What Is Mathematics?

Posted on 16 July 2018 by Richard Courant

For 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 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. Best Download Kindle ePUB What Is Mathematics? by Richard Courant – kino-fada.fr This is the ideal book to read during the last years at school, or early in an undergraduate degree School maths is often about understanding mathematical concepts intuitively via rote learning, repetition and visualization This book teaches you how mathematical knowledge is arrived at by looking carefully at a few simple ideas and building upon them.This book is also ideal reading for anybody who wants to improve their general mathematical literacy Perhaps many people who don t know much abo This is the ideal book to read during the last years at school, or early in an undergraduate degree School maths is often about understanding mathematical concepts intuitively via rote learning, repetition and visualization This book teaches you how mathematical knowledge is arrived at by looking carefully at a few simple ideas and building upon them.This book is also ideal reading for anybody who wants to improve their general mat...The difficulty is that it is easy to prove a problem is easy, but hard to prove that it is hard I m probably not unique in that I made it through a lot of math without ever really understanding what I was doing, just flipping equations around until an answer poured out I had a trigonometry professor who at least pushed understanding what you were doing It was in my first semester of the calculus that math started to make sense What Is Mathematics was a clear inspiration for some of the l ...Wow, that was absolutely beautiful Thanks for the heads up, Alex I really, really wish I d have had this book back as a senior or junior in high school I d have been able to plan out my math classes early on much better why on earth did I take Dynamics and Bifurcations and how did I avoid taking a serious vector spaces manifold calculus class would have been nice for upper level physics oh well I think this will be my default high school graduation present to anyone with an inkling Wow, that was absolutely beautiful Thanks for the heads up, Alex I really, really...Einstein put it best when he said this book is a lucid representation of the fundamental concepts and methods of the whole field of mathematics It really is.This is a magnificent book for laymen who want to know about mathematics This is a sensational book for amateurs who wish to widen and deepen understanding of mathematics This is an indispensable book for educators who need to find wonderful examples to inspire children and students Everyone does not want to miss this.I especially love the geometry part of this book, which contains chapter 3, 4 7 Chapter 3 introduces the ruler and compass construction This chapter firstly discusses th This is a magnificent book for laymen who want to know about mathematics This is a sensational book for amateurs who wish to widen and deepen understanding of mathematics This is an indispensable book for educators who need to find wonderful examples to inspire children and students Everyone does not want to miss this.I especially love the geometry part of this book, which contains chapter 3, 4 7 Chapter 3 introduces the ruler and compass construction This chapter firstly discusses the classical geometry of Des Cartes, namely how to construct the finite sums, differences, products, quotients and square roots of given line section Then explains the construtable problems Finally proves the impossibilities of the three ancient famous classical construction problems, squaring the circle, doubling the cube and angle trisection, which cost mathematicians hundreds of years to finally figure out Readers will be stunned by the connection between algebraic fields and classical geo... , .In another life, many many moons ago, I received this book as a gift from an English math professor I met on a plane It was not a completely haphazard encounter we were both on our way back from the Hong Kong IMO I was a contestant not a really successful one , and he was an elderly member of the committee I did not realize who he was during our pleasant conversation I only learned that from our team leader after we landed in Frankfurt and parted way with the British contingent In a cou In another life, many many moons ago, I received this book as a gift from an English math professor I met on a plane It was not a completely haphazard encounter we were both on our way back from the Hong Kong IMO I was a contestant not ...This is a book which changed my life I originally read it when I was 17, and it was the book which confirmed to me that I wanted to study mathematics at university Re reading it now, it is a clear and inspiring look at a wide range of interesting mathematics, presenting an elementary view of how it is viewed from a university rather than a high school perspective Some parts are a little dated even when I read it in the 1980s, the amount of ge...One of my favorite books on mathematics Also, one of Einstein s favorites.This is one of the best high school level extensions in mathematics Originally called Mathematics for Lori it was written for his daughter.

English
16 July 2018

Richard Courant