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

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Paperback, blz. | Engels
Springer International Publishing | e druk, 2018
ISBN13: 9783319717425
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Springer International Publishing e druk, 2018 9783319717425
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Samenvatting

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.

Specificaties

ISBN13:9783319717425
Taal:Engels
Bindwijze:paperback
Uitgever:Springer International Publishing

Inhoudsopgave

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.

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