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Birkhäuser

Mathematical Bridges

  • Textbook
  • © 2017

Overview

Authors:
  1. Titu Andreescu

    1. University of Texas at Dallas Natural Sciences and Mathematics, Richardson, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Cristinel Mortici

    1. Valahia University of Targoviste, Targoviste, Romania

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    You can also search for this author in PubMed   Google Scholar

  3. Marian Tetiva

    1. Gheorghe Rosca Codreanu National College, Barlad, Romania

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    You can also search for this author in PubMed   Google Scholar

  • Builds bridges between classical results and contemporary nonstandard problems

  • Embraces important topics in calculus, linear and abstract algebra, and analysis 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

  • Includes supplementary material: sn.pub/extras

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Mathematical (and Other) Bridges

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 1-23

  3. Cardinality

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 25-42

  4. Polynomial Functions Involving Determinants

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 43-55

  5. Some Applications of the Hamilton-Cayley Theorem

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 57-74

  6. A Decomposition Theorem Related to the Rank of a Matrix

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 75-92

  7. Equivalence Relations on Groups and Factor Groups

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 93-107

  8. Density

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 109-129

  9. The Nested Intervals Theorem

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 131-148

  10. The Splitting Method and Double Sequences

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 149-173

  11. The Number e

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 175-188

  12. The Intermediate Value Theorem

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 189-200

  13. The Extreme Value Theorem

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 201-211

  14. Uniform Continuity

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 213-226

  15. Derivatives and Functions’ Variation

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 227-251

  16. Riemann and Darboux Sums

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 253-287

  17. Antiderivatives

    • Titu Andreescu, Cristinel Mortici, Marian Tetiva
    Pages 289-307

  18. Back Matter

    Pages 309-309
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Keywords

About this book

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.

Reviews

“The book under review is an excellent collection of gems of undergraduate mathematics. … The book is very well written, and very pleasant to read.” (Mowaffaq Hajja, zbMATH 1421.00001, 2019)

Authors and Affiliations

  • University of Texas at Dallas Natural Sciences and Mathematics, Richardson, USA

    Titu Andreescu

  • Valahia University of Targoviste, Targoviste, Romania

    Cristinel Mortici

  • Gheorghe Rosca Codreanu National College, Barlad, Romania

    Marian Tetiva

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. 

Bibliographic Information

  • Book Title: Mathematical Bridges

  • Authors: Titu Andreescu, Cristinel Mortici, Marian Tetiva

  • DOI: https://doi.org/10.1007/978-0-8176-4629-5

  • Publisher: Birkhäuser New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media LLC 2017

  • License: CC BY

  • Hardcover ISBN: 978-0-8176-4394-2Published: 24 February 2017

  • Softcover ISBN: 978-1-4939-7918-9Published: 12 July 2018

  • eBook ISBN: 978-0-8176-4629-5Published: 17 February 2017

  • Edition Number: 1

  • Number of Pages: VIII, 309

  • Number of Illustrations: 3 b/w illustrations

  • Topics: Algebra

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