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.
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6 of 6 people found the following review helpful:
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Tells you so many facts nobody knows,
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This review is from: History of the Theory of Numbers (AMS Chelsea Publishing) (Hardcover)
"History of the Theory of Numbers" is a quite unusual type of reference/history book.
Rather than list entries in alphabetical order or in a strictly chronological order, "History of the Theory of Numbers" lists a very large number of important discoveries in number theory by topic in chronological order. Although the book will not enable a novice to understand most concepts within the field of number theory, the amount of detail it gives about how knowledge in such fields as prime and perfect numbers evolved in the centuries up to its publication in 1923 is quite remarkable. Where else can you find the name of the man who proved 1111111111111111111 (nineteen ones) to be prime - and see that remarkably there was no attempt to test it for primality even when mathematicians of the calibre of Lucas could prove it had almost certainly had not factor? Where else can you find the factor of (2^53-1)? I could list so many other facts in number theory that would surprise even those with the experience I have studying prime and other famous numbers like perfect and multiply perfect ones. Although using it can seem awkward at first, for those with a reasonable knowledge of number theory, "History of the Theory of Numbers" should become easy after a few reads as it is structured very logically. All in all, even if not for the beginner, this is one of the best reference mathematics books you will ever find.
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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100
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- Fermat's Last Theorem for Amateurs by Paulo Ribenboim on 10 pages
- Classical Theory of Arithmetic Functions (Chapman & Hall/CRC Pure and Applied Mathematics) by R Sivaramakrishnan on 4 pages
- Lure of the Integers (MAA Spectrum) by Joe Roberts on 4 pages
- Excursions in Calculus: An Interplay of the Continuous and the Discrete (Dolciani Mathematical Expositions) by Robert M. Young on 4 pages
- The Mathematical Career of Pierre de Fermat, 1601-1665 by Michael Sean Mahoney on page 289, page 292, and page 357
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