Titu Andreescu received his Ph.D. from the West University of Timisoara, Romania. The topic of his dissertation was "Research on Diophantine Analysis and Applications." Professor Andreescu currently teaches at The University of Texas at Dallas. He is past chairman of the USA Mathematical Olympiad, served as director of the MAA American Mathematics Competitions (1998–2003), coach of the USA International Mathematical Olympiad Team (IMO) for 10 years (1993–2002), director of the Mathematical Olympiad Summer Program (1995–2002), and leader of the USA IMO Team (1995–2002). In 2002 Titu was elected member of the IMO Advisory Board, the governing body of the world's most prestigious mathematics competition. Titu co-founded in 2006 and continues as director of the AwesomeMath Summer Program (AMSP). He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1994 and a "Certificate of Appreciation" from the president of the MAA in 1995 for his outstanding service as coach of the Mathematical Olympiad Summer Program in preparing the US team for its perfect performance in Hong Kong at the 1994 IMO. Titu’s contributions to numerous textbooks and problem books are recognized worldwide.
Dorin Andrica received his Ph.D. in 1992 from "Babes-Bolyai” University in Cluj-Napoca, Romania; his thesis treated critical points and applications to the geometry of differentiable submanifolds. Professor Andrica has been chairman of the Department of Geometry at "Babes-Bolyai" since 1995. He has written and contributed to numerous mathematics textbooks, problem books, articles and scientific papers at various levels. He is an invited lecturer at university conferences around the world: Austria, Bulgaria, Czech Republic, Egypt, France, Germany, Greece, Italy, the Netherlands, Portugal, Serbia, Turkey, and the USA. Dorin is a member of the Romanian Committee for the Mathematics Olympiad and is a member on the editorial boards of several international journals. Also, he is well known for his conjecture about consecutive primes called "Andrica's Conjecture." He has been a regular faculty member at the Canada–USA Mathcamps between 2001–2005 and at the AwesomeMath Summer Program (AMSP) since 2006.
Zuming Feng received his Ph.D. from Johns Hopkins University with emphasis on Algebraic Number Theory and Elliptic Curves. He teaches at Phillips Exeter Academy. Zuming also served as a coach of the USA IMO team (1997-2006), was the deputy leader of the USA IMO Team (2000-2002), and an assistant director of the USA Mathematical Olympiad Summer Program (1999-2002). He has been a member of the USA Mathematical Olympiad Committee since 1999, and has been the leader of the USA IMO team and the academic director of the USA Mathematical Olympiad Summer Program since 2003. Zuming is also co-founder and academic director of the AwesomeMath Summer Program (AMSP) since 2006. He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1996 and 2002.
Key features of Number Theory: Structures, Examples, and Problems:
* A rigorous exposition starts with the natural numbers and the basics.
* Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.
* Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.
* Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.
* Glossary, bibliography, and comprehensive index round out the text.
Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.
The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them.
The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented.
The book reflects the unique experience of the authors. It distills a vast mathematical literature, most of which is unknown to the western public, and captures the essence of an abundant problem culture. The target audience includes undergraduates, high school students and their teachers, mathematical contestants (such as those training for Olympiads or the W. L. Putnam Mathematical Competition) and their coaches, as well as anyone interested in essential mathematics.