Preface -- Acknowledgement -- Table of Contents -- Part I. Geometric Topics -- Chapter 1. Area and Dissection -- Section 1. Qualitative and Quantitative Treatments of Area -- Section 2. The Bolyai-Gerwin Theorem and Pythagoras’ Theorem -- Section 3. Dissection Problems -- Chapter 2. Projective Geometry -- Section 1. Synthetic Approach -- Section 2. Metric Approach -- Section 3. Analytic Approach -- Chapter 3. Conic Sections -- Section 1. Loci -- Section 2. The Parabola -- Section 3. Ellipses and Hyperbolas -- Chapter 4. Inversive Geometry -- Section 1. Inversion -- Section 2. Applications to Euclidean Geometry -- Section 3. Mohr-Mascheroni Constructions -- Chapter 5. Convexity -- Section 1. Figures -- Section 2. Convex Figures -- Section 3. Figures of Constant Width -- Part II. Other Topics -- Chapter 6. Balancing Problems -- Section 1. Identifying Fake Coins -- Section 2. Other Problems -- Section 3. Other Balances -- Chapter 7. Graph Theory -- Section 1. Basic Concepts -- Section 2. Trees -- Section 3. Directed Graphs -- Chapter 8. Beanstalks -- Section 1. Red and Blue Beanstalks -- Section 2. Infinite Beanstalks -- Section 3. Beansprouts -- Chapter 9. Inequalities -- Section 1. The Rearrangement Inequality -- Section 2. The Majorization Inequality -- Section 3. Trigonometric Inequalities -- Chapter 10. Polynomial Equations -- Section 1. Complex Numbers -- Section 2. Cubic Equations -- Section 3. Quartic Equations.

This book describes mini-courses in a Mathematical “Circle,” i.e., an organization that discovers and nurtures young mathematical talents through meaningful extra-curricular activities. This is the third volume in a trilogy describing in particular the S.M.A.R.T. Circle project, which was founded in Edmonton, Canada in 1981. The acronym S.M.A.R.T. stands for Saturday Mathematical Activities, Recreations & Tutorials. This book, Volume III, consists of mini-courses and explains what actually takes place in the Circle. Volume I describes how to run a Circle, and Volume II, consisting of student projects, addresses the purpose of the Circle. All three volumes provide a wealth of resources (mathematical problems, quizzes and games, together with their solutions). The books will be of interest to self-motivated students who want to conduct independent research, teachers who work with these students, and teachers who are currently running or planning to run Mathematical Circles of their own.