S.M.A.R.T. Circle Minicourses
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...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2018.
|
| Έκδοση: | 1st ed. 2018. |
| Σειρά: | Springer Texts in Education,
|
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.
