Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics.

Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. 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.

Table of Contents

1 Mathematical {and Other) Bridges

2 Cardinality

3 Polynomial Functions Involving Determinants

4 Some Applications of the Hamilton-Cayley Theorem

5 A Decomposition Theorem Related to the Rank of a Matrix

6 Equivalence Relations on Groups and Factor Groups

7 Density

8 The Nested Intervals Theorem

9 The Splitting Method and Double Sequences

10 The Number e

11 The Intermediate Value Theorem

12 The Extreme Value Theorem

13 Uniform Continuity

14 Derivatives and Functions' Variation

15 Riemann and Darboux Sums

16 Antiderivatives

About the Authors

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.