Mathematical Reflections

Two Beautiful Years (2018-2019)
Erscheinungsjahr 2021
ISBN: 978-0-9993428-9-3
Verlag: XYZ Press

Buch, Englisch, 551 Seiten, Hardback

Mathematical Reflections: Two Beautiful Years is a compilation and revision of the 2018 and 2019 volumes from the online journal of the same name. This book is aimed at high school students, participants in math competitions, undergraduates, and anyone who has a fire for mathematics. Passionate readers submitted many of the problems, solutions, and articles and all require creativity, experience, and comprehensive mathematical knowledge. This book is a great resource for students training for advanced national and international mathematics competitions such as USAMO and IMO.

Autoren/Hrsg.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

- Preface
- 1 Problems
- 1.1 Junior Problems
- 1.2 Senior Problems
- 1.3 Undergraduate Problems
- 1.4 Olympiad Problems
- 2 Solutions
- 2.1 Junior Solutions
- 2.2 Senior Solutions
- 2.3 Undergraduate Solutions
- 2.4 Olympiad Solutions
- 3 Articles
- 3.1. Searching for Homogeneity Across Multi-Variable Polynomials
- 3.2. Triangles Homothetic with the Intouch Triangle
- 3.3. Power-sum Problem, Bernoulli Numbers and Bernoulli Polynomials
- 3.4. Convergence of Root Location Algorithms with Random Initial Points
- 3.5. About an Old Romanian TST Problem
- 3.6. Unexpected Applications of Mean Value Theorem(s) in Number Theory
- 3.7. The Sequence ({nd?}) is Dense in [0,1]. An Elementary Proof
- 3.8. On a Special Center of Spiral Similarity
- 3.9. A Discrete Approach to a Result Concerning a Contour Integral
- 3.10. Linear Approximation Implies Unique Solution
- 3.11. Joining the Incenter and Orthocenter Configurations: Properties Associated with a Tangential Quadrilateral
- 3.12. Best Polynomial Estimates in a Triangle
- 3.13. On a Property of the Primitive Roots of Unity Leading to the Evaluation of Ramanujan’s Sums
- 3.14. Ptolemy’s Sine Lemma
- Problem Author Index
- Article Author Index