Number Theory

In this book, the author solves the problem of maintaining students' interest by offering a combinatorial approach to elementary number theory.
 
Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
 

• Accessible Introduction: This book offers a comprehensive and accessible introduction to number theory, catering to both mathematics majors and students in education and liberal arts who require a more basic understanding of the topic.
• Combinatorial Approach: By taking a combinatorial approach to elementary number theory, this book offers new insights to mathematics majors while providing simple proofs for many theorems to other students.
• Wide Range of Topics: The book covers multiplicativity-divisibility, fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots, prime numbers, quadratic congruences, additivity, partition theory, and geometric number theory.
• Emphasis on Numerical Examples: The author emphasizes the value of numerical examples in number theory and demonstrates the role of computers in obtaining such examples, allowing students to derive conjectures and develop a deeper understanding of the theorems.
• Opportunities for Practical Application: Exercises throughout the book allow students to construct numerical tables with or without a computer, encouraging them to explore the concepts through hands-on practice.

The Holy Grail of Number Theory
George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text Number Theory (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field — number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well.

In 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the "Lost Notebook" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations — mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years.

In the Author's Own Words:
"It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered." — George E. Andrews