» What Is Mathematics? An Elementary Approach to Ideas and Methods
Rating: 5.0 / 5.00 (30 reviews)
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Manufacturer: Oxford University Press, USA
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What Is Mathematics? An Elementary Approach to Ideas and Methods Details
Binding: PaperbackDewey Decimal Number: 510
EAN: 9780195105193
ISBN: 0195105192
Label: Oxford University Press, USA
Manufacturer: Oxford University Press, USA
Number Of Items: 1
Number Of Pages: 592
Publication Date: 1996-07-18
Publisher: Oxford University Press, USA
Studio: Oxford University Press, USA
What Is Mathematics? An Elementary Approach to Ideas and Methods Reviews
Customer Rating:
Summary: I need something more elementary
Comment: This book was (is) difficult for me. Although I managed to grind out B's and a few A's in introductory trig, analytic geometry and calculus in school, I felt overwhelmed by the author's methods of explanation. The text is elegantly written, but following the explanations often requires the reader to fill in a lot of steps which may seem obvious to the author (and apparently to many of the readers who gave the book such positive reviews) but which are not obvious to me.
I need something that goes into more detailed explanation of a more limited selection of material, with more explicit metaphors and visual analogies. Apparently my talent for math is pretty limited. A patient tutor is probably what I really need, but that doesn't seem to be a practical option for me. So I will keep looking for other texts that may help me understand it better.
Customer Rating:
Summary: What is "What is Mathematics"???
Comment: It's a lucid presentation of the ideas that govern the different domains of Mathematics. Clear but not too easy, it needs commitment by the reader in order to understand its essence to the full. Courant (as his mentor Hilbert) shows how important and useful it is to demystify the cumbersome technicalities that often dominate the subject.
Customer Rating:
Summary: Review by Undergraduate Math Major
Comment: As an above average undergraduate math major(by no means exceptional) I always had some nagging questions in the back of my mind. Questions like: what is the connection between e, pi, 1/x? Why does the Taylor series expansion work? How did we come across complex numbers? I found a lot of good answers in this book. This book is totally worth the price - I think I can speak for (and speak to) all who have at least an undergraduate preparation in math (and have some knawing questions).
Overall a great, broad overview of the discipline. Spread the word.
Customer Rating:
Summary: It's incredible (when read carefully with a controlled imagination)
Comment: Nevertheless, this book does in fact deserve 5 stars. I wanted to be the first to give it less than 4 stars, but the quality of the presentation of ideas is just too damn good.
An engineer or physicist would be quite happy with this book, which makes sense given Courant's career focus on applied mathematics. Still, a lot of "pure" mathematicians obviously enjoy it too. lol.
(By the way, this review really refers to original. No doubt Ian Stewart crapped it up a bit.)
Customer Rating:
Summary: Outstanding writing
Comment: Whether or not you are a mathematician or if it is just a hobby, this book is fantastic!!! You can open it up to any page and just begin reading...there is no need to start beginning to end. A great work to read as time allows!!!
More Reviews for What Is Mathematics? An Elementary Approach to Ideas and Methods
Editorial Review for What Is Mathematics? An Elementary Approach to Ideas and Methods:
"A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods."--Albert Einstein (on the first edition)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 not to real understanding or 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 a marvelously literate story: it opens a window onto the world of mathematics for anyone interested to view.
