Mathematics And Politics

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Mathematics and Politics

Author : Alan D. Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 0387776435
Total Pages : 378 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Mathematics and Politics by : Alan D. Taylor

Download or read book Mathematics and Politics written by Alan D. Taylor and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a text for an undergraduate mathematics course for nonmajors, Mathematics and Politics requires no prerequisites in either area while the underlying philosophy involves minimizing algebraic computations and focusing instead on some conceptual aspects of mathematics in the context of important real-world questions in political science. Five major topics are covered including a model of escalation, game theoretic models of international conflict, yes-no voting systems, political power, and social choice. Each topic is discussed in an introductory chapter and revisited in more depth in a later chapter. This new edition has added co-author, Allison Pacelli, and two new chapters on "Fairness" and "More Fairness." The examples and the exercises have been updated and enhanced throughout. Reviews from first edition: This book is well written and has much math of interest. While it is pitched at a non-math audience there is material here that will be new and interesting to the readers... -Sigact News For mathematicians, Taylor's book shows how the social sciences make use of mathematical thinking, in the form of axiomatic systems, and offers a chance to teach this kind of thinking to our students. - The College Mathematics Journal The writing is crisp and the sense of excitement about learning mathematics is seductive. The political conflict examples are well thought out and clear. -Michael C. Munger

Essential Mathematics for Political and Social Research

Author : Jeff Gill
Publisher : Cambridge University Press
ISBN 13 : 0521834260
Total Pages : 449 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Essential Mathematics for Political and Social Research by : Jeff Gill

Download or read book Essential Mathematics for Political and Social Research written by Jeff Gill and published by Cambridge University Press. This book was released on 2006-04-24 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: "More than ever before, modern social scientists require a basic level of mathematical literacy, yet many students receive only limited mathematical training prior to beginning their research careers. This textbook addresses this dilemma by offering a comprehensive, unified introduction to the essential mathematics of social science. Throughout the book the presentation builds from first principles and eschews unnecessary complexity. Most importantly, the discussion is thoroughly and consistently anchored in real social science applications, with more than 80 research-based illustrations woven into the text and featured in end-of-chapter exercises. Students and researchers alike will find this first-of-its-kind volume to be an invaluable resource."--BOOK JACKET.

The Mathematics of Politics, Second Edition

Author : E. Arthur Robinson
Publisher : CRC Press
ISBN 13 : 149879890X
Total Pages : 440 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis The Mathematics of Politics, Second Edition by : E. Arthur Robinson

Download or read book The Mathematics of Politics, Second Edition written by E. Arthur Robinson and published by CRC Press. This book was released on 2016-11-18 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is because mathematics is often misunderstood, it is commonly believed it has nothing to say about politics. The high school experience with mathematics, for so many the lasting impression of the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those believing this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoning about politics. In the search for ideal ways to make certain kinds of decisions, a lot of wasted effort can be averted if mathematics can determine that finding such an ideal is actually impossible in the first place. In the first three parts of this book, we address the following three political questions: (1) Is there a good way to choose winners of elections? (2) Is there a good way to apportion congressional seats? (3) Is there a good way to make decisions in situations of conflict and uncertainty? In the fourth and final part of this book, we examine the Electoral College system that is used in the United States to select a president. There we bring together ideas that are introduced in each of the three earlier parts of the book.

Game Theory and Politics

Author : Steven J. Brams
Publisher : Courier Corporation
ISBN 13 : 0486143635
Total Pages : 338 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Game Theory and Politics by : Steven J. Brams

Download or read book Game Theory and Politics written by Steven J. Brams and published by Courier Corporation. This book was released on 2013-01-17 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVMany illuminating and instructive examples of the applications of game theoretic models to problems in political science appear in this volume, which requires minimal mathematical background. 1975 edition. 24 figures. /div

A Mathematics Course for Political and Social Research

Author : Will H. Moore
Publisher : Princeton University Press
ISBN 13 : 0691159173
Total Pages : 450 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis A Mathematics Course for Political and Social Research by : Will H. Moore

Download or read book A Mathematics Course for Political and Social Research written by Will H. Moore and published by Princeton University Press. This book was released on 2013-08-11 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a semester-long or yearlong course to acquire the necessary skills. Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social sciences and a handy reference for seasoned researchers. The book begins with the fundamental building blocks of mathematics and basic algebra, then goes on to cover essential subjects such as calculus in one and more than one variable, including optimization, constrained optimization, and implicit functions; linear algebra, including Markov chains and eigenvectors; and probability. It describes the intermediate steps most other textbooks leave out, features numerous exercises throughout, and grounds all concepts by illustrating their use and importance in political science and sociology. Uniquely designed and ideal for students and researchers in political science and sociology Uses practical examples from political science and sociology Features "Why Do I Care?" sections that explain why concepts are useful Includes numerous exercises Complete online solutions manual (available only to professors, email david.siegel at duke.edu, subject line "Solution Set") Selected solutions available online to students

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

Author : Jonathan K. Hodge
Publisher : American Mathematical Soc.
ISBN 13 : 1470442876
Total Pages : 238 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Mathematics of Voting and Elections: A Hands-On Approach by : Jonathan K. Hodge

Download or read book The Mathematics of Voting and Elections: A Hands-On Approach written by Jonathan K. Hodge and published by American Mathematical Soc.. This book was released on 2018-10-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Mathematics of Politics

Author : E. Arthur Robinson
Publisher : CRC Press
ISBN 13 : 1498798888
Total Pages : 478 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis The Mathematics of Politics by : E. Arthur Robinson

Download or read book The Mathematics of Politics written by E. Arthur Robinson and published by CRC Press. This book was released on 2016-11-18 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is because mathematics is often misunderstood, it is commonly believed it has nothing to say about politics. The high school experience with mathematics, for so many the lasting impression of the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those believing this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoning about politics. In the search for ideal ways to make certain kinds of decisions, a lot of wasted effort can be averted if mathematics can determine that finding such an ideal is actually impossible in the first place. In the first three parts of this book, we address the following three political questions: (1) Is there a good way to choose winners of elections? (2) Is there a good way to apportion congressional seats? (3) Is there a good way to make decisions in situations of conflict and uncertainty? In the fourth and final part of this book, we examine the Electoral College system that is used in the United States to select a president. There we bring together ideas that are introduced in each of the three earlier parts of the book.

Numbers Rule

Author : George Szpiro
Publisher : Princeton University Press
ISBN 13 : 0691209081
Total Pages : 240 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Numbers Rule by : George Szpiro

Download or read book Numbers Rule written by George Szpiro and published by Princeton University Press. This book was released on 2020-11-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author takes the general reader on a tour of the mathematical puzzles and paradoxes inherent in voting systems, such as the Alabama Paradox, in which an increase in the number of seats in the Congress could actually lead to a reduced number of representatives for a state, and the Condorcet Paradox, which demonstrates that the winner of elections featuring more than two candidates does not necessarily reflect majority preferences. Szpiro takes a roughly chronological approach to the topic, traveling from ancient Greece to the present and, in addition to offering explanations of the various mathematical conundrums of elections and voting, also offers biographical details on the mathematicians and other thinkers who thought about them, including Plato, Pliny the Younger, Pierre Simon Laplace, Thomas Jefferson, John von Neumann, and Kenneth Arrow.

Political Geometry

Author : Moon Duchin
Publisher : Birkhäuser
ISBN 13 : 9783319691602
Total Pages : 436 pages
Book Rating : 4.6/5 (916 download)

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Book Synopsis Political Geometry by : Moon Duchin

Download or read book Political Geometry written by Moon Duchin and published by Birkhäuser. This book was released on 2022-04-02 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Why does my congressional district look like a salamander?” Politically engaged citizens have been asking this question for far too long. This volume collects perspectives from a wide cross-section of disciplines to explain what drives gerrymandering, why it can be hard to stamp out, and how we might go about fixing it. With topics ranging from the Voting Rights Act to Markov chains to the geography of communities, this book serves as a 21st century toolkit for how we can better approach this corrosive phenomenon. The volume editors gather experts from a variety of fields to provide as many different perspectives on gerrymandering as possible. Thanks to the breadth of expertise found across these chapters, ranging from lawyers to mathematicians to civil rights activists, readers will discover new ways of thinking about redistricting in the United States. Illustrations and helpful walkthroughs appear throughout to clearly explain otherwise complex ideas from these areas. Political Geometry is a must-have for anybody interested in political representation in the United States elections, and for anyone who’s ever thought, “There must be a better way to do this.”

Opening the Cage

Author : Ole Skovsmose
Publisher : Springer Science & Business Media
ISBN 13 : 9460918085
Total Pages : 387 pages
Book Rating : 4.4/5 (69 download)

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Book Synopsis Opening the Cage by : Ole Skovsmose

Download or read book Opening the Cage written by Ole Skovsmose and published by Springer Science & Business Media. This book was released on 2012-09-05 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: The picture on the front of this book is an illustration for Totakahini: The tale of the parrot, by Rabindranath Tagore, in which he satirized education as a magnificent golden cage. Opening the cage addresses mathematics education as a complex socio-political phenomenon, exploring the vast terrain that spans critique and politics. Opening the cage includes contributions from educators writing critically about mathematics education in diverse contexts. They demonstrate that mathematics education is politics, they investigate borderland positions, they address the nexus of mathematics, education, and power, and they explore educational possibilities. Mathematics education is not a free enterprise. It is carried on behind bars created by economic, political, and social demands. This cage might not be as magnificent as that in Tagore’s fable. But it is strong. Opening the cage is a critical and political challenge, and we may be surprised to see what emerges.

The New Math

Author : Christopher J. Phillips
Publisher : University of Chicago Press
ISBN 13 : 022618496X
Total Pages : 242 pages
Book Rating : 4.2/5 (261 download)

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Book Synopsis The New Math by : Christopher J. Phillips

Download or read book The New Math written by Christopher J. Phillips and published by University of Chicago Press. This book was released on 2015 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: An era of sweeping cultural change in America, the postwar years saw the rise of beatniks and hippies, the birth of feminism, and the release of the first video game. This book examines the rise and fall of the new math as a marker of the period's political and social ferment.

Constantin Carathéodory

Author : Maria Georgiadou
Publisher : Springer Science & Business Media
ISBN 13 : 3642185622
Total Pages : 651 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Constantin Carathéodory by : Maria Georgiadou

Download or read book Constantin Carathéodory written by Maria Georgiadou and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: With breathtaking detail, Maria Georgiadou sheds light on the work and life of Constantin Carathéodory, who until now has been ignored by historians. In her thought-provoking book, Georgiadou maps out the mathematician’s oeuvre, life and turbulent historical surroundings. Descending from the Greek élite of Constantinople, Carathéodory graduated from the military school of Brussels, became engineer at the Assiout dam in Egypt and finally dedicated a lifetime to mathematics and education. He significantly contributed to: calculus of variations, the theory of point set measure, the theory of functions of a real variable, pdes, and complex function theory. An exciting and well-written biography, once started, difficult to put down.

Mathematics and Democracy

Author : Steven J. Brams
Publisher : Princeton University Press
ISBN 13 : 1400835593
Total Pages : 390 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Mathematics and Democracy by : Steven J. Brams

Download or read book Mathematics and Democracy written by Steven J. Brams and published by Princeton University Press. This book was released on 2009-12-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.

The Mathematics of Voting and Apportionment

Author : Sherif El-Helaly
Publisher : Springer
ISBN 13 : 3030147681
Total Pages : 264 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Mathematics of Voting and Apportionment by : Sherif El-Helaly

Download or read book The Mathematics of Voting and Apportionment written by Sherif El-Helaly and published by Springer. This book was released on 2019-05-21 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook contains a rigorous exposition of the mathematical foundations of two of the most important topics in politics and economics: voting and apportionment, at the level of upper undergraduate and beginning graduate students. It stands out among comparable books by providing, in one volume, an extensive and mathematically rigorous treatment of these two topics. The text’s three chapters cover social choice, yes-no voting, and apportionment, respectively, and can be covered in any order, allowing teachers ample flexibility. Each chapter begins with an elementary introduction and several examples to motivate the concepts and to gradually lead to more advanced material. Landmark theorems are presented with detailed and streamlined proofs; those requiring more complex proofs, such as Arrow’s theorems on dictatorship, Gibbard’s theorem on oligarchy, and Gärdenfors’ theorem on manipulation, are broken down into propositions and lemmas in order to make them easier to grasp. Simple and intuitive notations are emphasized over non-standard, overly complicated symbols. Additionally, each chapter ends with exercises that vary from computational to “prove or disprove” types. The Mathematics of Voting and Apportionment will be particularly well-suited for a course in the mathematics of voting and apportionment for upper-level undergraduate and beginning graduate students in economics, political science, or philosophy, or for an elective course for math majors. In addition, this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications. No political science prerequisites are needed. Mathematical prerequisites (included in the book) are minimal: elementary concepts in combinatorics, graph theory, order relations, and the harmonic and geometric means. What is needed most is the level of maturity that enables the student to think logically, derive results from axioms and hypotheses, and intuitively grasp logical notions such as “contrapositive” and “counterexample.”

The Politics of Large Numbers

Author : Alain Desrosières
Publisher : Harvard University Press
ISBN 13 : 9780674009691
Total Pages : 386 pages
Book Rating : 4.0/5 (96 download)

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Book Synopsis The Politics of Large Numbers by : Alain Desrosières

Download or read book The Politics of Large Numbers written by Alain Desrosières and published by Harvard University Press. This book was released on 1998 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Begins with study of history of statistics, and shows how the evolution of modern statistics has been inextricably bound up with the knowledge and power of governments.

Social Choice and the Mathematics of Manipulation

Author : Alan D. Taylor
Publisher : Cambridge University Press
ISBN 13 : 9780521008839
Total Pages : 196 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Social Choice and the Mathematics of Manipulation by : Alan D. Taylor

Download or read book Social Choice and the Mathematics of Manipulation written by Alan D. Taylor and published by Cambridge University Press. This book was released on 2005-05-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system.

A Mathematical Look at Politics

Author : E. Arthur Robinson, Jr.
Publisher : CRC Press
ISBN 13 : 9781439819838
Total Pages : 0 pages
Book Rating : 4.8/5 (198 download)

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Book Synopsis A Mathematical Look at Politics by : E. Arthur Robinson, Jr.

Download or read book A Mathematical Look at Politics written by E. Arthur Robinson, Jr. and published by CRC Press. This book was released on 2010-12-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: What Ralph Nader's spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Dean’s method. How the US tried to use game theory to win the Cold War, and why it didn’t work. When students realize that mathematical thinking can address these sorts of pressing concerns of the political world it naturally sparks their interest in the underlying mathematics. A Mathematical Look at Politics is designed as an alternative to the usual mathematics texts for students in quantitative reasoning courses. It applies the power of mathematical thinking to problems in politics and public policy. Concepts are precisely defined. Hypotheses are laid out. Propositions, lemmas, theorems, and corollaries are stated and proved. Counterexamples are offered to refute conjectures. Students are expected not only to make computations but also to state results, prove them, and draw conclusions about specific examples. Tying the liberal arts classroom to real-world mathematical applications, this text is more deeply engaging than a traditional general education book that surveys the mathematical landscape. It aims to instill a fondness for mathematics in a population not always convinced that mathematics is relevant to them.