# Search Results for "what-is-mathematics-an-elementary-approach-to-ideas-and-methods"

## What is Mathematics?

*An Elementary Approach to Ideas and Methods*

**Author**: Richard Courant,Herbert Robbins,Ian Stewart**Publisher:**Oxford University Press, USA**ISBN:**9780195105193**Category:**Mathematics**Page:**566**View:**6362

A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

## What Is Mathematics?

*An Elementary Approach to Ideas and Methods*

**Author**: the late Richard Courant,Herbert Robbins**Publisher:**Oxford University Press**ISBN:**9780199754878**Category:**Mathematics**Page:**592**View:**679

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. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. 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. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, 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, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. 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*

**Author**: Richard Courant,Herbert Robbins**Publisher:**Oxford University Press, USA**ISBN:**0195105192**Category:**Mathematics**Page:**566**View:**4417

A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

## Concepts of Modern Mathematics

**Author**: Ian Stewart**Publisher:**Courier Corporation**ISBN:**0486134954**Category:**Mathematics**Page:**368**View:**6859

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

## What is Mathematics, Really?

**Author**: Reuben Hersh**Publisher:**Oxford University Press, USA**ISBN:**9780195130874**Category:**Medical**Page:**343**View:**8313

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

## Mathematics

*Its Content, Methods and Meaning*

**Author**: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev**Publisher:**Courier Corporation**ISBN:**0486157873**Category:**Mathematics**Page:**1120**View:**5094

Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

## Methods of Mathematical Physics, Volume 2

*Differential Equations*

**Author**: Richard Courant,D. Hilbert**Publisher:**John Wiley & Sons**ISBN:**3527617248**Category:**Science**Page:**852**View:**4688

Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.

## What is Mathematics?

*An Elementary Approach to Ideas and Methods*

**Author**: Richard Courant,Herbert Robbins**Publisher:**N.A**ISBN:**N.A**Category:**Mathematics**Page:**521**View:**8636

## Makers of Mathematics

**Author**: Stuart Hollingdale**Publisher:**Courier Corporation**ISBN:**0486174506**Category:**Mathematics**Page:**464**View:**8854

Each chapter of this accessible portrait of the evolution of mathematics examines the work of an individual — Archimedes, Descartes, Newton, Einstein, others — to explore the mathematics of his era. 1989 edition.

## Mathematics

**Author**: Timothy Gowers**Publisher:**Sterling Publishing Company, Inc.**ISBN:**9781402768972**Category:**Mathematics**Page:**180**View:**4440

Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

## Introduction to Calculus and Analysis

**Author**: Richard Courant,Fritz John**Publisher:**Springer Science & Business Media**ISBN:**9783540665694**Category:**Mathematics**Page:**556**View:**5078

Biography of Richard Courant Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence. For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John. (P.D. Lax) Biography of Fritz John Fritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was half-Jewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994. John's research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMO-functions (bounded mean oscillations). Fritz John's work exemplifies the unity of mathematics as well as its elegance and its beauty. (J. Moser)

## The Foundations of Mathematics

**Author**: Ian Stewart,David Orme Tall**Publisher:**Oxford University Press on Demand**ISBN:**9780198531654**Category:**Fiction**Page:**263**View:**6925

"There are many textbooks available for a so-called transition course from calculus to abstract mathematics. I have taught this course several times and always find it problematic. The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books

## Letters to a Young Mathematician

**Author**: Ian Stewart**Publisher:**Basic Books**ISBN:**0465008410**Category:**Mathematics**Page:**224**View:**7981

Mathematician Ian Stewart tells readers what he wishes he had known when he was a student. He takes up subjects ranging from the philosophical to the practical-what mathematics is and why it’s worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others.

## Mathematics for the Nonmathematician

**Author**: Morris Kline**Publisher:**Courier Corporation**ISBN:**0486316130**Category:**Mathematics**Page:**672**View:**1901

Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.

## Differential and Integral Calculus

**Author**: Richard Courant**Publisher:**John Wiley & Sons**ISBN:**1118031490**Category:**Mathematics**Page:**640**View:**2819

## Math Hysteria : Fun and games with mathematics

*Fun and games with mathematics*

**Author**: Ian Stewart**Publisher:**OUP Oxford**ISBN:**0191547395**Category:**Games**Page:**256**View:**3508

Welcome to Ian Stewart's strange and magical world of mathematics! In Math Hysteria, Professor Stewart presents us with a wealth of magical puzzles, each one spun around an amazing tale: Counting the Cattle of the Sun; The Great Drain Robbery; and Preposterous Piratical Predicaments; to name but a few. Along the way, we also meet many curious characters: in short, these stories are engaging, challenging, and lots of fun!

## Mathematics and the Imagination

**Author**: Edward Kasner,James Newman**Publisher:**Courier Corporation**ISBN:**0486320278**Category:**Mathematics**Page:**400**View:**3175

With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.

## Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces

**Author**: R. Courant**Publisher:**Springer Science & Business Media**ISBN:**1461299179**Category:**Mathematics**Page:**332**View:**2015