A Friendly Introduction to Number Theory

I am a working oceanographer with a physics background who is interested in browsing through various areas of mathematics, particularly ones like number theory which are not a common part of a physicist's background. I picked up and read Dr. Silverman's "Friendly Introduction to Number Theory" and was thoroughly charmed. The book presented many of the basic results of number theory in a clear, concise fashion, and also gave a bit of context and background to the results. Basis computations for "non-experts" are stressed, and the reader for whom this book was intended goes away with a nice feeling of having picked up a bit of knowledge of a new topic. I would also add my voice to those who chided the math majors for panning this book. There are plenty of high level "theorem-proof" books out there for mathematicians, and to criticise a book that popularizes mathematics is both snobbish and counterproductive. We should heartily applaud and value good popularizations of science and technology. This book is a first rate popularization.

I'm a bit shocked by the bad reviews of this book. I guess if a book is clear, understandable, and interesting it doesn't qualify as a worthy math book. I've noticed this in other math book reviews, there seems to be a real element of machismo among alot of mathematicians, if the book is very formal usually theorem proof theorem it gets high marks. If the book is like this, one where the author is clear and engaging the book is discounted. I personally found this book to be one of the great intellectual adventures of my life, but here again in college I only minored in math not majored.

I admit that this book might not be suitable especially for pure mathematicians. But I very much liked Silverman's way of writing: He cast questions and encourage readers to tackle them! Indeed, this is a unique number thoery book written in that way.

I very much enjoyed this book. The book is indeed an excellent and "friendly" introduction to number theory. Dr. Silverman writes in a conversation style. I felt like I had a friendly tutor standing over my shoulder explaining not only how the mathematics worked, but, more importantly, why the topics he described or was about to describe are important and their relevancy in either the world of mathematics or in the "real" world. While he has very few "formal" proofs compared to most number theory texts, Dr. Silverman thoroughly works through numerous numerical examples to give the reader a "feel" for what is going on.I was particularly pleased with Dr. Silverman's chapter explanation of why quadratic residues are important and how they are used. Dr. Silverman presents introductory explanations of a number of frequently mentioned number theory topics such as Mersenne Primes, number sieves, RSA cryptography, elliptic curves. He ties together lucid explanations of Pythagorean triples, x2 + y2 = z2, x4 + y4 = z4, and elliptic curves to build to an explanation of Wiles proof of Fermat's Last Theorem.

Although the book is intended for non-math majors in college, it's ideal for advanced high school or even junior high students. Only knowledge of high school algebra is needed for the book. I recommend that the book be made mandatory reading in a advanced high school math class such as calculus or precalculus. My reasoning is that most advanced high school math classes such as calculus are too application-oriented and students often mistake manipulation of formulas for what mathematics is about. A book like Silverman's can spark the beginning of a brilliant career in mathematics.