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Title: What Is Mathematics?: An Elementary Approach to Ideas and Methods by Richard Courant, Herbert Robbins, Ian Stewart ISBN: 0-19-510519-2 Publisher: Oxford University Press Pub. Date: May, 1996 Format: Paperback Volumes: 1 List Price(USD): $21.50 |
Average Customer Rating: 4.84 (19 reviews)
Rating: 4
Summary: Pretty good
Comment: For the most part I love this book. It is informative, and relatively simple to understand. This book is an "elementary approach to ideas and methods" for the whole field of mathmatics. In fact, this book is one of the reasons I changed my major to mathmatics.
However, there are two main problems with this book. First the quality of the print varies. Occasionally, whole sets of subscripts are blurred, which makes understanding the equation of the moment difficult, if not impossible.
Second, the order of steps for solving or understanding a problem are in an unexpected order, which is confusing. Often, I find that a difficult passage doesn't deal with difficult concepts, its just that the concepts are explained in an unusual way.
Aside from those problems, this is an extraordinary introduction to mathmatics.
Rating: 4
Summary: Not an 'easy' read
Comment: This is a demanding book. One cannot read it listening to Bach. [a clash of complexities]. The construction of he book is 'old style' [which is every seeming possible variation is mentioned] which has fallen into disfavor as confusing,
That written it is very complete and I really enjoyed many parts of this book.
Rating: 5
Summary: Extraordinary Book. Belongs on Your Bookshelf.
Comment: Courant's 500-page text is not entirely suitable for the layman. Its target audience includes those who enjoy reading and studying mathematics and have a good background through precalculus or higher. "What is Mathematics?" is a mathematics book, not a book about mathematics.
"What is Mathematics?" is not a new book. It was first published in 1941. New editions appeared in 1943, 1945, and 1947. My soft cover fourth edition by Oxford University Press is in its 12 printing.
The authors indicate that it is no means necessary to "plow through it page by page, chapter by chapter". I fully agree. I have skipped around, jumping to chapters of particular interest, but I have now read nearly every chapter.
I initially skipped to page 165 and delved directly into projective geometry (chapter IV), proceeded to topology (chapter V), and then jumped backwards to the beginning to explore the theory of numbers. After moving to geometry, I finally returned to the later chapters on functions and limits, maxima and minima, and the calculus.
Courant engages the reader in discussions on mathematical concepts rather than focusing on applications and problem solving. "What is Mathematics?" is a great textbook for students that have completed a year or more of calculus and wish to pull all of their mathematical learning together before moving on to more advanced studies. I suspect that it would even be welcomed by students that have completed an undergraduate degree in mathematics.
I cannot resist quoting Albert Einstein's comment on What is Mathematics? - "A lucid representation of the fundamental concepts and methods of the whole field of mathematics...Easily understandable."
Richard Courant was a highly respected mathematician. He taught in Germany and in Cambridge and was director of the Institute of Mathematical Sciences at New York University (now renamed the Courant Institute of Mathematical Sciences). Courant has authored other widely acclaimed mathematical texts including Methods of Mathematical Physics (co-authored with David Hilbert) and his popular Differential and Integral Calculus.
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Title: Concepts of Modern Mathematics by Ian Stewart ISBN: 0486284247 Publisher: Dover Pubns Pub. Date: 01 February, 1995 List Price(USD): $10.95 |
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Title: Foundations and Fundamental Concepts of Mathematics by Howard Eves ISBN: 048669609X Publisher: Dover Pubns Pub. Date: 20 May, 1997 List Price(USD): $14.95 |
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Title: Mathematics and the Physical World by Morris Kline ISBN: 0486241041 Publisher: Dover Pubns Pub. Date: 01 March, 1981 List Price(USD): $16.95 |
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Title: How to Solve It by G. Polya ISBN: 0691023565 Publisher: Princeton Univ Pr Pub. Date: 01 November, 1971 List Price(USD): $18.95 |
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Title: Mathematics for the Nonmathematician by Morris Kline ISBN: 0486248232 Publisher: Dover Pubns Pub. Date: 01 February, 1985 List Price(USD): $14.95 |
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