Synopses & Reviews
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.
Review
From the reviews: "In short, this book is a very valuable tool for any student/coach interested in preparing for mathematics competitions, especially the International Mathematical Olympiad.
Synopsis
This book contains 104 of the best problems used in the training and testing of the U. S. International Mathematical Olympiad (IMO) team. It is not a collection of very dif?cult, and impenetrable questions. Rather, the book gradually builds students number-theoretic skills and techniques. The ?rst chapter provides a comprehensive introduction to number theory and its mathematical structures. This chapter can serve as a textbook for a short course in number theory. This work aims to broaden students view of mathematics and better prepare them for possible participation in various mathematical competitions. It provides in-depth enrichment in important areas of number theory by reorganizing and enhancing students problem-solving tactics and strategies. The book further stimulates s- dents interest for the future study of mathematics. In the United States of America, the selection process leading to participation in the International Mathematical Olympiad (IMO) consists of a series of national contests called the American Mathematics Contest 10 (AMC 10), the American Mathematics Contest 12 (AMC 12), the American Invitational Mathematics - amination (AIME), and the United States of America Mathematical Olympiad (USAMO). Participation in the AIME and the USAMO is by invitation only, based on performance in the preceding exams of the sequence. The Mathematical Olympiad Summer Program (MOSP) is a four-week intensive training program for approximately ?fty very promising students who have risen to the top in the American Mathematics Competitions."
Synopsis
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 in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
Synopsis
This challenging problem book is written by renowned US Olympiad coaches, mathematics teachers, and researchers. It develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory.
About the Author
Titu Andreescu received his
Table of Contents
Preface.- Acknowledgments.- Abbreviations and Notation.- Foundations of Number Theory.- Introductory Problems.- Advanced Problems.- Solutions to Introductory Problems.- Solutions to Advanced Problems.- Glossary.- Further Reading.- Subject Index.