This book is a reader in number theory. Number theory is possibly the most accessible branch of higher mathematics and the author believes that senior high school, undergraduate and all amateur lovers of mathematics can actually just read this book, albeit slowly at times, and gain an appreciative knowledge of ways in which several major discoveries were made in number theory. There is a culinary theme to the book which becomes self-evident to the reader, hence the title, "A Taste of Number Theory". Unlike most introductory number theory textbooks, this book does not include any student homework - we want the reader to scan number theory, develop sufficient skills to read on, but not to be delayed by hours of problem solving. Unlike introductory number theory textbooks, it does explore quite complicated topics in number theory, requiring a mathematical background way beyond that of the typical high school curriculum. To this end, several "just-in-time" shopping excursions are included - the prerequisite is high school algebra - the excursions add the minimal amounts of complex number theory, calculus and trigonometry required to follow the story. An examination of discoveries from the years of development preceding three major theorems - Fermat's Last Theorem, Primes in arithmetic progression and the Prime Number theorem - form the major content of the book: the feast and the two banquets. There are many side paths: tastings, a degustation, even a sorbet. The book concludes by exploring a current unsolved challenge, the Riemann Hypothesis. This book would be an ideal reward for success in mathematics by senior high school students, undergraduates or personal strugglers. We hope you actually enjoy it!
About the Author: Keith James Timothy McDonald graduated B.Sc. from Sydney University in 1962 with a double major in mathematics and physics. His 33 year Australian career began as a teacher and high school headmaster, included a part-time Master's degree in education, and shifted to administration of State Government vocational education, public service board and health departments culminating in the CEO position of a private hospital group. He and his wife moved to the USA in 1995 for family reasons. After 8 more years in hospital administration, he was accepted into the mathematics graduate program at Rutgers University, Newark, NJ and in 2008 was awarded a Ph.D. in pure mathematics for work in p-adic number theory. He coordinated the elementary math program and taught courses at Rutgers Newark until 2013 when he and his wife retired to Palm Coast, Florida, where he has taught part-time at Flagler College in St. Augustine.