Author : Ivan Niven
Publisher : MAA
Page : 215 pages
File Size : 54,5 Mb
Release : 1965
Category : Mathematics
ISBN : 9780883856154
Mathematics of Choice
Ivan Niven
Mathematics Of Choice
Mathematics Of Choice Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Mathematics Of Choice book. This book definitely worth reading, it is an incredibly well-written.
Axiom of Choice
Horst Herrlich
Author : Horst Herrlich
Publisher : Springer
Page : 198 pages
File Size : 40,8 Mb
Release : 2006-07-21
Category : Mathematics
ISBN : 9783540342687
Axiom of Choice by Horst Herrlich Pdf
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.
Social Choice and the Mathematics of Manipulation
Alan D. Taylor
Author : Alan D. Taylor
Publisher : Cambridge University Press
Page : 196 pages
File Size : 47,6 Mb
Release : 2005-05-09
Category : Business & Economics
ISBN : 0521008832
Social Choice and the Mathematics of Manipulation by Alan D. Taylor Pdf
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.
Mathematics of Social Choice
Christoph Borgers
Author : Christoph Borgers
Publisher : SIAM
Page : 233 pages
File Size : 50,9 Mb
Release : 2010-01-01
Category : Political Science
ISBN : 9780898717624
Mathematics of Social Choice by Christoph Borgers Pdf
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.
Zermelo’s Axiom of Choice
G.H. Moore
Author : G.H. Moore
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394785
Zermelo’s Axiom of Choice by G.H. Moore Pdf
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.
The Axiom of Choice
Thomas J. Jech
Author : Thomas J. Jech
Publisher : Courier Corporation
Page : 226 pages
File Size : 55,9 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486466248
The Axiom of Choice by Thomas J. Jech Pdf
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.
Illustrating Mathematics
Diana Davis
Author : Diana Davis
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 49,6 Mb
Release : 2020-10-16
Category : Education
ISBN : 9781470461225
Illustrating Mathematics by Diana Davis Pdf
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.
Equivalents of the Axiom of Choice
Herman Rubin,Jean E. Rubin
Author : Herman Rubin,Jean E. Rubin
Publisher : Elsevier
Page : 159 pages
File Size : 55,7 Mb
Release : 1963
Category : Axiom of choice
ISBN : 9780444533999
Equivalents of the Axiom of Choice by Herman Rubin,Jean E. Rubin Pdf
Physical Mathematics
Kevin Cahill
Author : Kevin Cahill
Publisher : Cambridge University Press
Page : 128 pages
File Size : 46,7 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781107310735
Physical Mathematics by Kevin Cahill Pdf
Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
Numbers
Graham Flegg
Author : Graham Flegg
Publisher : Courier Corporation
Page : 304 pages
File Size : 52,9 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486166513
Numbers by Graham Flegg Pdf
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.
A Synopsis of Elementary Results in Pure and Applied Mathematics
George Shoobridge Carr
Author : George Shoobridge Carr
Publisher : Unknown
Page : 128 pages
File Size : 51,9 Mb
Release : 1880
Category : Mathematics
ISBN : OXFORD:600025093
A Synopsis of Elementary Results in Pure and Applied Mathematics by George Shoobridge Carr Pdf
Mathematics for Machine Learning
Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Author : Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Publisher : Cambridge University Press
Page : 391 pages
File Size : 44,8 Mb
Release : 2020-04-23
Category : Computers
ISBN : 9781108470049
Mathematics for Machine Learning by Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong Pdf
Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.
Sets for Mathematics
F. William Lawvere,Robert Rosebrugh
Author : F. William Lawvere,Robert Rosebrugh
Publisher : Cambridge University Press
Page : 280 pages
File Size : 47,6 Mb
Release : 2003-01-27
Category : Mathematics
ISBN : 0521010608
Sets for Mathematics by F. William Lawvere,Robert Rosebrugh Pdf
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Numbers Rule
George Szpiro
Author : George Szpiro
Publisher : Princeton University Press
Page : 240 pages
File Size : 53,7 Mb
Release : 2020-11-03
Category : History
ISBN : 9780691209081
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.
Statistical Universals of Language
Kumiko Tanaka-Ishii
Author : Kumiko Tanaka-Ishii
Publisher : Springer Nature
Page : 230 pages
File Size : 43,6 Mb
Release : 2021-04-01
Category : Mathematics
ISBN : 9783030593773
Statistical Universals of Language by Kumiko Tanaka-Ishii Pdf
This volume explores the universal mathematical properties underlying big language data and possible reasons why such properties exist, revealing how we may be unconsciously mathematical in our language use. These properties are statistical and thus different from linguistic universals that contribute to describing the variation of human languages, and they can only be identified over a large accumulation of usages. The book provides an overview of state-of-the art findings on these statistical universals and reconsiders the nature of language accordingly, with Zipf's law as a well-known example. The main focus of the book further lies in explaining the property of long memory, which was discovered and studied more recently by borrowing concepts from complex systems theory. The statistical universals not only possibly lie as the precursor of language system formation, but they also highlight the qualities of language that remain weak points in today's machine learning. In summary, this book provides an overview of language's global properties. It will be of interest to anyone engaged in fields related to language and computing or statistical analysis methods, with an emphasis on researchers and students in computational linguistics and natural language processing. While the book does apply mathematical concepts, all possible effort has been made to speak to a non-mathematical audience as well by communicating mathematical content intuitively, with concise examples taken from real texts.