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104 Number Theory Problems de Titu Andreescu

104 Number Theory Problems

Autor Titu Andreescu, Dorin Andrica, Zuming Feng
en Limba Engleză Paperback – 19 dec 2006

Exercițiile de antrenament și problemele de concurs reprezintă nucleul acestui volum, oferind o selecție de 104 enunțuri utilizate în pregătirea echipei Statelor Unite pentru Olimpiada Internațională de Matematică. Găsim în această carte nu doar o simplă culegere, ci un parcurs metodologic care transformă teoria abstractă în instrumente de lucru concrete. Ediția din 2007, publicată de BIRKHAUSER BOSTON INC, este structurată pentru a facilita o progresie naturală: începe cu un capitol dens dedicat fundamentelor teoriei numerelor, continuă cu o secțiune de probleme introductive pentru consolidarea tehnicilor de bază și culminează cu provocări avansate care necesită o gândire matematică sofisticată.

Recomandăm acest volum ca pe un manual de curs scurt, datorită modului în care autorii — coordonați de Titu Andreescu — au reorganizat strategiile de rezolvare a problemelor. Cititorii familiarizați cu Winning Solutions de Edward Lozansky vor aprecia aici abordarea mai aplicată și focalizarea pe tehnici specifice competițiilor de elită, precum Putnam sau USAMO. Spre deosebire de Problem-Solving and Selected Topics in Number Theory, care pune accent pe rigoarea demonstrațiilor teoretice pas cu pas, volumul de față prioritizează intuiția și tacticile de „atac” al problemelor.

Această lucrare se integrează perfect în vasta operă a lui Titu Andreescu, completând titluri precum 103 Trigonometry Problems sau Algebraic Inequalities: New Vistas. Dacă în Putnam and Beyond autorul explorează orizonturile matematicii universitare, în 104 Number Theory Problems el revine la puritatea teoriei numerelor, oferind soluții complete și elegante care servesc drept model de argumentare pentru orice viitor matematician.

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Specificații

ISBN-13: 9780817645274
ISBN-10: 0817645276
Pagini: 204
Ilustrații: XII, 204 p.
Dimensiuni: 156 x 234 x 17 mm
Greutate: 0.37 kg
Ediția:2007 edition
Editura: BIRKHAUSER BOSTON INC
Locul publicării:Boston, MA, United States

Public țintă

Lower undergraduate

De ce să citești această carte

Această carte este un instrument esențial pentru elevii de liceu și studenții care vizează excelența în competițiile matematice. Cititorul câștigă o înțelegere profundă a structurilor numerice și, mai important, învață să aplice strategii de rezolvare folosite la nivel internațional. Este resursa ideală pentru a trece de la simpla aplicare a formulelor la creativitatea matematică necesară pentru a aborda problemele de tip olimpiadă.

Despre autor

Titu Andreescu este un matematician de origine română, având doctoratul obținut la Universitatea de Vest din Timișoara cu o teză despre analiza diofantică. În prezent profesor la University of Texas at Dallas, acesta a avut o carieră prodigioasă în coordonarea competițiilor matematice din SUA, servind ca director al American Mathematics Competitions și antrenor principal al echipei SUA pentru Olimpiada Internațională de Matematică timp de un deceniu. Expertiza sa în teoria numerelor și pedagogia problemelor non-standard este recunoscută la nivel mondial, fiind autorul a numeroase tratate de referință în domeniu.

Descriere scurtă

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 ofnational 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.

Cuprins

Foundations of Number Theory.- Introductory Problems.- Advanced Problems.- Solutions to Introductory Problems.- Solutions to Advanced Problems.

Recenzii

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.  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 coursesat 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)

Notă biografică

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 theMathematics 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.

Textul de pe ultima copertă

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.

Caracteristici

Written by renowned US Olympiad coaches, mathematics teachers, and researchers Features a multitude of problem-solving skills needed to excel in mathematical contests and number theory research Can serve as a supplementary text for various number theory courses Unconventional techniques, strategies and motivation Valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches