problems in real analysis: advanced calculus, andreescu [pdf]
Problems in Real Analysis by Titu Andreescu, Teodora-Liliana T. Radulescum, Vicentiu D. Radulescu
(Advanced Calculus on the Real Axis)
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About this book :-
Problems in Real Analysis written by
The book is mainly geared toward students studying the basic principles of mathematical analysis. However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam and other high-level mathematical contests. We also address this work to motivated high-school and undergraduate students. This volume is meant primarily for students in mathematics, physics, engineering, and computer science, but, not without authorial ambition, we believe it can be used by anyone who wants to learn elementary mathematical analysis by solving problems. The book is also a must-have for instructors wishing to enrich their teaching with some carefully chosen problems and for individuals who are interested in solving difficult problems in mathematical analysis on the real axis.
The volume is intended as a challenge to involve students as active participants in the course. To make our work self-contained, all chapters include basic definitions and properties. The problems are clustered by topic into eight chapters, each of them containing both sections of proposed problems with complete solutions and separate sections including auxiliary problems, their solutions being left to our readers. Throughout the book, students are encouraged to express their own ideas, solutions, generalizations, conjectures, and conclusions.
The volume contains a comprehensive collection of challenging problems, our goal being twofold: first, to encourage the readers to move away from routine exercises and memorized algorithms toward creative solutions and nonstandard problem-solving techniques; and second, to help our readers to develop a host of new mathematical tools and strategies that will be useful beyond the classroom and in a number of applied disciplines. We include representative problems proposed at various national or international competitions, problems selected from prestigious mathematical journals, but also some original problems published in leading publications. That is why most of the problems contained in this book are neither standard nor easy. The readers will find both classical topics of mathematical analysis on the real axis and modern ones. Additionally, historical comments and developments are presented throughout the book in order to stimulate further inquiry.
Book Detail :-
Title: Problems in Real Analysis
Author(s): Titu Andreescu
Publisher: Springer-Verlag New York
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About Author :-
Author Titu Andreescu (born 1956) is a Romanian mathematician and an associate professor of mathematics at the University of Texas at Dallas. After graduating with a B.S. degree from the University of Timi?oara, Andreescu was appointed a professor of mathematics at the Constantin Diaconovici Loga school of Mathematics and Physics. Andreescu emigrated to the United States in 1990, where he first taught at the Illinois Mathematics and Science Academy. He earned a Ph.D. degree from the University of Timi?oara in 2003. He joined as an associate professor of mathematics at the University of Texas in 2005.
He is firmly involved in mathematics contests and olympiads, having been the Director of American Mathematics Competitions (as appointed by the Mathematical Association of America), Director of the Mathematical Olympiad Program, Head Coach of the United States International Mathematical Olympiad Team, and Chairman of the United States of America Mathematical Olympiad. He has also authored a large number of books on the topic of problem solving and olympiad style mathematics.
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Book Contents :-
Problems in Real Analysis written by
cover the following topics.
Part-I Sequences, Series, and Limits
Part-II Qualitative Properties of Continuous and Differentiable Functions
Part-III Applications to Convex Functions and Optimization
Part-IV Antiderivatives, Riemann Integrability, and Applications
A. Basic Elements of Set Theory
B. Topology of the Real Line
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