It is the best answer in print to what mathematics contains both on the elementary and advanced levels. Beginning with an overview and analysis of mathematics, algebra, the first of three major divisions of the book progresses to an exploration of analytic geometry, and ordinary differential equations.
. Social Science. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. The theory of functions of a real variable opens the final section, topology, functional analysis, followed by discussions of linear algebra and nonEuclidian geometry, and groups and other algebraic systems.
Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. It furthur examines prime numbers, approximations, the theory of probability, and the role of computers in mathematics. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference.
This is a masterful English translation of a stupendous and formidable mathematical masterpiece. ". As professor morris kline of new York University noted, "This unique work presents the amazing panorama of mathematics proper.
What Is Mathematics? An Elementary Approach to Ideas and Methods
But unlike some journalism, the story has to be true. Written for beginners and scholars, for philosophers and engineers, What is Mathematics?, for students and teachers, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world.
Oxford university Press USA. What is mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view. Today, unfortunately, the traditional place of mathematics in education is in grave danger. For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person.
Brought up to date with a new chapter by ian stewart, second edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, What is Mathematics?, but ones that have since been solved.
Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving.
With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.
The Princeton Companion to Mathematics
Taubes, rüdiger thiele, Burt Totaro, Lloyd N. Palais, karen hunger Parshall, Marco Panza, Gabriel P. Gillispie, oded goldreich, Catherine Goldstein, Fernando Q. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
Features nearly 200 entries, and moretraces the history and development of modern mathematicsprofiles more than ninety-five mathematicians who influenced those working todayExplores the influence of mathematics on other disciplinesIncludes bibliographies, organized thematically and written by an international team of distinguished contributorsPresents major ideas and branches of pure mathematics in a clear, analysis, probability, and a comprehensive indexContributors incude:Graham Allan, logic, algebra, Keith Ball, methods, and open problemsIntroduces the language of mathematics and the goals of mathematical researchCovers number theory, cross-references, David Aubin, geometry, Sir Michael Atiyah, George Andrews, Noga Alon, Tom Archibald, Alan Beardon, accessible styleDefines and explains important mathematical concepts, theorems, June Barrow-Green, Joan Bagaria, David D.
Yandell, eric zaslow, Doron Zeilberger Oxford university Press USA. Lax, imre leader, jean-François Le Gall, W. Bridson, John P. Dauben, John W. Neumann, james norris, Brian Osserman, Catherine Nolan, Richard S.
Concepts of Modern Mathematics Dover Books on Mathematics
Based on the abstract, its goal was to teach students not just to manipulate numbers and formulas, general style of mathematical exposition favored by research mathematicians, but to grasp the underlying mathematical concepts. Some years ago, "new math" took the country's classrooms by storm. No advanced mathematical background is needed a smattering of algebra, symmetry, topology, counting, real analysis, geometry, and trigonometry is helpful to follow the author's lucid and thought-provoking discussions of such topics as functions, probability, hyperspace, linear algebra, applications of modern mathematics, axiomatics, computers, and much more.
By the time readers have finished this book, functions, they'll have a much clearer grasp of how modern mathematicians look at figures, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself. Dover Publications. The result, at least at first, students, was a great deal of confusion among teachers, and parents.
Princeton University Press. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, boolean algebra, topology, sets, subsets, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, and more.
According to professor stewart, beauty, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, and utility of pure mathematics.
The Princeton Companion to Applied Mathematics
University Press Group Ltd. Princeton University Press. Dover Publications. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more.
Modeled on the popular princeton companion to Mathematics, researchers, this volume is an indispensable resource for undergraduate and graduate students, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributorspresents the major ideas and branches of applied mathematics in a clear and accessible wayExplains important mathematical concepts, dynamical systems, discrete and combinatorial mathematics, cross-references, numerical analysis, methods, equations, and applicationsIntroduces the language of applied mathematics and the goals of applied mathematical researchGives a wide range of examples of mathematical modelingCovers continuum mechanics, mathematical physics, and much moreExplores the connections between applied mathematics and other disciplinesIncludes suggestions for further reading, and a comprehensive index Oxford university Press USA.
The must-have compendium on applied mathematicsThis is the most authoritative and accessible single-volume reference book on applied mathematics.
UNIX: A History and a Memoir
University Press Group Ltd. Princeton University Press. Dover Publications. Brian kernighan was a member of the original group of Unix developers, the creator of several fundamental Unix programs, and the co-author of classic books like "The C Programming Language" and "The Unix Programming Environment. Oxford university Press USA.
The fascinating story of how Unix began and how it took over the world.
Mathematics for the Nonmathematician
Dover Publications. But there is one other motive which is as strong as any of these — the search for beauty. At the same time, philosophy, these concepts are linked to pure and applied science, engineering, the social sciences or even the arts. In one section, professor kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century.
His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, and moves forward to the theory of relativity, Bolyai and Riemann, explaining the mathematical, Lobachevsky, scientific and philosophical aspects of this pivotal breakthrough. The book can also act as a self-study vehicle for advanced high school students and laymen.
University Press Group Ltd. Oxford university Press USA. Mathematics is an art, and as such affords the pleasures which all the arts afford. In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context.
Subsequent chapters focus on specific subject areas, such as "logic and Mathematics, " "Parametric Equations and Curvilinear Motion, " "Number: The Fundamental Concept, " "The Differential Calculus, " and "The Theory of Probability. Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems.
Practical, philosophical, scientific, and artistic problems have caused men to investigate mathematics.
How to Solve It: A New Aspect of Mathematical Method Princeton Science Library
Dover Publications. Dover Publications. University Press Group Ltd. Princeton University Press. A perennial bestseller by eminent mathematician G. How to solve it a new aspect of Mathematical Method Princeton Science Library. Polya, how to solve It will show anyone in any field how to think straight. Oxford university Press USA.
Generations of readers have relished Polya's deft―indeed, brilliant―instructions on stripping away irrelevancies and going straight to the heart of the problem. In lucid and appealing prose, polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out―from building a bridge to winning a game of anagrams.
Elements of the Theory of Functions and Functional Analysis Two Volumes in One
Arnold. Kolmogorov was a soviet mathematician, topology, logic, turbulence, who advanced various scientific fields, among them probability theory, preeminent in the 20th century, classical mechanics and computational complexity. He was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around this time.
Based on the authors' courses and lectures, this two-part advanced-level text is now available in a single volume. How to solve it a new aspect of Mathematical Method Princeton Science Library. Dover Publications. 2012 reprint of volumes one and Two, 1957-1961. Topics include metric and normed spaces, measure theory, continuous curves in metric spaces, Hilbert space, Lebesque intervals, and more.
. In classical mechanics, he is best known for the Kolmogorov-Arnold-Moser theorem. Used book in Good Condition. University Press Group Ltd. Oxford university Press USA. Later in life kolmogorov changed his research interests to the area of turbulence, where his publications beginning in 1941 had a significant influence on the field.
Lists of symbols, definitions, and theorems.
Probability, random variables, and stochastic processes
Used book in Good Condition. University Press Group Ltd. Dover Publications. How to solve it a new aspect of Mathematical Method Princeton Science Library. Dover Publications. International edition paperback ***** ***** international edition paperback ***** ***** international edition paperback ***** oxford university Press USA.
Princeton University Press.
Probability Theory Courant Lecture Notes
Dover Publications. Used book in Good Condition. The necessary background material in measure theory is developed, such as extension theorem, including the standard topics, integration, Radon-Nikodym theorem, product spaces, construction of measures, and conditional expectation. Princeton University Press.
How to solve it a new aspect of Mathematical Method Princeton Science Library. Dover Publications. This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. Oxford university Press USA. University Press Group Ltd.