104 Number Theory Problems From the Training of the USA IMO Team - Andreescu, Titu.; Andrica, Dorin; Feng, Zuming; SpringerLink (Online service) (Boston, MA : Birkhäuser Boston, 2007)
This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory. Key features: * Contains problems developed for various mathematical contests, including the International Mathematical Olympiad (IMO) * Builds a bridge between ordinary high school examples and exercises in number theory and more sophisticated, intricate and abstract concepts and problems * Begins by familiarizing students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions * Combines unconventional and essay-type examples, exercises and problems, many presented in an original fashion * Engages students in creative thinking and stimulates them to express their comprehension and mastery of the material beyond the classroom 104 Number Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches preparing to participate in mathematical contests and those contemplating future research in number theory and its related areas.
Foundations of Number Theory -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems.
Keywords: MATHEMATICS; SEQUENCES (MATHEMATICS).; LOGIC, SYMBOLIC AND MATHEMATICAL; NUMBER THEORY; MATHEMATICS; NUMBER THEORY; SEQUENCES, SERIES, SUMMABILITY; MATHEMATICAL LOGIC AND FOUNDATIONS