Mathematics and Its History

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Springer Science & Business Media, Aug 2, 2010 - Mathematics - 662 pages
1 Review
From the reviews of the second edition:

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community."

(European Mathematical Society)

"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."

(Denis Bonheure, Bulletin of the Belgian Society)

This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.

 

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One of the better ways to learn mathematics is through its history.
Excellent narrative voice, very cohesive, only not giving it a five because ... well, not everything can get a five, can it?

Contents

1 The Theorem of Pythagoras
1
2 Greek Geometry
17
3 Greek Number Theory
37
4 Infinity in Greek Mathematics
53
5 Number Theory in Asia
68
6 Polynomial Equations
87
7 Analytic Geometry
109
8 Projective Geometry
126
15 Complex Numbers and Curves
295
16 Complex Numbers and Functions
313
17 Differential Geometry
335
18 NonEuclidean Geometry
359
19 Group Theory
382
20 Hypercomplex Numbers
415
21 Algebraic Number Theory
438
22 Topology
467

9 Calculus
157
10 Infinite Series
181
11 The Number Theory Revival
203
12 Elliptic Functions
224
13 Mechanics
243
14 Complex Numbers in Algebra
275
23 Simple Groups
495
24 Sets Logic and Computation
525
25 Combinatorics
553
Bibliography
589
Index
629
Copyright

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About the author (2010)

John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books with Springer, including The Four Pillars of Geometry; Elements of Algebra; Numbers and Geometry; and many more.

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