{"title":"Math - Theory","description":"\u003cmeta charset=\"utf-8\"\u003e\n\u003cp data-mce-fragment=\"1\"\u003eTheory remains one of our strongest mathematical publishing programs, with hundreds of low-priced texts available. Our comprehensive collection includes texts on abstract sets and finite ordinals, the algebraic theory of numbers, basic set theory, differential forms, group theory, matrix theory, permutation groups, symmetry, and more.\u003c\/p\u003e","products":[{"product_id":"9780486210964","title":"Recreations in the Theory of Numbers","description":"\u003cdiv\u003e\u003cdiv\u003e\u003cp\u003eNumber theory, the Queen of Mathematics, is an almost purely theoretical science. Yet it can be the source of endlessly intriguing puzzle problems, as this remarkable book demonstrates. This is the first book to deal exclusively with the recreational aspects of the subject and it is certain to be a delightful surprise to all devotees of the mathematical puzzle, from the rawest beginner to the most practiced expert. Almost every aspect of the theory of numbers that could conceivably be of interest to the layman is dealt with, all from the recreational point of view. Readers will become acquainted with divisors, perfect numbers, the ingenious invention of congruences by Gauss, scales of notation, endless decimals, Pythagorean triangles (there is a list of the first 100 with consecutive legs; the 100th has a leg of 77 digits), oddities about squares, methods of factoring, mysteries of prime numbers, Gauss's Golden Theorem, polygonal and pyramidal numbers, the Pell Equation, the unsolved Last Theorem of Fermat, and many other aspects of number theory, simply by learning how to work with them in solving hundreds of mathematical puzzle problems. The text is extremely clear and easy to follow, and it bears convincing evidence of the author's deep sense of humor and his outstanding ability to lure the reader through even the most difficult trails by skillfully revealing their fascination. The problems distributed throughout the book are explained in the final chapter and there is also a supplementary chapter containing 100 problems and their solutions, many original. There are over 100 tables.\u003cbr\u003eThe appeal of these stimulating puzzles lies in their ready comprehensibility and the fact that only high school math is needed to master the fundamental theory presented by the author. This theory is itself interesting and of use to the more serious math student, but it may be omitted by lay readers without diminishing the book's challenge or detracting from the pleasure-giving nuggets it contains.\u003c\/p\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eDover Original.\u003c\/div\u003e","brand":"Albert H. Beiler","offers":[{"title":"Default Title","offer_id":47159313301825,"sku":"9780486210964","price":15.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486210964.jpg?v=1710182768"},{"product_id":"9780486210100","title":"Essays on the Theory of Numbers","description":"\u003cdiv\u003e \u003cp\u003eThis volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.\u003cbr\u003eThe second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.\u003cbr\u003eThe contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by \"Vooster \" V. Beman.\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e \u003cp\u003eReprint of \"Stetigkeit und irrationale Zahlen\" and \"Was sind und was sollen die Zahlen?\" 1901 English translations.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"Richard Dedekind","offers":[{"title":"Default Title","offer_id":47159319626049,"sku":"9780486210100","price":9.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486210100.jpg?v=1710182799"},{"product_id":"9780486450100","title":"Differential Forms","description":"\u003cdiv\u003e\"Cartan's work provides a superb text for an undergraduate course in advanced calculus, but at the same time it furnishes the reader with an excellent foundation for global and nonlinear algebra.\" — \u003ci\u003eMathematical Review\u003c\/i\u003e\u003cbr\u003e\"Brilliantly successful.\" — \u003ci\u003eBulletin de l'Association des Professeurs de Mathematiques\u003c\/i\u003e\u003cbr\u003e\"The presentation is precise and detailed, the style lucid and almost conversational . . . clearly an outstanding text and work of reference.\" — \u003ci\u003eAnnales\u003c\/i\u003e\u003cbr\u003eCartan's \u003ci\u003eFormes Differentielles\u003c\/i\u003e was first published in France in 1967. It was based on the world-famous teacher's experience at the Faculty of Sciences in Paris, where his reputation as an outstanding exponent of the Bourbaki school of mathematics was first established.\u003cbr\u003eAddressed to second- and third-year students of mathematics, the material skillfully spans the pure and applied branches in the familiar French manner, so that the applied aspects gain in rigor while the pure mathematics loses none of its dignity. This book is equally essential as a course text, as a work of reference, or simply as a brilliant mathematical exercise.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the Kershaw Publishing Company Limited, London, 1971 edition.\u003c\/div\u003e\u003c\/div\u003e","brand":"Henri Cartan","offers":[{"title":"Default Title","offer_id":47159372316993,"sku":"9780486450100","price":14.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486450100.jpg?v=1710195676"},{"product_id":"9780486404554","title":"Variational Methods in Optimization","description":"\u003cdiv\u003e\u003cdiv\u003eFostering an increased appreciation of the fundamental theorem of calculus, this highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. A clear and well-illustrated treatment of techniques for solving a wide variety of optimization problems arising in a diverse array of fields, this volume requires only an elementary knowledge of calculus and can be used either by itself or as a supplementary text in a variety of courses. 1974 edition.\u003c\/div\u003e\u003c\/div\u003e","brand":"Donald R. Smith","offers":[{"title":"Default Title","offer_id":47159994188097,"sku":"9780486404554","price":19.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486404554.jpg?v=1710208885"},{"product_id":"9780486406824","title":"Differential Games","description":"\u003cdiv\u003e \u003cdiv\u003eOne of the definitive works in game theory, this fascinating volume offers an original look at methods of obtaining solutions for conflict situations. Combining the principles of game theory, the calculus of variations, and control theory, the author considers and solves an amazing array of problems: military, pursuit and evasion, games of firing and maneuver, athletic contests, and many other problems of conflict.\u003cbr\u003eBeginning with general definitions and the basic mathematics behind differential game theory, the author proceeds to examinations of increasingly specific techniques and applications: dispersal, universal, and equivocal surfaces; the role of game theory in warfare; development of an effective theory despite incomplete information; and more. All problems and solutions receive clearly worded, illuminating discussions, including detailed examples and numerous formal calculations. \u003cbr\u003eThe product of fifteen years of research by a highly experienced mathematician and engineer, this volume will acquaint students of game theory with practical solutions to an extraordinary range of intriguing problems.\u003cbr\u003e\n\u003c\/div\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the John Wiley and Sons, Inc., New York, 1965 edition.\u003c\/div\u003e","brand":"Rufus Isaacs","offers":[{"title":"Default Title","offer_id":47160013750593,"sku":"9780486406824","price":24.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486406824_619e55ad-2048-4c54-b5b9-78eab5823af3.jpg?v=1710179703"},{"product_id":"9780486417400","title":"Riemann's Zeta Function","description":"\u003cdiv\u003e\u003cp\u003eBernhard Riemann's eight-page paper entitled \"On the Number of Primes Less Than a Given Magnitude\" was a landmark publication of 1859 that directly influenced generations of great mathematicians, among them Hadamard, Landau, Hardy, Siegel, Jensen, Bohr, Selberg, Artin, and Hecke. This text, by a noted mathematician and educator, examines and amplifies the paper itself, and traces the developments in theory inspired by it. (An English translation of the original document appears in the Appendix.)\u003cbr\u003eTopics include Riemann's main formula, the prime number theorem, de la Vallée Poussin's theorem, numerical analysis of roots by Euler-Maclaurin summation, the Riemann-Siegel formula, largescale computations, Fourier analysis, zeros on the line, the Riemann hypothesis and Farey series, alternative proof of the integral formula, Tauberian theorems, Chebyshev's identity, and other related topics.\u003cbr\u003eThis inexpensive edition of Edwards' superb high-level study will be welcomed by students and mathematicians. Mathematically inclined general readers will likewise value this influential classic.\u003c\/p\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Academic Press, Inc., San Diego, 1974 edition.\u003c\/div\u003e prime obsession;complex variable;formal math;mathematical exposition;gamma function;complex mathematics;complex plane;reimann hypothesis;popular mathematics;popular math;math knowledge;math courses;marcus du;abstract algebra;primitive roots;mathematical world;mathematical topics;john derbyshire;college math;mathematical knowledge;du sautoy;advanced concepts;complex analysis;biographical background;mathematical background;famous mathematicians;math history;advanced math;math background;golden key;dollar prize;math major;energy levels;mathematical ideas;school math;mathematical concepts;math concepts;political context;white supremacist;mathematically inclined;chaos theory;liberal arts;quantum physics;job explaining;historical background;eigenvalues;titchmarsh;sabbagh;combinatorial;poussin;quadratic;even-numbered;non-math;fermat;non-mathematicians;fourier;euler;non-mathematical;odd-numbered;littlewood;matrices;non-trivial;hilbert;primes;gauss;zeros;theorems;zeroes;one-half;bernhard;1859;analytic;calculus;maths;proofs;distribution;mathematician;numbered;unsolved;infinite;dollars;riemann;books on popular mathematics;books on prime obsessions;books on complex mathematics;books on mathematical worlds;books on popular maths;books on mathematical topics;books on complex variables;books on math courses;books on abstract algebras;books on mathematical knowledges;books on mathematical expositions;books on college maths;books on math knowledges;books on formal maths;books on marcus du","brand":"H. M. Edwards","offers":[{"title":"Default Title","offer_id":47160126341441,"sku":"9780486417400","price":22.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486417400.jpg?v=1739294932"},{"product_id":"9780486421827","title":"Symmetry","description":"\u003cdiv\u003e\u003cdiv\u003e\u003cp\u003eThe crucial significance of symmetry to the development of group theory and in the fields of physics and chemistry cannot be overstated, and this well-organized volume provides an excellent introduction to the topic.\u003cbr\u003eThe text develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion, leading students to a point from which they can proceed easily to more elaborate applications. The finite groups describing the symmetry of regular polyhedral and of repeating patterns are emphasized, and geometric illustrations of all main processes appear here — including more than 100 fully worked examples.\u003cbr\u003eDesigned to be read at a variety of levels and to allow students to focus on any of the main fields of application, this volume is geared toward advanced undergraduate and graduate physics and chemistry students with the requisite mathematical background.\u003c\/p\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Macmillan Company, New York, 1963 edition.\u003c\/div\u003e","brand":"Roy McWeeny","offers":[{"title":"Default Title","offer_id":47160165368129,"sku":"9780486421827","price":16.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486421827_f81094f6-563f-49be-900e-2a2765dbdb74.jpg?v=1710207702"},{"product_id":"9780486435152","title":"Concepts of Mathematical Modeling","description":"\u003cdiv\u003e\u003cdiv\u003eAppropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the McGraw-Hill Book Company, New York, 1984 edition.\u003c\/div\u003e\u003c\/div\u003e","brand":"Walter J. Meyer","offers":[{"title":"Default Title","offer_id":47160321769793,"sku":"9780486435152","price":26.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486435152_06a236cf-7f48-475c-bce8-5b32e31d3080.jpg?v=1710206243"},{"product_id":"9780486435206","title":"The Philosophy of Set Theory","description":"\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003eA century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. \u003cbr\u003eAs Cantor's sometime collaborator, David Hilbert, remarked, \"No one will drive us from the paradise that Cantor has created.\" This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure. \u003cbr\u003ePhilosophers with only a basic grounding in mathematics, as well as mathematicians who have taken only an introductory course in philosophy, will find an abundance of intriguing topics in this text, which is appropriate for undergraduate-and graduate-level courses. \u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e \u003cdiv\u003e \u003cdiv\u003eReprint of the Basil Blackwell Ltd., Oxford, England, 1989 edition.\u003c\/div\u003e\n\u003c\/div\u003e\n\u003c\/div\u003e","brand":"Mary Tiles","offers":[{"title":"Default Title","offer_id":47160322195777,"sku":"9780486435206","price":19.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486435206.jpg?v=1710206241"},{"product_id":"9780486458069","title":"The Number System","description":"\u003cdiv\u003eThe teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.\u003cbr\u003eThis volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant concepts.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the 1967 Dover edition.\u003c\/div\u003e\u003c\/div\u003e","brand":"H. A. Thurston","offers":[{"title":"Default Title","offer_id":47160610226497,"sku":"9780486458069","price":9.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486458069.jpg?v=1710209029"},{"product_id":"9780486459165","title":"Problems in Group Theory","description":"\u003cdiv\u003eThe most effective way to study any branch of mathematics is to tackle its problems. This wide-ranging anthology offers a straightforward approach, with 431 challenging problems in all phases of group theory, from elementary to the most advanced.\u003cbr\u003eThe problems are arranged in eleven chapters: subgroups, permutation groups, automorphisms and finitely generated Abelian groups, normal series, commutators and derived series, solvable and nilpotent groups, the group ring and monomial representations, Frattini subgroup, factorization, linear groups, and representations and characters. Each chapter features a preface of pertinent definitions and theorems, and full solutions appear in a separate section.\u003cbr\u003eMost of these problems are derived from research papers published since 1950 (a listing of 102 references is supplied). This compilation makes them readily accessible as a supplement to courses in group theory. The presentation places equal emphasis on techniques and results, encouraging the development of both skill and comprehension.\u003cbr\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the Dover 1973 edition.\u003c\/div\u003e\u003c\/div\u003e","brand":"John D. Dixon","offers":[{"title":"Default Title","offer_id":47160617271617,"sku":"9780486459165","price":12.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486459165.jpg?v=1710193101"},{"product_id":"9780486462677","title":"Diophantine Approximations","description":"\u003cdiv\u003eThis self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts.\u003cbr\u003eThe author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discussion. Each chapter concludes with a bibliographic account of closely related work; these sections also contain the sources from which the proofs are drawn.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the John Wiley \u0026amp; Sons, Inc., New York, 1963 edition.\u003c\/div\u003e\u003c\/div\u003e","brand":"Ivan Niven","offers":[{"title":"Default Title","offer_id":47160646271297,"sku":"9780486462677","price":7.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486462677.jpg?v=1710176863"},{"product_id":"9780486466668","title":"Algebraic Theory of Numbers","description":"\u003cdiv\u003eAlgebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics — algebraic geometry, in particular.\u003cbr\u003eThis book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Galois theory, Noetherian rings and modules, and rings of fractions. It covers the basics, starting with the divisibility theory in principal ideal domains and ending with the unit theorem, finiteness of the class number, and the more elementary theorems of Hilbert ramification theory. Numerous examples, applications, and exercises appear throughout the text.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the Hermann, Paris, and Houghton Mifflin Company, Boston, 1970 edition.\u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e","brand":"Pierre Samuel","offers":[{"title":"Default Title","offer_id":47160678908225,"sku":"9780486466668","price":11.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486466668_18fd5958-0cac-4de4-bb7e-68a72c862bce.jpg?v=1710204115"},{"product_id":"9780486469218","title":"Set Theory and the Continuum Hypothesis","description":"\u003cdiv\u003eThis exploration of a notorious mathematical problem is the work of the man who discovered the solution. The independence of the continuum hypothesis is the focus of this study by Paul J. Cohen. It presents not only an accessible technical explanation of the author's landmark proof but also a fine introduction to mathematical logic. An emeritus professor of mathematics at Stanford University, Dr. Cohen won two of the most prestigious awards in mathematics: in 1964, he was awarded the American Mathematical Society's Bôcher Prize for analysis; and in 1966, he received the Fields Medal for Logic. \u003cbr\u003eIn this volume, the distinguished mathematician offers an exposition of set theory and the continuum hypothesis that employs intuitive explanations as well as detailed proofs. The self-contained treatment includes background material in logic and axiomatic set theory as well as an account of Kurt Gödel's proof of the consistency of the continuum hypothesis. An invaluable reference book for mathematicians and mathematical theorists, this text is suitable for graduate and postgraduate students and is rich with hints and ideas that will lead readers to further work in mathematical logic. \u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the W. A. Benjamin, Inc., New York, 1966 edition.\u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e","brand":"Paul J. Cohen","offers":[{"title":"Default Title","offer_id":47160715968833,"sku":"9780486469218","price":15.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486469218.jpg?v=1710193339"},{"product_id":"9780486469317","title":"Elementary Number Theory","description":"\u003cdiv\u003eIdeal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems—some computational and some classical, many original, and some with complete solutions. \u003cbr\u003eThe opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the W. H. Freeman and Company, San Francisco, second 1978 edition.\u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e   \u003c\/div\u003e A solutions manual to accompany this text is available for free download. \u003cu\u003e\u003ca target=\"_blank\" href=\"https:\/\/www.doverpublications.com\/solutions\/46931x.pdf\"\u003eClick here\u003c\/a\u003e\u003c\/u\u003e to download PDF version now.\u003cbr\u003e\u003cp\u003e\u003cb\u003eBonus Editorial Feature\u003c\/b\u003e\u003c\/p\u003e\u003cdiv\u003e \u003cp\u003eUnderwood Dudley: Cranking Out Classics  \u003c\/p\u003e\n\u003cp\u003eAny editor involved with publishing in mathematics for any length of time is familiar with the phenomena — the receipt, usually via snail mail, of generally handwritten, and generally interminable, really, really interminable, theses on some bizarre and unprovable point — theses hoping, trying against all hope, demanding in fact, to prove the unprovable, to rewrite some fundamental part of mathematics, often in my experience to demonstrate for one final time that, for example, Einstein didn't know what he was talking about — in short, the work of a mathematical crank!  \u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cp\u003eUnderwood Dudley (Woody to everyone in the math world), Professor Emeritus, Depauw University, provided an inestimable service to all math editors in the universe by demonstrating that they are not alone in their experience. His unique and wonderful book \u003ci\u003eMathematical Cranks\u003c\/i\u003e (The Mathematics Association of America, 1992) is a readable feast, especially for those who have been on the receiving end of mathematical crank mail. We're all in Woody's debt for having assembled this collection of failed squared circles, angle trisections, and much, much more.  \u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cp\u003eHowever, chronicling the cranks — as enjoyable as it may have been to the rest of us — is hardly a career, Woody has written many other books as well. And any reader who wants to check out a totally uncranky, reader- and student-friendly, time-tested basic text in \u003ci\u003eElementary Number Theory\u003c\/i\u003e could hardly do better than to look at the Dover edition of Woody's book by that name, which started its career with Freeman in 1969 and which Dover was pleased to reprint in 2008.\u003c\/p\u003e\n\u003c\/div\u003e math texts;abstract mathematics;popular math;square roots;education majors;zeta function;abstract algebra;primitive roots;studying mathematics;theory class;advanced concepts;mathematical proof;pure mathematics;complex analysis;mathematical background;wait awhile;pleasant memories;odd times;everyday language;liberal arts;polynomials;combinatorial;combinatorics;one-semester;quadratic;partitions;fermat;ogilvy;integers;self-study;primes;gauss;algebraic;computational;errata;theorems;cranks;cryptography;fractions;notation;calculus;generating;proofs;equations;excursion;mathematician;undergraduate;andrews;hardy;functions;textbook;exercises;study mathematics;books on combinatorics;books on advanced concepts;waiting awhile;books on math texts;books on square roots;books on theorems;books on notations;books on fermat;books on pure mathematics;books on functions;books on textbooks;books on complex analysis;books on proofs;books on studying mathematics;books on errata;books on cryptographies;books on excursions;books on odd times;books on calculus;books on partitions;books on exercises;books on fractions;books on popular maths;books on equations;books on theory classes;books on polynomials;books on abstract algebras;books on ogilvy;generate;books on everyday languages;books on andrews;books on cranks;books on education majors;books on zeta functions;books on self-studies;books on integers;books on abstract mathematics;books on liberal arts;books on mathematical proofs;books on gauss","brand":"Underwood Dudley","offers":[{"title":"Default Title","offer_id":47160718262593,"sku":"9780486469317","price":17.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486469317.jpg?v=1710181080"},{"product_id":"9780486471730","title":"Lattice Theory","description":"\u003cdiv\u003eLattice theory extends into virtually every area of mathematics and offers an ideal framework for understanding basic concepts. This outstanding text is written in clear, direct language and enhanced with many research problems, exercises, diagrams, and concise proofs. The author discusses historical developments as well as future directions and provides extensive end-of-chapter materials and references.\u003cbr\u003eBoth novices and experts will benefit from this treatment, which combines the techniques of an introductory text with those of a monograph. It begins with a concise development of the fundamentals of lattice theory and a detailed exploration of free lattices. The core of the text focuses upon the theory of distributive lattices. Diagrams constitute an integral part of the book, along with 500 exercises and 67 original research problems. Eight appendixes, contributed by a group of experts, complement this accessible and informative text.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the W. H. 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There follows a rigorous investigation of the relations holding between the mathematical and physical theories.\u003cbr\u003eTopics covered include: unitary geometry, quantum theory (Schrödinger's wave equation, transition probabilities, directional quantization, collision phenomena, Zeeman and Stark effects); groups and their representations (sub-groups and conjugate classes, linear transformations, rotation and Lorentz groups, closed continuous groups, invariants and covariants, Lie's theory); applications of group theory to quantum mechanics (simple state and term analysis, the spinning electron, multiplet structure, energy and momentum, Pauli exclusion principle, problem of several bodies, Maxwell-Dirac field equations, etc.); the symmetric permutation group; and algebra of symmetric transformation (invariant sub-spaces in group and tensor space, sub-groups, Young's symmetry operators, spin and valence, group theoretic classification of atomic spectra, branching laws, etc).\u003cbr\u003eThroughout, Dr. Weyl emphasizes the \"reciprocity\" between representations of the symmetric permutation group and those of the complete linear group. His simplified treatment of \"reciprocity,\" the Clebsch-Gordan series, and the Jordan-Hölder theorem and its analogues, has helped to clarity these and other complex topics.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the English, 1931 edition.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eBonus Editorial Feature\u003c\/b\u003e\u003c\/p\u003e\u003cdiv\u003e\u003cdiv\u003e\n\u003cp\u003eHermann Weyl: The Search for Beautiful Truths \u003c\/p\u003e\n\u003cp\u003eOne of the most influential mathematicians of the twentieth century, Hermann Weyl (1885–1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, \u003ci\u003eThe Theory of Groups and Quantum Mechanics\u003c\/i\u003e and \u003ci\u003eSpace, Time, Matter\u003c\/i\u003e. Two others, \u003ci\u003eThe Continuum\u003c\/i\u003e and \u003ci\u003eThe Concept of a Riemann Surface\u003c\/i\u003e were added to the Dover list in recent years. \u003c\/p\u003e\n\u003cp\u003e\u003cb\u003e\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eIn the Author's Own Words:\u003cbr\u003e\"My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.\" \u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.\" \u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.\" — Hermann Weyl \u003c\/p\u003e\n\u003cp\u003e\u003cb\u003e\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eCritical Acclaim for \u003ci\u003eSpace, Time, Matter\u003c\/i\u003e:\u003cbr\u003e\"A classic of physics . . . the first systematic presentation of Einstein's theory of relativity.\" — \u003ci\u003eBritish Journal for Philosophy and Science\u003c\/i\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003c\/div\u003e","brand":"Hermann Weyl","offers":[{"title":"Default Title","offer_id":47160794317121,"sku":"9780486602691","price":22.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486602691.jpg?v=1710193874"},{"product_id":"9780486604343","title":"Mathematical Foundations of Information Theory","description":"\u003cdiv\u003e\u003cdiv\u003eThe first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein, and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists, and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.\u003cbr\u003eIn his first paper, Dr. Khinchin develops the concept of entropy in probability theory as a measure of uncertainty of a finite “scheme,” and discusses a simple application to coding theory. The second paper investigates the restrictions previously placed on the study of sources, channels, and codes and attempts “to give a complete, detailed proof of both … Shannon theorems, assuming any ergodic source and any stationary channel with a finite memory.”\u003cbr\u003ePartial Contents: I. The Entropy Concept in Probability Theory — Entropy of Finite Schemes. The Uniqueness Theorem. Entropy of Markov chains. Application to Coding Theory. II. On the Fundamental Theorems of Information Theory — Two generalizations of Shannon’s inequality. Three inequalities of Feinstein. Concept of a source. Stationarity. Entropy. Ergodic sources. The E property. The martingale concept. Noise. Anticipation and memory. Connection of the channel to the source. Feinstein’s Fundamental Lemma. Coding. The first Shannon theorem. The second Shannon theorem.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the first English translation, 1957.\u003c\/div\u003e","brand":"A. I. Khinchin","offers":[{"title":"Default Title","offer_id":47160795988289,"sku":"9780486604343","price":10.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486604343.jpg?v=1710207088"},{"product_id":"9780486616308","title":"Axiomatic Set Theory","description":"\u003cdiv\u003e\u003cp\u003eOne of the most pressing\u003cb\u003e\u003c\/b\u003eproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: \"Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?\" Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level. \u003cbr\u003eThe opening chapter covers the basic paradoxes and the history of set theory and provides a motivation for the study. The second and third chapters cover the basic definitions and axioms and the theory of relations and functions. Beginning with the fourth chapter, equipollence, finite sets and cardinal numbers are dealt with. Chapter five continues the development with finite ordinals and denumerable sets. Chapter six, on rational numbers and real numbers, has been arranged so that it can be omitted without loss of continuity. In chapter seven, transfinite induction and ordinal arithmetic are introduced and the system of axioms is revised. The final chapter deals with the axiom of choice. Throughout, emphasis is on axioms and theorems; proofs are informal. Exercises supplement the text. Much coverage is given to intuitive ideas as well as to comparative development of other systems of set theory. Although a degree of mathematical sophistication is necessary, especially for the final two chapters, no previous work in mathematical logic or set theory is required. \u003cbr\u003eFor the student of mathematics, set theory is necessary for the proper understanding of the foundations of mathematics. Professor Suppes in \u003ci\u003eAxiomatic Set Theory \u003c\/i\u003eprovides a very clear and well-developed approach. For those with more than a classroom interest in set theory, the historical references and the coverage of the rationale behind the axioms will provide a strong background to the major developments in the field. 1960 edition.\u003c\/p\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the original, 1960 edition.\u003c\/div\u003e","brand":"Patrick Suppes","offers":[{"title":"Default Title","offer_id":47160802083137,"sku":"9780486616308","price":16.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486616308.jpg?v=1710207570"},{"product_id":"9780486623429","title":"Galois Theory","description":"\u003cdiv\u003e\u003cdiv\u003e\u003cp\u003eIn the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications.\u003cbr\u003eThe first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more.\u003cbr\u003eDr. Milgram's section on applications discusses solvable groups, permutation groups, solution of equations by radicals, and other concepts.\u003c\/p\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Notre Dame Press, 1944 edition.\u003c\/div\u003e algebra text;algebra textbook;mathematical objects;gamma function;level math;abstract algebra;self study;math text;algebra class;linear algebra;advanced math;highly disorganized;carefully explained;ivory tower;tensors;strang;kummer;algebras;polynomials;noether;lemma;factorization;solvability;evariste;hungerford;symmetric;self-study;permutation;algebraic;pinter;theorems;solvable;joining;foote;quotient;jacobson;mathematics;radicals;mathematicians;proofs;undergrad;equations;undergraduate;properties;applications;rigorous;exercises;fields;artin;books on factorizations;books on lemma;books on radicals;books on theorems;books on algebra textbooks;books on pinter;books on linear algebras;books on advanced maths;books on evariste;books on algebras;books on level maths;books on proofs;books on strang;books on tensors;books on algebra classes;books on permutations;books on mathematicians;books on self studies;books on kummer;books on exercises;books on hungerford;books on mathematical objects;books on properties;books on quotients;books on algebra texts;books on ivory towers;books on equations;books on polynomials;books on abstract algebras;books on undergrads;books on math texts;books on mathematics;books on foote;join;books on self-studies;books on jacobson;books on applications;books on fields","brand":"Edited by Arthur N. Milgram","offers":[{"title":"Default Title","offer_id":47160802607425,"sku":"9780486623429","price":9.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486623429.jpg?v=1710177649"},{"product_id":"9780486638294","title":"Set Theory and Logic","description":"\u003cdiv\u003e\u003cdiv\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e\n\u003ci\u003eSet Theory and Logic \u003c\/i\u003eis the result of a course of lectures for advanced undergraduates, developed at Oberlin College for the purpose of introducing students to the conceptual foundations of mathematics. Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. One of the most complex and essential of modern mathematical innovations, the theory of sets (crucial to quantum mechanics and other sciences), is introduced in a most careful concept manner, aiming for the maximum in clarity and stimulation for further study in set logic. \u003cbr\u003eContents include: Sets and Relations — Cantor's concept of a set, etc.\u003cbr\u003eNatural Number Sequence — Zorn's Lemma, etc.\u003cbr\u003eExtension of Natural Numbers to Real Numbers\u003cbr\u003eLogic — the Statement and Predicate Calculus, etc.\u003cbr\u003eInformal Axiomatic Mathematics\u003cbr\u003eBoolean Algebra\u003c\/div\u003e\n\u003cdiv\u003eInformal Axiomatic Set Theory\u003c\/div\u003e\n\u003cdiv\u003eSeveral Algebraic Theories — Rings, Integral Domains, Fields, etc.\u003cbr\u003eFirst-Order Theories — Metamathematics, etc.\u003cbr\u003eSymbolic logic does not figure significantly until the final chapter. The main theme of the book is mathematics as a system seen through the elaboration of real numbers; set theory and logic are seen s efficient tools in constructing axioms necessary to the system. \u003cbr\u003eMathematics students at the undergraduate level, and those who seek a rigorous but not unnecessarily technical introduction to mathematical concepts, will welcome the return to print of this most lucid work. \u003c\/div\u003e\n\u003cdiv\u003e\n\u003cbr\u003e\"Professor Stoll . . . has given us one of the best introductory texts we have seen.\" — \u003ci\u003eCosmos\u003c\/i\u003e. \u003c\/div\u003e\n\u003c\/div\u003e\n\u003cbr\u003e\"In the reviewer's opinion, this is an excellent book, and in addition to its use as a textbook (it contains a wealth of exercises and examples) can be recommended to all who wish an introduction to mathematical logic less technical than standard treatises (to which it can also serve as preliminary reading).\" —\u003ci\u003e Mathematical Reviews.\u003c\/i\u003e\n\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e \u003cdiv\u003eCorrected (1979) reprint of the W. H. Freeman \u0026amp; Co., San Francisco, 1963 edition.\u003c\/div\u003e\n\u003c\/div\u003e","brand":"Robert R. Stoll","offers":[{"title":"Default Title","offer_id":47160806015297,"sku":"9780486638294","price":22.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486638294.jpg?v=1710207545"},{"product_id":"9780486642161","title":"The Mathematics of Games of Strategy","description":"\u003cdiv\u003eMelvin Dresher, noted research mathematician for the Rand Corporation, puts forth an exceptionally clear presentation of the mathematical theory of games of strategy and its applications to many fields including: economics, military, business, and operations research. The mathematical presentation is elementary in the sense that no advanced algebra or non-elementary calculus occurs in most of the mathematical proofs.\u003cbr\u003eThe author presents game theory as a branch of applied mathematics. In addition to developing a mathematical theory for solving games, he shows how to formulate a game model associated with a given competitive or conflicting situation. Furthermore, he shows how some decision problems, such as timing of decisions, which do not resemble game situations, can be analyzed as a game, yielding rich insights into the decision problems.\u003cbr\u003eBeginning with an exposition of games of strategy, with examples from parlor games as well as military games, Dr. Dresher proceeds to treat the basic topics in the theory of finite games, i.e., the existence of optimal strategies and their properties. An elementary proof of the minimax theorem is given that provides an efficient method for computing optimal strategies.\u003cbr\u003eSince many games involve an infinite number of strategies, succeeding chapters deal with such games by first developing the necessary mathematics (e.g., probability distribution functions and Stieltjes integrals) for analyzing infinite games. The results of infinite games are then applied to two general classes of games — timing games and tactical games. A final chapter provides an application of moment space theory to the solution of infinite games.\u003cbr\u003eThis is a book about decision making in the absence of perfect information. In particular, it analyzes decision problems in a competitive environment where conflicting interests exist, and uncertainties and risk are involved. For the reader who is interested in the applications of the theory of games of strategy to military, economic, or political problems, or to decision making in business, operations research, or the behavior sciences, it will prove a most rewarding study.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of \u003ci\u003eGames of Strategy: Theory and Applications\u003c\/i\u003e, A Rand Corporation Research Study, 1981.\u003c\/div\u003e","brand":"Melvin Dresher","offers":[{"title":"Default Title","offer_id":47160809029953,"sku":"9780486642161","price":12.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486642161.jpg?v=1710177647"},{"product_id":"9780486656205","title":"Number Theory and Its History","description":"\u003cp\u003e\"A very valuable addition to any mathematical library.\" — \u003ci\u003eSchool Science and Math\u003cbr\u003e\u003c\/i\u003eThis book, written by a prominent mathematician and Sterling Professor of Mathematics at Yale, differs from most other books on number theory in two important ways: first, it presents the principal ideas and methods of number theory within a historical and cultural framework, making the subject more tangible and easily grasped. Second, the material requires substantially less mathematical background than many comparable texts. Technical complications and mathematical requirements have been kept to a minimum in order to make the book as accessible as possible to readers with limited mathematical knowledge. For the majority of the book, a basic knowledge of algebra will suffice.\u003cbr\u003eIn developing the importance and meaning of number theory in the history of mathematics, Professor Ore documents the contributions of a host of history's greatest mathematicians: Diophantos, Euclid, Fibonacci, Euler, Fermat, Mersenne, Gauss, and many more, showing how these thinkers evolved the major outlines of number theory. Topics covered include counting and recording of numbers, the properties of numbers, prime numbers, the Aliquot parts, indeterminate problems, theory of linear indeterminate problems, Diophantine problems, congruences, analysis of congruences, Wilson's Theorem, Euler's Theorem, theory of decimal expansions, the converse of Fermat's Theorem, and the classical construction problems.\u003cbr\u003eBased on a course the author gave for a number of years at Yale, this book covers the essentials of number theory with a clarity and avoidance of abstruse mathematics that make it an ideal resource for undergraduates or for amateur mathematicians. It has even been recommended for self-study by gifted high school students.\u003cbr\u003eIn short, \u003ci\u003eNumber Theory and Its History\u003c\/i\u003e offers an unusually interesting and accessible presentation of one of the oldest and most fascinating provinces of mathematics. This inexpensive paperback edition will be a welcome addition to the libraries of students, mathematicians, and any math enthusiast.\u003c\/p\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the McGraw-Hill Book Company, New York, 1948 edition.\u003c\/div\u003e","brand":"Oystein Ore","offers":[{"title":"Default Title","offer_id":47160820302145,"sku":"9780486656205","price":16.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486656205.jpg?v=1710207829"},{"product_id":"9780486659435","title":"Games and Decisions","description":"\u003cdiv\u003eSuperb non-technical introduction to game theory, primarily applied to social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, more. Bibliography.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the JohnWiley and Sons, New York, 1957 edition.\u003c\/div\u003e","brand":"R. Duncan Luce and Howard Raiffa","offers":[{"title":"Default Title","offer_id":47160824561985,"sku":"9780486659435","price":29.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486659435_ad71a603-5a7f-4117-a0ab-1d0544f80fcd.jpg?v=1710176919"},{"product_id":"9780486661650","title":"Theory and Application of Infinite Series","description":"\u003cdiv\u003e\u003cdiv\u003eThis classic work, written in a clear and interesting style, with many exercises, offers a thorough and reliable treatment of an important branch of higher analysis. It lends itself well to use in course work; however, because of its consistent clear illustrations of theoretical difficulties, the book is also ideal for self-study.\u003cbr\u003eSince all higher analysis depends on the theory of numbers, Professor Knopp (formerly Professor of Mathematics, University of Tübingen) begins with an introduction to the theory of real numbers, an indispensable foundation for what is to come. This introduction is followed by an extensive account of the theory of sequences and the actual theory of infinite series. The latter is covered in two stages: (1) the classical theory (2) later developments of the 19th century.\u003cbr\u003eCarefully selected exercises have been included throughout, emphasizing applications of the theory, rather than purely theoretical considerations.\u003cbr\u003eAimed at students already acquainted with the elements of differential and integral calculus, this work grew out of the author's lectures and course work at the universities of Berlin and Königsberg. This pedagogical background helped him achieve a work of utmost clarity and precision — one that belongs in the library of every serious mathematician or student of higher analysis.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Blackie \u0026amp; Son, Ltd., London and Glasgow, 1951 edition.\u003c\/div\u003e","brand":"Konrad Knopp","offers":[{"title":"Default Title","offer_id":47160828395841,"sku":"9780486661650","price":22.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486661650.jpg?v=1710193333"},{"product_id":"9780486663289","title":"Matrices and Linear Transformations","description":"\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003e\"Comprehensive . . . an excellent introduction to the subject.\" — \u003ci\u003eElectronic Engineer's Design Magazine\u003c\/i\u003e.\u003cbr\u003eThis introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. \u003cbr\u003eContents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. \u003cbr\u003eThe first seven chapters, which require only a first course in calculus and analytic geometry, deal with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Chapters 8 and 9, parts of which require the student to have completed the normal course sequence in calculus and differential equations, provide introductions to matrix analysis and numerical linear algebra, respectively. Among the key features are coverage of spectral decomposition, the Jordan canonical form, the solution of the matrix equation AX = XB, and over 375 problems, many with answers.\u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Addison-Wesley Publishing Company, Reading, Massachusetts, second, 1972 edition.\u003c\/div\u003e matrix operations;pure mathematics;differential equations;functional analysis;analytic geometry;optimal control;ordinary differential;theory stands;applied math;maximum information;number theory;vector spaces;signal processing;math majors;linear equations;markov chains;numerical methods;missing concepts;graph theory;abstract algebra;self study;primitive roots;partial differential;communication theory;mathematical notation;assigned textbook;mathematical rigor;pure math;math text;mathematical proofs;advanced concepts;linear algebra;mathematical background;probability theory;mathematical theory;claude shannon;advanced topics;information theory;classic text;graduate level;practical applications;introductory text;liberal arts;deeper understanding;firm grasp;farlow;pinsky;dieudonne;vectors;pugh;kemeny;berge;haberman;bostock;digits;krantz;eigenvalues;topology;chartrand;tenenbaum;bartle;polynomials;dudley;bessel;boyce;combinatorial;coefficients;one-semester;laplace;hamiltonian;axler;quadratic;fourier;diff;determinants;self-study;calculus;hardy;stewart;functions;manual;theorems;pollard;odes;trudeau;solutions;taylor;entropy;canonical;graphs;rigorous;suggestion;exercises;complaints;books on differential equations;books on self studies;books on numerical methods;books on theory stands;books on graph theories;books on analytic geometries;books on signal processings;books on applied maths;books on functional analysis;books on optimal controls;books on pure mathematics","brand":"Charles G. Cullen","offers":[{"title":"Default Title","offer_id":47160830984513,"sku":"9780486663289","price":25.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486663289.jpg?v=1710207771"},{"product_id":"9780486665214","title":"Information Theory","description":"\u003cdiv\u003e\u003cdiv\u003eDeveloped by Claude Shannon and Norbert Wiener in the late 1940s, information theory, or statistical communication theory, deals with the theoretical underpinnings of a wide range of communication devices: radio, television, radar, computers, telegraphy, and more. This book is an excellent introduction to the mathematics underlying the theory.\u003cbr\u003eDesigned for upper-level undergraduates and first-year graduate students, the book treats three major areas: analysis of channel models and proof of coding theorems (chapters 3, 7, and 8); study of specific coding systems (chapters 2, 4, and 5); and study of statistical properties of information sources (chapter 6). Among the topics covered are noiseless coding, the discrete memoryless channel, effort correcting codes, information sources, channels with memory, and continuous channels.\u003cbr\u003eThe author has tried to keep the prerequisites to a minimum. However, students should have a knowledge of basic probability theory. Some measure and Hilbert space theory is helpful as well for the last two sections of chapter 8, which treat time-continuous channels. An appendix summarizes the Hilbert space background and the results from the theory of stochastic processes necessary for these sections. The appendix is not self-contained but will serve to pinpoint some of the specific equipment needed for the analysis of time-continuous channels.\u003cbr\u003eIn addition to historic notes at the end of each chapter indicating the origin of some of the results, the author has also included 60 problems with detailed solutions, making the book especially valuable for independent study.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Interscience Publishers, New York, 1965 edition.\u003c\/div\u003e","brand":"Robert B. 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In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.\u003cbr\u003e Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.\u003cbr\u003e Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated.\u003c\/p\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the W. B. Saunders Co., Philadelphia, PA, 1971 edition.\u003c\/div\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eBonus Editorial Feature\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eThe Holy Grail of Number Theory  \u003c\/p\u003e\u003cp\u003eGeorge E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text \u003ci\u003eNumber Theory\u003c\/i\u003e (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field — number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well.  \u003c\/p\u003e\u003cp\u003eIn 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the \"Lost Notebook\" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations — mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years.  \u003c\/p\u003e\u003cp\u003e\u003cb\u003eIn the Author's Own Words: \u003cbr\u003e\u003c\/b\u003e\"It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered.\" — George E. Andrews elementary geometric combinatorial computational number theory; mathematics; math books; algorithms; Physics; Data Science; computers; Statistics; AI; Artificial Intelligence; algebra; geometry; Logic; Foundations; Machine Learning; Finance; lattice; partition; Basics; proof; tables; exercise; square; Topology; Cryptography; products; Probability; eCommerce; Combinatorics; Computer Science; infinite products; pure mathematics; theorems; Arithmetic; Prime numbers; combination; Generating functions; Analysis \u003c\/p\u003e","brand":"George E. Andrews","offers":[{"title":"Default Title","offer_id":47160847368513,"sku":"9780486682525","price":21.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486682525.jpg?v=1745947622"},{"product_id":"9780486689067","title":"Fundamentals of Number Theory","description":"\u003cdiv\u003e\u003cp\u003eThis excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect.\u003cbr\u003eThe author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, \u003ci\u003ep\u003c\/i\u003e-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of \u003ci\u003ee\u003c\/i\u003e, to mention a few.\u003cbr\u003eReaders will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.\u003c\/p\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Addison-Wesley Publishing Company, Reading, Massachusetts, 1977 edition.\u003c\/div\u003e","brand":"William J. LeVeque","offers":[{"title":"Default Title","offer_id":47160854610241,"sku":"9780486689067","price":14.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486689067.jpg?v=1710191910"},{"product_id":"9780486696300","title":"Continued Fractions","description":"\u003cdiv\u003e\u003cdiv\u003eIn this elementary-level text, eminent Soviet mathematician A. Ya. Khinchin offers a superb introduction to the positive-integral elements of the theory of continued functions, a special algorithm that is one of the most important tools in analysis, probability theory, mechanics, and, especially, number theory.\u003cbr\u003ePresented in a clear, straightforward manner, the book comprises three major chapters: the properties of the apparatus, the representation of numbers by continued fractions and the measure theory of continued fractions. The last chapter is somewhat more advanced and deals with the metric, or probability, theory of continued fractions, an important field developed almost entirely by Soviet mathematicians, including Khinchin.\u003cbr\u003eThe present volume reprints an English translation of the third Russian edition published in 1961. It is not only an excellent introduction to the study of continued fractions, but a stimulating consideration of the profound and interesting problems of the measure theory of numbers.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the University of Chicago Press, 1964 edition.\u003c\/div\u003e","brand":"A. Ya. Khinchin","offers":[{"title":"Default Title","offer_id":47160857919809,"sku":"9780486696300","price":15.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486696300.jpg?v=1710207897"},{"product_id":"9780486696843","title":"Information Theory and Statistics","description":"\u003cdiv\u003eHighly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Dover Publications, Inc., 1968 edition.\u003c\/div\u003e","brand":"Solomon Kullback","offers":[{"title":"Default Title","offer_id":47160858509633,"sku":"9780486696843","price":22.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486696843_ec9e5820-4e61-46b7-9b7c-ff207e81b7b5.jpg?v=1710177612"},{"product_id":"9780486143699","title":"Optimization Theory for Large Systems","description":"\u003cdiv\u003e\u003cdiv\u003eImportant text examines most significant algorithms for optimizing large systems and clarifying relations between optimization procedures. Much data appear as charts and graphs and will be highly valuable to readers in selecting a method and estimating computer time and cost in problem-solving. Initial chapter on linear and nonlinear programming presents all necessary background for subjects covered in rest of book. Second chapter illustrates how large-scale mathematical programs arise from real-world problems. Appendixes. List of Symbols.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Macmillan Company, New York, 1970 edition.\u003c\/div\u003e advanced mathematics; game theory; applied science and math; scientific exploration; significant algorithms; optimizing systems; clarifying relations between optimized procedures; selecting methods; estimating computer time; cost in problem solving; linear and nonlinear programming; large scale mathematical programs; real world problems; nonlinear programming; clarifying relations; advanced undergraduate studies; graduate level; college math; Optimization Theory; Large Systems; Linear and Nonlinear Programming; Dantzig-Wolfe Decomposition; Partition Procedures","brand":"Leon S. 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In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. He also covers special matrices — including complex numbers, quaternion matrices, and matrices with complex entries — and transpose matrices; the trace of a matrix; the cross product of matrices; eigenvalues and eigenvectors; and infinite series of matrices. Exercises at the end of each section give students further practice in problem solving. \u003cbr\u003ePrerequisites include a background in algebra, and in the later chapters, a knowledge of solid geometry. The book was designed as an introductory text for college freshmen and sophomores, but selected chapters can also be used to supplement advanced high school classes. 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Suitable for advanced undergraduates and graduate students, it assumes an understanding of the general principles of matrix algebra, including the Cayley-Hamilton theorem, characteristic roots and vectors, and linear dependence.\u003cbr\u003eAn introductory chapter covers the Lanczos algorithm, orthogonal polynomials, and determinantal identities. Succeeding chapters examine norms, bounds, and convergence; localization theorems and other inequalities; and methods of solving systems of linear equations. The final chapters illustrate the mathematical principles underlying linear equations and their interrelationships. Topics include methods of successive approximation, direct methods of inversion, normalization and reduction of the matrix, and proper values and vectors. Each chapter concludes with a helpful set of references and problems.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cdiv\u003eReprint of the Dover, 1975 edition.\u003c\/div\u003e\n\u003cdiv\u003e \u003c\/div\u003e\n\u003c\/div\u003e","brand":"Alston S. Householder","offers":[{"title":"Default Title","offer_id":47178762912065,"sku":"9780486145631","price":14.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486145631_85f12cd6-555c-45b9-9d7a-b36933932553.jpg?v=1758650662"},{"product_id":"9780486150765","title":"Elementary Theory of Numbers","description":"\u003cdiv\u003e\u003cdiv\u003e\u003cp\u003eThis superb text introduces number theory to readers with limited formal mathematical training. Intended for use in freshman- and sophomore-level courses in arts and science curricula, in teacher-training programs, and in enrichment programs for high-school students, it is filled with simple problems to stimulate readers' interest, challenge their abilities and increase mathematical strength.\u003cbr\u003eContents:\u003cbr\u003eI. Introduction\u003cbr\u003eII. The Euclidean Algorithm and Its Consequences\u003cbr\u003eIII. Congruences\u003cbr\u003eIV. The Powers of an Integer Modulo \u003ci\u003em\u003c\/i\u003e\u003cbr\u003eV. Continued Fractions\u003cbr\u003eVI. The Gaussian Integers\u003cbr\u003eVII. 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LeVeque","offers":[{"title":"Default Title","offer_id":47178884972865,"sku":"9780486150765","price":7.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486150765_20f09547-a832-4404-b30c-3753547db0d1.jpg?v=1758659149"},{"product_id":"9780486153179","title":"Boundary Value Problems and Fourier Expansions","description":"\u003cdiv\u003e\u003cdiv\u003eBased on modern Sobolev methods, this text for advanced undergraduates and graduate students is highly physical in its orientation. It integrates numerical methods and symbolic manipulation into an elegant viewpoint that is consonant with implementation by digital computer. The first five sections form an informal introduction that develops students' physical and mathematical intuition. The following section introduces Hilbert space in its natural environment, and the next six sections pose and solve the standard problems. The final seven sections feature concise introductions to selected topics, including Sturm-Liouville problems, Fourier integrals, Galerkin's method, and Sobolev methods. 1994 edition. 64 figures. Exercises.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eRevised republication (2004) of \u003ci\u003eBoundary Value Problems and Orthogonal Expansions: Physical Problems from a Sobolev Viewpoint, \u003c\/i\u003eoriginally published by IEEE Press, Piscataway, New Jersey, 1994. \u003c\/div\u003e\u003c\/div\u003e","brand":"Charles R. MacCluer","offers":[{"title":"Default Title","offer_id":47178918134081,"sku":"9780486153179","price":19.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486153179_55efda3a-b9c5-4d0a-b9db-d612de0b4171.jpg?v=1758661933"},{"product_id":"9780486153230","title":"Differential Geometry","description":"\u003cdiv\u003eThis first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of three dimensions. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. It also provides an introduction to the study of Riemannian geometry.\u003cbr\u003eSuitable for advanced undergraduates and graduate students, the text presupposes a knowledge of calculus. The first nine chapters focus on the theory, treating the basic properties of curves and surfaces, the mapping of surfaces, and the absolute geometry of a surface. The final chapter considers the applications of the theory to certain important classes of surfaces: surfaces of revolution, ruled surfaces, translation surfaces, and minimal surfaces. Nearly 200 problems appear throughout the text, offering ample reinforcement of every subject.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eUnabridged republication of the 1966 Dover edition. \u003c\/div\u003e\u003c\/div\u003e","brand":"William C. Graustein","offers":[{"title":"Default Title","offer_id":47178918461761,"sku":"9780486153230","price":14.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486153230_028e7277-e505-433b-bd4a-5ef0e102ed15.jpg?v=1758661821"},{"product_id":"9780486154374","title":"The Theory of Algebraic Numbers","description":"\u003cdiv\u003e\u003cdiv\u003eDetailed proofs and clear-cut explanations provide an excellent introduction to the elementary components of classical algebraic number theory in this concise, well-written volume.\u003cbr\u003eThe authors, a pair of noted mathematicians, start with a discussion of divisibility and proceed to examine Gaussian primes (their determination and role in Fermat's theorem); polynomials over a field (including the Eisenstein irreducibility criterion); algebraic number fields; bases (finite extensions, conjugates and discriminants, and the cyclotomic field); and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture (concluding with discussions of Pythagorean triples, units in cyclotomic fields, and Kummer's theorem). \u003cbr\u003eIn addition to a helpful list of symbols and an index, a set of carefully chosen problems appears at the end of each chapter to reinforce mathematics covered. Students and teachers of undergraduate mathematics courses will find this volume a first-rate introduction to algebraic number theory.\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Mathematical Association of America, second, 1975 edition.\u003c\/div\u003e algebra;number theory;number fields;divisibility;gaussian primes;fermats theorem;polynomials;eisenstein irreducibility criterion;bases;algebraic integers;integral bases;finite extensions;conjugates;discriminants;ideal theory;ideal classes;class numbers;fermat conjecture;pythagorean triples;cyclotomic fields;kummers theorem;symmetric functions;uft;congruences;proofs;math;mathematics;education;nonfiction;reference;textbook;undergraduate math;advanced math","brand":"Harry Pollard and Harold G. 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It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.\u003cbr\u003eFeatured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and \u003ci\u003en\u003c\/i\u003e squares; the number of solutions of quadratic congruences in \u003ci\u003en\u003c\/i\u003e unknowns; Liouville's series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and \u003ci\u003en;\u003c\/i\u003e sets of integers with equal sums of like powers; Waring's problem and related results; Fermat's last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eUnabridged republication of the edition published by Carnegie Institution, Washington, DC, 1919.\u003c\/div\u003e\u003c\/div\u003e","brand":"Leonard Eugene Dickson","offers":[{"title":"Default Title","offer_id":47178946216257,"sku":"9780486154602","price":31.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486154602_254d7d03-8402-4984-9e77-d4adf6540d85.jpg?v=1758662296"},{"product_id":"9780486319070","title":"Differential Topology","description":"\u003cdiv\u003e \u003cdiv\u003eOffering classroom-proven results, \u003ci\u003eDifferential Topology\u003c\/i\u003e presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces.\u003cbr\u003eThis self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curves, surgery, classification of orientable surfaces, and Whitney's embedding theorem. Suitable for advanced undergraduate courses in introductory or differential topology, this volume also serves as a supplementary text in advanced calculus and physics courses, as well as a key source of information for students of mechanics.\u003c\/div\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e \u003cdiv\u003e \u003cp\u003eReprint of the Marcel Dekker, Inc., New York, 1982 edition. \u003c\/p\u003e\n\u003c\/div\u003e\n\u003c\/div\u003e","brand":"David B. 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The text is designed to develop understanding and conceptual grasp, rather than mere manipulation.\u003cbr\u003eThe early chapters supply a far more detailed exposition than found in many texts, important for the student having his first experience with mathematical rigor. Concepts of vector space, linear transformation, and matrix are presented, then applied to solution of systems of linear equations. A self-contained development of the theory of determinants is given; the student is introduced to the general concept of invariant; then to the theory of similarity. Exposition of the bilinear and quadratic forms and of orthogonal equivalence follow. The last four chapters are more advanced in nature and the level of treatment somewhat higher. The standard theory of polynomials in one indeterminate is given; the development of the general theory of simple algebraic extensions of a field is presented in a form that can be used as a foundation for Galois theory and also for the general similarity theory. The standard canonical forms for matrices with integral or polynomial elements are presented, followed by the similarity theory, with applications to geometry and to differential equations. The final chapter provides an introduction to the important topic of linear inequalities, often neglected in elementary texts on matrix theory. The objective is to provide the student with sufficient background to read books and papers on game theory and linear programming. Exercises follow each exposition.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Wiley, New York, 1957 edition.\u003c\/div\u003e","brand":"Robert M. Thrall and Leonard Tornheim","offers":[{"title":"Default Title","offer_id":47179255382337,"sku":"9780486321059","price":14.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486321059.jpg?v=1758667726"},{"product_id":"9780486783482","title":"Special Matrices and Their Applications in Numerical Mathematics","description":"\u003cdiv\u003eThis revised and corrected second edition of a classic book on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference.\u003cbr\u003eAuthor Miroslav Fiedler, a Professor at the Institute of Computer Science of the Academy of Sciences of the Czech Republic, Prague, begins with definitions of basic concepts of the theory of matrices and fundamental theorems. In subsequent chapters, he explores symmetric and Hermitian matrices, the mutual connections between graphs and matrices, and the theory of entrywise nonnegative matrices. After introducing \u003ci\u003eM\u003c\/i\u003e-matrices, or matrices of class \u003ci\u003eK,\u003c\/i\u003e Professor Fiedler discusses important properties of tensor products of matrices and compound matrices and describes the matricial representation of polynomials. He further defines band matrices and norms of vectors and matrices. The final five chapters treat selected numerical methods for solving problems from the field of linear algebra, using the concepts and results explained in the preceding chapters.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of the revised and corrected second edition, Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 1986.\u003c\/div\u003e\u003c\/div\u003e","brand":"Miroslav Fiedler","offers":[{"title":"Default Title","offer_id":47179273306433,"sku":"9780486783482","price":19.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486783482.jpg?v=1758667981"},{"product_id":"9780486802251","title":"Transcendental and Algebraic Numbers","description":"Primarily an advanced study of the modern theory of transcendental and algebraic numbers, this treatment by a distinguished Soviet mathematician focuses on the theory's fundamental methods. The text also chronicles the historical development of the theory's methods and explores the connections with other problems in number theory. The problem of approximating algebraic numbers is also studied as a case in the theory of transcendental numbers.\u003cbr\u003eTopics include the Thue-Siegel theorem, the Hermite-Lindemann theorem on the transcendency of the exponential function, and the work of C. Siegel on the transcendency of the Bessel functions and of the solutions of other differential equations. The final chapter considers the Gelfond-Schneider theorem on the transcendency of alpha to the power beta. Each proof is prefaced by a brief discussion of its scheme, which provides a helpful guide to understanding the proof's progression.\u003cbr\u003e\u003cdiv\u003e \u003cdiv\u003eReprint of the Dover, 1960 edition.\u003c\/div\u003e\n\u003c\/div\u003e mathematical equations;approximating;mathematics;advanced algebra;advanced mathematics;gelfond schneider theorem;bessel functions;thue siegel theorem;hermite lindemann theorem;mathematical theories;alpha;beta;proofs;mathematical studies;books on math;algebra;differential equations;arithmetic","brand":"A. O. Gelfond. Translated by Leo F. Boron","offers":[{"title":"Default Title","offer_id":47179308073281,"sku":"9780486802251","price":14.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486802251.jpg?v=1758668446"},{"product_id":"9780486805825","title":"Philosophical Introduction to Set Theory","description":"The primary mechanism for ideological and theoretical unification in modern mathematics, set theory forms an essential element of any comprehensive treatment of the philosophy of mathematics. This unique approach to set theory offers a technically informed discussion that covers a variety of philosophical issues. Rather than focusing on intuitionist and constructive alternatives to the Cantorian\/Zermelian tradition, the author examines the two most important aspects of the current philosophy of mathematics, mathematical structuralism and mathematical applications of plural reference and plural quantification.\u003cbr\u003eClearly written and frequently cited in the mathematical literature, this book is geared toward advanced undergraduates and graduate students of mathematics with some aptitude for mathematical reasoning and prior exposure to symbolic logic. Suitable as a source of supplementary readings in a course on set theory, it also functions as a primary text in a course on the philosophy of mathematics.\u003cbr\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the University of Notre Dame Press, Notre Dame, Indiana, 1990 edition.\u003c\/div\u003e ideological and theoretical unification;philosophy of mathematics;college level mathematics;mathematical reasoning;symbolic logic;pure mathematics;advanced mathematics;math and science;graduate level mathematics;modern mathematics;set theory;mathematics;math books;cantorian;zermelian tradition;mathematical structuralism;mathematical applications of plural reference;plural quantification;mathematical literature","brand":"Stephen Pollard","offers":[{"title":"Default Title","offer_id":47179317772609,"sku":"9780486805825","price":14.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/files\/9780486805825.jpg?v=1758668620"},{"product_id":"9780486414553","title":"N-Person Game Theory","description":"\u003cdiv\u003e \u003cp\u003eN-person game theory provides a logical framework for analyzing contests in which there are more than two players or sets of conflicting interests-anything from a hand of poker to the tangled web of international relations. In this sequel to his \u003ci\u003eTwo-Person Game Theory,\u003c\/i\u003e Dr. Rapoport provides a fascinating and lucid introduction to the theory, geared towards readers with little mathematical background but with an appetite for rigorous analysis.\u003cbr\u003eFollowing an introduction to the necessary mathematical notation (mainly set theory), in Part I the author presents basic concepts and models, including levels of game-theoretic analysis, individual and group rationality, the Von Neumann-Morgenstern solution, the Shapley value, the bargaining set, the kernel, restrictions on realignments, games in partition function form, and Harsanyi's bargaining model. In Part II he delves into the theory's social applications, including small markets, large markets, simple games and legislatures, symmetric and quota games, coalitions and power, and more.\u003cbr\u003eThis affordable new edition will be welcomed by economists, political scientists, historians, and anyone interested in multilateral negotiations or conflicts, as well as by general readers with an interest in mathematics, logic, or games.\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e \u003cdiv\u003e \u003cdiv\u003e \u003cp\u003eReprint of the The University of Michigan Press, 1970 edition.\u003c\/p\u003e\n\u003c\/div\u003e\n\u003c\/div\u003e\n\u003c\/div\u003e game theory, mathematics, logical framework, analyzing contests, mathematical notation, set theory, game theoretic analysis, individual and group rationality, von neumann morgenstern solution, the shapley value, the bargaining set, the kernel, restrictions on realignments, games in partition function form, harsanyis bargaining model, symmetric and quota games, social game theory, political science, market economies;game-theoretical analysis; three-level analysis of elementary games; symmetric \u0026amp; quota games; bargaining set; Von Neumann-Morgenstern Solution","brand":"Anatol Rapoport","offers":[{"title":"Default Title","offer_id":47179463786817,"sku":"9780486414553","price":22.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486414553.jpg?v=1710176016"},{"product_id":"9780486434971","title":"Game Theory and Politics","description":"\u003cdiv\u003e\u003cdiv\u003e\u003cp\u003eIn this illuminating and instructive survey, author Steven J. Brams demonstrates both the insights and the pitfalls that can result from applying game theoretic models to the analysis of problems in political science. Using plenty of real-life examples, Brams shows how game theory can explain and elucidate complex political situations, from warfare to presidential vetoes. In these cases and others, game theory's mathematical structure provides a rigorous, consistent method for formulating, analyzing, and solving strategic problems. Minimal mathematical background is necessary, making the book accessible to a wide audience of students and teachers of politics and social science, as well as other readers with a serious interest in politics. New preface to the Dover edition. 1975 edition.\u003c\/p\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003eReprint of The Free Press, New York, 1975 edition.\u003c\/div\u003e\u003c\/div\u003e political science; history and theory; mathematics; politics; warfare; presidential vetoes; finance and economics; social science; sociological; theoretic models; math and science; scientific theory; formulating; analyzing; solving strategic problems; strategy; structure and analysis; government and governing; economy; statistics; hypothesis; test and evaluation; international relations games; qualitative voting games; quantitative voting games; coalition games; voting power","brand":"Steven J. Brams","offers":[{"title":"Default Title","offer_id":47179473387841,"sku":"9780486434971","price":17.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486434971.jpg?v=1710177118"},{"product_id":"9780486474847","title":"Set Theory and the Continuum Problem","description":"\u003cdiv\u003eA lucid, elegant, and complete survey of set theory, this volume is drawn from the authors' substantial teaching experience. The first of three parts focuses on axiomatic set theory. The second part explores the consistency of the continuum hypothesis, and the final section examines forcing and independence results.\u003cbr\u003ePart One's focus on axiomatic set theory features nine chapters that examine problems related to size comparisons between infinite sets, basics of class theory, and natural numbers. Additional topics include author Raymond Smullyan's double induction principle, super induction, ordinal numbers, order isomorphism and transfinite recursion, and the axiom of foundation and cardinals. The six chapters of Part Two address Mostowski-Shepherdson mappings, reflection principles, constructible sets and constructibility, and the continuum hypothesis. The text concludes with a seven-chapter exploration of forcing and independence results. This treatment is noteworthy for its clear explanations of highly technical proofs and its discussions of countability, uncountability, and mathematical induction, which are simultaneously charming for experts and understandable to graduate students of mathematics.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cdiv\u003e\u003cdiv\u003eRevised and corrected reprint of the Oxford University Press, New York, 1996 edition.\u003c\/div\u003e\u003c\/div\u003e\u003c\/div\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eBonus Editorial Feature\u003c\/b\u003e\u003c\/p\u003e\u003cdiv\u003e\n\u003cdiv\u003eRaymond Smullyan (1919–2017), mathematician, logician, magician, creator of extraordinary puzzles, philosopher, pianist, and man of many parts. The first Dover book by Raymond Smullyan was \u003ci\u003eFirst-Order Logic\u003c\/i\u003e (1995). Recent years have brought a number of his magical books of logic and math puzzles: \u003ci\u003eThe Lady or the Tiger\u003c\/i\u003e (2009); \u003ci\u003eSatan, Cantor and Infinity\u003c\/i\u003e (2009); an original, never-before-published collection, \u003ci\u003eKing Arthur in Search of His Dog and Other Curious Puzzles\u003c\/i\u003e (2010); and \u003ci\u003eSet Theory and the Continuum Problem\u003c\/i\u003e (with Melvin Fitting, also reprinted by Dover in 2010). More will be coming in subsequent years. \u003c\/div\u003e\n\u003cdiv\u003e\u003cdiv\u003e\n\u003cp\u003e\u003cb\u003e\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eIn the Author's Own Words:\u003cbr\u003e\"Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini.\" \u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\"Some people are always critical of vague statements. I tend rather to be critical of precise statements: they are the only ones which can correctly be labeled 'wrong.'\" — Raymond Smullyan \u003c\/p\u003e\n\u003c\/div\u003e\u003c\/div\u003e\n\u003c\/div\u003e axiomatic set theory;infinite sets;class theory;natural numbers;double induction principle;super induction;ordinal numbers;order isomorphism;transfinite recursion;axiom of foundation;cardinals;mostowski shepherdson mappings;reflection principles;constructible sets;constructability;continuum hypothesis;forcing;independence results;countability;uncountability;mathematical induction;math;mathematics;college math;graduate math;advanced math;modal logic;reference","brand":"Raymond M. Smullyan and Melvin Fitting","offers":[{"title":"Default Title","offer_id":47179496325441,"sku":"9780486474847","price":24.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486474847.jpg?v=1710194154"},{"product_id":"9780486481593","title":"Introduction to Matrices and Linear Transformations","description":"\u003cbr\u003eThis versatile undergraduate text can be used in a variety of courses in linear algebra. It contains enough material for a two-semester course, and it also serves as a support text and reference. Chapter Ten, on linear programming, will be of special interest to students of business and economics. A balanced combination of formal theory and related computational techniques, this treatment begins with the familiar problem of solving a system of linear equations. Subsequent chapters explore linear spaces and mappings, matrices, determinants, inner product spaces, scalar-valued functions, and linear differential equations. The author introduces metric notions of Euclidean space at an early stage and employs the computational technique of Gaussian elimination throughout the book. Solutions to selected exercises appear at the end.\u003cbr\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the W. H. Freeman \u0026amp; Company, San Francisco, 1978 edition.\u003c\/div\u003e math; science; mathematics; algebra; matrices; linear algebra; math textbooks; linear programming; business; economics; computational techniques; formal theory; linear equations; linear spaces and mappings; determinants; inner product spaces; scalar valued functions; and linear differential equations; euclidean space; gaussian elimination","brand":"Daniel T. 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The final chapter features thorough discussions of the work of Zassenhaus on Frobenius elements and sharply transitive groups in addition to an exploration of Huppert's findings on solvable doubly transitive groups.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003c\/div\u003e\u003cdiv\u003eReprint of the W. A. Benjamin, Inc., New York, 1968 edition.\u003c\/div\u003e mathematics; science and math; math; self study; permutation groups; reference; mathematic reference; modern algebra; abstract algebra; group extensions; transfer theorems; group representations and characters; college math; math professionals; department of mathematics; complex; engaging; students and teachers; career; realistic; scientists; experiments; sharply transitive groups; Huppert; Frobenius elements; solvable double transitive groups; classification theorems","brand":"Donald S. Passman","offers":[{"title":"Default Title","offer_id":47179575034177,"sku":"9780486485928","price":19.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486485928.jpg?v=1710193999"},{"product_id":"9780486488134","title":"An Introduction to the Theory of Groups","description":"\u003cdiv\u003eThis introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates, developing material of fundamental importance in a clear and rigorous fashion. The treatment is also useful as a review for more advanced students with some background in group theory. \u003cbr\u003eBeginning with introductory examples of the group concept, the text advances to considerations of groups of permutations, isomorphism, cyclic subgroups, simple groups of movements, invariant subgroups, and partitioning of groups. An appendix provides elementary concepts from set theory. A wealth of simple examples, primarily geometrical, illustrate the primary concepts. Exercises at the end of each chapter provide additional reinforcement.\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eReprint of the Hafner Publishing Co., New York, 1959 edition.\u003c\/div\u003e math; mathematics; mathematician; group; group theory; introduction to group theory; statistics; undergraduate study; student guide; study guide; chapter tests; quiz; science and math; electromagnetism; books with equations; Group Theory; Groups in Mathematics; Russian Mathematics; Paul Alexandroff","brand":"Paul Alexandroff","offers":[{"title":"Default Title","offer_id":47179584078145,"sku":"9780486488134","price":11.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0812\/3262\/5985\/products\/9780486488134_f78d85c6-b607-475e-a5b1-73390ddecc23.jpg?v=1710177828"}],"url":"https:\/\/store.doverpublications.com\/collections\/math-theory\/bisac-mathematics-reference.oembed","provider":"Dover Publications","version":"1.0","type":"link"}