THE MATH BOOK: BIG IDEAS SIMPLY EXPLAINED image
  • Book Title:
 The Math Book Big Ideas Simply Explained
  • Book Author:
D. K
  • Total Pages
675
  • Size of Book:
173 Mb
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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
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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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