104 Number Theory Problems (PDF)
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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 andextensive 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.
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 theMathematics Olympiad and is a member on the editorial boards of
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.
- Autoren: Titu Andreescu , Dorin Andrica , Zuming Feng
- 2007, 2007, 204 Seiten, Englisch
- Verlag: Springer Basel AG
- ISBN-10: 0817645616
- ISBN-13: 9780817645618
- Erscheinungsdatum: 05.04.2007
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- Dateiformat: PDF
- Größe: 1.36 MB
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"In short, this book is a very valuable tool for any student/coach interested in preparing for mathematics competitions, especially the International Mathematical Olympiad. College students participating in the Putnam competition might also find quite a few interesting problems. Moreover, any course in number theory could be supplemented with this book and could use some of the references included. Even research mathematicians working in number theory will find this book of value in their pursuits." -MAA Online
"The names of the authors sound familiar for teachers of mathematics and mathematicians who use books of these types … . I am sure about the success of this book. It is going to be a ‘bestseller’. It can be useful for high school students preparing for contests, and for teachers helping them all over the world. I am also reliant on being able to insert some excellent problems of the book into the syllabus of number theory courses at university level." (József Kosztolányi, Acta Scientiarum Mathematicarum, Vol. 73, 2007)
“The book starts with a gentle introduction to number theory. It serves for a training of the participants of the U. S. International Mathematical Olympiad. … The 104 problems are carefully selected. … The solutions are also carefully presented.” (J. Schoissengeier, Monatshefte für Mathematik, Vol. 156 (3), March, 2009)
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