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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.

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A 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.

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