© 2019


A Problem-Based Approach


Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages I-X
  2. Pavle Mladenović
    Pages 1-8
  3. Pavle Mladenović
    Pages 9-34
  4. Pavle Mladenović
    Pages 35-48
  5. Pavle Mladenović
    Pages 49-62
  6. Pavle Mladenović
    Pages 63-74
  7. Pavle Mladenović
    Pages 75-90
  8. Pavle Mladenović
    Pages 91-106
  9. Pavle Mladenović
    Pages 107-125
  10. Pavle Mladenović
    Pages 127-140
  11. Pavle Mladenović
    Pages 141-164
  12. Pavle Mladenović
    Pages 165-176
  13. Pavle Mladenović
    Pages 177-197
  14. Pavle Mladenović
    Pages 199-219
  15. Pavle Mladenović
    Pages 221-358
  16. Back Matter
    Pages 359-365

About this book


This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas.


enumerative combinatorics designs and configurations graph theory extremal combinatorics mathematical games mathematical Olympiads combinatorial mathematics magic and latin squares elementary probability multinomial theorems

Authors and affiliations

  1. 1.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia

About the authors

Pavle Mladenović is a professor at the Faculty of Mathematics of the University of Belgrade, Serbia, with research interests in probability theory and stochastic processes.

He was involved in organizing national mathematical competitions and was leader of the team of FR Yugoslavia first at the Balkan Mathematical Olympiad (1992-1996) and then at the International Mathematical Olympiad (1997-2001).

Bibliographic information

  • Book Title Combinatorics
  • Book Subtitle A Problem-Based Approach
  • Authors Pavle Mladenović
  • Series Title Problem Books in Mathematics
  • Series Abbreviated Title Problem Books Mathematics
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-030-00830-7
  • eBook ISBN 978-3-030-00831-4
  • Series ISSN 0941-3502
  • Series E-ISSN 2197-8506
  • Edition Number 1
  • Number of Pages X, 365
  • Number of Illustrations 98 b/w illustrations, 0 illustrations in colour
  • Topics Combinatorics
    Graph Theory
  • Buy this book on publisher's site