Pub. Date:
Springer New York
Mathematical Bridges

Mathematical Bridges


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Mathematical Bridges

Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and motivated mathematics students from high school juniors to college seniors will find the work a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students with an interest in mathematics competitions must have this book in their personal libraries.

Product Details

ISBN-13: 9780817643942
Publisher: Springer New York
Publication date: 02/24/2017
Edition description: 1st ed. 2017
Pages: 309
Product dimensions: 6.10(w) x 9.25(h) x (d)

About the Author

Titu Andreescu is an internationally acclaimed problem solving expert who has published more than 30 books in this area.

Cristinel Mortici is a Romanian mathematics professor who efficiently uses a problem base approach in his teaching.

Marian Tetiva is a Romanian high school teacher who strongly believes in the importance of meaningful problem solving in teaching and learning mathematics.

Table of Contents

Preface.- Glossary of Notation.- Cardinality.- Density.- Lemma of the Closed Intervals.- Sequences Given by Implicit Relations.- Recurrence Relations.- Complementary Sequences.- Quadratic Functions, Quadratic Equations.- Polynomial Functions Involving Determinants.- A Decomposition Theorem Related to the Rank of a Matrix.- Intermediate Value Property.- Uniform Continuity.- Toeplitz Theorem.- Derivatives and Functions Variation.- Weierstrass Theorem.- The Number e.- Riemann Sums, Darboux Sums.- References.- Subject Index.

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