What Is Mathematics? An Elementary Approach to Ideas and Methods

Oxford University Press #ad - Its goal is to put the meaning back into mathematics. 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.

. This new edition of richard Courant's and Herbert Robbins's classic work seeks to address this problem. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.

What Is Mathematics? An Elementary Approach to Ideas and Methods #ad - Oxford university Press USA. 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.

Written for beginners and scholars, for students and teachers, What is Mathematics?, for philosophers and engineers, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. 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. 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.


Mathematics: Its Content, Methods and Meaning 3 Volumes in One

Dover Publications #ad - 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, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations.

. 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.

. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. ". Nothing less than a major contribution to the scientific culture of this world.

Mathematics: Its Content, Methods and Meaning 3 Volumes in One #ad - The new york times book reviewthis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement.


Concepts of Modern Mathematics Dover Books on Mathematics

Dover Publications #ad - Dover Publications. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, topology, subsets, sets, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, Boolean algebra, and more.

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. According to professor stewart, beauty, in particular the power, an understanding of these concepts offers the best route to grasping the true nature of mathematics, and utility of pure mathematics.

No advanced mathematical background is needed a smattering of algebra, topology, computers, probability, counting, linear algebra, and trigonometry is helpful to follow the author's lucid and thought-provoking discussions of such topics as functions, axiomatics, applications of modern mathematics, real analysis, geometry, hyperspace, symmetry, and much more.

Concepts of Modern Mathematics Dover Books on Mathematics #ad - By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself. The result, students, was a great deal of confusion among teachers, at least at first, and parents.

Some years ago, "new math" took the country's classrooms by storm.


The Joy of x: A Guided Tour of Math, from One to Infinity

Mariner Books #ad - Delightful. Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x. Easily digestible chapters include plenty of helpful examples and illustrations. In the joy of x, with wit, steven strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, insight, and brilliant illustrations.

Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it, or determining how many people you should date before settling down, explaining just how Google searches the internet, Strogatz shows how math connects to every aspect of life. Dover Publications. But math plays a part in all of our lives all of the time, whether we know it or not.

The Joy of x: A Guided Tour of Math, from One to Infinity #ad - You'll never forget the pythagorean theorem again!"—Scientific AmericanMany people take math in high school and promptly forget much of it. Used book in Good Condition. Discussing pop culture, and business, philosophy, medicine, law, art, Strogatz is the math teacher you wish you’d had.


How to Solve It: A New Aspect of Mathematical Method Princeton Science Library

Princeton University Press #ad - Used book in Good Condition. 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. Dover Publications. A perennial bestseller by eminent mathematician G.

Generations of readers have relished Polya's deft―indeed, brilliant―instructions on stripping away irrelevancies and going straight to the heart of the problem. 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.


Mathematics for the Nonmathematician

Dover Books #ad - Dover Publications. Used book in Good Condition. The book can also act as a self-study vehicle for advanced high school students and laymen. Subsequent chapters focus on specific subject areas, " "parametric Equations and Curvilinear Motion, such as "Logic and Mathematics, " "The Differential Calculus, " "Number: The Fundamental Concept, " 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.

Mathematics for the Nonmathematician #ad - Dover Publications. 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.

At the same time, philosophy, engineering, these concepts are linked to pure and applied science, 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, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough.



Belknap Press: An Imprint of Harvard University Press #ad - Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work. How to solve it a new aspect of Mathematical Method Princeton Science Library. Belknap Press. Favoring plain english and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable.

Here lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living. In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying.

Measurement #ad - His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science. Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity.

Dover Publications. An impassioned critique of k–12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Dover Publications.


Journey through Genius: The Great Theorems of Mathematics

Penguin Books #ad - Dover Publications. How to solve it a new aspect of Mathematical Method Princeton Science Library. Now william Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, to Gerolamo Cardano, the absentminded theoretician whose absorption in his work often precluded eating or bathing, Georg Cantor.

. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. Like masterpieces of art, and literature, music, great mathematical theorems are creative milestones, works of genius destined to last forever. Used book in Good Condition.

Journey through Genius: The Great Theorems of Mathematics #ad - A rare combination of the historical, and mathematical, biographical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. Belknap Press.

It is mathematics by lightning flash. Isaac asimov Dover Publications.


Prelude to Mathematics Dover Books on Mathematics

Dover Publications #ad - Sawyer professor emeritus, University of Toronto defines mathematics as "the classification and study of all possible patterns. It is a broad definition, but one that seems appropriate to the great scope and depth of the topic. No mathematician can be a complete mathematician unless he is also something of a poet.

K. Indeed, mathematics seems to have few boundaries, either in applications to practical matters or in its mind-stretching excursions into realms of pure abstraction. Gearing his approach to the layman whose grasp of things mathematical may be a bit precarious, Professor Sawyer offers a lucid, accessible introduction to the mathematician's cast of mind.

Prelude to Mathematics Dover Books on Mathematics #ad - Belknap Press. Dover Publications. Five well-written preliminary chapters explore the beauty, power and mysticism of mathematics; the role of math as an adjunct in utilitarian matters; and the concepts of pattern, generalization and unification as both tools and goals of mathematical thought. After developing this conceptual groundwork, determinants, matrices, projective geometry, the author goes on to treat of more advanced topics: non-Euclidean geometry, transformations and group theory.

W. Dover Publications. Weierstrassin this lively and stimulating account, noted mathematician and educator W. How to solve it a new aspect of Mathematical Method Princeton Science Library.


Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

Plume #ad - The definitive story of the Riemann Hypothesis, a fascinating and epic mathematical mystery that continues to challege the world. In 1859, a little-known thirty-two year old mathematician, bernhard Riemann, made a hypothesis while presenting a paper to the Berlin Academy titled  “On the Number of Prime Numbers Less Than a Given Quantity.

Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics #ad - Belknap Press. How to solve it a new aspect of Mathematical Method Princeton Science Library. Plume Books. Used book in Good Condition. Dover Publications. Dover Publications.


The Foundations of Mathematics

Oxford University Press #ad - The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. Plume Books. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields.

This is exemplified by a new chapter on the theory of groups. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, and a more abstract development of general concepts, based on logic, based on set theory. The transition from school mathematics to university mathematics is seldom straightforward.

The Foundations of Mathematics #ad - Used book in Good Condition. Dover Publications. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking.

Dover Publications. Oxford university Press USA. How to solve it a new aspect of Mathematical Method Princeton Science Library.