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Jay R. Goldman
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The Queen of Mathematics: A Historically Motivated Guide to Number Theory

by Jay R. Goldman (Author)
3.7 3.7 out of 5 stars 6 ratings
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This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.
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  1. ISBN-10
    9781568810065
  2. ISBN-13
    978-1568810065
  3. Publisher
    A K Peters/CRC Press
  4. Publication date
    November 15, 1997
  5. Language
    English
  6. Dimensions
    6.5 x 1.5 x 9.5 inches
  7. Print length
    550 pages
  8. See all details
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Editorial Reviews

Review

A superb combination historical narrative and introductory mathematic text.
-- Math Works, May 2003



"A superb combination historical narrative and introductory mathematic text." -Math Works, May 2003

About the Author

Jay R. Goldman

Product details

  • ASIN ‏ : ‎ 1568810067
  • Publisher ‏ : ‎ A K Peters/CRC Press (November 15, 1997)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 550 pages
  • ISBN-10 ‏ : ‎ 9781568810065
  • ISBN-13 ‏ : ‎ 978-1568810065
  • Item Weight ‏ : ‎ 2 pounds
  • Dimensions ‏ : ‎ 6.5 x 1.5 x 9.5 inches
  • Customer Reviews:
    3.7 3.7 out of 5 stars 6 ratings

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Jay R. Goldman

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3.7 out of 5 stars
3.7 out of 5
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6 global ratings

Top reviews from the United States

Robin Hill
5.0 out of 5 stars Everything fine.
Reviewed in the United States on February 1, 2018
Verified Purchase
Condition exactly as described. Fast delivery. Everything fine.
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reader
2.0 out of 5 stars needs a makeover
Reviewed in the United States on November 10, 2014
This isn't a bad idea but there are simply too many errors
in this printing ranging from mild infelicity to outright howler.
In addition, there seems to be a systematic
error which turned subscripts into superscripts and played havoc
with a number of formulas.
As far as the material itself is concerned, the author is clearly more
at home with the classical theory while often struggling and out of his
element with the newer developments.
Would strongly suggest waiting for a second edition or at least a 2nd printing.
2 people found this helpful
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Darin Brown
5.0 out of 5 stars Broader introduction than usual
Reviewed in the United States on June 1, 2001
I would agree with everything the first reviewer has written. This book is very readable, and it introduces a large number of important general concepts in number theory. What separates this book from other "introduction" books is (1) it is pitched at a much higher level than most introductory number theory books, which often assume that proofs and induction are unfamiliar, and so there are many superfluous chapters at the beginning which are just a rehash of basic set theory, how to write proofs, and modular arithmetic. This book starts from the beginning with Fermat and assumes some mathematical maturity -- ability to read proofs, knowledge of calculus, linear algebra, basic definitions of groups, rings, and fields, about advanced undergraduate, roughly. But the difference in sophistication is more obvious towards the middle and end of the book, where more general concepts from algebra, geometry, and analysis start to appear. This allows the author to talk about a variety of topics that are rarely mentioned in "introductory" books. Put another way -- if you want to see what some of these topics are about, you either have THIS book, or else some rather technical graduate textbooks to start with. Where else is complex multiplication, transcendental number theory, quadratic forms, and p-adic numbers all discussed at an undergraduate level? The other aspect which is different is (2) everything is historically motivated, and this is more than a phrase -- passages of original historical text, problems originally studied, historical commentary, and other folklore are nicely put together with mathematics. The result is that the reader gets a very broad picture of number theory, the "big picture", seeing how number theory isn't some static piece of knowledge sitting somewhere in space, but a body of concepts, ideas, and techniques which naturally developed over the past 400 years. For an advanced undergraduate or graduate student who wants a simple answer to the question, "What is number theory?", I would just refer them to this book.
28 people found this helpful
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S. Little
5.0 out of 5 stars A skillful blend of history and solid number theory
Reviewed in the United States on June 11, 2004
A clearly written book that covers number theory at a graduate or advanced undergraduate level. Covers much of the material in Gauss's Disquisitiones, but without all the detail. The book covers elementary number theory, binary quadratic forms, cyclotomy, Gaussian integers, quadratic fields, ideals, algebraic curves, rational points on elliptic curves, geometry of numbers, and introduces p-adic numbers. Only a slight bit of analytic number theory is covered. A good book in my opinion to start learning algebraic number theory. Wonderfully fills the otherwise troublesome gap between undergraduate number theory and overly abstract graduate level algebraic number theory.
Full of historical information hard to find elsewhere, very well researched. To cover all the material in this book would likely take two semesters, though most of the important material could be covered in one semester. Requires a background in abstract algebra (undergraduate level), and a little advanced calculus. Some complex analysis for sections 19.7 and 19.8 would be helpful, but not at all a requirement. The author recommends Harold Davenport's 'The Higher Arithmetic' as a companion volume for the first 12 chapters, which according to Goldman is a gem of a book.
19 people found this helpful
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R. Ball
5.0 out of 5 stars A Modern Classic
Reviewed in the United States on October 4, 2000
This is a superb book. The level is a broad introduction to Number Theory quite unlike any other. Every other N.T. book I know is either of the elementary type that covers all the usual stuff on primes, continued fractions, congruences, diophantine equations, quadratic reciprocity, etc. and then stops without introducing any of the machinery of the modern (ie. the last century and more), algebraic and geometric theory; OR, it is an advanced textbook that assumes a sophisticated and comprehensive knowledge of analysis and Galois theory etc. This remarkable book has substantial sections on the geometry of numbers, elliptic curves, p-adic analysis and much else as well as the 'elementary' stuff and provides a large amount of fascinating historical motivation. The whole book is very clear, well presented and thoroughly pleasurable to read. How all this is achieved in about 550 pages is that the earlier elementary parts are economically presented without too much of the recreational number novelties that tend to pad out some other books, and also a less rigorous approch is taken to (the more difficult) theorems that uses looser, schematic proofs or emphasises explanation of the meaning and relevance rather than exhaustive rigor. This book breaches the vital gap between basic and advanced NT that is conspicuously unfilled elsewhere. More books of this type are desperately needed, although one could hardly expect many to be as good as this.
23 people found this helpful
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Top reviews from other countries

desiderata
3.0 out of 5 stars Contents excellent but mediocre printing, binding.
Reviewed in the United Kingdom on August 30, 2014
Verified Purchase
Excellent book contents but "print to order" print quality rather poor ! Years ago I used to have the original print issue of this book & it was rather disappointing to replace it with one of distinctly lower print & binding quality.
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