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

• Main Author: Liu, Andrew Chiang-Fung (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Springer Texts in Education,
• Subjects: Mathematics-Study and teaching .; Mathematics Education.

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...

Table of Contents:

• 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.