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Inequalities

An Approach Through Problems

  • Textbook
  • © 2018

Overview

Authors:
  1. B. J. Venkatachala

    1. Homi Bhabha Centre for Science Education (emeritus), Mumbai, India

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  • Discusses about the basic topics on inequalities and their applications
  • Contains over 400 problems with their solutions
  • Includes a chapter on geometric inequalities
  • Is useful to students preparing for various mathematical competitions and Olympiad
  • Is authored by mathematical Olympiad trainer to Indian students for over 25 years

Part of the book series: Texts and Readings in Mathematics (TRIM, volume 49)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Some basic inequalities

    • B. J. Venkatachala
    Pages 1-49

  3. Techniques for proving inequalities

    • B. J. Venkatachala
    Pages 51-110

  4. Geometric inequalities

    • B. J. Venkatachala
    Pages 111-171

  5. Applications involving inequalities

    • B. J. Venkatachala
    Pages 173-203

  6. Problems on inequalities

    • B. J. Venkatachala
    Pages 205-244

  7. Solutions to problems

    • B. J. Venkatachala
    Pages 245-514

  8. Back Matter

    Pages 515-519
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Keywords

About this book

This book discusses about the basic topics on inequalities and their applications. These include the arithmetic mean–geometric mean inequality, Cauchy–Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. The book contains over 400 problems with their solutions. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical Olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students who are consolidating their knowledge of inequalities and their applications. 

Authors and Affiliations

  • Homi Bhabha Centre for Science Education (emeritus), Mumbai, India

    B. J. Venkatachala

About the author

B.J. VENKATACHALA is professor emeritus at the Homi Bhabha Centre for Science Education–Tata Institute of Fundamental Research (HBCSE-TIFR), India. Earlier, he held several administrative and academic positions, such as a scientist at the Indian Institute of Science, Bengaluru; lecturer at the University of Mysore; reader at Kuvempu University, Shimoga; a scientific officer at the Department of Atomic Energy, Government of India, where he took charge of the mathematical Olympiad activity in India. He later joined HBCSE–TIFR, where he was completely involved in selecting and training students for International Mathematical Olympiad (IMO) for nearly 25 years, until his retirement in 2015. He has contributed to Olympiad literature in the form of problems and books. He was also the leader of the Indian team to IMO several times.

Bibliographic Information

  • Book Title: Inequalities

  • Book Subtitle: An Approach Through Problems

  • Authors: B. J. Venkatachala

  • Series Title: Texts and Readings in Mathematics

  • DOI: https://doi.org/10.1007/978-981-10-8732-5

  • Publisher: Springer Singapore

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

  • Copyright Information: Springer Nature Singapore Pte Ltd. and Hindustan Book Agency 2018

  • eBook ISBN: 978-981-10-8732-5Published: 09 May 2018

  • Series ISSN: 2366-8717

  • Series E-ISSN: 2366-8725

  • Edition Number: 2

  • Number of Pages: X, 519

  • Number of Illustrations: 42 b/w illustrations

  • Topics: Mathematics, general

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