30-Second

The 50 Most Mind-Expanding Theories in Mathematics, Each Explained in Half a Minute

Richard J. Brown

• Publisher: Icon Books
• Year: 2012
• ISBN:
  9781848313866
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

From Rubik's cubes to Godel's incompleteness theorem, everything mathematical explained, with colour illustrations, in half a minute. Maths is enjoying a resurgence in popularity. So how can you avoid being the only dinner guest who has no idea who Fermat was, or what he proved? The more you know about Maths, the less of a science it becomes. 30 Second Maths takes the top 50 most engaging mathematical theories, and explains them to the general reader in half a minute, using nothing more than two pages, 200 words and one picture. Read at your own pace, and discover that maths can be more fascinating than you ever imagined.

INDEX

A

Abel, Niels 1

abstract algebra 1

addition and subtraction 1, 2

algebra 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

algebraic expressions 1, 2

algebraic geometry 1, 2

algebraic number theory 1, 2

algebraic numbers 1, 2, 3

algorithms 1, 2, 3, 4, 5, 6

Al-Khwarizmi, Abu ‘Abdullah Muhammad Ibn Musa 1, 2, 3

analytical geometry 1

Archimedes of Syracuse 1, 2, 3

Archimedes’ Principle 1

Aristotle 1

arithmetic 1, 2, 3, 4, 5, 6, 7, 8

Aryabhata 1

B

base 2 (see binary system)

base 10 (see decimal system)

base 12 (see duodecimal system)

base 20 (see vigesimal system)

base 60 (see sexagesimal system)

Bayes, Rev. Thomas 1

Bayes’ theorem 1

bell curve 1

Bernoulli, Jacob 1

Bienaymé, Irénée-Jules 1

binary sequence 1, 2

binary system 1, 2, 3

Boolean logic (Boolean algebra) 1, 2, 3

Borel, Émile 1

Brahmagupta 1, 2

C

calculus 1, 2, 3, 4, 5, 6

Cantor, Georg 1

Cantor set 1

Cardano, Girolamo 1

Cartesian coordinates 1, 2, 3

central limit theorem 1

Church, Alonzo 1

complex numbers 1, 2, 3, 4, 5

continuum hypothesis 1

counting bases 1

cubic equations 1, 2...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Contents
• Introduction
• Numbers & Counting
• GLOSSARY
• Fractions & Decimals
• Rational & Irrational Numbers
• Imaginary Numbers
• Counting Bases
• Prime Numbers
• Fibonacci Numbers
• Pascal’s Triangle
• profile: Blaise Pascal
• Number Theory
• Making Numbers Work
• GLOSSARY
• Zero
• Infinity
• Addition & Subtraction
• Multiplication & Division
• Exponentials & Logarithms
• Functions
• profile: Gottfried Leibniz
• Calculus
• Chance is a Fine Thing
• GLOSSARY
• Game Theory
• Calculating the Odds
• profile: Girolamo Cardano
• The Law of Large Numbers
• The Gambler’s Fallacy – Law of Averages
• The Gambler’s Fallacy – Doubling Up
• Randomness
• Bayes’ Theorem
• Algebra & Abstraction
• GLOSSARY
• The Variable Placeholder
• The Equation
• Polynomial Equations
• profile: Abu ‘Abdallah Muhammad ibn Musa al-Khwarizmi
• Algorithms
• Sets & Groups
• Rings & Fields
• Geometry & Shapes
• GLOSSARY
• Euclid’s Elements
• Pi – The Circle Constant
• The Golden Ratio
• profile: Pythagoras
• Trigonometry
• Squaring the Circle
• Parallel Lines
• Graphs
• Another Dimension
• GLOSSARY
• Platonic Solids
• Topology
• Euler Bricks
• The Möbius Strip
• profile: Archimedes of Syracuse
• Fractals
• Origami Geometry
• Rubik’s Cube
• Knot Theory
• Proofs & Theorems
• GLOSSARY
• Fermat’s Last Theorem
• profile: Pierre de Fermat
• The Four Colour Mapping Problem
• Hilbert’s Program
• Gödel’s Incompleteness Theorem
• Poincaré’s Conjecture
• The Continuum Hypothesis
• Riemann’s Hypothesis
• APPENDICES
• Resources
• Notes on Contributors
• Index
• Acknowledgements