Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. But the focus is on quadratic reciprocity (several proofs are given including one that highlights the p q symmetry) and binary quadratic forms. The reader will come away with a good understanding of what Gauss intended in the Disquisitiones and Dirichlet in his Vorlesungen. The text also includes a lovely appendix by J. P. Serre titled =b2 4ac. The clarity of the author's vision is matched by the clarity of his exposition. This is a book that reveals the discovery of the quadratic core of algebraic number theory. It should be on the desk of every instructor of introductory number theory as a source of inspiration, motivation, examples, and historical insight.

Review

I really like this book...it sits on a nearby shelf every time I teach number theory. I use it as a source for ideas, examples, and problems. And sometimes, when I'm unhappy with the proof in our textbook, I will check to see if Flath has found the 'right' proof. He often has...I have often found that Flath's account of some topic is easier to understand than others. Most of all, Flath has good mathematical taste: the material he covers is beautiful and definitely worth learning. --Fernando Q. Gouv�a, MAA Reviews

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