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History of the Theory of Numbers, Volume I: Divisibility and Primality (Dover Books on Mathematics) Illustrated Edition

4.0 4.0 out of 5 stars 11 ratings
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The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This first volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subjects of divisibility and primality. It can be read independently of the succeeding volumes, which explore diophantine analysis and quadratic and higher forms.
Within the twenty-chapter treatment are considerations of perfect, multiply perfect, and amicable numbers; formulas for the number and sum of divisors and problems of Fermat and Wallis; Farey series; periodic decimal fractions; primitive roots, exponents, indices, and binomial congruences; higher congruences; divisibility of factorials and multinomial coefficients; sum and number of divisors; theorems on divisibility, greatest common divisor, and least common multiple; criteria for divisibility by a given number; factor tables and lists of primes; methods of factoring; Fermat numbers; recurring series; the theory of prime numbers; inversion of functions; properties of the digits of numbers; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.
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  1. ISBN-10
    0486442322
  2. ISBN-13
    978-0486442327
  3. Edition
    Illustrated
  4. Publisher
    Dover Publications
  5. Publication date
    June 3, 2005
  6. Part of series
    Dover Books on Mathematics
  7. Language
    English
  8. Dimensions
    5.54 x 1.04 x 8.54 inches
  9. Print length
    512 pages
  10. See all details
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Editorial Reviews

About the Author

Leonard Eugene Dickson taught at the University of Chicago.

Product details

  • Publisher ‏ : ‎ Dover Publications; Illustrated edition (June 3, 2005)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 512 pages
  • ISBN-10 ‏ : ‎ 0486442322
  • ISBN-13 ‏ : ‎ 978-0486442327
  • Item Weight ‏ : ‎ 1.16 pounds
  • Dimensions ‏ : ‎ 5.54 x 1.04 x 8.54 inches
  • Customer Reviews:
    4.0 4.0 out of 5 stars 11 ratings

Customer reviews

4 out of 5 stars
4 out of 5
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11 global ratings

Top reviews from the United States

Larry Whitmour II
5.0 out of 5 stars An excellent reference--only!
Reviewed in the United States on July 8, 2012
If you are looking for a quick concise history of any technical number theoretical topic (300BC--1900) this set of volumes is a masterpiece and stands alone--very few fields have such a fine authoritative concise summary of their history. The author clearly spent years combing libraries and trying to catalog all of what had been done in number theory. For this reason, these volumes are truly excellent reference books that all large libraries should own (but few individuals).

They are reference books, do not buy them to sit down and learn about the history of number theory. They are not narratives. No quaint stories. No pictures. Very few definitions. Just very long lists of very terse concise references arranged by topic and then listed chronologically. For example, if you want to know who created what length of prime number tables before 1900, no extra words, just a list of dates and references, these volumes are ideal! To fault these volumes for being boring is to entirely miss their purpose, they are not written to entertain you. They are not novels or text books. Just references.

I love my copies, and enjoy seeing who did what on areas of number theory that are no longer explored, but I think others should look in a library and know what they are buying before they do.
13 people found this helpful
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Donald Kahn
4.0 out of 5 stars Four Stars
Reviewed in the United States on February 23, 2016
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Concise, informative. The only reason it's not 5 stars, is that it doesn't cover the last 100 years.
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AM
1.0 out of 5 stars Unspeakably boring
Reviewed in the United States on September 23, 2007
Verified Purchase
I hate writing negative reviews, and I am not arguing about the completeness or accuracy of the mathematics of the book, but this is the most boring, useless, dreary, tedious, uninteresting, monotonous and dull book on mathematics that I have ever possessed.
The whole book is a catalog of mathematical facts and theorem, without proof, and with extremely vague corelations between them, proved by this or that author, each from 1 to 10 lines long. Reading a phone directory can often be more entertaining.
15 people found this helpful
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Catherine G. (Paris)
4.0 out of 5 stars A Landmark Writing, mainly of historical value
Reviewed in the United States on July 31, 2006
The author, L. E. Dickson, was a distinguished algebraist and number theorist in the first half of the 20th century. With collaborators, he compiled this "history", in three volumes, to get himself acquainted with the subject and to launch research on this topic (considered as important in other countries) in the US.

The book is a kind of "Mathematical Reviews" of number theory for the period until 1920: short, technical, notices on hundreds of articles and books, classified by topic, according to the classification valid in 1900. Dickson prefered "just the (mathematical) facts" and thus there is no biographical information, nor sweeping conceptual or sociological description. A useful, slightly more entertaining, introduction summarizes the development of the results in each volume.

Thus, if you are looking 1) for a popular, general presentation of the history of number theory 2) or for an up-to date synthesis of number theory or its history, forget it. It is rather technical and was written in the 1920s. But it is very interesting if your interest in history of maths is (semi-)professional, specially on the 19th century, or if you are looking for mathematical fun in old, mostly elementary, but certainly still fruitful, problems. Better to check the state-of-the-art, though, in both cases, if you have any hope for publication ( many new documents and of course many new theorems, even new research areas, have been found since the 1920s).

And then, it is such a classic for US (history of) maths that, especially in paperback, you may want it for your library in any case. If you want to know more on this book, there is a nice chapter devoted to it, written by D. Fenster (the best specialist of Dickson) in Landmark Writings in Western Mathematics, ed. I. Grattan-Guinness.
34 people found this helpful
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Top reviews from other countries

Peter Van Eetvelt
5.0 out of 5 stars Five Stars
Reviewed in the United Kingdom on September 24, 2015
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EXCELLENT
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