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Author : Ivan Niven
Publisher : MAA
ISBN 13 : 0883856158
Total Pages : 215 pages
Book Rating : 4.8/5 (838 download)
Download or read book Mathematics of Choice written by Ivan Niven and published by MAA. This book was released on 1965 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas J. Jech
Publisher : Courier Corporation
ISBN 13 : 0486466248
Total Pages : 226 pages
Book Rating : 4.4/5 (864 download)
Download or read book The Axiom of Choice written by Thomas J. Jech and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Author : G.H. Moore
Publisher : Springer Science & Business Media
ISBN 13 : 1461394783
Total Pages : 425 pages
Book Rating : 4.4/5 (613 download)
Download or read book Zermelo’s Axiom of Choice written by G.H. Moore and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.
Author : Christoph Borgers
Publisher : SIAM
ISBN 13 : 0898717620
Total Pages : 233 pages
Book Rating : 4.8/5 (987 download)
Download or read book Mathematics of Social Choice written by Christoph Borgers and published by SIAM. This book was released on 2010-01-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.
Author : Alan D. Taylor
Publisher : Cambridge University Press
ISBN 13 : 0521810523
Total Pages : 191 pages
Book Rating : 4.5/5 (218 download)
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 191 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 2005 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.
Author : Horst Herrlich
Publisher : Springer
ISBN 13 : 3540342680
Total Pages : 207 pages
Book Rating : 4.5/5 (43 download)
Download or read book Axiom of Choice written by Horst Herrlich and published by Springer. This book was released on 2006-07-21 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. It is shunned by some, used indiscriminately by others. This treatise shows paradigmatically that disasters happen without AC and they happen with AC. Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
Author : Herman Rubin
Publisher : Elsevier
ISBN 13 : 0444533990
Total Pages : 159 pages
Book Rating : 4.4/5 (445 download)
Download or read book Equivalents of the Axiom of Choice written by Herman Rubin and published by Elsevier. This book was released on 1963 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hannah Fry
Publisher : Simon and Schuster
ISBN 13 : 1476784892
Total Pages : 128 pages
Book Rating : 4.4/5 (767 download)
Download or read book The Mathematics of Love written by Hannah Fry and published by Simon and Schuster. This book was released on 2015-02-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this must-have for anyone who wants to better understand their love life, a mathematician pulls back the curtain and reveals the hidden patterns—from dating sites to divorce, sex to marriage—behind the rituals of love. The roller coaster of romance is hard to quantify; defining how lovers might feel from a set of simple equations is impossible. But that doesn’t mean that mathematics isn’t a crucial tool for understanding love. Love, like most things in life, is full of patterns. And mathematics is ultimately the study of patterns—from predicting the weather to the fluctuations of the stock market, the movement of planets or the growth of cities. These patterns twist and turn and warp and evolve just as the rituals of love do. In The Mathematics of Love, Dr. Hannah Fry takes the reader on a fascinating journey through the patterns that define our love lives, applying mathematical formulas to the most common yet complex questions pertaining to love: What’s the chance of finding love? What’s the probability that it will last? How do online dating algorithms work, exactly? Can game theory help us decide who to approach in a bar? At what point in your dating life should you settle down? From evaluating the best strategies for online dating to defining the nebulous concept of beauty, Dr. Fry proves—with great insight, wit, and fun—that math is a surprisingly useful tool to negotiate the complicated, often baffling, sometimes infuriating, always interesting, mysteries of love.
Author : Samuel B. Smith
Publisher : Cambridge University Press
ISBN 13 : 1107084520
Total Pages : 393 pages
Book Rating : 4.1/5 (7 download)
Download or read book Chance, Strategy, and Choice written by Samuel B. Smith and published by Cambridge University Press. This book was released on 2015-06-29 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague-Grundy theorem and Arrow's impossibility theorem. * Uses an integrative approach to probability, game, and social choice theory * Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies * Contains numerous exercises and examples of varying levels of difficulty * Requires only a high school mathematical background.
Author : Miklos Bona
Publisher : CRC Press
ISBN 13 : 1439850526
Total Pages : 478 pages
Book Rating : 4.4/5 (398 download)
Download or read book Combinatorics of Permutations written by Miklos Bona and published by CRC Press. This book was released on 2016-04-19 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Unified Account of Permutations in Modern CombinatoricsA 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, Second Edition continues to clearly show the usefuln
Author : Diana Davis
Publisher : American Mathematical Soc.
ISBN 13 : 1470461226
Total Pages : 90 pages
Book Rating : 4.4/5 (74 download)
Download or read book Illustrating Mathematics written by Diana Davis and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.
Author : Steven Brams
Publisher : Springer Science & Business Media
ISBN 13 : 3540791280
Total Pages : 412 pages
Book Rating : 4.5/5 (47 download)
Download or read book The Mathematics of Preference, Choice and Order written by Steven Brams and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn’s contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.
Author : Graham Flegg
Publisher : Courier Corporation
ISBN 13 : 0486166511
Total Pages : 307 pages
Book Rating : 4.4/5 (861 download)
Download or read book Numbers written by Graham Flegg and published by Courier Corporation. This book was released on 2013-05-13 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.
Author : Theodore G. Faticoni
Publisher : John Wiley & Sons
ISBN 13 : 111824382X
Total Pages : 361 pages
Book Rating : 4.1/5 (182 download)
Download or read book The Mathematics of Infinity written by Theodore G. Faticoni and published by John Wiley & Sons. This book was released on 2012-04-23 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.
Author : R. Duncan Luce
Publisher : Courier Corporation
ISBN 13 : 0486153398
Total Pages : 172 pages
Book Rating : 4.4/5 (861 download)
Download or read book Individual Choice Behavior written by R. Duncan Luce and published by Courier Corporation. This book was released on 2012-06-22 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise presents a mathematical analysis of choice behavior. Starting with a general axiom, it then examines applications of the theory to substantive problems: psychophysics, utility, and learning. 1959 edition.
Author : R.B.J.T. Allenby
Publisher : CRC Press
ISBN 13 : 1420082612
Total Pages : 440 pages
Book Rating : 4.4/5 (2 download)
Download or read book How to Count written by R.B.J.T. Allenby and published by CRC Press. This book was released on 2011-07-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.
Author : Gunter M. Ziegler
Publisher : CRC Press
ISBN 13 : 1466564911
Total Pages : 228 pages
Book Rating : 4.4/5 (665 download)
Download or read book Do I Count? written by Gunter M. Ziegler and published by CRC Press. This book was released on 2013-07-22 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of mathematics is not something distant, strange, and abstract that you can only learn about—and often dislike—in school. It is in everyday situations, such as housekeeping, communications, traffic, and weather reports. Taking you on a trip into the world of mathematics, Do I Count? Stories from Mathematics describes in a clear and captivating way the people behind the numbers and the places where mathematics is made. Written by top scientist and engaging storyteller Günter M. Ziegler and translated by Thomas von Foerster, the book presents mathematics and mathematicians in a manner that you have not previously encountered. It guides you on a scenic tour through the field, pointing out which beds were useful in constructing which theorems and which notebooks list the prizes for solving particular problems. Forgoing esoteric areas, the text relates mathematics to celebrities, history, travel, politics, science and technology, weather, clever puzzles, and the future. Can bees count? Is 13 bad luck? Are there equations for everything? What’s the real practical value of the Pythagorean Theorem? Are there Sudoku puzzles with fewer than 17 entries and just one solution? Where and how do mathematicians work? Who invented proofs and why do we need them? Why is there no Nobel Prize for mathematics? What kind of life did Paul Erdős lead? Find out the answers to these and other questions in this entertaining book of stories. You’ll see that everyone counts, but no computation is needed.
