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Mathematics and Its History (Undergraduate Texts in Mathematics) Hardcover – 29 Nov 2001


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Product details

  • Hardcover: 542 pages
  • Publisher: Springer; 2nd ed. 2002. Corr. 2nd printing edition (29 Nov. 2001)
  • Language: English
  • ISBN-10: 0387953361
  • ISBN-13: 978-0387953366
  • Product Dimensions: 15.6 x 3.2 x 23.4 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 957,878 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

"This book is highly recomended as the basis for courses, especially for students who want to besome teachers at secondary schools." Math Reviews

From the Back Cover

From the reviews of the first edition: "There are many books on the history of mathematics in which mathematics is subordinated to history. This is a book in which history is definitely subordinated to mathematics. It can be described as a collection of critical historical essays dealing with a large variety of mathematical disciplines and issues, and intended for a broad audience...we know of no book on mathematics and its history that covers half as much nonstandard material. Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer) "The discussion is at a deep enough level that I suspect most trained mathematicians will find much that they do not know, as well as good intuitive explanations of familiar facts. The careful exposition, lightness of touch, and the absence of technicalities should make the book accessible to most senior undergraduates." (American Mathematical Monthly) "...The book is a treasure, which deserves wide adoption as a text and much consultation by historians and mathematicians alike." (Physis - Revista Internazionale di Storia della Scienza) "A beautiful little book, certain to be treasured by several generations of mathematics lovers, by students and teachers so enlightened as to think of mathematics not as a forest of technical details but as the beautiful coherent creation of a richly diverse population of extraordinary people...His writing is so luminous as to engage the interest of utter novices, yet so dense with particulars as to stimulate the imagination of professionals." (Book News, Inc.) This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises expalining how they relate to the preceding section, and how they foreshadow later topics. The index has been given added structure to make searching easier, the references have been redone, and hundreds of minor improvements have been made throughout the text. --This text refers to an out of print or unavailable edition of this title.

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If there is one theorem that is known to all mathematically educated people, it is surely the theorem of Pythagoras. Read the first page
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4 of 4 people found the following review helpful By E. Clarke on 7 Feb. 2010
Format: Hardcover Verified Purchase
Excellent book, but take it at its word - you need to have undergraduate maths to appreciate it. It lost me many times.
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Format: Hardcover
I bought a copy of this book for the school library (as well as one for myself!), and it was on loan almost constantly, motivating many of my students towards taking mathematics to degree level. Although an advanced qualification makes for a fairly straightforward read, it is by no means necessary for a good appreciation of most of the chapters.

I learned much from reading right through, in particular what a poor substitute a degree is for a proper mathematical education. I'd never before seen a proof that non-singular cubic curves are incapable of being parametrised by algebraic functions: at first sight this seems surprising, in view of the fact that quadratics can be so expressed, but Stillwell makes it all so accessible and hypnotic. And when he moves on to doubly periodicity, elliptic functions, and geometrisation using the Riemann surface, leading all so naturally to the concept of genus, boy do you get a buzz!

And still I've drawn on only about 3 of the 23 chapters. It really is first-rate.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 13 reviews
88 of 91 people found the following review helpful
An intellectually satisfying history of mathematics 18 Feb. 2005
By Viktor Blasjo - Published on Amazon.com
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.
46 of 51 people found the following review helpful
concise and well written summary of mathematics 2 Oct. 2000
By G W Thielman - Published on Amazon.com
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.
9 of 9 people found the following review helpful
Publisher Springer prints with many pages missing (not physically - but many blank/missing pages) 8 Mar. 2014
By Bruce Sellers - Published on Amazon.com
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!!
28 of 34 people found the following review helpful
Relationship between algebra and geometry 2 Nov. 2003
By Ng Chi Chun - Published on Amazon.com
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.
8 of 10 people found the following review helpful
Simply Outstanding! 6 Oct. 2011
By Mathbuff - Published on Amazon.com
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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