Elementary Introduction to Number Theory

Rating:
Summary: Good Book for Self Study
Review: This is an intentionally small book that starts at a level somewhat below the usual introductory text. It presumes no background other than the equivalent of a course in college algebra. (Two brief sections in Chapter 3 do assume a knowledge of the Calculus but can be omitted if necessary). Since learning mathematics involves doing mathematics there are over 600 problems with detailed answers to selected exercises, including many proofs.

This book includes fewer topics than the typical introductiory text but the selection of material is excellent. Chapter 1 starts with a detailed treatment of the postulates of mathematical induction and well ordering. Congruences and the quadratic reciprocity law of Gauss are nicely covered. The Chinese Remainder Theorem gets a few pages of its own. Chapter 9 provides a brief look at simple continued fractions. Plus many others: The Euclidian Algorithm, the Fundamental Theorem of Arithmetic, the Prime Number Theorem, etc.

After you finish this book you will understand the essential methods of proofs and will be ready for introductory texts which take a more advanced approach to Number Theory. It's also a fun book to study.