Synopses & Reviews
Weintraub (mathematics, Lehigh U.) works through the concepts of factorization, an important feature of the system of natural numbers and their generalizations that can be written as a unique product of prime numbers and relates the ways in which factorization plays a key role in modern mathematics and its applications. After a fine introduction to basic notions, he covers unique factorization, the Gaussian integers, and Pell's equation, and moves on to algebraic number theory. He also offers very good appendices on mathematical induction and congruences, sets of exercises for each chapter, and examples throughout. This is well-suited for a first course in number theory or for self-study by motivated readers down to the high school level.
Synopsis
The concept of factorization, familiar in the ordinary system of whole numbers that can be written as a unique product of prime numbers, plays a central role in modern mathematics and its applications. This exposition of the classic theory leads the reader to an understanding of the current knowledge of the subject and its connections to other mathematical concepts, for example in algebraic number theory. The book can be used as a text for a first course in number theory or for self-study by motivated high school students or readers interested in modern mathematics.