Introduction to Number Theory

<p><em>Introduction to Number Theory</em> 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.</p><p>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.</p><p>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.</p><p>A final chapter discusses algebraic systems (like the Gaussian integers) presuming no previous exposure to abstract algebra. Studying general systems helps students to 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.</p><p>Applications of number theory include several sections on cryptography and other applications to further interest instructors and students alike.</p>