S.M.A.R.T. Circle Minicourses [Paperback]

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.

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.l“ˆ