Mathematics And Politics

Author : Alan D. Taylor,Allison M. Pacelli
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 42,5 Mb
Release : 2009-12-29
Category : Social Science
ISBN : 9780387776439

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Mathematics and Politics by Alan D. Taylor,Allison M. Pacelli Pdf

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

Author : Jeff Gill
Publisher : Cambridge University Press
Page : 449 pages
File Size : 55,6 Mb
Release : 2006-04-24
Category : Mathematics
ISBN : 9780521834261

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Essential Mathematics for Political and Social Research by Jeff Gill Pdf

"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.

Author : Will H. Moore,David A. Siegel
Publisher : Princeton University Press
Page : 450 pages
File Size : 47,6 Mb
Release : 2013-08-11
Category : Political Science
ISBN : 9780691159171

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A Mathematics Course for Political and Social Research by Will H. Moore,David A. Siegel Pdf

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

Author : E. Arthur Robinson,Daniel H. Ullman
Publisher : CRC Press
Page : 478 pages
File Size : 41,6 Mb
Release : 2016-11-18
Category : Mathematics
ISBN : 9781498798884

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The Mathematics of Politics by E. Arthur Robinson,Daniel H. Ullman Pdf

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.

Author : Jonathan K. Hodge,Richard E. Klima
Publisher : American Mathematical Soc.
Page : 238 pages
File Size : 49,7 Mb
Release : 2018-10-01
Category : Elections
ISBN : 9781470442873

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The Mathematics of Voting and Elections: A Hands-On Approach by Jonathan K. Hodge,Richard E. Klima Pdf

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.

Author : Sherif El-Helaly
Publisher : Springer
Page : 264 pages
File Size : 43,7 Mb
Release : 2019-05-21
Category : Mathematics
ISBN : 9783030147686

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The Mathematics of Voting and Apportionment by Sherif El-Helaly Pdf

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.”

Author : Steven J. Brams
Publisher : Courier Corporation
Page : 338 pages
File Size : 52,5 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9780486143637

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Game Theory and Politics by Steven J. Brams Pdf

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

Author : Ole Skovsmose,Brian Greer
Publisher : Springer Science & Business Media
Page : 387 pages
File Size : 49,6 Mb
Release : 2012-09-05
Category : Education
ISBN : 9789460918087

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Opening the Cage by Ole Skovsmose,Brian Greer Pdf

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.

Author : Moon Duchin,Olivia Walch
Publisher : Birkhäuser
Page : 436 pages
File Size : 49,9 Mb
Release : 2022-04-02
Category : Mathematics
ISBN : 3319691600

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Political Geometry by Moon Duchin,Olivia Walch Pdf

“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.”

Author : Christopher J. Phillips
Publisher : University of Chicago Press
Page : 242 pages
File Size : 52,6 Mb
Release : 2015
Category : Education
ISBN : 9780226184968

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The New Math by Christopher J. Phillips Pdf

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.

Author : Gordon Tullock
Publisher : Ann Arbor : University of Michigan Press
Page : 200 pages
File Size : 49,5 Mb
Release : 1967
Category : Mathematics
ISBN : UOM:39015002397258

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Toward a Mathematics of Politics by Gordon Tullock Pdf

Author : Maria Georgiadou
Publisher : Springer Science & Business Media
Page : 651 pages
File Size : 54,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642185625

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Constantin Carathéodory by Maria Georgiadou Pdf

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.

Author : George Szpiro
Publisher : Princeton University Press
Page : 240 pages
File Size : 51,8 Mb
Release : 2020-11-03
Category : History
ISBN : 9780691209081

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Numbers Rule by George Szpiro Pdf

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.

Author : Alain Desrosières
Publisher : Harvard University Press
Page : 386 pages
File Size : 49,6 Mb
Release : 1998
Category : History
ISBN : 067400969X

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The Politics of Large Numbers by Alain Desrosières Pdf

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.

Author : Joseph L. Bernd
Publisher : Unknown
Page : 156 pages
File Size : 42,9 Mb
Release : 1972
Category : Political science
ISBN : UCAL:B3935536

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Mathematical Applications in Political Science by Joseph L. Bernd Pdf

Vol. for 1964 contains papers presented at the Conference on Mathematical Applications in Political Science; vols. for 1965- consist chiefly of papers presented at institutes held at Southern Methodist University, 1965 and at Virginia Polytechnis Institute, 1966, 1968-