Dorin Andrica's Books

An Introduction to Diophantine Equations

A Problem-Based Approach

By: Titu Andreescu,Dorin Andrica,Ion Cucurezeanu

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An Introduction to Diophantine Equations

A Problem-Based Approach

By: Titu Andreescu,Dorin Andrica,Ion Cucurezeanu

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

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Page Count

350

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817645497

ISBN 13

9780817645496

104 Number Theory Problems

From the Training of the USA IMO Team

By: Titu Andreescu,Dorin Andrica,Zuming Feng

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104 Number Theory Problems

From the Training of the USA IMO Team

By: Titu Andreescu,Dorin Andrica,Zuming Feng

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.

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Page Count

214

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817645616

ISBN 13

9780817645618

Complex Numbers from A to ... Z

By: Titu Andreescu,Dorin Andrica

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Complex Numbers from A to ... Z

By: Titu Andreescu,Dorin Andrica

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory

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Page Count

406

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817684158

ISBN 13

9780817684150

Quadratic Diophantine Equations

By: Titu Andreescu,Dorin Andrica

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Quadratic Diophantine Equations

By: Titu Andreescu,Dorin Andrica

This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell’s equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.

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Page Count

224

Publisher

Springer

Published Date

ISBN 10

0387541098

ISBN 13

9780387541099

Recurrent Sequences

Key Results, Applications, and Problems

By: Dorin Andrica,Ovidiu Bagdasar

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Recurrent Sequences

Key Results, Applications, and Problems

By: Dorin Andrica,Ovidiu Bagdasar

This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students training for competitions. The content of the book is very recent, and focuses on areas where significant research is currently taking place. Among the new approaches promoted in this book, the authors highlight the visualization of some recurrences in the complex plane, the concurrent use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and links to many applications. It contains techniques which are fundamental in other areas of math and encourages further research on the topic. The introductory chapters only require good understanding of college algebra, complex numbers, analysis and basic combinatorics. For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex analysis. The first part of the book presents key theoretical elements required for a good understanding of the topic. The exposition moves on to to fundamental results and key examples of recurrences and their properties. The geometry of linear recurrences in the complex plane is presented in detail through numerous diagrams, which lead to often unexpected connections to combinatorics, number theory, integer sequences, and random number generation. The second part of the book presents a collection of 123 problems with full solutions, illustrating the wide range of topics where recurrent sequences can be found. This material is ideal for consolidating the theoretical knowledge and for preparing students for Olympiads.

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Page Count

410

Publisher

Springer Nature

Published Date

ISBN 10

3030515028

ISBN 13

9783030515027

Number Theory

Structures, Examples, and Problems

By: Titu Andreescu,Dorin Andrica

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Number Theory

Structures, Examples, and Problems

By: Titu Andreescu,Dorin Andrica

This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

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Page Count

383

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817646450

ISBN 13

9780817646455

Number Theory

Structures, Examples, and Problems

By: Titu Andreescu,Dorin Andrica

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Number Theory

Structures, Examples, and Problems

By: Titu Andreescu,Dorin Andrica

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Page Count

383

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817646450

ISBN 13

9780817646455

Complex Numbers from A to ... Z

By: Titu Andreescu,Dorin Andrica

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Complex Numbers from A to ... Z

By: Titu Andreescu,Dorin Andrica

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Solve jigsaw puzzle

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Page Count

406

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817684158

ISBN 13

9780817684150

Book's by Dorin Andrica

An Introduction to Diophantine Equations

An Introduction to Diophantine Equations

104 Number Theory Problems

104 Number Theory Problems

Complex Numbers from A to ... Z

Complex Numbers from A to ... Z

Quadratic Diophantine Equations

Quadratic Diophantine Equations

Recurrent Sequences

Recurrent Sequences

Number Theory

Number Theory

Number Theory

Number Theory

Complex Numbers from A to ... Z

Complex Numbers from A to ... Z

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