The Mathematics of Voting and Elections: A Hands-On Approach

Author: Jonathan K. Hodge,Richard E. Klima

Publisher: American Mathematical Soc.

ISBN: 1470442876

Category: Elections

Page: 238

View: 1797

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The Mathematics of Voting and Elections: A Hands-On Approach, Second Edition, is an inquiry-based approach to the mathematics of politics and social choice. The aim of the book is to give readers who might not normally choose to engage with mathematics recreationally the chance to discover some interesting mathematical ideas from within a familiar context, and to see the applicability of mathematics to real-world situations. Through this process, readers should improve their critical thinking and problem solving skills, as well as broaden their views of what mathematics really is and how it can be used in unexpected ways. The book was written specifically for non-mathematical audiences and requires virtually no mathematical prerequisites beyond basic arithmetic. At the same time, the questions included are designed to challenge both mathematical and non-mathematical audiences alike. More than giving the right answers, this book asks the right questions. The book is fun to read, with examples that are not just thought-provoking, but also entertaining. It is written in a style that is casual without being condescending. But the discovery-based approach of the book also forces readers to play an active role in their learning, which should lead to a sense of ownership of the main ideas in the book. And while the book provides answers to some of the important questions in the field of mathematical voting theory, it also leads readers to discover new questions and ways to approach them. In addition to making small improvements in all the chapters, this second edition contains several new chapters. Of particular interest might be Chapter 12 which covers a host of topics related to gerrymandering.
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The Mathematics of Voting and Elections

A Hands-on Approach

Author: Jonathan K. Hodge,Richard E. Klima

Publisher: American Mathematical Soc.

ISBN: 0821837982

Category: Mathematics

Page: 226

View: 1048

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The Mathematics of Voting and Elections: A Hands-on Approach will help you discover answers to these and many other questions. Easily accessible to anyone interested in the subject, the book requires virtually no prior mathematical experience beyond basic arithmetic, and includes numerous examples and discussions regarding actual elections from politics and popular culture.
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Learning and Understanding

Improving Advanced Study of Mathematics and Science in U.S. High Schools

Author: National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Programs for Advanced Study of Mathematics and Science in American High Schools

Publisher: National Academies Press

ISBN: 0309074401

Category: Education

Page: 588

View: 9039

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This book takes a fresh look at programs for advanced studies for high school students in the United States, with a particular focus on the Advanced Placement and the International Baccalaureate programs, and asks how advanced studies can be significantly improved in general. It also examines two of the core issues surrounding these programs: they can have a profound impact on other components of the education system and participation in the programs has become key to admission at selective institutions of higher education. By looking at what could enhance the quality of high school advanced study programs as well as what precedes and comes after these programs, this report provides teachers, parents, curriculum developers, administrators, college science and mathematics faculty, and the educational research community with a detailed assessment that can be used to guide change within advanced study programs.
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Probability, Decisions and Games

A Gentle Introduction using R

Author: Abel Rodríguez,Bruno Mendes

Publisher: John Wiley & Sons

ISBN: 1119302609

Category: Mathematics

Page: 240

View: 9049

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INTRODUCES THE FUNDAMENTALS OF PROBABILITY, STATISTICS, DECISION THEORY, AND GAME THEORY, AND FEATURES INTERESTING EXAMPLES OF GAMES OF CHANCE AND STRATEGY TO MOTIVATE AND ILLUSTRATE ABSTRACT MATHEMATICAL CONCEPTS Covering both random and strategic games, Probability, Decisions and Games features a variety of gaming and gambling examples to build a better understanding of basic concepts of probability, statistics, decision theory, and game theory. The authors present fundamental concepts such as random variables, rational choice theory, mathematical expectation and variance, fair games, combinatorial calculus, conditional probability, Bayes Theorem, Bernoulli trials, zero-sum games and Nash equilibria, as well as their application in games such as Roulette, Craps, Lotto, Blackjack, Poker, Rock-Paper-Scissors, the Game of Chicken and Tic-Tac-Toe. Computer simulations, implemented using the popular R computing environment, are used to provide intuition on key concepts and verify complex calculations. The book starts by introducing simple concepts that are carefully motivated by the same historical examples that drove their original development of the field of probability, and then applies those concepts to popular contemporary games. The first two chapters of Probability, Decisions and Games: A Gentle Introduction using R feature an introductory discussion of probability and rational choice theory in finite and discrete spaces that builds upon the simple games discussed in the famous correspondence between Blaise Pascal and Pierre de Fermat. Subsequent chapters utilize popular casino games such as Roulette and Blackjack to expand on these concepts illustrate modern applications of these methodologies. Finally, the book concludes with discussions on game theory using a number of strategic games. This book: · Features introductory coverage of probability, statistics, decision theory and game theory, and has been class-tested at University of California, Santa Cruz for the past six years · Illustrates basic concepts in probability through interesting and fun examples using a number of popular casino games: roulette, lotto, craps, blackjack, and poker · Introduces key ideas in game theory using classic games such as Rock-Paper-Scissors, Chess, and Tic-Tac-Toe. · Features computer simulations using R throughout in order to illustrate complex concepts and help readers verify complex calculations · Contains exercises and approaches games and gambling at a level that is accessible for readers with minimal experience · Adopts a unique approach by motivating complex concepts using first simple games and then moving on to more complex, well-known games that illustrate how these concepts work together Probability, Decisions and Games: A Gentle Introduction using R is a unique and helpful textbook for undergraduate courses on statistical reasoning, introduction to probability, statistical literacy, and quantitative reasoning for students from a variety of disciplines. ABEL RODRÍGUEZ, PhD, is Professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (UCSC), CA, USA. The author of 40 journal articles, his research interests include Bayesian nonparametric methods, machine learning, spatial temporal models, network models, and extreme value theory. BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA. BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA.INTRODUCES THE FUNDAMENTALS OF PROBABILITY, STATISTICS, DECISION THEORY, AND GAME THEORY, AND FEATURES INTERESTING EXAMPLES OF GAMES OF CHANCE AND STRATEGY TO MOTIVATE AND ILLUSTRATE ABSTRACT MATHEMATICAL CONCEPTS Covering both random and strategic games, Probability, Decisions and Games features a variety of gaming and gambling examples to build a better understanding of basic concepts of probability, statistics, decision theory, and game theory. The authors present fundamental concepts such as random variables, rational choice theory, mathematical expectation and variance, fair games, combinatorial calculus, conditional probability, Bayes Theorem, Bernoulli trials, zero-sum games and Nash equilibria, as well as their application in games such as Roulette, Craps, Lotto, Blackjack, Poker, Rock-Paper-Scissors, the Game of Chicken and Tic-Tac-Toe. Computer simulations, implemented using the popular R computing environment, are used to provide intuition on key concepts and verify complex calculations. The book starts by introducing simple concepts that are carefully motivated by the same historical examples that drove their original development of the field of probability, and then applies those concepts to popular contemporary games. The first two chapters of Probability, Decisions and Games: A Gentle Introduction using R feature an introductory discussion of probability and rational choice theory in finite and discrete spaces that builds upon the simple games discussed in the famous correspondence between Blaise Pascal and Pierre de Fermat. Subsequent chapters utilize popular casino games such as Roulette and Blackjack to expand on these concepts illustrate modern applications of these methodologies. Finally, the book concludes with discussions on game theory using a number of strategic games. This book: • Features introductory coverage of probability, statistics, decision theory and game theory, and has been class-tested at University of California, Santa Cruz for the past six years • Illustrates basic concepts in probability through interesting and fun examples using a number of popular casino games: roulette, lotto, craps, blackjack, and poker • Introduces key ideas in game theory using classic games such as Rock-Paper-Scissors, Chess, and Tic-Tac-Toe. • Features computer simulations using R throughout in order to illustrate complex concepts and help readers verify complex calculations • Contains exercises and approaches games and gambling at a level that is accessible for readers with minimal experience • Adopts a unique approach by motivating complex concepts using first simple games and then moving on to more complex, well-known games that illustrate how these concepts work together Probability, Decisions and Games: A Gentle Introduction using R is a unique and helpful textbook for undergraduate courses on statistical reasoning, introduction to probability, statistical literacy, and quantitative reasoning for students from a variety of disciplines. ABEL RODRÍGUEZ, PhD, is Professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (UCSC), CA, USA. The author of 40 journal articles, his research interests include Bayesian nonparametric methods, machine learning, spatial temporal models, network models, and extreme value theory. BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA.
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Encouraging mathematical thinkers

the basics and more : [a presenter's guide]

Author: Ruth E. Parker,Mathematics Education Collaborative

Publisher: Heinemann Educational Books

ISBN: 9780325009360

Category: Education

Page: 48

View: 9338

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Parents want to be supportive of math education. But they often feel frustration when they don't recognize the kind of instruction their children are getting and can't help them at home. The best way to guide parents toward an understanding of how their kids are learning is by engaging them in the very same mathematics students are experiencing at school. With the Supporting School Mathematicsseries, you'll find six comprehensive workshop modules for effectively engaging with parents or any stakeholder in mathematics education. Encouraging Mathematical Thinkers is designed to engage parents in a rich mathematical investigation involving probability. The importance of communication in mathematics classrooms is highlighted in the session, and parents experience how facility with numbers can be developed within important mathematical contexts. The content of this session is appropriate for teachers and parents of grades 3 - 8, and students of grades 4 - 8. Each of the six sessions of Supporting School Mathematicseach use explicit, thorough, hands-on examples to illustrate how key aspects of your math curriculum work. Parents will come to understand: what it means to teach for understanding and how meaningful, challenging, and engaging this type of learning is why and how the focus of instruction is different than traditional mathematics teaching how basic facts are both explicitly and implicitly addressed how to extend to home what students learn at school. Each Supporting School Mathematicspackage includes everything you need to conduct a successful parent workshop: a planning handbook that offers general advice on presenting mathematical content and even provides you a Q-and-A section featuring the questions you are most likely to get and good answers to them a module that includes scripts, content-specific talking points, overheads, and handouts that help audience members understand how their children are learning and discover new ways of helping them at home a CD that contains ready-to-print files for the overheads as well as printable versions of the handouts in both English and Spanish.The six workshops in the Supporting School Mathematicsseries help you demonstrate for parents the most important aspects of any mathematics curriculum: Helping with Math at Home: Ideas for Parents Helping with Math at Home: More Ideas for Parents Understanding Addition and Subtraction Across the Grades Understanding Multiplication Across the Grades Understanding Fractions Across the Grades Encouraging Mathematical Thinkers: The Basics and More Gain parents' support by using Supporting School Mathematicsto introduce them to high-quality, student-centered mathematics instruction. It's an easy, new way to change how they think about their children's math education.System Requirements for CD-ROMWindows/PC Pentium Processor 450Mhz (or higher)> Windows 98 (or higher) 64 MB RAM (more recommended) SVGA Color Display (or better) 8X CD-ROM Drive (or faster) Acrobat ReaderMac PowerPC Processor G3/333Mhz (or higher) System 8.6 (or higher) 64 MB RAM (more recommended) SVGA Color Display (or better) 8X CD-ROM Drive (or faster) Acrobat Reader
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