real Number System and Geometry You Try 2 Find the measures of angles A and B in this isosceles triangle. A 27Њ B 3. Learn and Apply Area, Perimeter, and Circumference Formulas The perimeter of a figure is the distance around the figure, while the area of a figure is the number of square units enclosed within the figure. | 677.169 | 1 |
The Normal Primary Arithmetic: Designed as an Introduction to a Thorough and Com.pdf 2. ReadMe.Important!.txt 3. The Normal Primary Arithmetic: Designed as an Introduction to a Thorough and Com.mobi 4. The Normal Primary Arithmetic: Designed as an Introduction to a Thorough and Com.epub 5. The Normal Primary Arithmetic: Designed as an Introduction to a Thorough and Com Normal Primary Arithmetic: Designed as an Introduction to a Thorough and Com.rar Detection ratio: 0 / 53 / Seems to be clean., Ebook PDF
RAR file contains
1. HOBART (THE COASTAL ADVENTURES OF A MIDWESTERNER)..pdf 2. ReadMe.Important!.txt 3. HOBART (THE COASTAL ADVENTURES OF A MIDWESTERNER)..mobi 4. HOBART (THE COASTAL ADVENTURES OF A MIDWESTERNER)..epub 5. HOBART (THE COASTAL ADVENTURES OF A MIDWESTERNER)..doc | 677.169 | 1 |
Teacher's Guide to the PARCC Model Content Frameworks for High School Mathematics October 16, 2012 Heather Brown Content contained is licensed under a.
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Presentation on theme: "Teacher's Guide to the PARCC Model Content Frameworks for High School Mathematics October 16, 2012 Heather Brown Content contained is licensed under a."— Presentation transcript:
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Teacher's Guide to the PARCC Model Content Frameworks for High School Mathematics October 16, 2012 Heather Brown Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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Objectives Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License To discover the elements of the Model Content Frameworks To use the Model Content Frameworks to aid in the implementation of the Common Core State Standards for Mathematics.
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Key Advances to Geometry Because concepts such as rotation, reflection, and translation were treated in the grade 8 standards mostly in the context of hands-on activities, and with an emphasis on geometric intuition, high school Geometry will put equal weight on precise definitions. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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Connecting Content and Practice: Algebra II MP7 Look for and make use of structure Delve deeper into transforming expressions that reveal meaning Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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How would you assess practices and content? school-seeing-structure-equation school-seeing-structure-equation Claim A Students solve problems involving the major content for their grade level with connections to practices. A.SSE Seeing structure in expressions Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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How would you assess practices and content? school-functions school-functions Claim A Students solve problems involving the major content for their grade level with connections to practices. F.IF.9 Compare properties of two functions each represented in a different way. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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Fluency F.IF.3 Fluency in translating between recursive definitions and closed forms is helpful when dealing with many problems involving sequences and series, with applications ranging from fitting functions to tables to problems in finance. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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Assessment Limits Tables for Standards Assessed on More than One End-of-Course Test Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Assessment Limits Tables for Standards Assessed in More than One Course | 677.169 | 1 |
A+ Pre-apprenticeship Maths and Literacy for Electrical (Part II)
By Andrew Spencer | Copyright Year:2017 | ISBN-13: 9780170374156
Pre-apprenticeship Maths and Literacy for Electrical (Part II) helps prepare students seeking to gain an apprenticeship or traineeship. This write-in workbook combines practical, real-world scenarios and terminology specific to the Electrical industry, and provides students with the skills they need to confidently pursue a career within this trade. It includes hundreds of example assessment questions and also supports concepts that students studying VET (Vocational Educational Training) may use.
STUDENTS:
PRODUCT:
ABOUT THE AUTHOR
Andrew Spencer has studied education both within Australia and overseas. He has a Bachelor of Education, as well as a Masters of Science in which he specialised in teacher education. Andrew has extensive experience in teaching secondary mathematics throughout New South Wales and South Australia for well over fifteen years. He has taught a range of subject areas including Maths, English, Science, Classics, Physical Education and Technical Studies. His sense of the importance of practical mathematics continued to develop with the range of subject areas he taught in.
FEATURES
Graduated difficulty – the book is divided into units that gradually increase in length, content and difficulty. For use throughout the course, not just before the actual assessment
No teacher preparation is required – students can write directly into the book, and can later use it for revision
Real-life scenarios and terminology – help motivate students and make the content specifically relevant to the students' chosen trade
Comprehensive practice questions – includes hundreds of questions
Bonus detachable test included – produced on perforated paper, it allows for easy tear-out and can be used as formal assessment tasks
Great value – designed and priced to be used by each individual student
Calculator-free – these workbooks have been designed to mirror current apprenticeship entry assessments and encourage students to attempt all questions without using a calculator. | 677.169 | 1 |
Helping Students Better Understand Nuclear Medicine with PTC Mathcad
At the British Columbia Institute of Technology (BCIT), Dr. Barry Pointon teaches nuclear medicine technology to students who hope one day to work in hospitals and clinics. As technologists, they'll produce the images that doctors use to diagnose problems like heart disease, cancers, bone fractures, and rheumatoid arthritis.
You can't overstate the importance of Dr. Pointon's job. Well-trained students produce better images, which lead to more accurate medical diagnoses, which lead to better health outcomes for people all over Canada.
If you think nuclear medicine sounds complicated, it is. "Students have to learn things like projection imaging, which involves line integrals, radon transforms, and objects called sinograms," says Dr. Pointon. "Then they have to learn about data filtering and spatial frequency domains. That involves Fourier transforms, convolution integrals, and an understanding of power spectra. Then, even further, they have to understand tomographic reconstruction, which gives the final images that the doctors look at."
Did that make sense to you? If so, my guess is you've had a few semesters of calculus. Many of Dr. Pointon's students have not.
As a public post-secondary institution with over 48,000 students enrolled into 350 programs annually, BCIT enrolls students with a solid understanding of algebra. How they learn complicated relationships among parameters in nuclear medicine and imaging outcomes—that's up to Dr. Pointon.
"My job is to give them an intuition of how the math works," he says. "I used to try to do that with an overhead projector, an acetate roll, and colored pens. I would try to draw an image on the overhead projector, and I would try show how things change as you varied the parameters." "I can tell you it was highly unsuccessful." Then several years ago, Dr. Pointon read a book about using PTC Mathcad to teach physics. Intrigued, he began developing interactive tutorials in the software that he could use in the classroom. The tutorials, composed on PTC Mathcad worksheets, laid out the complex calculations behind the images.
One of the benefits of PTC Mathcad is that it displays the math in the same way it would appear in a textbook, while other calculation software might introduce functions or words that confuse students.
Best of all, PTC Mathcad can combine equations and images on the same worksheet. So, Dr. Pointon can include simple geometry in a tutorial/worksheet. He asks students to predict what changing a parameter will do to the geometry, and then, on the fly, he changes that parameter. PTC Mathcad automatically regenerates the geometry to reflect the new value. The images become more and more sophisticated as students progress through the course, until they're working with a human-like model. Or more correctly, a "digital anthropomorphic phantom."
So, the images students see in PTC Mathcad actually look like the real images they'll encounter clinically. "But with PTC Mathcad, we can play with all the parameters and see how the parameters of the imaging and all the aspects of the field come into play in the final image."
Dr. Pointon says his approach works faster than the old acetate and overhead project method—and better. "Now you can see the lights go on in their heads as they begin to understand the relationships without actually having to calculate Fourier transforms on a piece of paper. They become very able to predict what the results will be if I change parameters. In the past it took students twice as long to understand these same concepts." Nuclear medicine imaging is a growing field that's becoming more sophisticated every year. With PTC Mathcad, students are mastering the complicated concepts, relationships, and theories behind the machines and the medicine. Dr. Pointon is integrating the latest ideas into the classroom more easily | 677.169 | 1 |
@Cody Johnson
–
My friends are only used to Mathcounts and some AMC... How hard are the problems expected to be? Even though it's not about winning, it wouldn't be worth it to drive that far just to participate in something we can hardly do.
Have you looked at Coach Monk's high school math competition playbook? It contains material that should be relevant at all levels of high school mathematics in the United States, from AMC 10/12 to USAMO and IMO. However, it's mostly a collection of formulas with minimal explanation, but it seems that is what's desired.
Also, try my problems. I think you'd find them interesting and they're good practice for AMC/AIME (well maybe not but they're still cool). :P | 677.169 | 1 |
MATLAB Linear Algebra
MATLAB is a high-level language and setting for numerical computation, visualization, and programming. utilizing MATLAB, you could study facts, advance algorithms, and create types and functions. The language, instruments, and integrated math features enable you discover a number of ways and achieve an answer quicker than with spreadsheets or conventional programming languages, corresponding to C/C++ or Java.
MATLAB Linear Algebra introduces you to the MATLAB language with sensible hands-on directions and effects, permitting you to speedy in attaining your objectives. as well as giving an creation to the MATLAB setting and MATLAB programming, this ebook offers the entire fabric had to paintings in linear algebra comfortably. as well as exploring MATLAB's matrix algebra features, it describes the MATLAB instructions which are used to create - and third-dimensional photographs, together with specific, implicit and parametric curve and floor plotting, and diverse tools of information illustration. tools for fixing platforms of equations are precise.
What you'll learn
• how one can use the MATLAB surroundings to unravel linear algebraic problems
Vector and Vector area basics
easy methods to use MATLAB for linear algebra difficulties, together with concepts for matrix decomposition
Basic matrix manipulation services in MATLAB
Who this booklet is for
This publication is for somebody who desires to paintings in a pragmatic, hands-on demeanour with MATLAB in a linear algebra context. you will have already got a center knowing of undergraduate point linear algebra, and feature entry to an put in model of MATLAB, yet no prior adventure of MATLAB is assumed.
Bob Miller's humor-laced, step by step studying information make even the main tough math difficulties regimen. in line with greater than 28 years of training and scholar suggestions, his easy-to-grasp ideas provide scholars much-needed self assurance.
This booklet introduces the maths that helps complicated laptop programming and the research of algorithms. the first objective of its famous authors is to supply an outstanding and correct base of mathematical abilities - the abilities had to resolve advanced difficulties, to judge horrendous sums, and to find refined styles in information. institution.
Word: it is a STAND on my own publication. entry CODE isn't incorporated WITH THIS e-book utilizing and realizing arithmetic: A Quantitative Reasoning strategy prepares scholars for the math they're going to stumble upon in collage classes, their destiny occupation, and lifestyles commonly. Its quantitative reasoning process is helping scholars to construct the talents had to comprehend significant concerns in daily life, and compels scholars to procure the problem-solving instruments that they're going to have to imagine significantly approximately quantitative matters in modern society. | 677.169 | 1 |
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find some solution; this leads into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.
Descartes's idea of coordinates is central to algebraic geometry, but it has undergone a series of remarkable transformations beginning in the early 19th century. Before then, the coordinates were assumed to be tuples of real numbers, but this changed when first complex numbers, and then elements of an arbitrary field became acceptable. Homogeneous coordinates of projective geometry offered an extension of the notion of coordinate system in a different direction, and enriched the scope of algebraic geometry. Much of the development of algebraic geometry in the 20th century occurred within an abstract algebraic framework, with increasing emphasis being placed on 'intrinsic' properties of algebraic varieties not dependent on any particular way of embedding the variety in an ambient coordinate space; this parallels developments in topology and complex geometry. | 677.169 | 1 |
Amsco trigonometry textbook answer key
Slader faster beaming IN your cheat sheet jusec There was an error saving. The links in the right column highlight the latest additions and revisions to jmap's resources.You may also download ExamView software.Be sure to include which edition of the textbook you are using!Written Exercises.17, mixed Review Exercises.20 1-4, sums and Differences, oral Exercises.23, written Exercises.24 1-5.Computer Exercises.5, mixed Review Exercises.5 1-2, simplifying Expressions, oral Exercises.10, written Exercises.10, calculator Key-In.12.Org brings you access to over 6 million free sets of flashcards covering everything from US History to Biology to Music Theory to the SAT.
Now is the time to redefine your true self using Sladers free Algebra and Trigonometry: Structure and Method, Book 2 answers.YOU are the protagonist of your own life.Mutually Exclusive and Independent Events Oral Exercises.758 Written Exercises.759 Self-Test.761 Chapter Review.764 Chapter Test.765 Chapter 16 Matrices And Determinants 16-1 Definition of Terms Oral Exercises.768 Mixed Review Exercises.769 Written Exercises.769 16-2 Addition and Scalar Multiplication Oral.Algebra I Study Guide, and, algebra I Lesson Plans. .Jmap offers teachers and other users of the Common Core State Standards free resources that simplify the integration of Regents exam questions into their curriculum.Get started by searching in the box below, click save on the flashcard set you'd like to review, and then select one of the following modes: Flashcard Mode lets you familiarize yourself with the material.Resources may be downloaded using the links in the left column or below.Common core state stan, dards classes, jMAP resources for the ccss include.Let Slader cultivate you that you are meant to be!Products, oral Exercises.30, written Exercises.30 Mixed Review Exercises.31 Computer Exercises.32 1-6"ents Oral Exercises.34 Written Exercises.35 Self-Test.36 1-7 Solving Equations in One Variable Written Exercises.40 Oral Exercises.40 Mixed Review Exercises.42 1-8 Words into Symbols. | 677.169 | 1 |
Martin Lotz – School of Mathematics – The University of Manchester
Week 1
In the first week, we will have a look at different types of optimization problems and see some Python code at work. We will encounter the definition of convexity (for sets and functions) and identify some problems as convex. After a brief overview of the computational environment, we will get started with the topic of unconstrained optimization and (if time permits) discover a first minimization algorithm.
Learning outcomes
Know examples of different types of optimization problems.
Have a vague idea of how to use Python.
Know the definition convexity, examples of convex functions, and its significance for optimization.
Tasks and Materials
Browse through the Preliminaries – don't worry if you are not familiar with everything in there, the more advanced concepts will be introduced as needed. | 677.169 | 1 |
This course is an introduction to numerical methods
for linear algebra.
Three types of problems are considered:
solving a linear system of equations (Ax=b),
computing the eigenvalues and eigenvectors of a matrix (Ax=\lambda x),
and
least squares problems
(min_x ||Ax-b||_2).
These problems arise in many scientific applications
and
much effort has gone into developing effective solution algorithms.
Standard mathematical expressions for the solution
(e.g. x=A^{-1}b)
and
naive implementations
(e.g. Gaussian elimination)
may fail in practice
either
because the operation count is prohibitive
or
because computer roundoff error ruins the answer.
The challenge for the numerical analyst
lies in deriving alternative expressions
which lead to practical algorithms.
This may involve exploiting a special property of the matrix
(e.g. positive definite)
or a radical approach
(e.g. QR algorithm for computing eigenvalues).
In this class,
we shall study some of the main algorithms in use today for linear algebra.
For example,
we shall see how the singular value decomposition of a matrix leads to
an algorithm for image compression.
Two important issues we shall discuss are the
efficiency and stability of an algorithm.
In addition,
for the case of approximate iterative methods,
we shall also discuss the rate of convergence.
We shall study the rigorous derivation
of each algorithm,
as well as practical implementation issues.
Applications and examples will be provided throughout. | 677.169 | 1 |
This book was developed to fill the need for a high-school level
discrete mathematics text [8]. It is addressed to
the student, and is less sophisticated mathematically
than either FAPP or Excursions. Teachers of students in
grades 7-9 (or average students in grades 10-12) have been very pleased
with it; but teachers of more advanced students have found it
less useful. Overall, the comments on this book
have been more mixed than those on the previous three. However,
the book can provide a good introduction for a teacher who has not
seen discrete mathematics previously.
Content.
The book includes the following chapters:
1.
Election Theory;
2.
Fair Division;
3.
Matrix operations and applications;
4.
Graphs and applications;
5.
Recursion.
Each chapter begins with a group exploration and a set of
exercises to introduce the topic. This is followed
by short lessons and exercises.
In another article in this volume [8], the authors
give more detail on the content and development of the text.
Classroom Use.
One teacher used it as a text for a
course called ``Math in the Real World'',
for students at the 11th- and 12th-grade level with
poor mathematics backgrounds. Another used it as a text for
a discrete mathematics course for grades 9-10,
while another used a draft version for an 11th-grade
discrete mathematics course.
Comments.
A teacher who used it as a text, who felt that FAPP and
Excursions were too abstract and notation-heavy
for her students, said:
It's an excellent book.
It's very concrete, interesting, and to the point.
Starting with the first chapter, where there's an election
activity on soda preferences, there are many good activities
that involve the students. The exercises are conducive
to group work, and range from very basic to challenging.
(Diane DePriest LP `93, private communication.)
She supplemented the text with logic puzzles, and
material on permutations and combinations which she created.
A teacher who chose not to use the book for a
12th-grade course felt
that it ``looked too easy,'' and feared it could have a
``bad effect on the reputation of the course.''
A college faculty member was disappointed that the book ``does not
point out where the mathematical structure is,'' and does not do more
``summing up'' of the mathematics topics learned.
On the other hand, an elementary school teacher advises teachers of elementary or middle
grades to use the text:
It lends itself
best of all the texts to adapting ideas to the elementary and
middle grades. Also, the instructor's manual is
user-friendly
for teachers who are not familiar with discrete math,
and would otherwise be
afraid to try it. I also encourage them to order the COMAP
modules on graphs.
(Penni Ross LP `94, private communication.) | 677.169 | 1 |
The Best Software Downloads
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GeoGebra 5. 0. 226. 0-Flexible and free mathematical software
GeoGebra is a complex mathematical program for those that study or work with arithmetic, geometry, algebra plus calculus .
Aimed at math experts
It's a rather complex app that's aimed firmly at those comfortable with difficult math, but the advantage GeoGebra offers over similar apps is it provides multiple representations of items that are all dynamically linked. The concept is to connect geometric, algebraic, plus numeric representations in an interactive method. This can be done with points, vectors, ranges, and conic sections.
GeoGebra allows you to directly enter and manipulate equations and coordinates , enabling you to plot features; work with sliders to investigate parameters; discover symbolic derivatives; and use effective commands like Root or Sequence.
Mind boggling
The particular complexity of the program is thoughts boggling for those a new comer to such mathematical applications. It's very hard to work out how to use from scratch, although there are a variety very detailed tutorials to help you on the way.
Not for the faint hearted
GeoGebra isn't a mathematical program for the faint hearted but if you have to cope with arithmetic, geometry, algebra and calculus on a regular basis, it is very versatile .
What's brand new in GeoGebra
The latest version of GeoGebra includes tangent to Freehand Functions, as well as the ability to save projections regarding 3D view (unless "Gray-scale" and "Omit green channel"), a "Use Lighting" option for 3D view (turns off shadows), and a "Show All of the Objects" button for 3D view. | 677.169 | 1 |
Plan
· Deliver the new GCSE maths curriculum with confidence with a detailed introduction to support you in interpreting the significant change · Help students achieve a smooth transition from KS3 using our thorough explanations of the new assessment objectives · Plan ahead with detailed, practical schemes of work for 2, 3 and 5 year teaching · Pick up and teach with detailed lesson plans – perfect for cover lessons, NQTs and full of ideas for more experienced teachers. New features include: - literacy prompts to help students ask the right questions - extra teacher support on the new, harder topics from AS level and IGCSE · Link the course together with all relevant resources and curriculum and specification references included · Access answers to the accompanying student book
Book Description HARPER COLLINS, 2015. Paperback. Book Condition: NEW. 9780008113940 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE0988417 | 677.169 | 1 |
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