An Introduction to Number Theory (Mit Press)

This book is nice. It mixes in interesting history that motivates the major topics. I've had a graduate class in number theory and was simply mystified by why the topics in it were of interest.

Good !

If numbers are over your head, you might not enjoy this book... But, if you want to take your good math skills and make them better, a good study of number theory will do it and this book is a good way to get moving down that path... Now, it is a bit dated, being almost as old as I am... Some of the discussion of work done in the field may be out of date... but the internet can help you check those facts... Otherwise, numbers haven't changed since Adam (1) & Eve (1) = Couple (2)... Did Adam understand number theory... I don't know, but if he had this book, he certainly would have...

This book served as the primary text for my undergraduate course on number theory. It starts off how you would expect it to with sections on the Euclidean algorithm, linear diophantine equations, Euler's totient function, congruences and primitive roots. It is pretty conventional until you arrive at the chapter on magic squares (some really cool stuff). I remember being asked to construct a 9-by-9 filled, magic square using integers from 0 to 80 with the property that when divided into ninths, each 3-by-3 subsquare is also magic. While you are most likely to encounter exercises at the beginning of the book that deal with topics such as Fermat's little theorem and perhaps proving that a number like 1729 is a pseudoprime or verifying that there are infinitely many primes of the form 4n-1 and 4n+1, there are some unique problems in this book that explore topics like the sieve of Eratosthenes and continued fractions. I would say that with regards to the content of the book, Stark's introduction to number theory is not your standard, run-of-the-mill text, which is good. I found it incorporated a lot of neat topics like this and the later chapters on quadratic fields prove to be a good insight into algebraic number theory. Highly recommend!

This book was the required text for an independent study class I enrolled in. The class has been more difficult than I thought it would be, as has the text. It is complex material and doesn't provide a lot of clear-cut examples - instead assuming that you make the connection yourself. However, I am learning all on my own and the material may be more understandable with the help of a live professor.

In general, this book gives a comprehensive account on elementary number theory. The first few chapters include some fundamental concepts like divisibility and congruences (i.e. a simple kind of modular arithmetic), as well as famous yet basic theorems like the fundamental theorem of arithmetic. Important topics in number theory such as Diophantine equations, fractional approximations for irrational numbers and Quadratic fields are there, and if you're interested in magic squares, I'd like to say that a whole chapter is devoted to it. There're some good points featuring this book. It assumes no prerequisite in number theory. Just a bit knowledge about numbers and operations on them are needed. Results and theorems are closely related, allowing you to observe how things are connected. Although not many examples are available, some are really instructive and helpful enough to avoid misconceptions. However, it's a pity to say that the materials contained are not really well-organized, especially those in Chapter 7: the geometric arguments used in the development of the continued fraction algorithm lack concision, and a few proofs are quite annoying because the author failed to justify some claims that shuold not be treated as something "obvious". It can be motivating just to provide readers guidelines about how to work out those minor stuff, but such things shouldn't have been misleadingly called "proofs". Another problem is that the illustratons presented are occasionally insufficient, and this is particularly the case in the chapter about Diophantine equations. Novices in the subject can hardly rely on the text to solve harder exercises contained without tracing out more technique which is not emphasized. Overall, the book deserves to be a fine reading for the interested ones new to number theory. But if you're serious about the topic, find an even better book instead.