S.M.A.R.T. Circle Minicourses

Description

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. Front Matter ....Pages i-xiv Front Matter ....Pages 1-1 Area and Dissection (Andy Liu)....Pages 3-28 Projective Geometry (Andy Liu)....Pages 29-54 Conic Sections (Andy Liu)....Pages 55-78 Inversive Geometry (Andy Liu)....Pages 79-104 Convexity (Andy Liu)....Pages 105-134 Front Matter ....Pages 135-135 Balancing Problems (Andy Liu)....Pages 137-158 Graph Theory (Andy Liu)....Pages 159-186 Beanstalks (Andy Liu)....Pages 187-206 Inequalities (Andy Liu)....Pages 207-232 Polynomial Equations (Andy Liu)....Pages 233-244