History of the Theory of Numbers (AMS Chelsea Publishing) Volumes I; II; III. THREE VOLUME SET (Vol. 2) [Hardcover]

Leonard Eugene Dickson (Author)

Book Description

Publication Date: May 31, 1999 | ISBN-10: 0821819380 | ISBN-13: 978-0821819388

Dickson's History is truly a monumental account of the development of one of the oldest and most important areas of mathematics. It is remarkable today to think that such a complete history could even be conceived. That Dickson was able to accomplish such a feat is attested to by the fact that his History has become the standard reference for number theory up to that time. One need only look at later classics, such as Hardy and Wright, where Dickson's History is frequently cited, to see its importance. The book is divided into three volumes by topic. In scope, the coverage is encyclopedic, leaving very little out. It is interesting to see the topics being resuscitated today that are treated in detail in Dickson. The first volume of Dickson's History covers the related topics of divisibility and primality. It begins with a description of the development of our understanding of perfect numbers. Other standard topics, such as Fermat's theorems, primitive roots, counting divisors, the Mobius function, and prime numbers themselves are treated. Dickson, in this thoroughness, also includes less workhorse subjects, such as methods of factoring, divisibility of factorials and properties of the digits of numbers. Concepts, results and citations are numerous. The second volume is a comprehensive treatment of Diophantine analysis. Besides the familiar cases of Diophantine equations, this rubric also covers partitions, representations as a sum of two, three, four or $n$ squares, Waring's problem in general and Hilbert's solution of it, and perfect squares in arithmetical and geometrical progressions. Of course, many important Diophantine equations, such as Pell's equation, and classes of equations, such as quadratic, cubic and quartic equations, are treated in detail. As usual with Dickson, the account is encyclopedic and the references are numerous. The last volume of Dickson's History is the most modern, covering quadratic and higher forms. The treatment here is more general than in Volume II, which, in a sense, is more concerned with special cases. Indeed, this volume chiefly presents methods of attacking whole classes of problems. Again, Dickson is exhaustive with references and citations.

Product Details

• Hardcover: 1602 pages
• Publisher: American Mathematical Society (May 31, 1999)
• Language: English
• ISBN-10: 0821819380
• ISBN-13: 978-0821819388
• Product Dimensions: 9.4 x 6.3 x 4 inches
• Shipping Weight: 6 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #4,513,906 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

5.0 out of 5 stars Not what you might expect., December 26, 2000

By 

D. Taylor (Colorado, USA) - See all my reviews
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This review is from: History of the Theory of Numbers (AMS Chelsea Publishing) Volumes I; II; III. THREE VOLUME SET (Vol. 2) (Hardcover)

The author was himself an expert in number theory and modern algebra (as it was) in his day. These volumes were published in 1919-23 so don't expect the latest results. In fact, the terminology won't even be the same since much of the theory has undergone a great deal of mollycoddling and reformulation...publish or perish, you know.

If you plan to do original research in the theory of numbers, these volumes are a must (even with the heavy price tag). Why? There is so much work constantly being done, results are often lost with time - what seems like something new is probably not. Like the constant rediscovery of Bernoulli and Striling numbers.

The volumes are probably not what you expect. They're really just a large annotated bibliography without detailed proofs or much immediate historic motivation (long-term history is the over-riding theme). Dickson catalogs near-misses as well as sometime pointless generalizations, so the text is not all meat. (Perhaps he's being more journalist here, than editor). In fact, it can become quite tiresome. You may be content to read these in a library, as any results will probably require you to look up the original source for more details. You'd better take notes and write down the page numbers while perusing. It's hard to find your way back, so many papers, so many authors, and the index is not optimal.

Andre Weil's "Number Theory: An approach through history" is a more literary and biographical account, but less comprehensive in the excruciating details.

5 stars for being an indispensable reference (if only for the historically-minded). Not without shortcomings.

14 of 14 people found the following review helpful:

5.0 out of 5 stars Absolutely essential reference, February 11, 2001

By 

Victor A. Vyssotsky "mandvav" (Orleans, MA USA) - See all my reviews
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This review is from: History of the Theory of Numbers (AMS Chelsea Publishing) Volumes I; II; III. THREE VOLUME SET (Vol. 2) (Hardcover)

This long book is sort of the equivalent of an extremely long review paper, with innumerable references. It is the only work of its kind on Theory of Numbers. Written in the early 1920s, it is still the only place where one can find information on who did what in various topics of number theory, and many of those topics are still fertile ground for further research. So if one wants to do research on any topic in theory of numbers, or on related aspects of algebra, topology, Ramsey Theory, theory of graphs, etc. one *must* have Dickson's book handy. It's expensive; if you're lucky, a colleague or your departmental library may have a copy handy for you, but if not, go ahead and spend the money to buy it. It has been of great use to me.