- Book Title:
| The Math Book Big Ideas Simply Explained |

- Book Author:
| D. K |

- Total Pages
| 675 |

- Size of Book:
| 173 Mb |

- Book Views:
| 983 total views, 4 views today |

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| PDF Direct Download Link |

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| Click for Hard Copy from Amazon |

The Math Book: Big Ideas Simply Explained – Book Sample

## CONTENTS – *The Math Book: Big Ideas Simply Explained*

### ANCIENT AND CLASSICAL PERIODS 6000 BCE–500 CE

- Numerals take their places • Positional numbers
- The square as the highest power • Quadratic equations
- The accurate reckoning for inquiring into all things • The Rhind papyrus
- The sum is the same in every direction • Magic squares
- Number is the cause of gods and daemons • Pythagoras
- A real number that is not rational • Irrational numbers
- The quickest runner can never overtake the slowest • Zeno’s paradoxes of motion
- Their combinations give rise to endless complexities • The Platonic solids
- Demonstrative knowledge must rest on necessary basic truths • Syllogistic logic
- The whole is greater than the part • Euclid’s
*Elements* - Counting without numbers • The abacus
- Exploring pi is like exploring the Universe • Calculating pi
- We separate the numbers as if by some sieve • Eratosthenes’ sieve
- A geometrical tour de force • Conic sections
- The art of measuring triangles • Trigonometry
- Numbers can be less than nothing • Negative numbers
- The very flower of arithmetic • Diophantine equations
- An incomparable star in the firmament of wisdom • Hypatia
- The closest approximation of pi for a millennium • Zu Chongzhi

### THE MIDDLE AGES 500–1500

- A fortune subtracted from zero is a debt • Zero
- Algebra is a scientific art • Algebra
- Freeing algebra from the constraints of geometry • The binomial theorem
- Fourteen forms with all their branches and cases • Cubic equations
- The ubiquitous music of the spheres • The Fibonacci sequence
- The power of doubling • Wheat on a chessboard

### THE RENAISSANCE 1500–1680 – *The Math Book: Big Ideas Simply Explained*

- The geometry of art and life • The golden ratio
- Like a large diamond • Mersenne primes
- Sailing on a rhumb • Rhumb lines
- A pair of equal-length lines • The equals sign and other symbology
- Plus of minus times plus of minus makes minus • Imaginary and complex numbers
- The art of tenths • Decimals
- Transforming multiplication into addition • Logarithms
- Nature uses as little as possible of anything • The problem of maxima
- The fly on the ceiling • Coordinates
- A device of marvelous invention • The area under a cycloid
- Three dimensions made by two • Projective geometry
- Symmetry is what we see at a glance • Pascal’s triangle
- Chance is bridled and governed by law • Probability
- The sum of the distance equals the altitude • Viviani’s triangle theorem
- The swing of a pendulum • Huygens’s tautochrone curve
- With calculus I can predict the future • Calculus
- The perfection of the science of numbers • Binary numbers

### THE ENLIGHTENMENT 1680–1800 – *The Math Book: Big Ideas Simply Explained*

- To every action there is an equal and opposite reaction • Newton’s laws of motion
- Empirical and expected results are the same • The law of large numbers
- One of those strange numbers that are creatures of their own • Euler’s number
- Random variation makes a pattern • Normal distribution
- The seven bridges of Königsberg • Graph theory
- Every even integer is the sum of two primes • The Goldbach conjecture
- The most beautiful equation • Euler’s identity
- No theory is perfect • Bayes’ theorem
- Simply a question of algebra • The algebraic resolution of equations
- Let us gather facts • Buffon’s needle experiment
- Algebra often gives more than is asked of her • The fundamental theorem of algebra

### THE 19TH CENTURY 1800–1900

- Complex numbers are coordinates on a plane • The complex plane
- Nature is the most fertile source of mathematical discoveries • Fourier analysis
- The imp that knows the positions of every particle in the Universe • Laplace’s demon
- What are the chances? • The Poisson distribution
- An indispensable tool in applied mathematics • Bessel functions
- It will guide the future course of science • The mechanical computer
- A new kind of function • Elliptic functions
- I have created another world out of nothing • Non-Euclidean geometries
- Algebraic structures have symmetries • Group theory
- Just like a pocket map • Quaternions
- Powers of natural numbers are almost never consecutive • Catalan’s conjecture
- The matrix is everywhere • Matrices
- An investigation into the laws of thought • Boolean algebra
- A shape with just one side • The Möbius strip
- The music of the primes • The Riemann hypothesis
- Some infinities are bigger than others • Transfinite numbers
- A diagrammatic representation of reasonings • Venn diagrams
- The tower will fall and the world will end • The Tower of Hanoi
- Size and shape do not matter, only connections • Topology
- Lost in that silent, measured space • The prime number theorem

### MODERN MATHEMATICS 1900–PRESENT – *The Math Book: Big Ideas Simply Explained*

- The veil behind which the future lies hidden • 23 problems for the 20th century
- Statistics is the grammar of science • The birth of modern statistics
- A freer logic emancipates us • The logic of mathematics
- The Universe is four-dimensional • Minkowski space
- Rather a dull number • Taxicab numbers
- A million monkeys banging on a million typewriters • The infinite monkey theorem
- She changed the face of algebra • Emmy Noether and abstract algebra
- Structures are the weapons of the mathematician • The Bourbaki group
- A single machine to compute any computable sequence • The Turing machine
- Small things are more numerous than large things • Benford’s law
- A blueprint for the digital age • Information theory
- We are all just six steps away from each other • Six degrees of separation
- A small positive vibration can change the entire cosmos • The butterfly effect
- Logically things can only partly be true • Fuzzy logic
- A grand unifying theory of mathematics • The Langlands Program
- Another roof, another proof • Social mathematics
- Pentagons are just nice to look at • The Penrose tile
- Endless variety and unlimited complication • Fractals
- Four colors but no more • The four-color theorem
- Securing data with a one-way calculation • Cryptography
- Jewels strung on an as-yet invisible thread • Finite simple groups
- A truly marvelous proof • Proving Fermat’s last theorem
- No other recognition is needed • Proving the Poincaré conjecture

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