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 andstrategies 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. Builds bridges between classical results and contemporary nonstandard problems Embraces important topics in calculus, linear and abstract algebra, analysis and differential equations from a problem-solving perspective Makes connections between various concepts from different areas of mathematics Students from high school juniors to college seniors interested in math and mathematics competitions must have this book INDICE: 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.
- ISBN: 978-0-8176-4394-2
- Editorial: BIRKHAUSER VERLAG.
- Encuadernacion: Rústica
- Páginas: 300
- Fecha Publicación: 01/02/2012
- Nº Volúmenes: 1
- Idioma: Inglés
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- MATEMÁTICAS /
- ÁLGEBRA