Introduction to Number Theory covers the essential content of an
introductory number theory course including divisibility and prime
factorization, congruences, and quadratic reciprocity. The
instructor may also choose from a collection of additional topics.
Aligning with the trend toward smaller, essential texts in
mathematics, the author strives for clarity of exposition. Proof
techniques and proofs are presented slowly and clearly. The book
employs a versatile approach to the use of algebraic ideas.
Instructors who wish to put this material into a broader context
may do so, though the author introduces these concepts in a
non-essential way. A final chapter discusses algebraic systems
(like the Gaussian integers) presuming no previous exposure to
abstract algebra. Studying general systems urges students realize
unique factorization into primes is a more subtle idea than may at
first appear; students will find this chapter interesting, fun and
quite accessible. Applications of number theory include several
sections on cryptography and other applications to further interest
instructors and students alike.
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