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Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads
The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).
338 pages, Hardcover
First published December 2, 2010
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March 20, 2011
This is part of the book review by Preda Mihailescu (Göttingen, Germany), published in the Newsletter of the European Mathematical Society, March Issue 2011, pp. 45-47, available at http://www.ems-ph.org/journals/newsle... .
"... Every single collection adds its own accent and focus. This book has a few particular characteristics which make it unique among similar problem books. While most of these books have been written by experienced mathematicians after several decades of practising their skills as a profession, Michael wrote this book during his undergraduate years in the Department of Electrical and Computer Engineering of the National Technical University of Athens. It is composed of some number theory fundamentals and also includes some problems that he undertook while training for the Olympiads. He focused on problems of number theory, which was the field of mathematics that began to capture his passion. It appears like a confession of a young mathematician to students of his age, revealing to them some of his preferred topics in number theory based on solutions of particular problems – most of which also appear in this collection. Michael does not limit himself to those particular problems. He also deals with topics in classical number theory and provides extensive proofs of the results, which read like “all the details a beginner would have liked to find in a book” but are often omitted. ...
I could close this introduction with the presentation of my favourite problem but instead I shall present and briefly discuss another short problem which is included in the book. It is a conjecture that Michael Th. Rassias conceived of at the age of 14 and tested intensively on the computer before realising its intimate connection with other deep conjectures of analytic number theory. These conjectures are still considered intractable today. ..."
"... Every single collection adds its own accent and focus. This book has a few particular characteristics which make it unique among similar problem books. While most of these books have been written by experienced mathematicians after several decades of practising their skills as a profession, Michael wrote this book during his undergraduate years in the Department of Electrical and Computer Engineering of the National Technical University of Athens. It is composed of some number theory fundamentals and also includes some problems that he undertook while training for the Olympiads. He focused on problems of number theory, which was the field of mathematics that began to capture his passion. It appears like a confession of a young mathematician to students of his age, revealing to them some of his preferred topics in number theory based on solutions of particular problems – most of which also appear in this collection. Michael does not limit himself to those particular problems. He also deals with topics in classical number theory and provides extensive proofs of the results, which read like “all the details a beginner would have liked to find in a book” but are often omitted. ...
I could close this introduction with the presentation of my favourite problem but instead I shall present and briefly discuss another short problem which is included in the book. It is a conjecture that Michael Th. Rassias conceived of at the age of 14 and tested intensively on the computer before realising its intimate connection with other deep conjectures of analytic number theory. These conjectures are still considered intractable today. ..."
November 24, 2011
This is an excellent book! Here are some of the reviews it obtained (i checked them out here http://www.springer.com/mathematics/n...
“Number Theory problems are among the most tricky in Mathematical Olympiads (MO). For students who are going to participate in such a tournament, and also for their teachers, a book that covers the main topics of fundamental number theory and contains various problems related to MOs is very useful. The book under review is exactly such a friendly volume, arranged in two main parts: Topics and Problems....The book under review is not the only book which focuses on olympiad problems in number theory, but because of its structure (containing topics and problems), it is also useful for teaching. I highly recommend this book for students and teachers of MOs.”
—Mehdi Hassani, MAA Reviews
“Number theory is one of the most active and important fields in Mathematics with a substantial and large variety of applications in several disciplines including representation theory, cryptography, coding theory, dynamical systems, [and] theoretical physics. The present book provides a wonderful presentation of concepts and ideas as well as problems with their solutions in Number Theory. Although most of the problems solved in this book were given in international mathematical contests and hence are of high level of complexity, the author has succeeded in providing solutions and extensive step-by-step proofs in a rigorous yet very simple and fascinating way. Even though the author is a very young mathematician (of only 23 years), he is an outstanding specialist in this field.
—Dorin Andrica, Zentralblatt MATH
“Number Theory problems are among the most tricky in Mathematical Olympiads (MO). For students who are going to participate in such a tournament, and also for their teachers, a book that covers the main topics of fundamental number theory and contains various problems related to MOs is very useful. The book under review is exactly such a friendly volume, arranged in two main parts: Topics and Problems....The book under review is not the only book which focuses on olympiad problems in number theory, but because of its structure (containing topics and problems), it is also useful for teaching. I highly recommend this book for students and teachers of MOs.”
—Mehdi Hassani, MAA Reviews
“Number theory is one of the most active and important fields in Mathematics with a substantial and large variety of applications in several disciplines including representation theory, cryptography, coding theory, dynamical systems, [and] theoretical physics. The present book provides a wonderful presentation of concepts and ideas as well as problems with their solutions in Number Theory. Although most of the problems solved in this book were given in international mathematical contests and hence are of high level of complexity, the author has succeeded in providing solutions and extensive step-by-step proofs in a rigorous yet very simple and fascinating way. Even though the author is a very young mathematician (of only 23 years), he is an outstanding specialist in this field.
—Dorin Andrica, Zentralblatt MATH
Displaying 1 - 2 of 2 reviews