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...
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| Médium: | Elektronický zdroj E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
Cham :
Springer International Publishing,
2018.
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| Vydání: | 1st ed. 2018. |
| Edice: | Springer Texts in Education,
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| Témata: | |
| ISBN: | 9783319717432 |
| ISSN: | 2366-7672 |
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Obsah:
- 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.