© 2012


Theorems, Techniques and Selected Problems


Table of contents

  1. Front Matter
    Pages I-X
  2. Zdravko Cvetkovski
    Pages 19-25
  3. Zdravko Cvetkovski
    Pages 49-60
  4. Zdravko Cvetkovski
    Pages 61-67
  5. Zdravko Cvetkovski
    Pages 69-77
  6. Zdravko Cvetkovski
    Pages 117-119
  7. Zdravko Cvetkovski
    Pages 155-160
  8. Zdravko Cvetkovski
    Pages 161-167
  9. Zdravko Cvetkovski
    Pages 169-175
  10. Zdravko Cvetkovski
    Pages 177-182

About this book


This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.


Cauchy-Schwarz inequality Hölder’s inequality Inequalities Jensen's inequality Olympiads

Authors and affiliations

  1. 1.of the Republic of Macedonia, Faculty of InformaticsEuropean UniversitySkopjeMacedonia

About the authors

Dipl. Math. Zdravko Cvetkovski, European University-Skopje, R. Macedonia, Informatics Department.

Bibliographic information


From the reviews:

“The book is aimed at the more advanced students about to enter university and is particularly useful to candidates, and their trainers, for mathematical competitions such as the Olympiads. The themes and methods are introduced in 19 chapters of the book, which include exercises and their solutions.” (Peter Shiu, The Mathematical Gazette, Vol. 98 (541), March, 2014)

“This volume collects problems of various degrees of difficulty in the field of elementary inequalities. This book is intended as a valuable source for the training of high-school students in view of mathematical Olympiads. School teachers will also gain benefit from this book. … It would be a particularly valuable resource for those who participate in mathematics competitions at the high school or college level. … this book is a ‘must have’ for a university’s library, and I recommend it highly to its ‘ideal audience’.” (Teodora-Liliana Radulescu, Zentralblatt MATH, Vol. 1233, 2012)