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Number Theory (Dover Books on Mathematics) Paperback – October 12, 1994
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About the Author
The Holy Grail of Number Theory
George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text Number Theory (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field — number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well.
In 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the "Lost Notebook" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations — mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years.
In the Author's Own Words:
"It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered." — George E. Andrews
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Top Customer Reviews
I am glad I did. I am working my way through it -- problems and all -- and have finished the first three chapters. I find the material well presented and satisfying my needs. As a statistician I appreciate the fact that Dr. Andrews elected to take a combinatorial approach to the topic. Being familiar with this type of reasoning makes certain topics easier for me to comprehend. The book is not for the layman and takes an individual with a solid mathematical background to get through it in its entirety. However, if you're interested in the topic and willing to put in the effort, the book will pay off.
Here are the titles of the chapters with their starting pages:
// PART I Multiplicativity-Divisibility // 1. Basis Representation-3 / 2. The Fundamental Theorem of Arithmetic-12 / 3. Combinatorial and Computational Number Theory-30 / 4. Fundamentals of Congruences-49 / 5. Solving Congruences-58 / 6. Arithmetic Functions-75 / 7. Primitive Roots-93 / 8. Prime Numbers-100 // PART II Quadratic Congruences // 9. Quadratic Residues-115 / 10. Distribution of Quadratic Residues-128 // PART III Additivity // 11. Sums of Squares-141 / 12. Elementary Partition Theory-149 / 13. Partition Generating Functions-160 / 14. Partition Identities-175 // PART IV Geometric Number Theory // 15. Lattice Points-201 / There are four mathematical appendices and the full set of indices after the 15 chapters--213-259.
From the complicated table of contents above, one can see a broad sweep of combinatorial number theory. Part I is mostly pretty straight number theory, and that is what I did read. Part III on additivity is almost fully combinatorics more than number theory though. Still the price of this book is quite low to have access to all of this big range of mathematics to pick and choose what is most interesting to any given reader. Recommended.
I can't say which viewpoint is the correct one (they both are, I guess) but, since the books are so inexpensive, I would suggest try each or using both. It is often eye-opening to see the same conclusion derived from attacking the problem from more than one angle.
leading to deeper insight of the subject.
The use of computer-aided analysis is well-worth noting, since such calculating devices are commonly available.
The chosen examples are simple and allowthe text to be used also for self-study purposes.
Most Recent Customer Reviews
One huge complaint though for the Kindle Edition. On the big iPad Pro, some formulas are just about unreadable.Read more
Other than that, no complaints, it's exactly what it says it is and is in perfect condition other than...Read more