Mathematical Beauty: What Is Mathematical Beauty And Can Anyone Experience It?
US$ 27.59
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Description
Contents
Reviews
Language
English
ISBN
9781915361929
Title page
Copyright
Contents
Dedication
Foreword: By Mark McCourt
Introduction
An example of ‘objectively beautiful mathematics’
Defining mathematics
Chapter 1: What is mathematics? Patterns and significant form
The nature of mathematics: A quick note
The pursuit of mathematics
Significant form
Significant form: An example with The Towers of Hanoi puzzle
Concluding remarks
Historical notes: What are complex numbers and are they as scary as non-mathematicians might think?
Criterion for mathematical beauty
Chapter 2: A framework for mathematical aesthetics
Mathematical Beauty Pillar 1
Chapter 3: The accessibility of mathematical beauty
An elemental example of pattern and order: What is mathematical symmetry?
Mathematical Beauty Pillar 2
The power of algebra and the pros and cons of symbolic representation
Simplicity: A thought for the aesthetic framework
Mathematical Beauty Pillar 3a
Visual vs. mathematical beauty
Explaining fractals: Julia sets and how they connect to the Mandelbrot set
A misrepresented number: The golden ratio
Understanding ‘what’ vs. understanding ‘why’: Two proofs of the same theorem
What does it mean to understand ‘why’ in mathematics?
Mathematical Beauty Pillar 3b
Adaptive appreciation responses: Euler’s identity
The book: Can both pure and applied mathematics be considered beautiful?
Generalisations in mathematics: A pattern for the book
How do rainbows form? A more technical example
The Goldbach conjecture
Prime numbers and the Riemann hypothesis
Patterns and fitness indicators
Mathematical Beauty Pillar 4
Unexpected simplicity in complexity
Chapter 4: A deeper analysis of important aesthetic criteria
Unexpected connections
Unexpectedness: Five concepts which defy intuition
The beautiful, the sublime and the mysterious: Ramanujan’s sum
Returning to the pure vs. applied debate: the unreasonable effectiveness of mathematics
Mathematical Beauty Pillar 5
Mathematical Beauty Pillar 6
The aesthetic canon: Computer-assisted proofs
An attempt at an aesthetic framework for mathematics
Summary
Teaching to develop aesthetic sensibility
How to explain mathematical beauty to ‘almost’ anyone
Appendices
Bibliography
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$15.59
