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Mathematics and Its History (Undergraduate Texts in Mathematics) 3rd ed. 2010 Edition

4 out of 5 stars 16 customer reviews
ISBN-13: 978-1441960528
ISBN-10: 144196052X
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Editorial Reviews

Review

From the reviews of the third edition:

"The author’s goal for Mathematics and its History is to provide a “bird’s-eye view of undergraduate mathematics.” (p. vii) In that regard it succeeds admirably. ... Mathematics and its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. ... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics. ... While Stillwell does a wonderful job of tying together seemingly unrelated areas of mathematics, it is possible to read each chapter independently. I would recommend this fine book for anyone who has an interest in the history of mathematics. For those who teach mathematics, it provides lots of information which could easily be used to enrich an opening lecture in most any undergraduate course. It would be an ideal gift for a department’s outstanding major or for the math club president. Pick it up at your peril ― it is hard to put down!"

(Richard Wilders, MAA Reviews)

“I appreciate and recommend Stillwell’s presentation of mathematics and history written in a lively style. The author’s concept (history mostly as the means of approaching mathematics) remains a matter of interest for both the mathematician and the historian … .” (Rüdiger Thiele, Zentralblatt MATH, Vol. 1207, 2011)

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)

From the Back Cover

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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Product Details

  • Series: Undergraduate Texts in Mathematics
  • Hardcover: 662 pages
  • Publisher: Springer; 3rd ed. 2010 edition (August 2, 2010)
  • Language: English
  • ISBN-10: 144196052X
  • ISBN-13: 978-1441960528
  • Product Dimensions: 6.1 x 1.4 x 9.2 inches
  • Shipping Weight: 2.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #161,448 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Hardcover
This is a brilliant book that conveys a beautiful, unified picture of mathematics. It is not an encyclopedic history, it is history for the sake of understanding mathematics. There is an idea behind every topic, every section makes a mathematical point, showing how the mathematical theories of today has grown inevitably from the natural problems studied by the masters of the past.

Math history textbooks of today are often enslaved by the modern curriculum, which means that they spend lots of time on the question of rigor in analysis and they feel obliged to deal with boring technicalities of the history of matrix theory and so on. This is of course the wrong way to study history. Instead, one of the great virtues of a history such as Stillwell's is that it studies mathematics the way mathematics wants to be studied, which gives a very healthy perspective on the modern customs. Again and again topics which are treated unnaturally in the usual courses are seen here in their proper setting. This makes this book a very valuable companion over the years.

Another flaw of many standard history textbooks is that they spend too much time on trivial things like elementary arithmetic, because they think it is good for aspiring teachers and, I think, because it is fashionable to deal with non-western civilisations. It gives an unsound picture of mathematics if Gauss receives as much attention as abacuses, and it makes these books useless for understanding any of the really interesting mathematics, say after 1800. Here Stillwell saves us again. The chapter on calculus is done by page 170, which is about a third of the book. A comparable point in the more mainstream book of Katz, for instance, is page 596 of my edition, which is more than two thirds into that book.

Petty details aside, the main point is the following: This is the single best book I have ever seen for truly understanding mathematics as a whole.
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Format: Hardcover
Stillwell covers a lot of ground in a short undergraduate text intended to unify various mathematical disciplines. Naturally, _Mathematics_and_its_History_ begins with the early Greeks and in particular geometry (which is how mathematics was typically expressed then). The development of algebra and polynomial forms is described followed by perspective geometry. The invention of calculus and the closely related discovery of infinite series provide the backdrop for short biographies of prominent mathematicians (mostly dead white males to multicultural deconstructionists). The development of elliptic integrals (used in solving functions with specified boundary conditions such as a Neumann problem found in fluid mechanics). The treatment then diverges to physical problems including the vibrating string and hydrodynamics, together with a note on the renown Bernoulli family. Then Stillwell returns to the esoteric in complex numbers, topology, group theory and logic with some comments on computation at the end. Some mathematicians may find the overview to lack comprehensiveness, but the book's brevity for each topic and biographical notes present a balanced approach to the more casual reader about this important field of study and how it developed.
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Format: Hardcover Verified Purchase
This review is not negative based on the content of the book.
This review is negative because of the poor job by the publisher
in printing this book.

The problem is: the "new" copy of the book I received had 15 to 20
page ranges which were totally unprinted. To phrase it another way,
all the correct number of pages were in the book but there were places
where anywhere from 2 to 12 consecutive pages were not printed -
not even the page numbers were printed on such page.

The material on 90%+ of the 600+ seemed fine but several of the
sections I had intended to read had large (and important) gaps.

Springer this was an inferior print job - I have never seen a single
book so poorly printed.

I would still like a "good" copy of this book but I will never pay for it!!
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Format: Hardcover
It is a very good book. It has presented very clearly some difficult-to-understand relationship especially the link between algebra and geometry. It is a very good balance - history, Mathmatics, biography all mixed very well together. Highly recommended.
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Format: Hardcover
Every page is filled with fresh insights, genuine scholarships, clarity, connections, and understandings. Leaves all other textbooks on history of math in the dust. Never blindly follows the crowd of other authors to repeat after each other the muddled, and often untrue, interpretations and stories. Makes me want to have a photographic memory to take in everything in the book and use them to motivate and inspire my own teaching. Also makes me want to read many of the original sources Professor Stillwell's vast scholarship has traveled through.

It's a great page-turner and at the same time a fine wine to be sipped and appreciated sentence by sentence.
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Format: Hardcover Verified Purchase
While I've enjoyed the first 10 pages, my copy was very poorly printed. There have to be at least 30 pages worth of text which are just blank.
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Format: Hardcover Verified Purchase
A very readable and comprehensive history of mathematics with actual mathematics included - in the text and in the problems - as opposed to merely talking about mathematics with names and dates. Of course there are enough of the names and dates included to make it a real history too.
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