Train Your Brain
Challenging Yet Elementary Mathematics
- Available for pre-order. Item will ship after November 14, 2020
The book contains selected problems aimed for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions. The problems are mostly selected from an extensive collection of problems from Polish Mathematical Olympics and many appear here in English for the first time. Each chapter consists of many sections devoted to a collection of related topics. Each of these sections starts with a problem followed by the necessary background (definitions and theorems used), careful and detailed solution, and discussion of possible generalizations
Table of Contents
Preface 1 Inequalities 2 Equalities and Sequences 3 Functions, Polynomials, and Functional Equations 4 Combinatorics 5 Number Theory 6 Geometry 7 Hints 8 Solutions A Introduction to Julia Programming A.1 Installing Julia A.2 Understanding the Examples from the Book A.2.1 Finding Reminders—Problem 5.4 A.2.2 Rolling of three dice—Problem 4.9.3 A.2.3 Sum of Four-digit Numbers—Problem 4.3.3 A.2.4 Legendre’s Formula—Problem 5.2 A.2.5 Subset Selection—Problem 5.7.2 A.2.6 Sicherman Dice—Problem 4.9 A.2.7 Painting 13-gon—Problem 4.7.2 A.2.8 Ski Jumping Tournament—Problem 4.6.2 A.2.9 Number of Solutions—Problem 2.5 A.2.10 The Maximum GCD—Problem 5.1.3 Further Reading Index
Dr. Pawel Prałat is an associate professor at Ryerson University whose main research interests are in graph theory and complex networks. He is the Assistant Director of Industry Liaison at The Fields Institute for Research in Mathematical Sciences, and has pursued collaborations with various industry partners as well as the Government of Canada.