Combinatorics: A Problem-Based Approach

✍ Scribed by Pavle Mladenović

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 372
• Series: Problem Books in Mathematics
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages I-X
Introduction (Pavle Mladenović)....Pages 1-8
Arrangements, Permutations, and Combinations (Pavle Mladenović)....Pages 9-34
Binomial and Multinomial Theorems (Pavle Mladenović)....Pages 35-48
Inclusion-Exclusion Principle (Pavle Mladenović)....Pages 49-62
Generating Functions (Pavle Mladenović)....Pages 63-74
Partitions (Pavle Mladenović)....Pages 75-90
Burnside’s Lemma (Pavle Mladenović)....Pages 91-106
Graph Theory: Part 1 (Pavle Mladenović)....Pages 107-125
Graph Theory: Part 2 (Pavle Mladenović)....Pages 127-140
Existence of Combinatorial Configurations (Pavle Mladenović)....Pages 141-164
Mathematical Games (Pavle Mladenović)....Pages 165-176
Elementary Probability (Pavle Mladenović)....Pages 177-197
Additional Problems (Pavle Mladenović)....Pages 199-219
Solutions (Pavle Mladenović)....Pages 221-358
Back Matter ....Pages 359-365

✦ Subjects

Mathematics; Combinatorics; Graph Theory