This book provides an overview of how to run a Mathematical “Circle,” i.e., an organization that discovers and nurtures young mathematical talents through meaningful extra-curricular activities. This is the first 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 I, offers a sampling of many aspects, including projects and mini-courses. Volume II, which consists of student projects, addresses the purpose of the Circle, and Volume III, consisting of mini-courses, explains what actually takes place in 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.
About the Author
Andy Liu is an established author with eleven books to his credit. He is Professor Emeritus of the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. He has won numerous international awards in Mathematics teaching and outreach, as have several of his former students. He was the leader of the Canadian team to the International Mathematical Olympiad in 2000 (South Korea) and in 2003 (Japan), acts as Vice President of the Tournament of Towns and ran the S.M.A.R.T. Circle for over 30 years.
Table of ContentsA Brief History of the S.M.A.R.T. Circle.- Table of Contents.- Part I Mathematical Conversations.- Chapter 1 Three Sample Projects : Counting Problems.- Section 1 River-Crossing with Alibaba.- Section 2 Martian Citizenship Quiz.- Section 3 Rook Paths.- Chapter 2 A Sample Minicourse : Tessellations.- Section 1 Platonic and Archimedean Tilings.- Section 2 From Tessellations to Rectifications.- Section 3 Frieze and Wallpaper Patterns.- Part II Mathematical Competitions.- Chapter 3 Past Papers of the Edmonton Junior High Mathematics Invitational.- Section 1 Problems.- Section 2 Solutions.- Chapter 4 International Mathematics Tournament of the Towns : Selected Problems.- Section 1 A Problem on Area.- Section 2 A Problem on Series.- Section 3 A Problem on Communication.- Section 4 A Problem on Divisors.- Section 5 A Problem on Merge-Sort Algorithms.- Section 6 A Problem on Complex Numbers in Geometry.- Section 7 A Problem on Polyhedra.- Section 8 A Problem on Majorization.- Section 9 A Problem on Sequences.- Section 10 A Problem on Lottery.- Section 11 A Problem on Angles.- Section 12 A Problem on Balance.- Section 13 A Problem on Magic Tricks.- Section 14 A Problem on Polyomino Dissections.- Section 15 A Problem on Chess Tournaments.- Section 16 A Problem on electrical Networks.- Section 17 Another Problem on Communication.- Section 18 A Problem on Inversion.- Section 19 A Problem on Sharing.- Section 20 Yet Another Problem on Communication.- Section 21 A Problem on Finite State Machines.- Section 22 A Problem on Tangent Circles.- Section 23 A Problem on Graph Algorithms.- Section 24 A Problem on Fixed Points.- Part III Mathematical Congregations.- Appendix A Canadian Geography.- Appendix B Mathematical Jeopardy.- Appendix C Answers.- Chapter 5 “From Earth to Moon” Sample Contests.- Section 1 Problems.- Section 2 Answers.- Section 3 Solutions.- Chapter 6 Past Papers of the Peking University Mathematics Invitational for Youths.- Section 1 Problems.- Section 2 Solutions.- Part IV Mathematical Celebrations.- Chapter 7 Sample SNAP Math Fair Projects.- Section 1 Problems.- Section 2 Solutions.- Chapter 8 Sample GAME Math Unfair Games.- Section 1 Problems.- Section 2 Solutions.