Starting with nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers.
Features an informal writing style and includes many numerical examples. Emphasizes the methods used for proving theorems rather than specific results. Includes a new chapter on big-Oh notation and how it is used to describe the growth rate of number theoretic functions and to describe the complexity of algorithms. Provides a new chapter that introduces the theory of continued fractions. Includes a new chapter on “Continued Fractions, Square Roots and Pell’s Equation.” Contains additional historical material, including material on Pell’s equation and the Chinese Remainder Theorem.
Silverman (Brown U.) originally wrote the book as a text for a course designed to attract non-science majors with little interest in pursuing the standard calculus sequence, and convince them to study some college mathematics. He expects readers to have some facility with high school algebra and access to a calculator, though he points out that those who know how to program a computer have great fun generating reams of data and implementing assorted algorithms. He mentions concepts from calculus now and then, but does not lay them down as barriers to cross. The first edition appeared in 1997. Annotation c. Book News, Inc., Portland, OR (booknews.com)