An Introduction to Diophantine Equations ریاضیات

An Introduction to Diophantine Equations دانلود

آشنایی با معادلات دیوفانتی، تیتو آندرسکو

معادلات ديوفانتی يكی از شاخه‌هاي علم نظريه‌ی اعداد است. معمولا پيدا كردن همه‌ی جواب‌های صحيح يك معادله از جذابيت خاصی برخوردار است. هرچند ممكن است برای اين دسته معاملات، روش‌های حل مختلفی وجود داشته باشد، ولی بايد اذعان كرد كه مسائل بی‌شماري نيز در اين حيطه، بدون حل باقي مانده‌اند.
اين كتاب، به سه بخش كلی «رو‌ش‌های مقدماتی برای حل معادلات ديوفانتی»، «معادلات كلاسيك ديوفانتی» و «معادلات پل» تقسيم شده‌ است و در هر بخش، شما با روش‌های حل معادلات مختلف، آشنا می‌شويد. خواندن اين كتاب، به شركت‌كنندگان در المپياد رياضی، دانشجويان رشته‌ی رياضی و عموم علاقمندان به علم رياضی، توصيه مي‌شود.

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 material is organized in two parts: Part I introduces the reader to elementary methods necessary in solving Diophantine equations, such as the decomposition method, inequalities, the parametric method, modular arithmetic, mathematical induction, Fermat's method of infinite descent, and the method of quadratic fields; Part II contains complete solutions to all exercises in Part I. 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.

Dr. Titu Andreescu is an associate professor of mathematics in the Science and Mathematics Education department at the University of Texas at Dallas (UTD). Much of his career has been devoted to competition math, an efficient medium for teaching creative problem-solving for a wide-range of math topics.

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