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Purchasing Options: Description This text explores the beauty of topology and homotopy theory in a direct, engaging, and accessible manner while illustrating the power of the theory through many, often surprising, applications. It offers a comprehensive presentation that uses a combination of rigorous arguments and extensive illustrations to facilitate an understanding of the material. The author covers basic topology, ranging from the axioms of topology to proofs of important theorems. He also discusses the classification of compact, connected manifolds, ambient isotopy, and knots, which leads to coverage of homotopy theory. Related Subjects Name: An Illustrated Introduction to Topology and Homotopy (Hardback) – Chapman and Hall/CRC Description: By Sasho Kalajdzievski. This text explores the beauty of topology and homotopy theory in a direct, engaging, and accessible manner while illustrating the power of the theory through many, often surprising, applications. It offers a comprehensive presentation that uses a... Categories: Geometry, Mathematical Analysis, Mathematical Physics
Essential reading for any student teacher who wishes to reflect upon and improve their math's knowledge and understanding. Miss Emma Morris School of Education, Newman University College Mar 25 2013 Report this review Part of a set of books these make a good foundation that are easily tackled. A good starting point. Mrs Kathryn Peckham Childhood Studies : Early Years, Chichester University Mar 24 2013 Report this review Helpful book for students on FdA intending to progress onto QTS – supports Supporting Teaching and Learning module which looks at English and mathematics at KS1. M-level extension activities and helpful linkls to new teaching standards Mrs Janet Harvell Early Years, Bridgwater College Jan 08 2013 Report this review A good overview of essential knowledge and understanding. Ms helen yorke School of Primary Education, Birmingham City University Oct 31 2012 Report this review This book will provide a useful reference text for students with regard to reference to the standards and mathematical knowledge and understanding required. It has some useful reflective and practical activities. Mr Colin Howard Institute of Education, Worcester University Oct 10 2012 Report this review Helpful revision of a previously used book. Mr Ralph Manning Please Select Your Department, University of East Anglia Sep 14 2012 Report this review updated version of a very useful book for ITE students studying and levels 4 and 5 Ms Sylvia Turner Faculty of Education, Winchester University Aug 15 2012 Report this review Good general background. Mrs Alison Flint School of Education (Park Campus), Northampton University Jul 24 2012 Report this review Valuable text book for students developing the knowledge of mathematics curriculum at primary level. Ms Sue Kellas Child Care and education, Penwith College Jul 20 2012 Report this review This updated version of an ever popular series, aligned to the new standards, will be well received by our students. Mrs Pauline Palmer Institute of Education, Manchester Metropolitan University Jul 19 2012 Report this review higher mathematics is explained Miss anita chamberlain Education (Lancaster), St Martin's College Jul 06 2012 Report this review Ideally linked to standards so students are aware of the essential duty to develop and enhance their subject knowledge Mrs Carmen Mohamed School of Education, University of Leicester Jul 05 2012 Report this review Recommended for students who may need support with personal numeracy skills. Mrs Rachel Wallis Swansea School of Education, Swansea Metropolitan University Jun 27 2012 Report this review This book is very good for a primary school teacher, however I do not feel it will be of use to me Mrs Noelle Wilson Childhood Studies, Hull College Jun 20 2012 Report this review Essential reading for teacher trainees needing to revisit their maths skills. Clear guidance given with practical tasks and a useful self assessment. Mrs Helen Handyside Teacher Education, CB Learning and Assessment Ltd Jun 01 2012 Report this review Clear links to practice with diagrams to make understanding easier. Mrs amanda thomas Education, Glamorgan University May 28 2012 Report this review Report this review If you believe this review contains offensive or inappropriate content, please report it using the button below. SAGE will be notified and will take appropriate action.
Saxon Algebra 1 - Home School Bundle with DIVE CD Algebra 1 covers topics typically treated in a first-year algebra course. Specific topics include exponents and roots, properties of real numbers, absolute value, scientific notation, polynomials and rational expressions, Pythagorean theorem, algebraic proofs, functions, quadratic equations, exponential growth, computation of the perimeter and area of two dimensional regions, computation of the surface area and volume of a wide variety of geometric solids, statistics and probability, and more. (120 lessons) The student textbook, which contains answers to the odd problems; the Home Study Packet (the complete answer key and tests); the Solutions Manual, and the DIVE CD-ROM are all included.
Precalculus Concepts Through Functions, a Right Triangle Approach to Trigonometry This edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books a la Carte also offer a great value-this format costs significantly less than a new textbook. Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, Second Edition embodies Sullivan/Sullivan's hallmarks-accuracy, precision, depth, strong student support, and abundant exercises-while exposing readers to functions in the first chapter. To ensure that students master basic skills and develop the conceptual understanding they need for the course, this text focuses on the fundamentals: "preparing "for class, "practicing "their homework, and "reviewing" the concepts. After using this book, students will have a solid understanding of algebra and functions so that they are prepared for subsequent courses, such as finite mathematics, business mathematics, and engineering calculus. show more show less List price: $136.00 Edition: 2nd 2011 Publisher: Addison Wesley Binding: Looseleaf - sheets only Pages: 1130 Size: 8.36" wide x 10.30" long x 1.37" tall Weight: 4calculus Concepts Through Functions, a Right Triangle Approach to Trigonometry - 9780321645241 at TextbooksRus.com.
Discrete Mathematics 9780130890085 ISBN: 0130890081 Edition: 5 Pub Date: 2000 Publisher: Prentice Hall PTR Summary: For one or two term introductory courses in discrete mathematics. This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has woven techniques of proofs into the text as a running theme. Each chapter has a problem-solving corner that shows students how to attack and solve problems. Ships From:Hillsboro, ORShipping:Standard, Expedited, Second Day, Next Day
Find a Plainfield, IL StatisticsStudents seem to find it overwhelming to remember how exactly a differential equation can be classified as homogeneous, non-homogeneous, linear, nonlinear, first order, or second order. There are just so many things to keep track of! Both my knowledge of this subject and my ability to explain it may be able to help you with all of the linear thinking that goes into solving these equations
Mathematics Upper School Mathematics Department Philosophy The mathematics department's goal is to prepare each student for life and for future academic training in the area of mathematics. Mathematics is a sequential subject with each course building upon the work of the previous course, adding new concepts and approaches with a minimum reinforcement of previous knowledge. To hone critical thinking skills, students will have to analyze and synthesize concepts in order to solve problems. The teachers strive to create a positive, caring, and encouraging environment. Algebra I CP This course places emphasis on the understanding of the properties of real numbers and the application of those properties to the solution of problems. The course covers solving equations and inequalities, operations on polynomials, factoring, rational expressions, radicals, graphs, and quadratics. Algebra I Lyceum This course places strong emphasis on understanding the properties of the real number system and their application to the solution of problems which can be analyzed algebraically. Problem solving techniques are developed for various types of problems, including problems dealing with mixtures, uniform motion, percent, age, money, consecutive integers, and angle relationships. The course covers the operations with real numbers and solving equations and inequalities. Throughout the year, students will participate in enrichment activities and will calculate advanced problems.Prerequisites Geometry CP Students are introduced to the properties and relationships of congruency, similarity, parallelism, and perpendicularity. The course covers the properties of circles and various convex polygons. Algebraic skills are reviewed and strengthened as they are applied to the solutions of geometric problems. Geometry Lyceum The student is introduced to the principles of logic, deductive reasoning, formal proof, and indirect proof. The course covers the properties and relationships of congruency, similarity, parallelism, and perpendicularity. Other topics covered include the properties of circles and convex polygons as well as trigonometry and coordinate geometry. Advanced algebraic techniques are used in solving geometric problems. Throughout the year, students will participate in enrichment activities and will calculate advanced problems.Prerequisites Algebra II CP This course begins by reviewing the major concepts of Algebra I and going into further depth as each topic is covered. The major topics include linear equations and inequalities, absolute value, polynomials, factoring, solving quadratic equations by factoring, rational expressions, fractional equations, literal equations, radicals, integral exponents, rational number exponents, complex numbers, solving quadratic equations using the quadratic formula and completing the square, graphing linear equations and inequalities, solving systems of linear equations (by graphing, substitution, and linear combination), graphing parabolas, solving quadratic systems, and inverse functions. Word problems are included in all topics involving equation solving. Students are introduced to inverse and logarithmic relations. Algebra II Lyceum In this course, it is assumed that students are acquainted with the language of algebra, have an understanding of the structure of number systems, and can manipulate algebraic expressions. Students will be reintroduced to the algebraic properties of the real number system, solve first and second degree equations and inequalities, and begin working with graphing calculators. During the second semester, students work with complex numbers, functions, and logarithms, and begin a study of trigonometric functions. Sequences, series, probability and matrices may be introduced. Throughout the year, students will participate in enrichment activities and will calculate advanced problems. Prerequisites Discrete Math CP Use of the textbook in conjunction with a calculator will guide students to an understanding of equations and inequalities; polynomials, factoring, and rational expressions; radicals; imaginary and complex numbers; quadratic equations; relations and functions; exponential and logarithmic functions; circles; circular functions; trigonometric identities; graphs of trigonometric functions; trigonometric equations; and solutions of right and oblique triangles. Pre-Calculus Lyceum Students study the functions, trigonometry and algebra necessary for the study of calculus. Topics include circular functions, trigonometric identities, graphs of trigonometric functions, particular and general solutions of trigonometric equations, solutions of right and oblique triangles, polynomial functions, and exponential and logarithmic functions. Throughout the year, students will participate in enrichment activities and will calculate advanced problems.Prerequisites Calculus Lyceum The purpose of this course is to provide the students with the understanding of the concepts of calculus and experience with its methods and applications. Topics will include elementary functions, limits and continuity, derivatives, applications of derivatives, integrals, applications of integrals, logarithmic and exponential functions, trigonometric functions, and techniques of integration. Prerequisites AP Calculus AB In this course, students learn to understand the concept of calculus and are provided experience with its methods and applications. Topics include elementary functions, limits and continuity; derivatives, applications of derivatives; integrals, applications of integrals, logarithmic and exponential functions, trigonometric functions, and techniques of integration. Graphing calculators are required and will be used regularly. This material is explored extensively and word problem applications, in particular, are covered at an accelerated pace. Prerequisites AP Calculus BC In addition to expanding on the topics covered in Calculus AB, sequences and series, statistics, probability, vectors and matrices are covered. Graphing calculators are required and used regularly. Prerequisites Probability and Statistics CP This course includes topics on probability, descriptive statistics, and regression analysis. Graphing calculators are required. Enrollment limited to juniors and seniors AP Statistics This course deals with four major themes: exploratory data analysis, planning a study, probability, and statistical inference. Students incorporate current technology and use graphing calculators and statistical software to analyze real world problems. Prerequisites Upper School students are pictured in the video production classroom. Students are pictured in front of the Mack Building between classes. Pictured are Upper School students entering Pou Chapel. Middle and Upper School students wear casual dress Mon., Wed., Thurs., and Fri. and traditional dress on Tues.
Maths Plus Year 2: Student Book Stude... read full description below. Sorry, availability of this title has not been updated from publisher recently so availability is uncertain. Description of this Textbook Student Books relate directly to the Mentals and Homework Books as well as the Teaching Guides. The revised series: focuses teaching to clearly defined outcomes promotes differentiated learning to cater for all students' needs is designed to give students a thorough understanding of mathematics follows a clear progression of mathematical skills and understandings from Kindergarten to Year 6 encourages students to realise that there are many different ways of solving a problem and that there may be multiple solutions to a given problem develops students' mental computation skills builds students' confidence and enthusiasm for mathematics.
Introductory And Intermediate Algebra For College Students - With 2 Cds - 3rd edition Summary: TheBlitzer Algebra Seriescombines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum student appeal. Blitzer's personality shows in his writing, as he draws students into the material through relevant and thought-provoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success! KEY TOPICS: Variables, Real Numbers, and Mathematical Models; Linear Equations and Inequ...show morealities in One Variable; Linear Equations in Two Variables; Systems of Linear Equations; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Basics of Functions; Inequalities and Problem Solving; Radicals, Radical Functions, and Rational Exponents; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conic Sections and Systems of Nonlinear Equations; Sequences, Series, and the Binomial Theorem. MARKET: for all readers interested in algebra This book is in Like New Used Condition. STUDENT US EDITION. CD INCLUDED. All pages are clean and intact. There is No highlighting or underlines. Best buy. Shipped promptly and packaged ca...show morerefully. ...show less $55.65 +$3.99 s/h LikeNew DINOSBOOKS Bellevue, WA Fine Book Is In Like New Condition. Includes Sealed CD. Best Buy. Shipping Same Day
This best selling book reviews that basic arithmetic required to calculate drug dosages accurately and quickly - an essential skill for every nurse. Examples are drawn from clinical practice. Explanations and graded exercises (with answers) cover the calculations required to administer injections, tablets and mixtures, to dilute solutions, to arrive at different drip rates and to administer paediatric dosages safely. In this new edition all drug usage material has been reviewed and updated. New exercises have been added to assist in the learning process. - A diagnostic test at the start allows readers to review their knowledge of maths and identify their weak points - Numerous exercises give plenty of practice in making drug calculations - Answers to questions aid self-study - Revision and summary exercises ensure that the reader fully understands the calculations - The nursing context allows the application of theory to every day practice
Philosophie der Mathematik [Philosophy of Mathematics] For students and teachers in mathematics and philosophy as well as the general public Aims and Scope This elementary introduction to philosophical problems and issues in mathematical thought, speech, teaching, and learning is now available in a revised and expanded second edition. It is designed for teachers and students of mathematics and philosophy alike. Real numbers form the basis for discussion and remain a continuous touchstone throughout the work, which incisively addresses a range of mathematical and philosophical problems and questions. The work provides an overview and engages in an in-depth discussion of viewpoints held throughout the history of mathematics and philosophy up to the present day. 24 x 17 cm Includes a print version and an ebook Language: German Type of Publication: Monograph Keywords: Axiomatics; Logic; Mathematics; Set Theory; Philosophy Readership: Teachers and Students of Mathematics and Philosophy at Universities and Schools; Libraries
Algebra enables pupils to hone their maths skills with endless practice. The software offers guidance with on-screen help. The program then enables pupils to work step-by-step towards the correct answer. This program, written by teachers David Benjamin and Justin Dodd, is far and away the best available for developing algebra skills. For use on one single computer. To meet the challenges of success in school and today's technology-rich work world, students must develop mathematical skills in a meaningful and retrievable way. With Discovering Algebra, the sequence of topics, content emphasis, hands-on activities, and use of technology combine to form a program that gives students a solid, lasting foundation in algebra. CLICK ON PICTURE FOR FULL DETAILS AND PRICES. Paul Kunkel, Steven Chanan, Scott Steketee. This collection of more than 55 activities compiled specifically for Algebra 1 including updated activities from Exploring Algebra with The Geometer's Sketchpad and many new ones. Click for longer description. Help Your Students Visualize Algebra 2 Concepts. More than 55 activities, some updated from Exploring Algebra with The Geometers Sketchpad and many new cover Algebra 2 from functions and relations to systems of equations to matrices. Price: £36.00 excl Vat Price: £36.00 inc Vat A total of 16 items are available. You are currently viewing page 1 of 2.
A collection of the various old and new results, centered around the following simple observation of J L Walsh. This book is particularly useful for researchers in approximation and interpolation theory. more... Mathematics for Dyslexics: Including Dyscalculia, 3rd Edition discusses the factors that contribute to the potential difficulties many dyslexic learners may have with mathematics, and suggests ways of addressing these difficulties. The first chapters consider the theoretical background. The later chapters look at practical methods, which may help dyslexic... more... Veteran educators share proven solutions to guide a new secondary math teacher through the challenging first few months and provide the more experienced teacher with interesting alternatives to familiar methods. more... Shows how well-meant teaching strategies and approaches can in practice exacerbate underachievement in maths by making inappropriate demands on learners. As well as criticizing some of the teaching and grouping practices that are considered normal in many schools, this book also offers an alternative view of attainment and capability. more... What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding... more... Deals with the specific characteristics of mathematical communication in the classroom. This book offers a presentation and an application of the fundamental research method in mathematics education that establishes a reciprocal relationship between everyday classroom communication and epistemological conditions of mathematical knowledge. more... This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Discussion focuses on how computers, writing and oral discourse transform education at an epistemological as well as a political level. Building on examples, research and theory, the authors propose that knowledge... more... The advancement of a scientific discipline depends not only on the "big heroes" of a discipline, but also on a community?s ability to reflect on what has been done in the past and what should be done in the future. This volume combines perspectives on both. It celebrates the merits of Michael Otte as one of the most important founding fathers... more...
Logistic Growth In this lesson, our instructor John Zhu gives an introduction to logistic growth. He explains the logistic growth function, defines the variables and the parts of the equation. He finishes with example problems. This content requires Javascript to be available and enabled in your browser. Logistic Growth Logistic Growth Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
Geometry Reasoning, Measuring, Applying Author: ISBN-13: 9780395937778 ISBN: 0395937779 Edition: 10 Pub Date: 2000 Publisher: Houghton Mifflin College Div Summary: The theorems and principles of basic geometry are clearly presented in this workbook, along with examples and exercises for practice. All concepts are explained in an easy-to-understand fashion to help students grasp geometry and form a solid foundation for advanced learning in mathematics. Each page introduces a new concept, along with a puzzle or riddle which reveals a fun fact. Thought-provoking exercises encourag...e students to enjoy working the pages while gaining valuable practice in geometry2001. An acceptable used copy with heavy cover wear and school markings. Book only-does not include additional resources. Booksavers receives donated books and recycles them [more] 2001
DescriptionThe concept of function is one of the most important ideas in the learning of mathematics (Dubinsky & Harel, 1992). Yet it is considered by many researchers to be the least understood by high-school and college students (Breidenbach, Dubinsky, Hawks, & Nichols, 1992; Sfard, 1992). Reforming early mathematics curricula in algebra, therefore, is justified. To this end, the National Council of Teachers of Mathematics (2000) called for a longitudinal view of algebra, from elementary to advanced mathematics education. As a strand in the Rutgers-Kenilworth longitudinal study in 1993, Robert B. Davis introduced early algebra ideas to eleven-year-old students during the sixth grade. Research prior to Davis' intervention with the students showed how they built their understanding of linear, quadratic, and exponential functions (Spang, 2009; Giordano, 2008; Mayansky, 2007). Building on Davis' approach to early algebra and the learning of function, Emily Dann designed a study to determine whether these students, now seventh graders, could extend their understanding to the concept of inverse function. The present study analyzes videotaped work of seventh-grade students who were engaged in a series of activities that Dann had devised.The Guess-My-Rule activities, as they were called, were conducted over three consecutive days. Using the model that Powell, Francisco, and Maher (2003) described for analyzing videotaped data, this study examines in detail the students' work as they collaborated in small groups to develop rules for function and inverse; the study also investigates the obstacles students had experienced. This research demonstrates that seventh-graders understood the idea of function by writing rules, symbolically, to describe the relationships of quantities. Understanding function as action, they progressed to the process concept when creating their own function tables and corresponding rules. Using inverse operations, students wrote inverse rules; however, due to difficulties with integer and fraction arithmetic, they needed to adjust their initial attempts in order to be successful. This study maintains that having facility with function and inverse function concepts will permit students to learn the subject matter, to communicate ideas and solutions, and to interconnect mathematical ideas. In the process of exploring these related concepts, students will be encouraged to think independently and to devise original strategies in their work with function and inverse. The results demonstrate to researchers and educators how students build the concepts of function and of inverse function through group work in a specific environment. Seventh-grade students can engage in activities, similar to those described above, that are essential to the study of algebra.
10 Units 6000 Level Course Available in 2013 This course will extend students understanding of calculus and related applications. The course will examine topics such as ordinary differential equations, multiple integrals, limits and continuity, real or complex variable analysis. The course will also examine current related pedagogical models within the field of secondary mathematics. Objectives On satisfactory completion of this course students should be able to: - Understand study of calculus (analysis) involving topics such as ordinary differential equations, multiple integrals, limits and continuity, real or complex variable analysis. - appreciate the mathematical knowledge and beliefs that learners bring to a learning task - apply a range of strategies for teaching secondary mathematics - recognise the common misconceptions that students may have in regard to the mathematical content covered.
Mathematics What will I study? Mathematics at AS and Advanced GCE is a course worth studying not only as a supporting subject for the physical and social sciences, but in its own right. It is challenging but interesting. It builds on work you will have met at GCSE, but also involves new ideas produced by some of the greatest minds of the last millennium. While studying mathematics you will be expected to: use mathematical skills and knowledge to solve problems solve problems by using mathematical arguments and logic. You will also have to understand and demonstrate what is meant by proof in mathematics simplify real-life situations so that you can use mathematics to show what is happening and what might happen in different circumstances use the mathematics that you learn to solve problems that are given to you in a real-life context use calculator technology and other resources (such as formulae booklets or statistical tables) effectively and appropriately; understand calculator limitations and when it is inappropriate to use such technology. Is this the right subject for me? Mathematics is rather different from many other subjects. An essential part of mathematical study is the challenge of analysing and solving a problem and the satisfaction and confidence gained from achieving a 'correct' answer. If you choose mathematics you will not have to write essays, but you will need to be able to communicate well in written work to explain your solutions. Mathematics is not about learning facts. You will not achieve success by just reading a textbook or by producing and revising from detailed notes... you actually need to 'do' mathematics. How will I be assessed? This will depend on your choice of units of study. For AS Level you will take 3 units and for a full A Level you will take a further 3 units. Each unit is tested by a 1½ hour written examination and the units are equally weighted. What can I do after I've completed the course? An AS in mathematics is very valuable as a supporting subject to many courses at Advanced GCE and degree level, especially in the sciences and geography, psychology, sociology and medical courses. Advanced GCE mathematics is a much sought-after qualification for entry to a wide variety of fulltime courses in higher education. There are also many areas of employment that see a Mathematics Advanced GCE as an important qualification and it is often a requirement for the vocational qualifications related to these areas. Higher Education courses or careers that either require Advanced GCE mathematics or are strongly related include: economics medicine architecture engineering accountancy teaching psychology physics computing information and communication technology. If you wanted to continue your study of mathematics after Advanced GCE you could follow a course in mathematics at degree level or even continue further as a postgraduate and get involved in mathematical research. People entering today's most lucrative industries such as IT, banking and the stock market need to be confident using mathematics on a daily basis. To be sure of this, many employers still look for a traditional mathematics A-level qualification. Researchers at the London School of Economics have recently found that people who have studied mathematics can expect to earn up to 11% more than their colleagues, even in the same job! Even in areas where pure mathematics isn't required, other mathematics skills learned at AS and A level, such as logical thinking, problem solving and statistical analysis, are often very desirable in the workplace. Mathematics is the new lingua franca of commerce, business and even journalism. Next steps! Find out more about the course by talking to your mathematics teachers or by visiting the Edexcel website. Advanced Subsidiary Mathematics Core Mathematics units C1 and C2 plus one of the Applications units M1, S1 or D1. When studying pure mathematics at AS and A2 level you will be extending your knowledge of such topics as algebra and trigonometry as well as learning some brand new ideas such as calculus. While many of the ideas you will meet in pure mathematics are interesting in their own right, they also serve as an important foundation for other branches of mathematics, especially mechanics and statistics. Mechanics (M1, M2, M3, M4, M5) Mechanics deals with the action of forces on objects. It is therefore concerned with many everyday situations, e.g. the motion of cars, the flight of a cricket ball through the air, the stresses in bridges, the motion of the earth around the sun. Such problems have to be simplified or modelled to make them capable of solution using relatively simple mathematics. The study of one or more of the Mechanics units will enable you to use the mathematical techniques which you learn in the Core units to help you to produce solutions to these problems. Many of the ideas you will meet in the course form an almost essential introduction to such important modern fields of study such as cybernetics, robotics, bio-mechanics and sports science, as well as the more traditional areas of engineering and physics. Statistics (S1, S2, S3, S4) When you study statistics you will learn how to analyse and summarise numerical data in order to arrive at conclusions about them. You will extend the range of probability problems that you looked at in GCSE using the new mathematical techniques learnt in the pure mathematics units. Many of the ideas in this part of the course have applications in a wide range of other fields, from assessing what your car insurance is going to cost to how likely it is that the Earth will be hit by a comet in the next few years. Many of the techniques are used in sciences and social sciences. Even if you are not going on to study or work in these fields, in today's society we are bombarded with information (or data) and the statistics units will give you useful tools for looking at this information critically and efficiently. Decision Mathematics (D1, D2) In decision mathematics you will learn how to solve problems involving networks, systems, planning and resource allocation. You will study a range of methods, or algorithms, which enable such problems to be tackled. The ideas have many important applications in such different problems as the design of circuits on microchips to the scheduling of tasks required to build a new supermarket. Entry requirements This course is suitable for students who have achieved at least a grade B at Higher tier in GCSE Mathematics.
This course is designed to teach students spatial and relational mathematics through the use of logic, reasoning, coordinate planes, diagrams, constructions, and real world applications. Students will be using a variety of technology and media to explore basic geometry problems and how geometry plays a role in our daily lives. Basic knowledge of Algebra concepts in finding solutions, using real numbers and basic operations, and problem solving are the basis for starting this course. Goals/Objectives: To teach and apply the skills to use reason and think logically when confronted with geometrical and real life situations. To build an understanding of spatial relationships to be used in practical applications. To foster a greater appreciation for the art of mathematics. To fulfill the credit requirement for high school mathematics and graduation.
More from this developer Description Can help in a class like Linear Algebra. Solve a system of equations or find the inverse or determinant of a matrix. Use spaces between numbers in a row and a new line between rows. Numbers can be decimals or fractions; 0.75, .75, 3/4, and 1.5/2 are valid. Updates: Help Keypad /.- buttons Fixed determinants Clear button
MathMagic is a feature-rich software application that supplies users with the necessary tools for creating and editing mathematical equations effortlessly. It can be used for various purposes, whether you are a student or a professor. MathMagic Personal Edition 7.4.3.48 is a Trial. Please read this article and discover what exactly does Trial mean. Whether you're happy or not testing and using MathMagic Personal Edition 7.4.3.48, be our guest and let's solve all the problems related to this software together. Feel free to use: MathMagic Personal Edition 7.4.3.48
MATH 0960 Accelerated Beginning Algebra Lecture/Lab/Credit Hours 6 - 0 - 6 This course is for students who need to review basic algebra skills. It is a fast-paced course that contains all of the content of both MATH 0930 Beginning Algebra Part 1 and MATH 0931 Beginning Algebra Part 2 in a single course. Topics include positive and negative real-numbers, solving linear equations and inequalities along with their applications, integer exponents, operations with polynomials, factoring, rational expressions, equations of lines, and graphing of equations and inequalities10 or MATH 0930 with a grade of P, or MCC placement test
enjoy Mathematics, wish to study it beyond GCSE and want to see it applied into various areas of real life. It introduces students to mathematical ideas and concepts and shows how they can be used in the modelling of real life situations. Further Details At AS all students study units in 'Algebra' and 'Data Analysis'. Students can then take a further optional unit which has been either 'Dynamics' or 'Principles of Personal Finance' in the past. Two of the three units are Free Standing Mathematics Qualifications (FSMQs) which are Level 3 qualifications in their own right. Please note that at the moment this is a pilot qualification and so the exact course details are subject to change. Progression Options The course provides a sound basis for students studying subjects with mathematical content. AS / A Level Navigation Use of Maths Student Quotes "I enjoy Use of Maths as you learn all of the maths knowledge while applying it to real life situations. It allows you to see how you could use maths in everyday life, rather than just learning mathematical equations." - Emma Rose
Quantitative Literacy Assessment Level 2 Mathematical Connections Bypass The Mathematical Connections bypass assessment consists of three sections, representing data, predicting data, and measurement concepts, with each part consisting of word problem applications. The topics covered in the sections are Representing Data Using descriptive statistics (mean, median, mode) to represent a set of data Using graphs (bar graph, line graph, circle graph, histogram, frequency polygon) to represent a set of data Converting measures between the American and Metric measurement systems Using Pythagorean Theorem to determine unknown lengths Determining geometric quantities of perimeter, area, surface area and volume Connecting concepts of volume, capacity and mass The assessment is not timed. As a guideline, most students spend about an hour and one-half for the bypass assessment. Additional time is available if needed. You may use a calculator and a 4" x 6" note card on the assessment.
The CCSS for Mathematical Practice reflect "how" students should interact with math content to master essential skills and their underlying concepts. Math Solutions Common Core courses are specifically designed to align what teachers already know with what they need to know about developing expertise in the "processes and proficiencies" outlined in the Standards for Mathematical Practice. Students with a strong start to their mathematics education—one that encourages conceptual understanding, procedural fluency, and computational automaticity—will be better prepared for academic success. Math Solutions helps teachers deepen content understanding, which will allow them to build a strong mathematical foundation for their students. Math Solutions helps teachers incorporate literature and communication to promote thinking and reasoning and increase their students' problem-solving ability. In addition, real-life scenarios and classroom discussion advance students' understanding and ability to use and apply mathematical concepts in a multitude of contexts. Within a mathematics class, students exhibit a wide variety of learning styles and instructional needs. Math Solutions helps teachers develop strategies for adapting lessons to facilitate understanding for the diversity of learners in their classroom. Some students need more support, more time, and specialized instruction to learn. Math Solutions helps teachers provide intervention instruction that meets the needs of these struggling students and helps them succeed. Math Solutions helps high school classroom teachers understand how students learn mathematics, explores ways to make math accessible for students, and focuses on problem solving in the strands of algebra and geometry.
Book Description: This manual allows students to use Derive as an investigative tool to explore the concepts behind calculus. Each chapter begins with worked examples, followed by exercises and exploration and discovery problems which encourage students to investigate ideas on their own or in groups.
guide to learning activities developed for use with Microsoft Office 97 software programs. Communication topics include filling out forms; creating personal letters using a word processor; writing letters of request or complaint; using email; formatting a report; performing a job search using a computer; creating a newsletter; and writing a résumé and a cover letter. Among the mathematics learning activities are a variety of uses for Excel, including finding perimeter, area and volume; graphing linear and non-linear equations, graphing trigonometric functions; and creating and using spreadsheets. Rubrics for measuring success and answer keys for the mathematics portion are also included. Citation Share This video tutorial uses a variety of examples to introduce the concept of averages. The instructor explains that finding the average, or mean, involves taking a total value and dividing it by the number of units represented by that total. For example, if three students score 90, 85 and 80 respectively on a test, the total value of their marks is 255. To find the average mark, it is necessary to divide the total of 255 by three, the number of students, which shows they had an average score of 85. Citation Share This video tutorial gives learners a chance to reinforce their knowledge of averages by trying three progressively more challenging problems. They are asked to pause the video to work out the problems on their own, then restart it to see the instructor's solutions. The first problem simply requires the learner to find the average of three numbers. In the third problem, the learner is given the average of three numbers, along with two of those three numbers, and must find the third numberDesigned for educators, trainers, tradespeople, apprentices and people considering construction careers, this Essential Skills workbook offers exercises that students can use to refresh their math skills. The curriculum-based exercises are built around typical construction workplace tasks. It includes sections on measuring; dimension and area; elevation and grade; problems involving the Pythagorean Theorem; and weight-load estimation. Each section is independent of the others, which means that learners will not need information from one section to solve problems in another. You can purchase a hard copy of this document on the Construction Sector Council's website at Comments Citation Share This booklet offers an introduction to Communications and Math Employment Readiness Assessment (CAMERA), a series of standardized tests providing placement and diagnostic information about adult learners' abilities to manage workplace communications and numeracy tasks. The CAMERA system was developed by PTP Adult Learning and Employment Programs, a non-profit literacy organization based in Ontario. It uses real-life workplace documents and tasks to test and develop adult learners' reading, document use, writing, and numeracy skills. In this booklet, the authors provide information about the rationale for the system; its components, including tests, curriculum guidelines, and workbooks; training requirements; and costs. They have also included sample tests and contact information for PTP. Citation Share This workbook is part of a series developed through a two-year project initiated by the Canadian Gaming Centre of Excellence (CGCE), a subsidiary of Manitoba Lotteries. While the project focused on meeting the training needs of Aboriginal or new Canadians, the material could be relevant for any new or potential employees in the gaming industry. Designed to be used by both learners and teachers, the document is divided into two separate parts. The first section offers a review of the underlying math skills required in most gaming jobs, including working with fractions; counting cash; converting currency; and estimating. For each topic, the authors provide a description of the skill; practice exercises for the learner; and teaching tips. The second section deals with what the authors call "job families" and contains practice questions organized according to specific kinds of gaming and casino jobs. For example, learners who need to develop skills for calculating odds and payouts specific to table games will find relevant math skills exercises in the "Casino Table Games" section. Comments Citation Share This document is a manual for teaching basic math to adults. It was written as part of a project funded by the National Office of Literacy and Learning (NOLL) and is intended for adult basic education math instructors who are interested in changing their teaching practice to bring it more in line with recommendations from the research literature on teaching numeracy to adults. The manual sets out some "best practices" from the literature, then outlines some difficulties instructors may face in implementing them, and makes suggestions for overcoming those difficulties. There are also many pages of activities ready for immediate classroom use that provide examples of some ways to implement the best practices.
8th Grade Algebra For students: The Important Files (documents and power points) are located at the bottom of the page. Overview of 8th Grade Algebra GOALS: There are several major goals for students in Algebra: 1. to identify and define a function, 2. to graph and solve functions, 3. to perform operations with polynomials and factor them, 4. to apply the skills learned to real world problems, and 5. to use technology to assist us in solving and representing mathematical concepts. INTRO TO FUNCTIONS: Students begin the year introducing the concept of functions. We define functions and relations and learn various ways to represent relations-- equations, graphs, tables, and mapping diagrams. From those representations, we identify what relations are and are not functions. LINEAR FUNCTIONS:The first family of functions we study is linear functions. We investigate the various general equations to represent these functions such as slope-intercept form, standard form, direct variation form, and point-slope form. We learn how to graph these functions in these different forms and convert from one form to another. We practice writing equations to represent real world situations, graph data, and interpret what these graphs of these functions mean. We use both Microsoft Excel and graphing calculators to apply skills we learn in this unit. We culminate this unit with a chapter project in which students collect data from an experiment they design. LINEAR SYSTEMS:We extend our investigation of linear functions by studying linear systems. We learn what a solution of a linear system means and study various methods of how to solve a linear system. Students write a persuasive essay of which method they feel is the best way to solve a linear system. INEQUALITIES:Students review the basic concept of inequalities and analyze what their solutions mean graphically. They learn about a new type of inequality--an absolute value inequality. They also learn how to graph inequalities on the coordinate plane. POLYNOMIALS:We shift from functions and graphing to defining polynomials. We first learn how to perform operations with polynomials and then we learn various methods of factoring polynomials. We will analyze various polynomials and determine which method is necessary to factor them. QUADRATIC FUNCTIONS & EXPONENTIAL FUNCTIONS: We finally move on to new families of functions other than linear! We examine the famililes of quadratic and exponential functions and learn their equations and graphic patterns. We also learn how to solve quadratic and exponential equations using a variety of methods. All of these skills are applied to word problems involving quadratic functions. TECHNOLOGY:Graphing calculators will be used throughout the year to enhance our study of functions. Microsoft Excel will also be used to show another method of graphing data. END OF THE YEAR EXAM: Students will take an Algebra Acuity Test at the end of the year for the Archdiocese. Neither I nor the Archdiocese make the exam. It is made through a computer program that the Archdiocese hired. What we learn throughout the year will prepare the students for the exam. Certain high schools within the Archdiocese ask for the exam scores to determine math placement. However, public schools and other private schools do not typically ask to see these scores.We will most likely not cover every single concept on the exam but that is typical. I give more information as the exam approaches toward the end of May. SETUP: There is a focus on vocabulary. Students must keep up with the key terms in the vocabulary section of their notebooks. There are several quizzes throughout a chapter. Quizzes involve vocabulary and word problems. There is a major test at the end of a chapter. There are some projects and/or writing assignments throughout the year.
MTH/HMTH202 Linear Mathematics 2 Duration :1 semester Core Course for Major 24 lectures Aim: This course, which assumes and builds upon a basic knowledge of matrix theory from MTH102, is designed to give a good grounding in all linear aspects of mathematics. The emphasis in sections A and B will be on actual examples and only basic results are proved. A more abstract approach is offered in the course in Algebra 1 (MTH005). The main aim in section C (which could be studied before section B) is to expose the link between matrix theory and linear transformations. This material, together with that in Section D, has applications to almost all areas of pure and applied mathematics. It is applied (within this course) to diagonalization of matrices and solutions of differential equations. (B) INNER PRODUCT SPACES. Basic definitions with many examples, the notions of norm (length) and distance (emphasis will be on the Euclidean inner product), the Cauchy-Schwarz inequality, the angle between two vectors, orthogonal vectors --- the Gram-Schmidt orthogonalization process, orthonormal basis. 3 (C) LINEAR TRANSFORMATIONS. Basic definitions and results, including images and kernels, with examples; matrix representations of linear transformations from $\BbbR^n$ to $\BbbR^n$, geometric interpretations of linear transformations from $\BbbR^2$ to $\BbbR^2$. 4 (D) EIGENVALUES AND EIGENVECTORS. The eigenvalues and eigenvectors of a matrix, the characteristic polynomial of a matrix, linear independence and orthogonality of eigenvectors, algebraic and geometric multiplicity of eigenvalues, eigenspaces, eigenvalues of powers of matrices, formulas for finding inverses of matrices and powers of matrices. 3 (E) VARIOUS TYPES OF MATRICES. Symmetric, skew symmmetric, unitary, hermitian matrices etc., their eigenvalues and eigenvectors, some basic results and theorems about them. 3 (F) DIAGONALISATION OF MATRICES. Similar matrices and their eigenvalues and vectors, identification of matrices that are diagonalizable, the Cayley-Hamilton theorem and its applications, quadratic forms and canonical forms. 3 (G) DIFFERENTIAL EQUATIONS. Application of diagonalization of matrices to solutions of systems of differential equations; the emphasis is on method --- no theorems are proved.
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Intended for schools that want a single text covering the standard topics from Beginning and Intermediate Algebra. Topics are organized by using the principles of the AMATYC standards as a guide, giving strong support to teachers using the text. The book's organization and pedagogy are designed to work for students with a variety of learning styles and for teachers with varied experiences and backgrounds. The inclusion of multiple perspectives -- verbal, numerical, algebraic, and graphical -- has proven popular with a broad cross section of studentsHall and Mercer's text is intended for schools that want a single book covering the standard topics from elementary algebra through intermediate algebra. The text is fully integrated, rather than being simply the joining of two, separate texts. Topics are organized not following the historical pattern, but by using as the guiding principles, the AMATYC standards as outlined in Crossroads in Mathematics. BEGINNING AND INTERMEDIATE ALGEBRA: THE LANGUAGE AND SYMBOLISM OF MATHEMATICS is oriented toward recent reforms in college level mathematics curricula. [via] More editions of Beginning and Intermediate Algebra: The Language and Symbolism of Mathematics: This practical and comprehensive sourcebook sets out to strengthen the practitioner's understanding of clinically important auditory evoked responses (AERs). It enhances understanding of the anatomy, measurement and interpretation of AERs, helps improve AER recording procedures using stimulus techniques, and introduces new evoked response patient services. This book describes electrocochleography, auditory middle latency response, auditory late response, and the P300 response, and details the anatomy, measurement and interpretation of each. The author provides specific clinical applications, practical guidelines and helpful hints drawn from his clinical experience. [via]
Summertime Maths Our students say "I didn't realise how much Maths I could forget over the long summer break!". Different subjects and different degrees require different specific mathematical skills. This site is for students who wish to identify what specific skills are required for their first session of studies. It will also be of use for students who need to review their Mathematics skills, in the summer, before starting at Uni. The site is based on the skills required in subjects at the University of Wollongong. This will be similar to subjects elsewhere, but there will also be differences.
Dinah Zike's Big Book of Math for Middle and High School features instructions for 28 manipulatives, with approximately 100 full-color photographed examples. Math topics are divided into five catagories, Number Systems, Algebraic Patterns and Functions, Geometry, Measurement, Data Analysis and Probablility. The book contains thousands of ideas for teaching math concepts using graphic organizers, as well as five black-line art examples per page and an additional 40 black and white photographed examples throughout the book. 128 pages, 8 1/2" x 11"
Department of Mathematical Sciences The United States Military Academy West Point, New York Abstract The Department of Mathematical Sciences at the United States Military Academy (USMA) is fostering an environment where students and faculty become confident and competent problem solvers. This assessment will reevaluate and update the math core curriculum's program goals to incorporate the laptop computer, enabling exploration, experimentation, and discovery of mathematical and scientific concepts. Background and Goals: Technology has made a dramatic impact on both education and the role of the educator. Graphing calculators and computer algebra systems have provided the means for students to quickly and easily visualize the mathematics that once took effort, skill, and valuable classroom time. The Calculus Reform movement sought to improve instruction, in part, by taking advantage of these technological resources. Mathematical solutions could now be represented analytically, numerically, and graphically. The shift in pedagogy went from teaching mathematics to teaching mathematical modeling, problem solving, and critical thinking. Ideally the problem solving experiences that students encountered in the classroom were interdisciplinary in nature. Mathematics has truly become the process of transforming a problem into another form in order to gain valuable insight about the original problem. Portable notebook computers provide an even greater technological resource that has led us to once again reexamine our goals for education. Storage and organization coupled with powerful graphical, analytical, and numerical capabilities allow students to transfer their learning across time and discipline. The Department of Mathematical Sciences at USMA is committed to providing a dynamic learning environment for both students and faculty to develop self-confidence in their abilities to explore, discover, and apply mathematics in their personal and professional lives. The core math program attempts to expose the importance of mathematics, providing opportunities to solve complex problems. The program is ideally suited and committed to employing emerging technologies to enhance the problem solving process. Since 1986, all students at USMA have been issued desktop computers with a standard suite of software; this year the incoming class of students (class of '06) will be issued laptop computers with a standard suite of software. The focus of this assessment is to reevaluate the program goals of the math core curriculum and update these goals to incorporate the ability of the laptop computer to not only explore, experiment, and discover mathematical and scientific concepts in the classroom, but provide a useful medium to build and store a progressive library of their analytical and communicative abilities. Description The general educational goal of the United States Military Academy is "to enable its graduates to anticipate and to respond effectively to the uncertainties of a changing technological, social, political, and economic world.‰ The core math program at USMA supports this general educational goal by stressing the need for students to think and act creatively and by developing the skills required to understand and apply mathematical, physical, and computer sciences to reason scientifically, solve quantitative problems, and use technology effectively. Cadets who successfully complete the core mathematics program should understand the fundamental principles and underlying thought processes of discrete and continuous mathematics, linear and nonlinear mathematics, and deterministic and stochastic mathematics. The core program consists of four semesters of mathematics that every student must study during his/her first two years at USMA. The first course in the core is Discrete Dynamical Systems and an Introduction to Calculus (4.0 credit-hours). The second course is Calculus I and an Introduction to Differential Equations (4.5 CH). The sophomore year's first course is Calculus II (4.5 CH), and the final core course is Probability and Statistics (3 CH). Five learning thread objectives have been established for each core course. They are: Mathematical Modeling, Mathematical Reasoning, Scientific Computing, Communicating Mathematics, and the History of Mathematics. Each core course builds upon these threads in a progressive yet integrated fashion. The assessment focuses on the following aspects of our core math program. 1) Innovative curriculum, instructional, and assessment strategies brought on by the integration of the laptop computer. 2) Student attainment of departmental goals. Innovative Curriculum and Assessment Strategies Projects: In-class problem solving labs serve as a chance for the students to synthesize the material covered in the course over the previous week or two. Students use technology to explore, discover, analyze, and understand the behavior of a mathematical model of a real world phenomenon. Following the classroom experience, students will be given an extension to the problem in which they are required to adapt their model and prepare a written analysis of the extension. Students are given approximately seven-ten days to complete the project. For the most part, these out-of-class projects will be accomplished in groups of two or three. An example of a project is provided in Appendix A. Two-day Exams: Assessment of student understanding and problem-solving skills will take place over the course of two days. Paramount in this process is determining what concepts and/or skills we want our students to learn in our core program. We understand that, what you test is what you get; therefore, we have adapted our exams to assess these desired concepts and skills. The first day of the exam will be a traditional in-class exam in which students do not have access to technology (calculator or laptop computer). This exam portion focuses on basic fundamental skills and concepts associated with the core mathematics program. Students are also expected to develop mathematical models of real world situations. Upon completion of this portion, students are given a take-home scenario that outlines a real world problem. They have the opportunity to explore the scenario on their own or in groups. Upon arrival in the classroom the next day, the scenario is and/or adapted to allow students to apply their problem-solving skills in a changing environment. An example of a take-home scenario and the adapted scenario is provided in Appendix B. Modeling and Inquiry Problems: To continue to develop competent and confident problem solvers, students are not given traditional examinations in the second core mathematics course. Instead, they are assessed with Modeling and Inquiry Problems (MIPs). Each MIP is designed as an in-class word problem scenario to engage the student for about 45 minutes in solving an applied problem with differentiable or integral calculus or differential equation methods. The student must effectively communicate the situation, the solution, and then discuss any follow-on scenarios, similar to the Day Two portion outlined above, all in a report format. As an example, a MIP may involve using differential calculus to solve a related rates problem. The Situation portion of the MIP involves transforming the words into a mathematical model that can be solved, by drawing a picture, defining variables with units, determining what information is pertinent, what assumptions should be made, and most importantly, what needs to be found. Finally, the Situation ends with the student stating which method (related rates in this case) will be used to solve the problem. The Solution portion involves writing the step-by-step details of the problem and determining what is needed to be found. Any asides or effects of assumptions can be written in as work progresses, and this portion ends with some numerical value, to include appropriate units. For example, the rate at which the oil slick approaches the shore is two meters per minute. The MIP itself has a second paragraph that asks follow-on questions. Suppose the volume of the oil slick is now doubled. How does that affect your rate? Or what is the exact rate the moment the slick reaches the shore? These follow-on questions prod the student to go back to the method and rework the problem with new information. The final portion of the MIP write-up is the Inquiry/Discussion section. The MIP write-up must be coherent and logical in its flow. Students must tie together the work and stress the solution back in the context of the problem. The Inquiry section is vital in student understanding of the problem. Students do not stop once they determine a numerical answer. They must continue and communicate how that answer relates to the problem, and more importantly, if the answer passes the common sense test. As of the time of this writing, the third core course has also incorporated MIPs, in addition to traditional exams. The probability and statistics course is considering the use of MIPs in future years. An example of a MIP (focusing on a differential equations problem) is provided in Appendix C. Electronic Portfolio: The notebook computer provides a tremendous resource for storage and organization of information. This resource avails the opportunity for students to transfer learning across time and between courses. In the novel, Harry Potter and the Goblet of Fire, Dumbledore refers to this capability as a pensieve. At these times, says Dumbledore, indicating the stone basin, I use the Pensieve. One simply siphons the excess thoughts from one's mind, pours them into a basin, and examines them at one's leisure. It becomes easier to spot patterns and links, you understand, when they are in this form. The portable notebook computer provides the resource for students to create their own pensieve. Creative exercises offer the student exposure to mathematical concepts with the ability to explore their properties, determining patterns and connections which facilitate the process of constructing understanding. Thorough understanding is feasible in either a controlled learning environment or at the student's leisure. Instructors will provide early guidance to incoming students on organizational strategies and file-naming protocol. Informal assessments of a student's electronic portfolio will provide information regarding the ability to understand relationships between mathematical concepts. Attitude and Perceptions Survey: One tool that will be used to assess if students are confident and competent problem solvers in a rapidly changing world is a longitudinal attitude and perceptions survey. Students will be given a series of sixteen common questions upon their arrival at the Academy and as part of a department survey at the conclusion of each of the four core math courses. A comparison of their confidence, attitudes, and perceptions will be made against those students who in prior years took the core math sequence without a laptop computer. The questions used in the survey are provided in Appendix D. Revisions Based on Initial Experience: The assessment began in the Fall of 2002 and will track students over a period of four semesters. A pilot study was run in the Spring of 2002 and the following lessons were learned. Student use of computers on exams: In the initial implementation of the two-day exam, students were allowed to use the computer on both days. Many students used their computers as electronic crib sheets. This problem may be further exacerbated when student computers in the classroom have access to a wireless network. The day one portion of the exam has been reengineered to assess skills and concepts that do not require technology of any sort. Electronic imprints of exams: Core math courses are all taught in the first four hours of the day. The students' dorms are all networked and word travels very quickly. It is currently against our policy to prohibit students from talking about exams with students who have not yet taken the exam. Enabling the use of laptops on exams creates a situation in which an imprint of the exam is on some cadet's computer following the first hour of classes. The day two portion of the exam, which is designed to test the students' ability to explore mathematics concepts using technology, will be given to all students at the same time, during a common lab period after lunch. Power: Computer reliability, particularly in the areas of power is an area of concern. Students will be issued a backup battery for their laptops. It is forecasted that an exchange facility will be available in the academic building for cadets who experience battery problems in the middle of a test. Findings Projects: Students overwhelmingly stated that the course projects helped to integrate the material that was taught in the course. The students' ability to incorporate the problem-solving process (i.e., modeling) increased with each successive project. Two-Day Exams: The two-day exams provided a thorough assessment of the course objectives. Course-end surveys revealed that the students felt that these two-day examinations were fair assessments of the concepts of the course. The technology portion (Day two) magnified the separation between those who demonstrated proficiency in solving problems using technology and those who didn't; there was no significant in-between group of students. Electronic Portfolios: Assessment of the electronic portfolios consisted of individual meetings of all students with their individual instructors. The results of these meetings brought out the point that students needed assistance in determining what material should be retained and how it should be kept. Students realized that material in this course would be needed in follow-on courses, so file naming would be key. Guidance was given to students to incorporate a file management system for later use, but no universal scheme was provided; in this manner, students could best determine their own system. Additional Findings: Unless assessed (tested), the students did not take the opportunity to learn how to effectively use the computer algebra system, Mathematica. Students embraced the use of the graphing calculator (TI-89) as the preferred problem-solving tool; they overwhelmingly reported that the laptop computer was a hindrance to their learning. Use of the Findings: Projects: We will continue to use group projects to assess knowledge; however, we will phase the submission of the projects to provide greater feedback and opportunity for growth in problem-solving and communication skills. Our plan is to have students submit the projects as each portion (Introduction, Facts and Assumptions, Analysis, and Recommendations and Conclusions) is completed. Two-Day Exams: Content on the Day-one (non-technology) portion needs to be more straightforward, emphasizing the concepts we want students to internalize and understand without needing technology. For the Day-two (technology) portion, questions should be asked to get students to outline and explain their thought processes, identifying possible errant methods. We need to keep in mind that problems with syntax should not lead to severe grade penalties. Additional Use of the Findings: We are going to introduce graded homework sets designed to demonstrate the advantage of the computer algebra system and the laptop as a problem-solving tool. Use of the graphing calculator will be limited to avoid confusion and overwhelming students with too many technology options. We plan to review course content and remove unessential material, thus providing more lessons for exploration and self-discovery. Next Steps and Recommendations: The assessment cycle will continue as we implement the changes outlined above into the first course. The majority of students will enter the second core course, Calculus I which will continue the use of laptops. Six Modeling and Inquiry Problems and one project will be used to assess the progress of our students' problem-solving capabilities. Acknowledgements We would like to thank the leaders of the Supporting Assessment in Undergraduate Mathematics (SAUM) for their guidance and support. In particular, our team leader, Bernie Madison, has been instrumental in keeping our efforts focused. Appendix A Sample Project The following Problem Solving Lab is an in-class exercise that allows the students to model and solve a system of interacting Discrete Dynamical Systems. Humanitarian Demining Background The country of Bosnia-Herzegovina has approximately 750,000 land mines that remain in the ground after their war ended in November 1995. The United Nations (UN) has decided to establish a Mine Action Center (MAC) to coordinate efforts to remove the mines. You are serving as a U.S. military liaison to the director of the UN-MAC. The UN-MAC will initially have 1000 trained humanitarian deminers working in country. Each of these trained personnel can remove 65 mines per week during normal operations. Unfortunately, there is a rebel force of about 8,000 soldiers that opposes the UN-MAC's efforts to support the legitimate government of Bosnia-Herzegovina. They conduct two major activities to oppose the UN-MAC: killing the deminers and emplacing more mines. They terrorize the deminers, killing 1 deminer for every 1,000 rebels each week. However, due to poor training and funding, each of these soldiers can only emplace an average of 5 additional mines per week. Meanwhile, the accidental destruction of the mines maim and kill some of both the deminers and the rebel forces. For every 1,000,000 mines, 1 deminer is permanently disabled or killed each week. The mines have the exact same quantitative impact on the rebel forces. Modeling and Analysis Your current goal is to determine the outcome of the UN-MAC's efforts, given the current resources and operational environment. 1. Model the strength of the demining organization, the rebels, and the number of mines in the ground. Ensure you define your variables and domain and state any initial conditions and assumptions. 2. Write the system of equations in matrix form A(n+1) = R * A(n). 3. If the interaction between the rebels and deminers as well as their respective efforts to affect the minefields remain constant, what happens during the first five years of operations? 4. Graphically display your results. Ensure you display your results for each of the three entities you model. 5. What is the equilibrium vectors, D or Ae, for this system? Is it realistic? 6. The General and Particular Solution for the new system of DDS's using eigenvalue and eigenvector decomposition. We add a little more realism to the scenario by creating interaction between the model's components. The following extension is the project that forces the students to adapt their model and prepare a written analysis. Humanitarian Demining BETTER ESTIMATE ON CASUALTIES DUE TO MINES We now have more accurate data on the casualties due to mines; it may (or may not) change part of your model. Better estimates show that for every 100,000 mines, 2 deminers are permanently disabled or killed each week. The mines have the exact same quantitative impact on the rebel forces. OTHER MINEFIELD LOSSES Other factors take their toll on the number of emplaced mines as well. Weather and terrain cause some of the mines to self-destruct, and civilians occasionally detonate mines. Approximately 1% of the mines are lost to these other factors each week. NATURAL ATTRITION OF FORCES Due to other medical problems, infighting, and desertion, the rebel forces lose 4% of their force from one week to the next. The deminers have a higher attrition due to morale problems; they lose 5% of their personnel from one week to the next. RECRUITING EFFORTS Both the rebel forces and the deminers recruit others to help. Each week, the rebels are able to recruit an additional 10 soldiers. Meanwhile, the UN-MAC is less successful. They only manage to recruit an additional 5 deminers each week. For the project, your report should address the following at a minimum: 1. Executive Summary in memo format that summarizes your research. 2. The purpose of the report. 3. Facts bearing on the problem. 4. Assumptions made in your model, as well as the viability of these assumptions. 5. An analysis detailing: a. The equilibrium vector, D or Ae, for the system and discuss its relevance. b. The General and Particular Solution for the new system of DDS's using eigenvalue and eigenvector decomposition. c. A description of what is happening to each of the entities being modeled during the first five (5) years of operations. 6. The director of the UN-MAC also wants your recommendation on the following: a. If the demining effort is going to be successful within the first five years, when will it succeed in eradicating all mines? If the demining effort is not going to be successful, determine the minimum number of weekly demining recruits needed to remove all mines within five years of operations. b. Describe at least one other strategy the UN-MAC can employ to improve its efforts to eradicate all of the mines. Quantify this strategy within a mathematical model and show the improvement (graphically, numerically, analytically, etc.). 7. Discussion of the results. a. Reflect on your assumptions and discuss what might happen if one or more of the assumptions were not valid. b. Integrate graphs and tables into your report, discuss them, and be sure to label them correctly. 8. Conclusion and Recommendations. Appendix B Example Day Two Exam Take Home Scenario While home on Spring Break, you explain to your parents the fundamental concepts that you have learned in your Discrete Dynamical Systems course. Following dinner one evening you provide them a quick 10 minute presentation on how you were able to use DDS to assist with car buying decisions. Due to your improved ability to communicate about mathematics, your parents immediately say, "Hey, I think you might be able to help us". They share with you the fact that they are negotiating the purchase of a 2003 Toyota Camry. The Wasko Federal Credit Union has agreed to finance a vehicle loan of up to $20,000 at a yearly interest rate of 6%. Adapted Scenario Recall from the read-ahead that your parents have asked for your assistance to help them determine the financing option for their purchase of a 2003 Toyota Camry. They have successfully negotiated a price of $18,000 for the car. In order to boost slumping car sales, the dealer has offered two financing options. In Option One the dealer has offered to finance the car at a rate of 1.9% interest for 48 months. Develop a model that predicts the car loan balance after n months, given the loan requires 48 equal payments of p dollars. Define all variables, state the domain, and any initial conditions. Determine the payment p, to the nearest cent, if your parents bought the Camry using the 1.9% loan financed by Toyota? Explain how you used technology to obtain this figure. Include the actual formulas used in EXCEL or the TI-89. In Option Two, the dealer has offered a $1500 rebate in lieu of the 1.9% financing. The finance rate for this option is 5.2% interest over 48 months. Develop a model that predicts the car loan balance after n months, given the loan requires 48 equal payments of q dollars. Define all variables and state the domain, and any initial conditions. Should your parents take the 1.9% financing or the $1500 rebate with a 5.2% financing rate? Explain how you used technology to assist in your decision. Provide clear mathematical backing to support your decision. Include the actual formulas used in EXCEL or the TI-89. Appendix C Example Modeling and Inquiry Problem Scenario: Your friend borrowed a 1 kg mass and two springs from the Physics Department. The springs have the following properties: Spring Spring Constant (N/m) A ( B (2 She wants to build an undamped harmonic oscillator to keep time like a watch. After displacing the mass an initial 5 cm and letting it go, she wants it to move through the position of the system's natural length (equilibrium) every second. Which spring will accomplish this? Justify your answer with appropriate differential equation(s), solution(s), and/or graph(s). Follow-up: What's fundamentally wrong with your friend's plan to build a spring-mass system to keep time? Explain your answer using terminology from the course. The format used for assessment is broken down as follows: Part I: Modeling the Situation 1. Draw a picture. 2. Define variables with appropriate units. 3. What are you trying to find? 4. What information is given? 5. What are your assumptions? (They must be valid and necessary.) 6. Describe the technique you will use to solve the model. Part II: Determining a solution 1. The solution follows logically from the equations. 2. The solution to the follow-up question follows logically. 3. No magical "leaps of faith". 4. The solutions are given in correct units. Part III: Inquiries and Discussion 1. Summarize your answer to the MIP in the context of the problem. 2. Discuss your solution to the follow-on question in context. 3. Perform a common sense check. 4. Explanations are communicated clearly. This format is given to the students. Appendix D Questions used in Attitude and Perceptions Survey The following questions were given to students and were rated on a Likert-Scale from 1 (strongly disagree) to 5 (strongly agree). 1. An understanding of mathematics is useful in my everyday life. 2. I believe that mathematics involves exploration and experimentation. 3. I believe that mathematics involves curiosity. 4. I can structure (model) problems mathematically. 5. I am confident in my ability to solve problems using mathematics. 6. Mathematics helps me to think logically. 7. There are many different ways to solve most mathematics problems. 8. I am confident in my ability to communicate mathematics orally. 9. I am confident in my ability to communicate mathematics in writing. 10. I am confident in my ability to transform a word problem into a mathematical expression. 11. I am confident in my ability to transform a mathematical expression into my own words. 12. I believe that mathematics is a language which can be used to describe the world around us. 13. Learning mathematics is in individual responsibility. 14. Mathematics is useful in my other courses. 15. I can use numerical and tabular displays of data to solve problems. 16. I can use graphs and their properties to solve problems. USMA Academic Board and Office of the Dean Staff (1998), Educating Army Leaders for the 21st Century, West Point, New York.
accessible introduction to the essential quantitative methods for making valuable business decisions Quantitative methods-research techniques used to analyze quantitative data-enable professionals to organize and understand numbers and, in turn, to make good decisions. Quantitative Methods: An Introduction for Business Management presents the application of quantitative mathematical modeling to decision making in a business management context and emphasizes not only the role of data in drawing conclusions, but also the pitfalls of undiscerning reliance of software packages that implement standard statistical procedures. With hands-on applications and explanations that are accessible to readers at various levels, the book successfully outlines the necessary tools to make smart and successful business decisions. Progressing from beginner to more advanced material at an easy-to-follow pace, the author utilizes motivating examples throughout to aid readers interested in decision making and also provides critical remarks, intuitive traps, and counterexamples when appropriate. The book begins with a discussion of motivations and foundations related to the topic, with introductory presentations of concepts from calculus to linear algebra. Next, the core ideas of quantitative methods are presented in chapters that explore introductory topics in probability, descriptive and inferential statistics, linear regression, and a discussion of time series that includes both classical topics and more challenging models. The author also discusses linear programming models and decision making under risk as well as less standard topics in the field such as game theory and Bayesian statistics. Finally, the book concludes with a focus on selected tools from multivariate statistics, including advanced regression models and data reduction methods such as principal component analysis, factor analysis, and cluster analysis. The book promotes the importance of an analytical approach, particularly when dealing with a complex system where multiple individuals are involved and have conflicting incentives. A related website features Microsoft Excel® workbooks and MATLAB® scripts to illustrate concepts as well as additional exercises with solutions. Quantitative Methods is an excellent book for courses on the topic at the graduate level. The book also serves as an authoritative reference and self-study guide for financial and business professionals, as well as readers looking to reinforce their analytical skills.
Support Material With new CD The CD has our new 'self-tutoring' software. For every worked example in this book, a student can listen to a teacher's voice explain each step in the worked example – 'click' anywhere in the worked example where you see the icon. Sample chapters for download About the book This is the first of two books to choose from for the Pre-Diploma Grade/Year: this book (MYP 5) aims to cover the Presumed Knowledge required for 'Mathematical Studies SL' at Diploma level; its companion (MYP 5 Plus) aims to cover the Presumed Knowledge required for either 'Mathematics SL' or 'Mathematics HL' at Diploma level. Pre-Diploma Studies SL (MYP 5) is our interpretation of the Presumed Knowledge required for the IB Diploma course 'Mathematical Studies'. It is not our intention to define the PK and we encourage teachers to use a variety of resources. The text is not endorsed by the International Baccalaureate Organization (IBO). We have developed the book independently of the IBO with advice from several experienced teachers of IB Mathematics. This book may also be used as a general textbook at about Grade 10 level in schools where students might be expected to embark on an 'Applications' type of Mathematics course in their final two years of high school. About the accompanying CD A feature of the accompanying CD is our new 'self-tutoring' software where a teacher's voice explains each step in every worked example in the book. Click anywhere on any worked example where you see the icon to activate the self-tutoring software. Other features include: Areas of interaction links to printable pages printable chapters for review and extension graphing and geometry software computer demonstrations and simulations statistics packages video clips For a complete list of all the active links on the MYP 5 CD, click here. The CD is ideal for independent study and revision. It also contains the full text of the book so that if students load it onto a home computer, they can keep the textbook at school and access the CD at home. Table of contents Graphics calculator instructions 9 A Basic calculations 10 B Basic functions 12 C Secondary function and alpha keys 15 D Memory 15 E Lists 18 F Statistical graphs 20 G Working with functions 21 1 Measurement and units 25 A Standard units 26 B Converting units 29 C Area units 32 D Volume units 33 E Capacity 34 F Mass 35 G Time 36 H 24-hour time 39 Review set 1A 40 Review set 1B 41 2 Number operations 43 A Operations with integers 44 B Operations with fractions 49 C Index notation 53 D Laws of indices 57 Review set 2A 59 Review set 2B 60 3 Sets, sequences and logic 61 A Set notation 62 B Important number sets 63 C Constructing sets (Interval notation) 66 D Venn diagrams 67 E Union and intersection 69 F Simple set problems 72 G Number sequences 73 H Introduction to logic 75 Review set 3A 79 Review set 3B 80 4 Rounding and estimation 81 A Rounding numbers 82 B Rounding money 83 C One figure approximations 86 D Rounding decimal numbers 88 E Using a calculator to round off 90 F Significant figure rounding 92 G Rounding time 94 Review set 4A 95 Review set 4B 96 5 The Rule of Pythagoras 97 A The Rule of Pythagoras (Review) 99 B Further problem solving 103 C Testing for right angles 106 D Navigation 107 Review set 5A 109 Review set 5B 110 6 Algebra 111 A Changing words into symbols 112 B Generalising arithmetic 113 C Converting into algebraic form 115 D Formula construction 116 E Number patterns and rules 118 F The value of an expression 120 Review set 6A 124 Review set 6B 125 7 Length and area 127 A Perimeter and length 128 B Area 133 C Surface area 139 D Problem solving 145 Review set 7A 147 Review set 7B 148 8 Decimals and percentage 149 A Decimal numbers 150 B Percentage 152 C Working with percentages 154 D Unitary method in percentage 156 E Percentage increase and decrease 157 F Scientific notation (Standard form) 159 Review set 8A 163 Review set 8B 164 9 Algebraic simplification and expansion 167 A Collecting like terms 168 B Product notation 170 C The distributive law 172 D The expansion of (a+b)(c+d) 177 E The expansion rules 179 F Perimeters and areas 183 Review set 9A 185 Review set 9B 185 10 Statistics 187 A Terminology for the study of statistics 189 B Quantitative (numerical) data 194 C Grouped discrete data 197 D Frequency histograms 199 E Measuring the centre 202 F Cumulative data 208 G Measuring the spread 211 H Box-and-whisker plots 213 I Statistics from technology 217 Review set 10A 218 Review set 10B 219 11 Equations 221 A Solution by inspection or trial and error 223 B Maintaining balance 224 C Formal solution of linear equations 226 D Equations with a repeated unknown 228 E Fractional equations 230 F Unknown in the denominator 231 G Forming equations 233 H Problem solving using equations 235 I Finding an unknown from a formula 237 J Formula rearrangement 240 Review set 11A 243 Review set 11B 244 12 Ratios and rates 245 A Ratio 246 B Simplifying ratios 247 C Equal ratios 249 D The unitary method for ratios 251 E Using ratios to divide quantities 252 F Scale diagrams 254 G Rates 255 H Rate graphs 259 I Travel graphs 261 Review set 12A 262 Review set 12B 264 13 Algebraic factorisation 265 A Common factors 266 B Factorising with common factors 268 C Factorising expressions with four terms 272 D Factorising quadratic trinomials 273 E Factorisation of ax2+bx+c (a ≠ 1) 275 F Difference of two squares factorising 278 Review set 13A 278 Review set 13B 279 14 Congruence and similarity 281 A Congruence of figures 282 B Congruent triangles 283 C Similarity 287 D Similar triangles 289 E Problem solving with similar triangles 292 Review set 14A 295 Review set 14B 296 15 Volume and capacity 297 A Volume 298 B Capacity 304 C Problem solving 307 Review set 15A 309 Review set 15B 310 16 Trigonometry 311 A Labelling sides of a right angled triangle 312 B Trigonometric ratios 315 C Using the sine ratio 316 D Using the cosine ratio 318 E Using the tangent ratio 319 F Problem solving with trigonometry 321 G Bearings 325 Review set 16A 326 Review set 16B 328 17 Coordinates and lines 329 A Plotting points on the Cartesian plane 330 B Distance between two points 332 C Midpoints 334 D Gradient (or slope) 335 E Linear relationships 338 F Linear functions 340 G Finding equations of straight lines 342 H Graphing lines 347 I Points on lines 348 J Other line forms 349 K Parallel and perpendicular lines 350 L Using gradients 353 Review set 17A 354 Review set 17B 355 18 Simultaneous linear equations 357 A The point of intersection of linear graphs 358 B Simultaneous equations 360 C Algebraic methods for solving simultaneous equations 362 D Problem solving 366 E Using a graphics calculator to solve simultaneous equations 368 Review set 18A 370 Review set 18B 370 19 Probability 371 A Probability by experiment 373 B Theoretical probability 374 C Expectation 376 D Probabilities from tabled data 378 E Representing combined events 379 F Probabilities from lists and diagrams 381 G Multiplying probabilities 384 H Using tree diagrams 385 I Sampling with and without replacement 388 J Mutually exclusive and non-mutually exclusive events 390 K Independent events 392 Review set 19A 393 Review set 19B 394 20 Functions, graphs and notation 395 A Graphical interpretation 396 B Interpreting line graphs 398 C Conversion graphs 400 D Time series data 402 E Step graphs 403 F Mappings 405 G Functions 406 H Function notation 409 Review set 20A 410 Review set 20B 412 21 Geometry 413 A Angle properties 417 B Triangles 422 C Isosceles triangles 424 D Angles of a quadrilateral 427 E Polygons 430 F The exterior angles of a polygon 433 G Nets of solids 434 Review set 21A 435 Review set 21B 437 22 Quadratic and other equations 439 A Quadratic equations 440 B Problem solving with quadratics 443 C Exponential equations 446 D Solving harder equations with technology 447 Review set 22A 449 Review set 22B 450 23 Finance 451 A Profit and loss 452 B Percentage profit and loss 454 C Discount 456 D Using a multiplier 459 E Chain percentage problems 461 F Simple interest 463 G Compound interest 467 H Foreign exchange 470 Review set 23A 472 Review set 23B 474 24 Quadratic functions 475 A Graphs of quadratic functions 476 B Axes intercepts 478 C The axis of symmetry 480 D Quadratic modelling 483 Review set 24A 485 Review set 24B 486 25 Transformation geometry (Chapter on CD only) 487 A Reflection 3 B Rotation 6 C Translation 9 D Enlargement 11 Review set 25A 14 Review set 25B 15 26 Sine and cosine rules (chapter on CD only) 488 Chapter on CD only A Obtuse angles 2 B Area of a triangle using sine 4 C The sine rule 5 D The cosine rule 10 E Problem solving with the sine and cosine rules 13 Review set 26A 14 Review set 26B 15 ANSWERS 489 INDEX 526 Using the interactive CD The interactive CD is ideal for independent study. Students can revisit concepts taught in class and undertake their own revision and practice. The CD also has the text of the book, allowing students to leave the textbook at school and keep the CD at home. By clicking on the relevant icon, a range of new interactive features can be accessed: SELF TUTOR is a new exciting feature of this book. The icon on each worked example denotes an active link on the CD. Simply 'click' on the (or anywhere in the example box) to access the worked example, with a teacher's voice explaining each step necessary to reach the answer. Play any line as often as you like. See how the basic processes come alive using movement and colour on the screen. Ideal for students who have missed lessons or need extra help. Areas of interaction The International Baccalaureate Middle Years Programme focuses teaching and learning through five areas of interaction: Approaches to learning Community and service Human ingenuity Environments Health and social education The Areas of Interaction are intended as a focus for developing connections between different subject areas in the curriculum and to promote an understanding of the interrelatedness of different branches of knowledge and the coherence of knowledge as a whole. In an effort to assist busy teachers, we offer the following printable pages of ideas for projects and investigations: Chapter 1: Measurement and units (p. 39) Errors in measurement Approaches to learning Chapter 4: Rounding and estimating (p. 88) Area and volume errors Approaches to learning Chapter 5: The Rule of Pythagoras (p. 99) Pythagoras Human ingenuity Chapter 7: Length and area (p. 137) Estimating areas Approaches to learning/Human ingenuity Chapter 10: Statistics (p. 217) How many trout are in the lake? Environments/Human ingenuity Chapter 12: Ratios and rates (p. 252) All that glitters in not gold Human ingenuity Chapter 14: Congruence and similarity (p. 294) How wide is the canal? Human ingenuity Chapter 16: Trigonometry (p. 326) How far away is the moon and how large is it? Human ingenuity Chapter 19: Probability (p. 392) What are your survival prospects? Environments/Health and social education Chapter 21: Geometry (p. 434) What region can be eaten by a goat? Approaches to learning/Environments Chapter 23: Finance (p. 472) How much can I save by not smoking? Envionments/Health and social education Chapter 24: Quadratic functions (p. 485) What is the strongest arch? Approaches to learning/Environments/Human ingenuity Foreword Pre-Diploma Studies SL (MYP 5) is an attempt to cover, in one volume, the Presumed Knowledge required for the IB Diploma course "Mathematical Studies SL" as well as including some extension topics. It may also be used as a general textbook at about Grade 10 level in classes where students might be expected to embark on an "Applications" type of Mathematics course in their final two years of high school. In terms of the IB Middle Years Programme (MYP), this book does not pretend to be a definitive course. In response to requests from teachers who use "Mathematics for the International Student" at Diploma level, we have endeavoured to interpret their requirements, as expressed to us, for a book that would prepare students for Mathematical Studies SL at Diploma level. We have developed the book independently of the International Baccalaureate Organization (IBO) in consultation with experienced teachers of IB Mathematics. The text is not endorsed by the IBO. It is not our intention that each chapter be worked through in full. Time constraints may not allow for this. Teachers must select exercises carefully, according to the abilities and prior knowledge of their students, to make the most efficient use of time and give as thorough coverage of content as possible. To avoid producing a book that would be too bulky for students, we have presented these chapters on the CD as printable pages: Chapter 25: Transformation geometry Chapter 26: Sine and cosine rules The above were selected because the content could be regarded as extension beyond what might be regarded as an essential prerequisite for Diploma. This package is language rich and technology rich. We hope the combination of textbook and interactive Student CD will foster the mathematical development of students in a stimulating way. Frequent use of the interactive features on the CD should nurture a much deeper understanding and appreciation of mathematical concepts. The inclusion of our new software (see p. 5) is intended to help students who have been absent from classes or who experience difficulty understanding the material. The book contains many problems from the basic to the advanced, to cater for a range of student abilities and interests. While some of the exercises are simply designed to build skills, every effort has been made to contextualise problems, so that students can see everyday uses and practical applications of the mathematics they are studying, and appreciate the universality of mathematics. We understand the emphasis that the IB MYP places on the five Areas of Interaction and in response there are links on the CD to printable pages which offer ideas for projects and investigations to help busy teachers (see p. 8). The interactive CD also allows immediate access to our own specially designed geometry packages, graphing packages and more. In this changing world of mathematics education, we believe that the contextual approach shown in this book, with the associated use of technology, will enhance the students' understanding, knowledge and appreciation of mathematics, and its universal application.
Teaching algebra Mathematics teachers can use the ideas in this collection when planning to integrate key processes and problem solving into the teaching of algebra. By adopting an integrated approach, teachers can enable pupils to experience mathematics as a coherent, worthwhile and engaging subject. As you plan, ensure that opportunities exist for connections to be made between algebra and the three other mathematical content strands of number, geometry and measures and statistics. The collection includes: ideas for developing pupils' key process skills while they learn about algebra materials to support and develop teachers' subject knowledge examples of teaching approaches that can be used to develop algebraic knowledge, skills and understanding teaching and learning resources that encourage more active ways of learning through the use of group work, discussion and open questioning. Attachments Improve your understanding of the key processes relating to algebra and learn how to develop pupils' problem-solving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problem-solving cycle of representing, analysing, interpreting and evaluating, and communicating and reflecting. These algebra-based lesson plans and activities, and links to useful computer programs, are part of 'Teaching algebra', which is designed to transform the teaching, training and learning of mathematics in secondary schools.
Good book for 2nd grader It shows student how to understand some fundamental math concepts step-by-step. However, if your kids have kinds of math talents, this will be a boring book for him/her. Share this review: -1point 0of1voted this as helpful. Review 2 for Singapore Math: Primary Math Textbook 2A US Edition Overall Rating: 5out of5 The very best! Date:September 14, 2011 Wiconi Location:La Crosse, Wisconisn Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 Skills are clearly outlined with simple and straightforward examples and the corresponding workbook assignments are easy to identify. If I had to criticize something, I'd say that sometimes there's too little practice, but there are other, additional practice books that round it out nicely. Share this review: 0points 0of0voted this as helpful. Review 3 for Singapore Math: Primary Math Textbook 2A US Edition Overall Rating: 5out of5 Date:August 16, 2011 414lat Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5
25.1.1.9.2 -- Students will make and justify predictions based on patterns. 25.1.1.9.3 -- Students will identify the characteristics of functions and relations including domain and range. 25.1.1.9.11 -- Students will apply the concepts of limits to sequences and asymptotic behavior of functions. 25.1.2.9.3 -- Students will recognize and explain the meaning of the slope and x- and y-intercepts as they relate to a context, graph, table or equation1 MATHEMATICS - ALG REASONING: PATTERNS & FUNCTS 25.1.2.9.7 -- Students will recognize that the slope of the tangent line to a curve represents the rate of change. 25.1.3.9.2 -- Students will determine equivalent representations of an algebraic equation or inequality to simplify and solve problems. 25.2 MATHEMATICS - NUMERICAL & PROP REASONING 25.2.2.9.1 -- Students will select and use appropriate methods for computing to solve problems in a variety of contexts. 25.2.2.9.3 -- Students will develop and use a variety of strategies to estimate values of formulas, functions and roots; to recognize the limitations of estimation; and to judge the implications of the results. 25.3 MATHEMATICS - GEOM & MEASUREMT 25.3.1.9.2 -- Students will use geometric properties to solve problems in two and three dimensions. 25.3.2.9.2 -- Students will describe how a change in measurement of one or more parts of a polygon or solid may affect its perimeter, area, surface area and volume and make generalizations for similar figures. 25.3.2.9.4 -- Students will visualize three-dimensional objects from different perspectives and analyze cross-sections, surface area, and volume. 25.3.2.9.5 -- Students will use Cartesian, navigational, polar, and spherical systems to represent, analyze, and solve geometric and measurement problems. 1) What are limits? How are they analyzed? Why are they important to the study of calculus? 2) What is a derivative? What techniques are used to find derivatives? How is a derivative related to a tangent line? How can the derivative concept be applied to real world problems? 3) What is integration, and how does it relate to differentiation? What are techniques used to find an anti-derivative, and what does the answer represent? How can the integral concept be applied to real world problems? This course focuses on the following concepts: Analysis of Graphs Limits of Functions Asymptotic and Unbounded Behavior Continuity as a Property of Functions Concept of Derivative Derivative at a Point Derivative as a Function Higher Order Derivatives Techniques of Differentiation Rolle's Theorem Mean Value Theorem L'Hopital's Rule Applications of Derivatives Interpretations and Properties of Definite Integrals Applications of Integrals Fundamental Theorem of Calculus Techniques of Antidifferentiation Applications of Antidifferentiation Numerical Approximations to Definite Integrals Students will develop the ability to: -- Determine the relationship between the geometric and analytic representations of functions and how to use calculus to explain and predict both local and global behavior, -- Explain the limiting process, -- Estimate limits from graphs or tables of data, -- Calculate limits using algebra, -- Explain asymptotes in terms of graphical behavior, -- Describe asymptotic behavior in terms of limits involving infinity, -- Explain what makes a function continuous or discontinuous, -- Relate continuity to limits, -- Present the derivative graphically and analytically, -- Relate the derivative to instantaneous rate of change, -- Use the definition of the derivative to find the derivative, -- Explain the relationship between differentiability and continuity, -- Find the derivative at a point, -- Identify where there are vertical tangents and removable discontinuities, -- Relate the graph of a function to the graph of its derivative, -- Translate verbal descriptions into equations involving derivatives and vice versa, -- Relate the graph of a function to its second derivative graph, -- Use Rolle's Theorem and Mean Value Theorem in problem solving -- Identify points of inflection, -- Analyze curves in terms of increasing and decreasing intervals and concavity, -- Find maximums and minimums through equation analysis, -- Model rates of change including related rate problems, -- Solve optimization poblems using differentiation -- Solve exponential growth and decay problems using differential equations -- Use a tangent line to approximate the graph of a function -- Use L'Hopital's Rule to find the limit of a quotient -- Differentiate implicitly, -- Differentiate power, exponential, logarithmic, trigonometric, and inverse trigonometric functions, --Differentiate sums, products, and quotients of functions, -- Differentiate using the chain rule, -- Compute Riemann sums using left, right, and midpoint evaluation points, -- Explain the definite integral as a limit of Riemann sums over equal subdivisions, -- Explain the definite integral as the change of the quantity over the interval, -- Explain the properties of definite integrals, -- Use the Fundamental Theorem of Calculus to represent and evaluate definite integrals, -- Use derivatives of basic functions to antidifferentiate, -- Use u-substitution of variables to antidifferentiate, -- Solve separable differential equations and use them in modeling, -- Use Riemann and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values. All students will: -- Have daily exposure to both mechanical, theoretical, and application-based problems, -- Utilize the graphing calculator extensively to supplement pencil and paper techniques. Students will be assessed by: 1. Daily homework assignments, which will acount for 10% of their final grade 2. Quizzes, approximately one every one to two weeks 3. Unit tests, comprised of 60-70% application, 30-40% computation 4. A final exam that will cover an entire semester's material, andwill account for 20% of the student's final grade Projects involving hands-on experience with differentation and integration (e.g.related rates, optimization, area, or volume) and research into areas not specifically covered by the curriculum (e.g. math history).
This book provides an easy introduction to the theory of differentiable manifolds. The authors then show how the theory can be used to develop, simply but rigorously, the theory of Lanrangian mechanics directly from Newton's laws. Unnecessary abstraction has been avoided to produce an account suitable for students in mathematics or physics who have taken courses in advanced calculus.
Math model The final reduced model of math skill acquisition confirms many common sense generalizations. The math skill model is the strongest of the five models, with 54% of the variance explained. There are many interesting conclusions that can be drawn from this model including, but not limited to the following: Math courses directly and substantially contribute to math skills. (OK, if this is the first of the model you've looked at, then this may sound trite. It is not. Other skills are not as easily attributed to specific course work.) Science courses also directly and substantially contribute to math skills. However, this may be a connection that is miss-specified in the model. It may be that this is spurious relationship because higher skills in math may contribute to taking more science courses. (This is mentioned as a warning that modeling is not a test of causation. The process of modeling imposes an order to the data that structural equations do not test for appropriateness.) As a tangent it is interesting to note that the path from study time to GPA is positive. Thus, controlling for work, and prior knowledge spending time does pay off with higher grades. The direction of the path from GPA to skill may also be questioned in that it may be possible to argue that higher skills should lead to a higher GPA. The absence of paths between the Non-native speaker of English and math skill confirms the observation that these individuals are not at a substantial disadvantage in math skill acquisition as contrasted with that of more language based skills such as critical thinking.
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Perhaps most important--this book effectively prepares readers for further courses in mathematics. Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications.The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of... Less Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this text like you. The book also provides calculator examples, including specific keystrokes that show you how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares you for further courses in mathematics. This book differs from others on Chaos Theory in that it focuses on its applications for understanding complex phenomena. The emphasis is on the interpretation of the equations rather than on the details of the mathematical derivations. The presentation is interdisciplinary in its approach to real-life problems: it integrates nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. An effort has been made to present the material ina reader-friendly manner, and examples are chosen from real life situations. 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In AS Further Mathematics three modules will be studied. One of them (FP1) builds on the mathematics covered in the AS Core modules. As well as continuing the work on coordinate geometry and calculus in introduces exciting new topics such as complex numbers and matrices. The other two units are both applied Mathematics modules. One of them is a second Decision Mathematics module, which extends the work begun in the AS Mathematics course. The other is Statistics 1. Students will be familiar with some of the topics in this module from the work covered in GCSE mathematics. In studying statistics we learn how to analyse and summarise numerical data in order to arrive at conclusions about it. You will extend the range of probability problems that you looked at in GCSE using the new mathematical techniques learnt in the core mathematics units. Many of the ideas in this part of the course have applications in a wide range of other fields, from assessing what your car insurance is going to cost to how likely it is that the Earth will be hit by a comet in the next few years. Many of the techniques are used in sciences and social sciences. Even if you are not going on to study or work in these fields, in today's society we are bombarded with information (or data) and the statistics units will give you useful tools for looking at this information critically and efficiently. For A2 Further Mathematics three more units are studied. Two more pure (core) mathematics modules are taken along with another Statistics module. Module FP2 introduces differential equations (which are of great importance on University Science and Engineering courses). In module FP3 the work on matrices and vectors is extended and hyperbolic functions are introduced for the first time – at last students find out what the 'hyp' key on the calculator is for! In the Statistics 2 unit the problem solving power of Statistics is greatly increased by the study of Hypothesis Tests (Significance testing). This has applications even in such areas as medical research on new drugs. What do I need to have to study the course? To study AS Further Mathematics you should have achieved a grade B or higher at GCSE mathematics and you should also be taking AS Mathematics. Where will it take me? The study of Further Mathematics at either AS or A2 level would give you a very strong mathematical background should you be going on to study Mathematics, Science or Engineering at a university, or if you were going into any of the career areas where mathematics is valued (see the list given under A level Mathematics). What else should I know? To do this course you should enjoy the challenges that mathematics presents, even if you don't always find it easy! Also it should be noted that Further Mathematics modules are interchangeable with those of A level Mathematics. This means that if you achieved a good mark on a Further Mathematics module you could if you wanted to exchange it for a poor result in one of the A level mathematics modules, thus giving you a better chance of getting a higher grade in your a level Mathematics. Even without this option of swapping module results, studying Further Mathematics will help you with your work on A level Mathematics, as the two subjects are linked in content and support each other.
1598639 Math: Algebra (Master Math Series) Get ready to master the principles and operations of algebra! Master Math: Algebra is a comprehensive reference guide that explains and clarifies algebraic principles in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced topics that will help prepare you for pre-calculus and calculus, the book helps clarify algebra using step-by-step procedures and solutions, along with examples and applications Master Math: Algebra will help you master everything from simple algebraic equations to polynomials and graphing
3.10.4 Operators Basic Mathematical Operators Note that the for \[Cross] is distinguished by being drawn slightly smaller than the for \[Times]. xy Times[x,y] multiplication xy Divide[x,y] division x Sqrt[x] square root xy Cross[x,y] vector cross product x PlusMinus[x] (no built-in meaning) xy PlusMinus[x,y] (no built-in meaning) x MinusPlus[x] (no built-in meaning) xy MinusPlus[x,y] (no built-in meaning) Interpretation of some operators in basic arithmetic and algebra. Operators in Calculus and Algebra form full name alias \[Del] del \[PartialD] pd \[DifferentialD] dd \[Sum] sum \[Product] prod form full name alias \[Integral] int \[ContourIntegral] cint \[DoubleContourIntegral] \[CounterClockwiseContourIntegral] cccint \[ClockwiseContourIntegral] ccint Operators used in calculus. form full name aliases  \[Conjugate] co, conj  \[Transpose] tr form full name alias  \[ConjugateTranspose] ct  \[HermitianConjugate] hc Operators for complex numbers and matrices. Logical and Other Connectives form full name aliases \[And] &&, and \[Or] ||, or ¬ \[Not] !, not \[Element] el \[ForAll] fa \[Exists] ex \[NotExists] !ex \[Xor] xor \[Nand] nand \[Nor] nor form full name alias \[Implies] => \[RoundImplies] \[Therefore] tf \[Because] \[RightTee] \[LeftTee] \[DoubleRightTee] \[DoubleLeftTee] \[SuchThat] st \[VerticalSeparator] | : \[Colon] : Operators used as logical connectives. The operators , and are interpreted as corresponding to the built-in functions And, Or and Not, and are equivalent to the keyboard operators &&, || and !. The operators , and correspond to the built-in functions Xor, Nand and Nor. Note that is a prefix operator. xy and xy are both taken to give the built-in function Implies[x,y]. xy gives the built-in function Element[x,y]. This is interpreted using the built-in functions And and Implies. In[1]:= 3 < 4 x > 5 y < 7 Out[1]= Mathematica supports most of the standard syntax used in mathematical logic. In Mathematica, however, the variables that appear in the quantifiers , and must appear as subscripts. If they appeared directly after the quantifier symbols then there could be a conflict with multiplication operations.
Intermediate Algebra - 4th edition Summary: Algebra can be like a foreign language. But one text delivers an interpretation you can fully understand. Building a conceptual foundation in the ''language of algebra,'' iNTERMEDIATE ALGEBRA, 4e provides an integrated learning process that helps you expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Packed with real-life applications of math, it blends instructional approaches that include vocabulary, practice, and well-defined pedagogy w...show moreith an emphasis on reasoning, modeling, communication, and technology skills. The authors' five-step problem-solving approach makes learning easy. More student-friendly than ever, the text offers a rich collection of student learning tools, including Enhanced WebAssign online learning system. With INTERMEDIATE ALGEBRA, 4e, algebra makes sense
For Students Contact us Mathematics At Norwich University, we believe mathematics is the universal tool. The skills you develop as an undergraduate can be applied to a host of disciplines, including biology, engineering, physics and beyond. Outside of the hard sciences, these tools can be applied to many fields: Computer scientists write algorithms every day that have a firm foundation in mathematics; psychology and criminal justice specialists regularly use statistical methods. Mathematics has a mesmerizing dual nature; it is a source of problems and beautiful results in its own right: Can we calculate the rate at which fluid is entering or leaving a region of the brain? How can "imaginary numbers" help us compute real quantities? Can we trust the conclusions of a poll in the newspaper? At Norwich, we offer flexibility, hands-on experience, world-class faculty and extracurricular opportunities matched by few small universities. Flexibility and experiential learning Norwich offers enough free electives for math students to earn a minor or a double major in another field of interest. Our students pursue secondary areas of study in a variety of areas, including engineering, biology, economics, computer science, information assurance, and teacher education and licensure Once students have mastered the foundations of mathematics, they work directly with faculty to design and carry out original research. Many have gone on to publish or present their findings at regional and national conferences. Experience across disciplines The department has developed a community of scholars with specialties in both pure and applied mathematics. Areas of expertise include wavelets, oceanography, ocean surveillance, graph theory, real analysis, Fourier analysis, actuarial science, statistical methods, extensions of trigonometry, abstract algebra and secondary education. Professors with graduate degrees in mathematics are responsible for teaching all courses.
First Year Physics First Year Physics I've always had problems with learning physics. It's not that I don't like it or can't do the calculations, but rather the memorization of thousands of equations that can easily derived. Of course, memorizing the important ones are necessary, so we don't have to constantly rederive them. So, my question is: What is a rigorous first year college (AP Physics C) leveled physics text WITH the use of calculus? With mechanics, electricity, magnetism, modern physics. I didn't know colleges required students to memorize formulas at that level. I don't recall having to memorize formulas at all until my junior year in physics degree. Maybe I was at a crappy college. Or are you talking about the AP physics C test? As for books, I can definitely say Kleppner's Mechanics is wonderful. Purcell is good for E&M if you have had some E&M before. I don't know of a dedicated modern physics text at that level with calculus. I'm just talking about my school's physics program. It's all memorization. We're given a bunch of fornulas and told to memorize them. I'd just like to have an actual book(s) that give the reader how the result is derived. Regardless, I will be taking the AP Physics C exam, so I would like to be prepared too. Thanks for those suggestions. If Kleppner is as good as you say, I'll definitely getting them! Isn't AP physics C purely mechanics? Either way, the standard calculus based physics textbook is Halliday and Resnick Fundamentals of Physics. Get yourself a previous edition like the 6th and that'll cover everything you need for the AP test and includes EM
Find an AntiochIt can be a very confusing class, but I hope to make it fun for your student. As their understanding grows they will find that it is a very systematic subject and following the procedures will get you to the right place. Reading is such an integral part of any learning experience that it is important to make sure that the comprehension is there. ...It also includes a review of major topics in Algebra II in the beginning chapters. My
Intermediate Algebra : Functions and AuthenticUnique in its approach, the Lehmann Algebra Series uses curve fitting to model compelling, authentic situations, while answering the perennial question "But what is this good for?" Lehmann begins with interesting data sets, and then uses the data to find models and derive equations that fit the scenario. This interactive approach to the data helps students connect concepts and motivates them to learn. The curve-fitting approach encourages students to understand functions graphically, numerically, and symbolically. Because of the multi-faceted u... MOREnderstanding that they gain, students are able to verbally describe the concepts related to functions. 11.2 Linear Inequalities in Two Variables; Systems of Linear Inequalities Key Points of Section 11.2 11.3 Performing Operations with Complex Numbers Key Points of Section 11.3 11.4 Pythagorean Theorem, Distance Formula, and Circles Key Points of Section 11.4 11.5 Ellipses and Hyperbolas Key Points of Section 11.5 11.6 Solving Nonlinear Systems of Equations Key Points of Section 11.6 A. Reviewing Prerequisite Material A.1 Plotting Points A.2 Identifying Types of Numbers A.3 Absolute Value A.4 Performing Operations with Real Numbers A.5 Exponents A.6 Order of Operations A.7 Constants, Variables, Expressions, and Equations A.8 Distributive Law A.9 Combining Like Terms A.10 Solving Linear Equations in One Variable A.11 Solving Equations in Two or More Variables A.12 Equivalent Expressions and Equivalent Equations B Using a TI-83 or TI-84 Graphing Calculator B.1 Turning a Graphing Calculator On or Off B.2 Making the Screen Lighter or Darker B.3 Entering an Equation B.4 Graphing an Equation B.5 Tracing a Curve without a Scattergram B.6 Zooming B.7 Setting the Window Format B.8 Plotting Points in a Scattergram B.9 Tracing a Scattergram B.10 Graphing Equations with a Scattergram B.11 Tracing a Curve with a Scattergram B.12 Turning a Plotter On or Off B.13 Creating a Table B.14 Creating a Table for Two Equations B.15 Using "Ask" in a Table B.16 Finding the Regression Curve for Some Data B.17 Plotting Points in Two Scattergrams B.18 Finding the Intersection Point(s) of Two Curves B.19 Finding the Minimum Point(s) or Maximum Point(s) of a Curve B.20 Storing a Value B.21 Finding Any x-Intercepts of a Curve B.22 Turning an Equation On or Off B.23 Finding Coordinates of Points B.24 Graphing Equations with Axes "Turned Off" B.25 Entering an Equation by Using Yn References B.26 Responding to Error Messages In the words of the author: Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful. My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country has made it all worthwhile! I'm proud to have played even a small role in raising peoples' respect and enthusiasm for mathematics. I have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024). In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, and of course, a large bank of skill problems. The curve-fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course.
Search Mathematical Communication: Mathematical Communication Welcome to MathDL Mathematical Communication Topic Teaching Tip(s): Courses in which students communicate about mathematics | Including writing in math classes | Including oral communication in math classes | General principles of mathematical communication This website is by and for educators whose students write, give presentations, or communicate informally about mathematics. Some educators would like students to learn to communicate as mathematicians; others would like students to talk or write about math in order to better learn math. This site supports both goals by offering pedagogical advice, materials, and links to helpful resources.
Using the Standards - Algebra, Grade 4 Book Description Communi... More Communication, Connections, and Representation. The vocabulary cards reinforce math terms and the correlation chart and icons on each page help to easily identify which content and process standards are being utilized. Includes a pretest, post test, and answer key. Reproducible.
About integralCALC Academy integralCALC Academy is an interactive learning tool designed specifically to guide students through the depth and complexity of a comprehensive calculus curriculum. Learn from Krista King Krista King, the creator of integralCALC, takes a new approach to calculus education. A calculus tutor with 10 years experience, Krista makes calculus accessible to everyone with her simple, step-by-step tutorials.
Eastchester Physics latter appear when students learn about averages and medians. Of course the biggest focus of elementary school math remains on addition, subtraction, multiplication, division, fractions, decimals, percents, and ratios. Differential equations are equations that involve an unknown function and one or more of its derivatives.
Perfect for either undergraduate mathematics or science history courses, this account presents a fresh and detailed reconstruction of the development of two mathematical fundamentals: numbers and infinity. One of the rare texts that offers a friendly and conversational tone, it avoids tedium and cont... read more Customers who bought this book also bought: Our Editors also recommend: A Source Book in Mathematics by David Eugene Smith The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhereElementary Number Theory: Second Edition by Underwood Dudley Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition. History of the Theory of Numbers by Leonard Eugene Dickson Save 10% when you buy all 3 volumes of this set. Includes "Volume I: Divisibility and Primality," "Volume II: Diophantine Analysis," and "Volume III: Quadratic and Higher Forms."Product Description: Perfect for either undergraduate mathematics or science history courses, this account presents a fresh and detailed reconstruction of the development of two mathematical fundamentals: numbers and infinity. One of the rare texts that offers a friendly and conversational tone, it avoids tedium and controversy while maintaining historical accuracy in defining its concepts' profound mathematical significance. The authors begin by discussing the representation of numbers, integers and types of numbers, and cubic equations. Additional topics include complex numbers, quaternions, and vectors; Greek notions of infinity; the 17th-century development of the calculus; the concept of functions; and transfinite numbers. The text concludes with an appendix on essay topics, a bibliography, and an index
Prealgebra - 4th edition Addressing individual learning styles,Tom Carsonpresents targeted learning strategies and a complete study system to guide students to success. Carson's Study System, presented in the ''To the Student'' section at the front of the text, adapts to the way each student learns, and targeted learning strategies are presented throughout the book to guide students to success. Tom speaks to students in everyday language and walks them through the concepts, ex...show moreplaining not only how to do the math, but also where the concepts come from and why they work142.83 +$3.99 s/h Good recycleabook CENTERVILLE, OH used book - free tracking number with every order. book may have some writing or highlighting, or used book stickers on front or back
Subject: Mathematics (9 - 12) Title: Now, where did THAT come from? Deriving the Quadratic Formula Description: Generally, teachers expect students to memorize the quadratic formula and to know that you use it after exhausting all other means of solving a quadratic equation, i.e. as a last resort. This technology-based lesson is designed to assist students with deriving the formula on their own. Students must first be familiar with complex numbers and the process of "completing the square." This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Expand your ability to visualize and reason about geometric ideas. In this section About This Course Course Name/Code: Advanced Geometry, ASMA 335 Catalog Description: Examines concepts of Euclidean and non-Euclidean Geometries. Students will use the computer program Geometer's Sketchpad to discover the logic of Geometry. The Students will make predictions and Sketchpad to confirm or refute their predictions. Credits/Hours: 3 Instructors and Texts Instructors Who Teach This Course:Mrs. Marsha Jackson Required Text(s)Students must purchase and possess the required text(s) by the first day of class. Order early: Geometer's Sketchpad, Keycurriculum This is the program you will use for all your assignments except for forums and tests. You may order the student unlimited version, the 1 year rental version, or the instructors version. The instructors version allows you to save and make tools within the program ISBN-10: 978-1-60440-095-3 Kimberling, Clark. Geometry in Action. Key College Publishing, 2003 ISBN-13: 978-1-93191-402-4 Course Workload Preview The following preview of anticipated course workload is subject to instructor change. Expand your ability to visualize and reason about geometric ideas. Use inductive reasoning to make conjectures and use deductive reasoning. Learn and understand Euclid¹s postulates and mathematical system. Use Analytical Geometry as a tool to solve geometric problems, and develop a realization of the relationships between Algebra and Geometry.
September 2007 This is the second installment of a new feature in Plus : the teacher package. Every issue contains a package bringing together all Plus articles about a particular subject from the UK National Curriculum. Whether you're a student studying the subject, or a teacher teaching it, all relevant Plus articles are available to you at a glance. A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling . Mathematical models are used not only in the natural sciences (such as physics , biology , earth science , meteorology ) and engineering disciplines (e.g. computer science , artificial intelligence ), but also in the social sciences (such as economics , psychology , sociology and political science ); physicists , engineers , statisticians , operations research analysts and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour. Mathematical models can take many forms, including but not limited to dynamical systems , statistical models , differential equations , or game theoretic models . The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is subtracted from the desired value to create the error signal, which is amplified by the controller. A signal-flow graph (SFG) is a special type of block diagram [ 1 ] —and directed graph —consisting of nodes and branches. Its nodes are the variables of a set of linear algebraic relations. An SFG can only represent multiplications and additions. Little Green Book Nearly everything that occurs in the universe can be considered a part of some system, and that certainly includes human behavior and, potentially, human attitudes as well. But this does not mean that systems theory, and thus graph algebra, is appropriate for use in all situations. There are many competing approaches to the study of social and political phenomena, and systems theory using graph algebra is only one such approach. From the publisher's description of the book: Graph Algebra: Mathematical Modeling with a Systems Approach introduces a new modeling tool to students and researchers in the social sciences. Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modeling that offers social scientists a variety of tools that are both sophisticated and easily applied. Key Features: (This is the first in a series on the use of Graph Algebraic models for Social Science.) Linear Difference models are a hugely important first step in learning Graph Algebraic modeling. That said, linear difference equations are a completely independent thing from Graph Algebra. (This is the second of a series of ongoing posts on using Graph Algebra in the Social Sciences.) First-order linear difference equations are powerful, yet simple modeling tools. They can provide access to useful substantive insights to real-world phenomena. They can have powerful predictive ability when used appropriately. Additionally, they may be classified in any number of ways in accordance with the parameters by which they are defined. And though they are not immune to any of a host of issues, a thoughtful approach to their application can always yield meaningful information, if not for discussion then for further refinement of the model. Data must be selected carefully. The predictive usefulness of the model is grossly diminished if outliers taint the available data. Figure 1, for instance, shows the Defense spending (as a fraction of the national budget) between 1948 and 1968. Note how the trend curve (as defined by our linear difference model from the last post : see appendix for a fuller description) is a very poor predictor. Whatever is going on here isn't a first-order process. This is sort-of related to my sidelined study of graph algebra. I was thinking about data I could apply a first-order linear difference model to, and the stock market came to mind. After all, despite some black swan sized shocks, what better predicts a day's closing than the previous day's closing? So, I hunted down the data and graphed exactly that:
Algebra Concepts is a tool for introducing many of the difficult concepts that are necessary for success in higher level math courses. This program includes a special feature, the Algebra Tool Kit, wh... More: lessons, discussions, ratings, reviews,... Algebra Concepts is an interactive learning system designed to provide instruction in mathematics at the 7th grade enrichment through adult levels. The instructional goals for Algebra Concepts include
7 Steps To Solving Any Word Problem 1) This class is designed to briefly present my 7 step method for solving word problems. 2) This class will use introductory examples from the following disciplines: Math, Chemistry, Statistics, and Physics. However, a student does not have to be in these disciplines to benefit from this class. 3) After this class the student should be able utilize the seven strategies to solve standard word problems found in most mathematics, statistics, and sciences courses. 4) The student or individual who is experiencing challenges with solving word problems will benefit from this class
Mathland The Expert Version 9780521468022 ISBN: 0521468027 Publisher: Cambridge University Press Summary: Mathland is a problem-solving adventure. Pupils are given a problem to solve by an inhabitant of Mathland - the answer determines the next page they go to. The problems come from all areas of maths (apart from statistics) and are intended to stimulate both analytical and empirical approaches.
Introductory Algebra and Trigonometry With Applications 9780471368762 ISBN: 0471368768 Pub Date: 1999 Publisher: Wiley & Sons, Incorporated, John Summary: Introductory Algebra and Trignometry with Applications by Paul Calter and Carol Felsinger Rogers This textbook introduces all the important topics for a student who needs preparatory, review, or remedial work in mathematics. Adapted from Calter's Technical Mathematics, it uses an intuitive approach and gives information in very smallsegments. Careful page layout and numerous illustrations make the material easy to fo...llow. Features of Introductory Algebra and Trigonometry with Applications include the following.Graphing Calculator: The graphing calculator has been fully integrated throughout the text, and calculator problems are given in the exercises. The book does not present any particular calculator. Keystrokes are shown in the early chapters, with verbal descriptions given thereafter.Common Error Boxes: Many of the mistakes that students repeatedly make have been identified and are presented in the text as Common Error boxes.Summary of Facts and Formulas: All important formulas are boxed and numbered in the text and are listed in the Summary of Facts and Formulas at the end of the book.Examples: The many fully worked examples are specifically chosen to help the student do the exercises.Exercises: A large number of exercises is given after each section, graded by difficulty and grouped by type.Chapter Review Exercises: Every chapter ends with a set of Chapter Review Exercises. In contrast to the exercises, most are scrambled as to type and difficulty, requiring the student to be able to identify type.Applications: Applications drawn from many fields are included in the examples, the exercises, and the Chapter Review.Writing Questions: The "writingacrossthecurriculum" movement urges writing in every course as an aid to learning. In response, this text provides a writing question at the end of every chapter.Team Projects: As an aid to collaborative learning, a team project is included at the end of most chapters.Thorough Support Material: Among valuable components found at the end of the book are the Summary of Facts and Formulas, Conversion Factors, Answers to Selected Exercises, Index to Applications, Index to Writing Questions, Index to Team Projects, and General Index.For the Instructor: An Instructor's Manual contains workedout solutions to every evennumbered problem in the text. This most valuable supplement is available to any instructor using the textbook.For more information on this book or any of Prentice Hall's other new technology titles, visit our Web site at
Mathematical Methods in Science George Pólya "Mathematics, taught and learned appropriately, improves the mind and implants good habits of thought." This tenet underlies all of Professor Pólya's works on teaching and problem-solving. The distinctive feature of Mathematical Methods in Science is the stress on the history of certain elementary chapters of science; these can be a source of enjoyment and deeper understanding of mathematics even for beginners who have little, or perhaps no, knowledge of physics. Print on demand (POD) books are not returnable because they are printed at your request. Damaged books will, of course, be replaced (customer support information will be on your receipt).
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0495558885 9780495558880 111178230X 9781111782306 features and patient explanation to give students a book that preserves the integrity of mathematics, yet does not discourage them with material that is confusing or too rigorous. Long respected for its ability to help students quickly master difficult problems, this book also helps them develop the skills they'll need in future courses and in everyday life. This new edition has the mathematical precision instructors have come to expect, and by bringing in new co-author, Jeff Hughes, the authors have focused on making the text more modern to better illustrate to students the importance of math in their world. «Show less... Show more» Rent College Algebra 10th Edition today, or search our site for other Frisk
The chapter begins with an exploratory problem designed to introduce the concept of linear programming with an objective function to maximize profits by optimizing a company's product mix. The problem context involves assembling two types of computers with different profit margins and labor requirements. Students are led through a graphical solution to a two decision variable problem involving two constraints.The second product mix example involves a detailed totally worked-out example involving the manufacture of skateboards. Students are shown step-by-step how to formulate and solve this two decision variable problem graphically. A third decision variable is then added to motivate the need for EXCEL to solve larger problems. Students are taught how to use SOLVER as standard add-in to EXCEL to solve linear programming problems. This section also discusses how to use the linear programming output to perform sensitivity analysis. There is also an optional section that discusses the Simplex algorithm that is the basis for computational solution of LP problems. The third example is a sports shoe company and focuses on interpretation of results. The text presents a fully formulated and solved problem involving six decision variables and six constraints. The emphasis is on interpreting the output from SOLVER and answering a variety of what-if questions. Binary programming is a form of integer programming. The word "binary" refers to the decision variables. When decision variables are binary, this means that they can only take on the values of either 0 or 1. That might seem overly restrictive, but there are many situations that can easily be modeled using binary decision variables. For example, the following decisions could be modeled with binary decision variables: - Should we located a new automobile dealership at this location? - Should I choose to apply to this college? - Should I invest in this stock? We all make decisions everyday in our lives that involve uncertainty. Decision Trees is the first chapter in the Probabilistic material and introduces the concept of making decisions under uncertainty and risk. The decision tree methodology involves accounting for every possible decision and random event. The best alternative generally maximizes the expected value of profit or minimized the expected cost, however, other non-financial variables are also considered. Expected value does not also capture an individual's risk tolerance. This risk aversion is the foundation for the insurance industry. The final problem in this chapter follows Jee Min a high school junior as he tries to determine how much collision insurance he needs.
Elementary Surveying : An Introduction to Geomatics freshman and sophomore courses in surveying.This is a highly readable best-selling text that presents basic concepts and practical material in each of the areas fundamental to modern surveying (geomatics) practice. Its depth and breadth are ideal for self-study. The Eleventh Edition includes more than 400 figures and illustrations to help clarify discussions, and numerous worked example problems to illustrate computational procedures.
Overview Because of the fact that we will be extending so many areas, this is a perfect opportunity to solidify everything that you have done before, or to get little tastes of things you haven't seen before. We'll start with some basics of real numbers, then earn the basics of what and why complex numbers are. After that we will see interplay with geometry, linear algebra, and then head toward topics from calculus: series, differentiation and end with the richest area of all - integration. Grading Half of your grade will come from problem sets. Another tenth will come from a final project and each of two midterm exams. The final fifth will come from the final exam. Problem Sets After we finish each chapter problem sets will be collected. They will be returned with a letter grade based on the following factors: number of exercises correctly completed, difficulty of exercises correctly completed, number of exercises completed by classmates, and some subjective determination on my part as to what seems appropriate. Each problem set will be scaled using a linear function of the number of exercises completed (problems correctly completed by only one student will earn two points). Submitting no problem set by the day it is due will earn a score of zero. I strongly recommend consulting with me as you work on these problem sets. I also recommend working together on them, however I want to carefully emphasise that each must write up their own well-written solutions. A good rule for this is it is encouraged to speak to each other about the problem, but you should not read each other's solutions. A violation of this policy will result in a zero for the entire assignment and reporting to the Dean of Students for a violation of academic integrity. Final Project Your final project will constitute writing up a detailed explanation (filling in the gaps) of a topic in the text that we will omit (or another topic selected by you and approved by me) , and a completion of a problem set (graded as above) from the exercises in that section. Exams The exams will consist of a few straightforward problems designed to emphasise a personal understanding of the basicsAcademic Dishonesty While working on homework with one another is encouraged, all write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. The Student Academic Dishonesty Policy and Procedures of observance of religious holidays the opportunity to make up missed work. You are responsible for notifying me by September 11 of plans to observe a holiday. Schedule (loose and subject to variations) August 29 Introduction 31 Chapter 1 (1-3, 4, 5) September 2 7 9 12 14 Chapter 2 (1, 2, 6, 7, 8) 16 PS1 due 19 21 23 26 28 Chapter 3 (1, 2, 4, 5) PS2 due 30 October 3 exam (Chapter 1-2) 5 7 12 14 17 Chatper 4 (2.3, 2.4, 2.5, 1, 2) 19 21 PS3 due 24 26 28 31 November 2 Chapter 5 (1, 2, 3, 4, half of 5) PS4 due 4 7 exam (Chapter 3-4) 9 11 14 16 18 Chapter 6 (1, 2, 4, 5) 21 PS5 due 28 30 December 2 5 Chapter 7 (1, 2) 7 9 12 Review, PS6-7 due, Final Project due Monday, December 19 12N - 3p Final Exam (half 5-7, half 1-4) Learning Outcomes Upon successful completion of this course, a student will be able to Express complex numbers in the important equivalent forms - rectangular, polar and exponential.
Saxon Advanced Mathematics, Second Edition, is the third book in a three-book high school series designed to prepare students for calculus, chemistry and physics. It is intended to follow Saxon Algebra 1 and 2 and to come before calculus and physics. (Saxon does not have a separate geometry course. Geometry is spread throughout Algebra 1, Algebra 2, and Advanced Math.) The homeschool packet includes the student text, test forms, and test and problem set answers. An optional solutions manual is also available, and I strongly recommend that you purchase it. Advanced Mathematics begins with a review of algebra and geometry. Topics covered in Advanced Mathematics include trigonometry, logarithms, analytic geometry, and advanced algebra concepts. Advanced Mathematics has 125 lessons and 31 tests. The following information is contained in the preface: "For high school students who complete Algebra 2 in the ninth grade, this is a three-semester book. These students can begin their study of calculus the second semester of their junior year. The book is a two-semester book only for the top third of high school students, i.e., those who complete Algebra 2 in the ninth grade and are highly motivated. They can begin their study of calculus in the fall of their junior year. For high school students who complete Algebra 2 in the tenth grade, this is a four-semester book. This will assure high College Board scores and will prepare these students for calculus as college freshmen." After a thorough examination of Advanced Math, I think that many students will need three semesters to finish the course because numerous lessons will take two or more hours to complete. A student who finishes Saxon Advanced Mathematics with a test average of 85% or better will be well prepared for college level mathematics. Saxon math is taught in a spiral cycle. Students are introduced to small bits of a concept at a time. They are not required to master the material at the first introduction. Initially I loved the approach; it let us move on when we did not get it. At the higher levels this will be a problem for some students who need to see the whole picture at once. For this reason it is essential that students DO NOT skip problems in the problem set. Learn from my mistake and don't do only odd or even problems to shorten a lesson. Use two days if it takes too long! In an interview with Art Robinson, John Saxon Jr. said this about his math program, "Understanding more often than not follows doing rather than precedes it. If I'm going to teach you how to drive, I don't lecture you on the theory of the internal-combustion engine. I get you behind the wheel of the car and drive around the block." It is this presupposition that is the driving force behind each Saxon Math course. I like the Advanced Mathematics curriculum. The lessons are presented so that most students will understand them with minimal outside help (this does mean Mom or Dad needs to go over the lessons too). Saxon math programs were originally written for the public school math teacher who presented the lesson to the student before the student read the book and were not intended to be do-it-yourself programs. Saxon recommends that parents do not allow the student to do independent study. I realize that many parents cannot teach at this level of math, so a tutor may be a necessity to help your student succeed. A cheaper alternative than a tutor is a DIVE CD by Dr. David Shormann. These CDs ARE NOT produced by Saxon, nor are they necessary for every student. But most students will benefit from Dr. Shormann's explanations on the later lessons, and I believe many students will benefit from his explanation for each lesson. Another thing I like about Saxon Advanced Mathematics is that it is still available in the homeschool kit as a hardback book. The lower level paperback textbooks look and feel cheap. My hardback Saxon books have withstood the use of three to four students and still look good. While this is not a reason to buy or avoid Saxon, it is something every family with multiple students must consider. In my ten years using Saxon Math, I have never regretted using what many consider the Cadillac of math programs. Saxon Math is the winner of many awards, including Cathy Duffy's Top 100 Picks of 2005 and The Old Schoolhouse 2005 Award of Excellence in Education as the best math company (again!). A few years ago there were few competitors in the high school math market for Saxon, and now there are many who claim to be better. I can't say if they are or not, but I do know that they do not have Saxon's track record. After comparing Saxon Advanced Mathematics to VideoText, Singapore New Elementary Math, Math-U-See, Jacobs, and Teaching Textbooks, I find it to be a first-rate program that will prepare most students for success in college (see the table below on areas I looked at). Does this mean that all students will succeed with Saxon? NO! Not all students need the repetition or drill, and some students need to hear or see the lesson in a video format (the reason I love the DIVE CDs). Saxon Saxon with DIVE CD VideoText Geometry Jacobs Geometry Teaching Textbooks Aleks Math*U*See Geometry, Trigonometry, Pre-Calculus covered in the course Yes Yes Yes Only Geometry Only Algebra 1 and 2 or Geometry Either geometry or Trig & Pre-Calculus (1) Either Geometry or Pre-Calculus Teaches via video/audio and textbook No Yes Yes No Yes Online only Yes Consumable No No No No No Yes Student Text is Requires daily parent instruction Yes Minimal Minimal Yes No No Yes Math help via email or phone Yes Yes Yes No Yes Yes Yes Cost Approx. $75 Approx. $100 $660 Approx. $100 $185 $20 per month $80-$90 Need a computer? No Yes No No Yes Yes No Need a DVD player? No No Yes No No No Yes Hours per day (based on company and student reports) 1 1/2 to 2 1 1/2 to 2 1 1 to 1 1/2 1 1 Less than 1 Complete solutions included Yes Yes Yes Answer key only Yes Yes Answer key only Average number of problems per lesson 30 30 15 30 Unable to get this information Varies by student desire Varies (1) Aleks is an online subscription math program. Your student moves at their own pace and can finish one course in less than a year and move on at their own pace to the next course. This said, would I change anything about Advance Mathematics? Yes. There are too many problems per lesson. I call this drill and kill. From past experience I know you should not skip problems, so I won't even suggest doing only odd or even problems; but the amount of time for a student to complete the required work is excessive. Even a highly motivated student will find that he rarely finishes in less than 1 1/2 hours. A student who does not like math will most likely be turned off by the amount of work involved in each lesson. What I did to counter the amount of time involved was to take two days to do most lessons. I know this takes a lot longer than most families want to spend on advanced math, but after an hour of math my brain begins to make careless mistakes and my frustration level goes way up when working difficult problems. Some lessons could be done in that hour window. I suspect this is why Saxon advises Advanced Mathematics as a three-semester course. Will I recommend Advanced Mathematics to most of my homeschooling friends? YES! It is affordable, fairly easy to use, covers the standard advanced math scope and sequence, is a tried and true program used by thousands of students for more than 20 years, and was written by a man who had a passion for teaching math to his students. I think that most unschoolers will dislike Saxon Advanced Mathematics, so I would not recommend it to them. It is well suited to a Classical Educator and the visual student. If you did not use Saxon for Algebra 1 and 2, you will need a geometry program before beginning Advanced Mathematics because Saxon covers geometry in Algebra 1 and 2. "Saxon works" is my motto.
MAS 099. Presentation Attendance. The aim of this course is exposure to mathematics beyond the classroom curriculum. The course requirement is attendance at a minimum of six formal presentations on mathematical topics given at conferences, colloquia or symposia at a minimum of two separate events (that is, a conference or event). Presentations should have a title and abstract and may be given by faculty or students; poster sessions do not count. 0 credits. MAS 100. Concepts of Mathematics. A study of a variety of topics in mathematics. Many introduce modern mathematics and most do not appear in the secondary school curriculum. Fulfills general education requirement: Liberal Studies Area 4 (Mathematics). 3 credits. MAS 102. Pre-Calculus. A review of precalculus mathematics including algebra and trigonometry. A student may not receive credit for this course after completing MAS 111, 161, or the equivalent. 3 credits. MAS 170. Elementary Statistics. An introduction to elementary descriptive and inferential statistics with emphasis on conceptual understanding. Fulfills general education requirement: Liberal Studies Area 4 (Mathematics). A student may not receive credit for MAS 170 after completing MAS 372. A student may not receive credit for both MAS 170 and MAS 270. 3 credits. MAS 270. Intermediate Statistics. A more advanced version of MAS 170 intended for students with some calculus background. Fulfills general education requirement: Liberal Studies Area 4 (Mathematics). A student may not receive credit for both MAS 170 and MAS 270
This is the revised and expanded second edition of the hugely popular Numerical Recipes: the Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner, it proceeds from mathematical and theoretical considerations to actual, practical computer routines. With over 100 new routines, bringing the total to well over 300, plus upgraded versions of many of the original routines, this new edition is the most practical, comprehensive handbook of scientific computing available today. The book retains the informal, easy-to-read style that made the first edition so popular, even while introducing some more advanced topics. It is an ideal textbook for scientists and engineers, and an indispensable reference for anyone who works in scientific computing. The second edition is availabLe in FORTRAN, the quintessential language for numerical calculations, and in the increasingly popular C language.
This one year course covers the National Curriculum levels 5 - 8 in Number, Algebra, Shape & Space and Statistics, and GCSE grades A - G through both Foundation and Higher Tiers can be awarded. A text ... This one year course covers the National Curriculum levels 5 - 8 in Number, Algebra, Shape & Space and Statistics, and GCSE grades A - G through both Foundation and Higher Tiers can be awarded. A text book particularly designed for the course is used and this is supported with worksheets and practice exam questions. →
ABSTRACT ALGEBRA: A STUDY GUIDE FOR BEGINNERS John A. Beachy Department of Mathematical Sciences Northern Illinois University This study guide is intended for students who are working through the Third Edition of our textbook Abstract Algebra (co-authored with William D. Blair). The guide is focused on solved problems, and covers Chapters One through Six.` My goal throughout is to help students learn how to do proofs, as well as computations. The study guide now contains well over 500 problems, and more than half have detailed solutions, while about a quarter have either an answer or a hint. That number of problems can be quite overwhelming, so if you don't have enough time to try all of the solved problems, you can at least read the solutions. The file is in pdf format, suitable for viewing with Adobe Acrobat Reader. It can also be downloaded and printed, with only minor restrictions (see page ii of the study guide). Please send me email if you find typos or mathematical mistakes.
The first half part of the course is based on assigned chapters of Mathematics of the Discrete Fourier Transform (DFT), also by the same author, which contains a more detailed development of the mathematics of signals and spectra in the discrete-time case. The course presents fundamental elements of digital audio signal processing, such as sinusoids, spectra, the Discrete Fourier Transform (DFT), digital filters, z transforms, transfer-function analysis, and basic Fourier analysis in the discrete-time case. Due to the nature of CCRMA research, this book will emphasize audio and music applications, although the material on the subject of digital filters itself is not specific to audio or music. Intended Audience: The only prerequisite to the course is a good high-school level algebra and trigonometry, some calculus, and prior exposure to complex numbers.
Linear Algebra With Application - 6th edition ISBN13:978-0763757533 ISBN10: 0763757535 This edition has also been released as: ISBN13: 978-0763746315 ISBN10: 0763746312 Summary: Linear Algebra with Applications, Sixth Edition is designed for the introductory course in linear algebra typically offered at the sophomore level.� The new Sixth Edition is reorganized and arranged into three natural parts that improve the flow of the material.� Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of Rn, matrices, linear transformations, determinants, and eigenvectors.� Part 2 builds on this material, introducing the conc...show moreept of a general vector space, discussing properties of bases, developing the rank/nullity theorem and introducing spaces of matrices and functions.� Part 3 completes the course with many of the important ideas and methods of Numerical Linear Algebra, such as ill-conditioning, pivoting, and LU decomposition.� New applications include discussions of linear algebra in the operation of the search engine Google and in the global structure of the worldwide air transportation network.� Clear, Concise, Comprehensive - Linear Algebra with Applications, Sixth Edition continues to educate and enlighten students, leading to a mastery of the mathematics and an understanding of how to apply
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Why Minus Times Minus Is Plus : The Very Basic Mathematics of Real and Complex Numbers [Back cover text:]MATHEMATICS / ALGEBRAThis book is written for a very broad audience. There are no particular prerequisites for reading this book. We hope students of High Schools, Colleges, and Universities, as well as hobby mathematicians, will like and benefit from this book. The book is rigorous and self-contained. All results are proved (or the proofs are optional exercises) and stated as theorems. Important points are covered by examples and optional exercises. Additionally there are also two sections called "More optional exercises (with answers)."Modern technology uses complex numbers for just about everything. Actually, there is no way one can formulate quantum mechanics without resorting to complex numbers.Leonard Euler (1707-1786) considered it natural to introduce students to complex numbers much earlier than we do today. Even in his elementary algebra textbook he uses complex numbers throughout the book.Nils K. Oeijord is a science writer and a former assistant professor of mathematics at Tromsoe College, Norway. He is the author of The Very Basics of Tensors, and several other books in English and Norwegian. Nils K. Oeijord is the discoverer of the general geneticcatastrophe (GGC). show more show less Edition: 2010 Publisher: iUniverse, Incorporated Binding: Trade Paper Pages: 136 Size: 7.50" wide x 9 Minus Times Minus Is Plus : The Very Basic Mathematics of Real and Complex Numbers - 9781450240635 at TextbooksRus.com.
Basic Mathematical Tools for Imaging and Visualization Administrative Info (For CSE students, this lecture is credited with 2 ECTS with the restriction that it has to be taken together with either the Computer Aided Medical Procedures lecture or the 3D Computer Vision lecture.) The lecture is given in English. Time & Location Monday, 14:00 - 15:30 Thursday, 16:00 - 17:30 The lessons will take place in room MI 03.013.010. The programming exercises will take place in room MI 03.013.008. Site Content Announcements Final Results are available. The grades have been sent by e-mail to the people who gave their e-mail address at the final exam. Otherwise, you can get your grade at the MyTUM portal. New regulation for CSE students: For CSE students, the lecture is credited with 2 ECTS with the restriction that it has to be taken together with either the Computer Aided Medical Procedures (CAMP) lecture or the 3D Computer Vision (3DCV) lecture. Overview In order to solve real-world problems in applied engineering areas of computer science, knowledge of basic mathematical tools is essential. The aim of this lecture is to provide a basic mathematical toolbox for selected topics of Imaging and Visualization. We The lecture will have three main parts: Basics, Tools and Practise. In the first part, we will give a reminder of linear algebra, analysis, geometry, probability and statistics basics. We go on by presenting the use of these basic concepts in methods such as parameter estimation and optimization. And finally, the students will have the opportunity to gain a deep understanding and hands-on experience of the methods by implementing them and/or using them to solve real-world problems during the exercises. In order to solve real-world problems in applied engineering areas of computer science, knowledge of basic mathematical tools is essential. The aim of this lecture is to provide a basic mathematical toolbox for selected topics of Imaging and Visualization. We The lecture will have three main parts: Basics, Tools and Practise. In the first part, we will give a reminder of linear algebra, analysis, geometry, probability and statistics basics. We go on by presenting the use of these basic concepts in methods such as parameter estimation and optimization. And finally, the students will have the opportunity to gain a deep understanding and hands-on experience of the methods by implementing them and/or using them to solve real-world problems during the exercises.
books.google.com - An experienced math instructor and teacher trainer helps to make PreCalculus easy—even for students who feel intimidated by more advanced math topics. His orderly, step-by-step approach begins with concepts and skills typically introduced in a first-year high-school-level algebra course then progresses... The Easy Way
From the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests, these programs strengthen student understanding and provide the tools students need to succeed.
The essential skills needed for learning mathematics at Robert College are based on an understanding of operations and a sound knowledge of basic facts. These basic facts were taught in an elementary school mathematics program which included concepts from Arithmetic, Algebra and Geometry. The Robert College mathematics department encourages students to: Ø concentrate on the problem-solving process rather than on the calculations associated with the problem. Ø perform those tedious computations that arise when working with real datain a problem-solving situation with a graphing calculator. Ø gain access to mathematics beyond the students' level of computational skill. Ø discover and reinforce mathematical concepts including estimation, computation,approximation, and properties. Ø experiment with mathematical ideas and discover patterns. Ø go from concrete experience to abstract mathematical ideas. Conceptual understanding of Lise mathematics is developed in three different modes:
Scheme of Work Overview Year 7 Overview Year Aims To develop confidence in using algebra to describe situations and aid problem solving; To understand the meaning of expressions, for example seeing the difference between 2x and x²; To work confidently with negative numbers; To see the connection between the area of squares, square numbers, the meaning of x² and Pythagoras' theorem; To find unknowns from given information, e.g. finding the missing lengths in shapes & solids, or solving purely abstract equations;
COURSE GOALS: 1. To further develop your skill as a mathematical problem solver. 2. To explore pedagogical issues regarding the use of problem-solving in the elementary/middle school classroom. 3. To explore problem resources, particularly using the Internet. COURSE OBJECTIVES: 1. To solve problems of various types: (a) Puzzles and Logic Problems (b) Numerical Problems (c) Problems about Infinity (d) Geometry Problems (e) Probability and Statistics 2. To explore some of the literature regarding the use of problem-solving in the classroom: (a) NCTM Documents (b) Articles on the Internet 3. Problem Resources: (a) Student reports of Internet searches (b) Other literature COURSE PROCEDURES: This course is aimed at education majors who have a particular interest in mathematics. The Wisconsin DPI requires Elementary Education Mathematics minors to take a course in Problem Solving, so in that sense we are satisfying a specific requirement, but let us hope there is also worthwhile work to be done here. There is one line from the summary of the text which I find appropriate here: "We hope the life lessons of this book expand your repertoire of strategies and modes of thought." In one sense, it matters little what specific types of problems we solve – it is the practice which is important. Problem of the Week: In a course about problem solving it is extremely important that you solve problems! We will be solving problems on a daily basis throughout the semester, but I am going to specifically require you to turn in you solution to a specific problem each week. It is necessary that I get a chance to see your approach to various problems and to give you feedback on your work. Homework: It is always important that you do the assigned homework, but in particular when the focus is on solving problems it is absolutely necessary that you try problems so that we will have something to discuss in class. Exams: There will be two exams during the course, one after chapters 1 & 2, and the second after chapters 3, 4 & 7. These will include some take-home problems, but will also include an in-class exam – I want to see what you can do on your own, with you feet held to the fire, as it were. The final exam will be cumulative 25
The Math Place What is The Math Place? The Math Place is a free tutoring service specifically designed for students enrolled in Learning Center mathematics courses (ULC 147 & 148), and MTH 115, 121, 122, 141, 142 Students should feel free to drop in any time the Math Place is open for help with their math work. How Can Students Use It? Students can bring problems or questions to the Math Place and the tutors will provide assistance. Students should rememberto bring their textbook and notes in order to aid the tutors in explaining the relevant material.
The Geometry and Geometry Honors summer assignment is designed to prepare students for the new school year. The assignment should be completed during late July, early August and should be turned in during the first week of school. Those students that turn in the assignment on the first day of school will receive a bonus. The Algebra II and Algebra II Honors summer assignment is designed to prepare students for the new school year. The assignment covers all the prerequisite skills taught in Algebra I as well as some applications taught in Geometry. The assignment should be completed during late July, early August and should be turned in during the first week of school. Those students that turn in the assignment on the first day of school will receive a bonus. This packet is to be handed in to your Precalculus teacher on the first day of the school year. All work must be shown in the packet OR on separate paper attached to the packet. Completion of this packet will be counted toward your first quarter grade.
REA'S Problem Solvers®: The Complete Step-by-Step Solution Guides Useful, practical, and informative, these study aids are excellent review books and textbook companions, making them perfect for high school, undergraduate and graduate studies, and beyond. Ideal for helping students with the toughest subjects Simplify study and learning tasks Spend study time wisely and constructively, avoiding frustrating hours of trying to work out answers Superb index helps locate specific problems quickly and easily Educators consider Problem Solvers® the most effective and reliable study aids; students describe them as "fantastic"—the best review books available. To learn more about REA and browse other Test Preps and Study Guides, click here. Products in Problem Solvers Algebra & Trigonometry Problem SolverŪ by Jerry R. Shipman REA's Algebra and Trigonometry Problem Solver Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient source f... read more Our Price:$25.95 Calculus Problem SolverŪ byChemistry Problem SolverŪ by A. Lamont Tyler,Geometry Problem SolverŪ by The Editors of REA, Ernest Woodward REA's Plane and Solid (Space) Geometry Problem Solver Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient ... read more Our Price:$25.95 Linear Algebra Problem SolverŪ by The Editors of REA The Problem Solvers are an exceptional series of books that are thorough, unusually well-organized, and structured in such a way that they can be used with any text. No other series of study and solution guides has come close to the Problem Solvers in usefulness, quality, and... read more Our Price:$30.95 Physics Problem SolverŪ by The Editors of REA, Joseph Molitoris REA's Physics Problem Solver Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient source from one of the mo... read more
Numbers: Rational and Irrational Ivan Niven A fine job of presenting the materials at a level which is attainable for the intended reading public. — The Mathematics Teacher A superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, you will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of algebra and analysis. Professor Niven's book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics.
In modern society there are very few areas of knowledge and practice in which mathematics does not play a part. These increasingly include areas which affect our quality of life, such as health-related studies and environmental issues, as well as the contributions mathematics continues to make in commerce, science and technology. Consequently, as a subject of study, mathematics possesses great diversity, and it offers a wide range of opportunities to identify areas, which relate to your own interests, concerns, and aspirations. TEACHING AND ASSESSMENT Small tutorial groups in which problems are considered and individual work discussed, form an integral part of each course along with larger formal lectures, 'surgeries' and problem classes are held to deal with specific individual difficulties. To encourage an increasingly independent approach to learning, courses are delivered through lectures only, and individual tutorial assistance is given by lectures on the student's initiative. Current methods of student assessment include conventional written examinations, a variety of coursework assignments and, in some cases, a combination of these methods. SKILLS AND CAREERS As well as the specific expertise and skills relating to course content, students will continually be developing the kind of logical and analytical thinking which characterizes the discipline of mathematics. It is this quality which marks out the mathematics graduate, not only as a skilled practical scientist, but also as a potential strategic planner and decision maker in any complex situation. Therefore there are many opportunities open to well qualified mathematicians in industry, commerce, finance, education and research. About three-quarters of our graduates enter careers associated with computing, statistics, operational research, actuarial and insurance fields, accountancy and teaching.
This book is a guided tour of geometry, from Euclid through to algebraic geometry. It shows how mathematicians use a variety of techniques to tackle problems, and it links geometry to other branches of mathematics. It is a teaching text, with a large number of exercises woven into the exposition. Topics covered include: ruler and compass r s1tructions, transformations, triangle and circle theorems, classification of isometries and groups of isometries in dimensions 2 and 3, Platonic solids, conics, similarities, affine, projective and Mobius transformations, non-Euclidean geometry, projective geometry, the beginnings of algebraic geometry. Stock Availability: This title will be ordered from the publisher and usually ships by us within 15 days. Allow a few extra days for delivery
Pasadena, TX PhysicsMatlab is mainly used in colleges to teach algorithms including Runge Kutta for integrating differential equations. I use Mathematica mostly in heavily formulated physics problems such as molecular spins and fractional calculus where equations are concise but complex. It is always advisable for a student to be conversant in both languages
Used by more than half a million students each year!Actual Regents Examsdevelop your subject knowledge and test-taking skills and show you where you need more study.Answers to All Questionsprovide the guidance you need to learn on your ow Sequential Math III Power Pack Editorial review When students and teachers purchase Let's Review: Sequential Math III in combination with Barron's Regents Exams and Answers: Sequential Math III (the "Red Book"), they save $2.95 over the cost of both books purchased separately. Algebra I (Cliffs Study Solver) Editorial review Basic Math and Pre-Algebra (Cliffs Study Solver) Editorial review Algebra II (CliffsStudySolver) Editorial review CliffsQuickReviewMath Word Problems (Cliffs Quick Review (Paperback)) Editorial review Karen Anglin, a mathematics instructor at Blinn College in Brenham, Texas, since 1990, regularly presents workshops to teachers on best practices for teaching math word problems. She holds an MS in Statistics and a BS in Mathematics from Algebra for Dummies Editorial review Reviewed by Aaron S. Rutledge, (Kalamazoo, MI) this is definitely the book for you. If you want to learn algebra, look elsewhere. Reviewed by "nguido", (Tampa, FL USA) ry for Dummies a 5, since Geometry has always been my favorite subject and Algebra has not... Reviewed by a reader I had gone back to college and had not been in an algebra class in about 16 years...this book helped me tremendously! The book is very easy to follow and I found it short and to the point. Reviewed by a reader, (Prince Frederick, MD United States) Even though there are a lot of pages in this book, the number of concepts covered is extremely small. This would be better titled "Pre-Algebra for Dummies"; in fact, you'd be hard pressed to pass an Algebra I class with the mate
Summary: Lecture 1. Real numbers. Constants, variables, and mathematical modeling. In this lecture we briefly sketch the structure of Real numbers and recall properties of addition and subtraction. Then we will discuss the notions of variables and constants and basic ideas of mathematical modeling. 1.1. Real Numbers We will try to sketch the structure of numbers by ranging them by the increase of com- plexity. Most people agree that the simplest are the counting numbers. 1, 2, 3, 4, 5 The next step is the whole numbers (a "zero" element was added) 0, 1, 2, 3, 4, 5 to make whole numbers even more useful the addition and multiplication were invented. The addition and the multiplication were invented in such a way to satisfy commutative properties a + b = b + a a · b = b · a, and the associative properties a + (b + c) = (a + b) + c a · (b · c) = (a · b) · c,
Outcomes: Upon successful completion of this course, students will: • Understand and apply concepts in Algebra including slope , solving equations for unknowns , graphing equalities and inequalities, and quadratic equations . • Students will gain comprehension of the relationship of independent and dependent variables, equations with multiple solutions, and recognize graphical representations of these relationships. • Solve and graph equalities and inequalities, demonstrate the concept of slope and realize its application to everyday problems. • Distinguish between expressions and graphs of functions and non-functions. Use a graphing calculator to graph expressions . Student Evaluation and Grading Policies: As this course is designed to prepare the student for Algebra 1 in the fall , assessments will be utilized to gauge student comprehension and progress. A narrative evaluation will be prepared at the end of the course regarding student progress. Target Group: Algebra 1 students (generally 9th grade) Special education students required to obtain a Regents Diploma as per their IEP. "15:1" Meaning a ratio fifteen students to one teacher. Curriculum is modified to student needs. Procedure: Students will make a notebook entry containing the necessary math language for unit . (See Teacher note sheet) Review location of keys on TI-82 needed for finding square root. Reference the teacher chart located on front board. Write five visual prompts on the board to find their square root. Use Glencoe algebra 1, Resource Master, 2-7, page 111, numbers 1,3,4,7,12,6 Introduce finding square root on the TI-84 using the overhead projector connected to TI View Screen™ Panel Turn the calculator "on" Press 2nd "x "squared to get the radical symbol , followed by" 64". Press "enter". The answer which is calculated should be "8" Use the same procedure for the next four examples. Have a different student volunteer act as the teacher during this guided practice. Monitor to ensure proper procedure while using the calculator/overhead. Turning the TI-82 ON: Find the "on" button on the bottom left hand column. Press the "On " button". If the last thing on the calculator is displayed, press the "Clear" button. This will place the cursor at the upper left hand of the screen to begin. Finding "Square Root" on the TI-82: Press "blue second" , then x squared The radical symbol will appear on the screen. Press the keys for the number for which square root are needed. Press "enter". The square root will be shown on the screen. Session two Prior knowledge: Student will use the proper steps to find the square root of a given number on the TI-82 calculator. Student can classify the set of numbers to which a real number belongs. (Rational or irrational) Student can apply place values to the ten thousandths place. Objectives: Student will determine if square root of a number is rational or irrational. Student will display proficiency using TI-82 to find the square root of a number. Put five square root problems on the overhead, project on the screen using Resource Master 2-7 Sills Practice page 113 Students are to independently find the square root of each to the nearest hundredth. Ask a student volunteer to choose a problem to answer at the overhead. Query the class,"Is the answer correct?" The student volunteer will confirm his/her answer using the calculator attached to the overhead. If the student has answered the problem correctly, ask if the answer is rational or irrational. Note next to answer. Repeat for all example problems. For independent practice, use a separate sheet of paper, include proper heading. Students will use Algebra 1 page 107, complete, numbers 38, 41, 43, 46, 49 Collect independent practice to be used as participation grade. Notebook Entry Rational numbers are numbers that can be expressed in the form of a fraction. (a/b) A and B are integers. B cannot equal 0. (B≠0) Example #1 ¼, -¾, ½ A rational number can be expressed as a decimal that terminates or repeats indefinitely. Example # 2 .231 Or .3333 An irrational number can not be repeating or terminating numbers. Example # 3 Session Three Prior Knowledge: Student will use the proper steps to find the square root of a given number on a TI-82. Objectives: Student will independently find the square roots for given Numbers using a TI -82. Student will independently classify the square root of the number as rational or irrational. Procedure: Student will complete independently as per directions Algebra 1 page 825; lesson 2-7, numbers 1 through 8. Time limit is to be 15 minutes. After completing worksheets, students will determine as Group the values from least to greatest. Group will confirm answers using the TI-84 Plus Silver Connected to the overhead using the TI View Screen™Panel. Collect independent practice work to be used as a participation grade Session Four Prior Knowledge: Student is able to classify a number as rational or irrational. Student will recognize and use symbols of inequalities Objectives: Determine the setoff numbers to which each real number belongs. Ordering real numbers from the least to the greatest. Procedure: Teacher will review using the overhead projector, Use examples from page 107 Algebra text, numbers 32 through 49. Students are to classify as rational and irrational numbers. Solicit responses from students to come and write their answer for the class on the overhead. Teacher will give a series of fractions and square roots to Examine as a group from Resource Master Skill sheet 2-7 page 113, numbers 7 through 12. Using the overhead calculator, student volunteer will find the square root and/or the decimal equivalent of a fraction. The student group will determine the answer as rational or irrational. Teacher will demonstrate to students ordering a given set of real numbers from least to greatest. Using above page Students are given independent practice to order real numbers. Collect as a participation grade. Session five Previous knowledge: Student can round a decimal to the nearest hundredth. Student can find the square root of a number using a TI-82 Objective: Given a set of numbers, student will find the square root of the number and round to the nearest hundredth. Procedure: Teacher will use the overhead projector when demonstrating place value for decimals to the thousandths place. Teacher created prompts. Time permitting, review as a group using the overhead calculator to find square root of the given. Nearest hundredth will then be determined
Secondary Mathematics I [2011] The fundamental purpose of Mathematics I is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Mathematics 1 uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Critical Area 1: By the end of eighth grade students have had a variety of experiences working with expressions and creating equations. In this first unit, students continue this work by using quantities to model and analyze situations, to interpret expressions, and by creating equations to describe situations. Critical Area 2: In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions. Critical Area 3: By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation and to justify the process used in solving a system of equations. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. Students explore systems of equations and inequalities, and they find and interpret their solutions. All of this work is grounded on understanding quantities and on relationships between them. Critical Area 4: This unit builds upon prior students' prior experiences with data, providing students with more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit. Critical Area 5: In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work. Critical Area 6: Building on their work with the Pythagorean Theorem in eighth grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines.Core Standards of the Course Unit 1: Relationships Between Quantities By the end of eighth grade students have had a variety of experiences working with expressions and creating equations. In this first unit, students continue this work by using quantities to model and analyze situations, to interpret expressions, and by creating equations to describe situations. (ViewSecondary One Textbook.) Reason quantitatively and use units to solve problems. Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions. N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Interpret the structure of expressions. Limit to linear expressions and to exponential expressions with integer exponents. A.SSE.1 Interpret expressions that represent a quantity in terms of its context.*Create equations that describe numbers or relationships. Limit A.CED.1 and A.CED.2 to linear and exponential equations, and, in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs. Limit A.CED.3 to linear equations and inequalities. Limit A.CED.4 to formulas with a linear focus. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. SKILLS TO MAINTAIN Reinforce understanding of the properties of integer exponents. The initial experience with exponential expressions, equations, and functions involves integer exponents and builds on this understanding. Unit 2: Linear and Exponential Relationships In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions. Represent and solve equations and inequalities graphically. For A.REI.10 focus on linear and exponential equations and be able to adapt and apply that learning to other types of equations in future courses. For A.REI.11, focus on cases where f(x) and g(x) are linear or exponential. A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A.REI.11 Explain A.REI.12 Graph Understand the concept of a function and use function notation. Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples from linear and exponential functions. In F.IF.3, draw connection to F.BF.2, which requires students to write arithmetic and geometric sequences. Emphasize arithmetic and geometric sequences as examples of linear and exponential functions. F.IF.1 .IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Interpret functions that arise in applications in terms of a context. For F.IF.4 and 5, focus on linear and exponential functions. For F.IF.6, focus on linear functions and intervals for exponential functions whose domain is a subset of the integers. Mathematics II and III will address other function types. N.RN.1 and N.RN.2 will need to be referenced here before discussing exponential models with continuous domains. F.IF.4 For.* F.IF.5 Rel.* F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* Analyze functions using different representations. For F.IF.7a, 7e, and 9 focus on linear and exponential functions. Include comparisons of two functions presented algebraically. For example, compare the growth of two linear functions, or two exponential functions such as y=3n and y=100·2n. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* Graph linear and quadratic functions and show intercepts, maxima, and minima. F.IF.9 Compare Build a function that models a relationship between two quantities. Limit F.BF.1a, 1b, and 2 to linear and exponential functions. In F.BF.2 connect arithmetic sequences to linear functions and geometric sequences to exponential functions. F.BF.1 Write a function that describes a relationship between two quantities.*F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* Build new functions from existing functions. Focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y-intercept. While applying other transformations to a linear graph is appropriate at this level, it may be difficult for students to identify or distinguish between the effects of the other transformations included in this standard. F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f Construct and compare linear, quadratic, and exponential models and solve problems. For F.LE.3, limit to comparisons between exponential and linear models. F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Interpret expressions for functions in terms of the situation they model. Limit exponential functions to those of the form f(x) = bx + k . F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. Unit 3: Reasoning with Equations By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation and to justify the process used in solving a system of equations. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. Students explore systems of equations and inequalities, and they find and interpret their solutions. All of this work is grounded on understanding quantities and on relationships between them. Understand solving equations as a process of reasoning and explain the reasoning. Students should focus on and master A.REI.1 for linear equations and be able to extend and apply their reasoning to other types of equations in future courses. Students will solve exponential equations with logarithms in Mathematics III. A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve equations and inequalities in one variable. Extend earlier work with solving linear equations to solving linear inequalities in one variable and to solving literal equations that are linear in the variable being solved for. Include simple exponential equations that rely only on application of the laws of exponents, such as 5x = 125 or 2x = 1/16. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Solve systems of equations. Build on student experiences graphing and solving systems of linear equations from middle school to focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution); connect to GPE.5, which requires students to prove the slope criteria for parallel lines. A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Unit 4: Descriptive Statistics Experience with descriptive statistics began as early as Grade 6. Students were expected to display numerical data and summarize it using measures of center and variability. By the end of middle school they were creating scatterplots and recognizing linear trends in data. This unit builds upon that prior experience, providing students with more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit. Summarize, represent, and interpret data on a single count or measurement variable. In grades 6 - 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points. S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Summarize, represent, and interpret data on two categorical and quantitative variables. Students take a more sophisticated look at using a linear function to model the relationship between two numerical variables. In addition to fitting a line to data, students assess how well the model fits by analyzing residuals. S.ID.6b should be focused on situations for which linear models are appropriate. S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. Informally assess the fit of a function by plotting and analyzing residuals. Fit a linear function for scatter plots that suggest a linear association. Interpret linear models Build7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. S.ID.9 Distinguish between correlation and causation. Unit 5: Congruence, Proof, and Constructions In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work. Experiment with transformations in the plane. Build on student experience with rigid motions from earlier grades. Point out the basis of rigid motions in geometric concepts, e.g., translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle. G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another Understand congruence in terms of rigid motions. Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems. G.CO.6 Use Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Make geometric constructions. Build on prior student experience with simple constructions. Emphasize the ability to formalize and defend how these constructions result in the desired objects. Some of these constructions are closely related to previous standards and can be introduced in conjunction with them. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Unit 6: Connecting Algebra and Geometry Through Coordinates Building on their work with the Pythagorean Theorem in 8th grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines. Use coordinates to prove simple geometric theorems algebraically. This unit has a close connection with Unit 5. Reasoning with triangles in this unit is limited to right triangles; e.g., derive the equation for a line through two points using similar right triangles. Relate work on parallel lines in G.GPE.5 to work on A.REI.5 in Mathematics I involving systems of equations having no solution or infinitely many solutions. G.GPE.7 provides practice with the distance formula and its connection with the Pythagorean theorem. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). G.GPE.5 Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *
TechTools Resource Kits for TI Graphing Calculators The TechTools Resource Kit for the TI Graphing Calculators can be used in a variety of instructional settings. The How-To Cards are a quick reference tool for students and teachers. The projects can be easily integrated into middle school and high school math and science curriculum. Kit Includes: 60 math and science projects 100 step-by-step How-To Cards Management & References book featuring guides for the applications and probes
By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins, detailed algorithm descriptions, and many figures and worked examples. The book will appeal, in whole or in part, to mathematicians, computer scientists, and engineers.
TI-Nspire Video Tutorials Sign up for a Webinar to get an Overview of Media4Math+! Need help with the TI-Nspire? Media4Math has a library of YouTube videos for the TI-Nspire, the TI-Nspire CAS, the TI-Nspire Touchpad, the TI-Nspire CX, and the TI-Nspire CX CAS. Learn to use the TI-Nspire with these byte-size segments. These video-based (which are embedded videos from our YouTube channel) tutorials can be used in multiple ways: Learn the basic keystrokes for using Nspire Explore key concepts in Algebra and Geometry using the Nspire Whether you use the Nspire Clickpad or the newer Touchpad and CX models, we have a video-based tutorial from our YouTube channel. Many of our video tutorials come with worksheets that show all the relevant keystrokes shown in the video. (Subscribe to our YouTube channel.) Are you looking to take your knowledge of the Nspire CX to the next level? Check out our DOWNLOADABLE VIDEO SERIES FOR ALGEBRA. Click here. TI-Nspire CX Tutorial: Slope Between Two Points TI-Nspire CX Tutorial: Slope for Randomly Generated Points In this Nspire CX tutorial, randomly create two points in a Spreadsheet Window. Graph them as a scatterplot. Connect the two points using the Line tool, then measure the slope of the line. Creating new random coordinates will yield a new line with a new slope. TI-Nspire CX Tutorial: Slope Formula 2 In this TI-Nspire CX tutorial, the Graph Window and Spreadsheet Window are used to calculate the slope of the line between two points. The coordinates of the points are linked to variables, which are then used in the Spreadsheet Window to calculate the slope. The split-screen, dynamically linked windows allow you to manipulate the points, while getting an updated value for the slope.
Costs Course Cost: $300.00 Materials Cost: None Total Cost: $300 Special Notes State Course Code 02052Algebra I provides a curriculum focused on the mastery of critical skills and the understanding of key algebraic concepts, preparing students to recognize and work with these concepts. Through a "Discovery-Confirmation-Practice" based exploration of algebraic concepts, students are challenged to work toward a mastery of computational skills, to deepen their conceptual understanding of key ideas and solution strategies, and to extend their knowledge in a variety of problem-solving applications. Course topics include an Introductory Algebra review; measurement; an introduction to functions; problem solving with functions; graphing; linear equations and systems of linear equations; polynomials and factoring; and data analysis and probability. Within each Algebra I Algebra I assessments include a computer-scored test and a scaffolded, teacher-scored test. To assist students for whom language presents a barrier to learning or who are not reading at grade level, Algebra I includes audio resources in both Spanish and English. The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards.
Intermediate Algebra 2nd Edition+ MathZone Allocation 1st Edition 9780073312682 ISBN: 0073312681 Edition: 2 Pub Date: 2006 Publisher: McGraw-Hill Higher Education Summary: Miller/O'Neill/Hyde, built by teachers just like you, continues continues to offer an enlightened approach grounded in the fundamentals of classroom experience in the 2nd edition of Intermediate Algebra. The practice of many instructors in the classroom is to present examples and have their students solve similar problems. This is realized through the Skill Practice Exercises that directly follow the examples in the ...textbook. Throughout the text, the authors have integrated many Study Tips and Avoiding Mistakes hints, which are reflective of the comments and instruction presented to students in the classroom. In this way, the text communicates to students, the very points their instructors are likely to make during lecture, helping to reinforce the concepts and provide instruction that leads students to mastery and success. The authors included in this edition, Problem-Recognition exercises, that many instructors will likely identify to be similar to worksheets they have personally developed for distribution to students. The intent of the Problem-Recognition exercises, is to help students overcome what is sometimes a natural inclination toward applying problem-sovling algorithms that may not always be appropriate. In addition, the exercise sets have been revised to include even more core exercises than were present in the first edition. This permits instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills and develop the knowledge they need to make a successful transition into College Algebra. In this way, the book perfectly complements any learning platform, whether traditional lecture ordistance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class, as they do inside class with their instructor. For even more support, students have access to a wealth of supplements, including McGraw-Hill's online homework management system, MathZone2008. An acceptable used copy with heavy cover wear and school markings. Book only-does not include additional resources. Booksavers receives donated books and recycles them [more] 2008