The Art of Mathematics

Coffee Time in Memphis

Author: Béla Bollobás

Publisher: Cambridge University Press

ISBN: 0521872286

Category: Mathematics

Page: 359

View: 8990


A collection of mathematical problems chosen to illustrate the mathematician's art.

The Art of the Infinite

The Pleasures of Mathematics

Author: Robert Kaplan,Ellen Kaplan

Publisher: Bloomsbury Publishing USA

ISBN: 1608198693

Category: Mathematics

Page: 416

View: 7880


Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.

The Art of Mathematical Problem Solving

Author: Richard M. Beekman


ISBN: 1329428900


Page: 266

View: 4070


Mathematics is a fine art, like painting, sculpture, or music. This book teaches the art of solving challenging mathematics problems. Part I presents a general process for solving problems. Part II contains 35 difficult and challenging mathematics problems with complete solutions. The goal is to teach the reader how to proceed from an initial state of "panic and fear" to finding a beautiful and elegant solution to a problem.

Discovering Mathematics

The Art of Investigation

Author: A. Gardiner

Publisher: Courier Corporation

ISBN: 0486452999

Category: Mathematics

Page: 206

View: 4149


The term "mathematics" usually suggests an array of familiar problems with solutions derived from well-known techniques. Discovering Mathematics: The Art of Investigation takes a different approach, exploring how new ideas and chance observations can be pursued, and focusing on how the process invariably leads to interesting questions that would never have otherwise arisen. With puzzles involving coins, postage stamps, and other commonplace items, students are challenged to account for the simple explanations behind perplexing mathematical phenomena. Elementary methods and solutions allow readers to concentrate on the way in which the material is explored, as well as on strategies for answers that aren't immediately obvious. The problems don't require the kind of sophistication that would put them out of reach of ordinary students, but they're sufficiently complex to capture the essential features of mathematical discovery. Complete solutions appear at the end.

Art in the Life of Mathematicians

Author: Anna Kepes Szemerédi

Publisher: American Mathematical Soc.

ISBN: 1470419564

Category: Mathematics

Page: 282

View: 1506


Why are mathematicians drawn to art? How do they perceive it? What motivates them to pursue excellence in music or painting? Do they view their art as a conveyance for their mathematics or an escape from it? What are the similarities between mathematical talent and creativity and their artistic equivalents? What are the differences? Can a theatrical play or a visual image capture the beauty and excitement of mathematics? Some of the world's top mathematicians are also accomplished artists: musicians, photographers, painters, dancers, writers, filmmakers. In this volume, they share some of their work and reflect on the roles that mathematics and art have played in their lives. They write about creativity, communication, making connections, negotiating successes and failures, and navigating the vastly different professional worlds of art and mathematics.

The Gentle Art of Mathematics

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486164063

Category: Science

Page: 160

View: 7519


This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games, chance and choice, automatic thinking, and more.

The Art of Proof

Basic Training for Deeper Mathematics

Author: Matthias Beck,Ross Geoghegan

Publisher: Springer Science & Business Media

ISBN: 9781441970237

Category: Mathematics

Page: 182

View: 5696


The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

The Art of the Intelligible

An Elementary Survey of Mathematics in its Conceptual Development

Author: J. Bell

Publisher: Springer Science & Business Media

ISBN: 9401142092

Category: Science

Page: 250

View: 902


A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl. Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background.

Street-Fighting Mathematics

The Art of Educated Guessing and Opportunistic Problem Solving

Author: Sanjoy Mahajan,Carver A. Mead

Publisher: MIT Press

ISBN: 0262265591

Category: Mathematics

Page: 152

View: 2443


In problem solving, as in street fighting, rules are for fools: do whatever works -- don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge -- from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool -- the general principle -- from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

The Joy of Finite Mathematics

The Language and Art of Math

Author: Chris P. Tsokos,Rebecca D. Wooten

Publisher: Academic Press

ISBN: 0128029854

Category: Mathematics

Page: 554

View: 666


The Joy of Finite Mathematics: The Language and Art of Math teaches students basic finite mathematics through a foundational understanding of the underlying symbolic language and its many dialects, including logic, set theory, combinatorics (counting), probability, statistics, geometry, algebra, and finance. Through detailed explanations of the concepts, step-by-step procedures, and clearly defined formulae, readers learn to apply math to subjects ranging from reason (logic) to finance (personal budget), making this interactive and engaging book appropriate for non-science, undergraduate students in the liberal arts, social sciences, finance, economics, and other humanities areas. The authors utilize important historical facts, pose interesting and relevant questions, and reference real-world events to challenge, inspire, and motivate students to learn the subject of mathematical thinking and its relevance. The book is based on the authors’ experience teaching Liberal Arts Math and other courses to students of various backgrounds and majors, and is also appropriate for preparing students for Florida’s CLAST exam or similar core requirements. Highlighted definitions, rules, methods, and procedures, and abundant tables, diagrams, and graphs, clearly illustrate important concepts and methods Provides end-of-chapter vocabulary and concept reviews, as well as robust review exercises and a practice test Contains information relevant to a wide range of topics, including symbolic language, contemporary math, liberal arts math, social sciences math, basic math for finance, math for humanities, probability, and the C.L.A.S.T. exam Optional advanced sections and challenging problems are included for use at the discretion of the instructor Online resources include PowerPoint Presentations for instructors and a useful student manual

The Cauchy-Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

Author: J. Michael Steele

Publisher: Cambridge University Press

ISBN: 9780521546775

Category: Mathematics

Page: 306

View: 3660


This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

Counting: The Art of Enumerative Combinatorics

Author: George E. Martin

Publisher: Springer Science & Business Media

ISBN: 1475748787

Category: Mathematics

Page: 252

View: 6566


This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

The Invention of Infinity

Mathematics and Art in the Renaissance

Author: Judith Veronica Field

Publisher: Oxford University Press, USA

ISBN: 0198523947

Category: Mathematics

Page: 250

View: 3704


Fully illustrated, this story brings together the histories of arts and mathematics and shows how infinity at last acquired a precise mathematical meaning.

Mathematics and Art

A Cultural History

Author: Lynn Gamwell

Publisher: Princeton University Press

ISBN: 0691165289

Category: Art

Page: 576

View: 8688


This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked “What is art?” in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.

Mathematics and Plausible Reasoning: Induction and analogy in mathematics

Author: George Pólya

Publisher: Princeton University Press

ISBN: 9780691025094

Category: Mathematics

Page: 280

View: 8673


A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. I, on Induction and Analogy in Mathematics, covers a wide variety of mathematical problems, revealing the trains of thought that lead to solutions, pointing out false bypaths, discussing techniques of searching for proofs. Problems and examples challenge curiosity, judgment, and power of invention.

Investigating Patterns in Number Relationships

Author: Paul Swan

Publisher: R.I.C. Publications

ISBN: 1863118195

Category: Form perception

Page: 84

View: 7178


"Pattern work that introduces and develops the relationship between numbers. The activities predominantly focus on number relationships in tables... range from completing addition tables, to number sequences, to "finding the rule'"--Foreword.

Noble Numbers, Subtle Words

The Art of Mathematics in the Science of Storytelling

Author: Barbara Milberg Fisher

Publisher: Fairleigh Dickinson Univ Press

ISBN: 9780838637401

Category: Literary Criticism

Page: 168

View: 310


This study approaches the use of mathematics in fiction in an entirely new way, as a potent instrument of language. Following Wittgenstein's description of mathematical constructs as a component of ordinary language, Fisher shows how number, geometric figuration, algebraic coding, and transcendent abstractions have been made to function as practical narrative tools. Far from rehearsing the various paradigms of numerology, whether Pythagorean, Elizabethan, or Cabalistic, this book explores the tactical deployment of mathematical objects as shaping and framing agents. It reveals how mathematical objects may be subordinated to the storyteller's art.

The Art of Mathematics in Business

Analyzing Facts and Figures for Smart Business Decisions

Author: Jae K. Shim

Publisher: Global Professional Pub

ISBN: 9781906403324

Category: Business & Economics

Page: 395

View: 2441


This book is a comprehensive, one-stop desk reference for managers and owners of small businesses who must use quantitative calculations to make daily operating and investing decisions. Its purpose is to provide the fundamentals of business math techniques that can be quickly applied to real-word problems. This unique resource will save countless hours of research time by making sound financial planning truly easy. It provides analyses as well as clear and understandable explanations of complex small business problems. Basic mathematical techniques are presented in a step-by-step fashion that takes the reader through each stage of the problem-solving process. The examples in this book provide an invaluable and effective operating tool. This book also contains user-friendly personal computer techniques. The examples enable the businessperson to measure results and to report the data in an easy-to-understand format.