PREFACE

LECTURE ONE. Scratches and grunts

  1. Keeping count by a one-to-one correspondence (many millennia ago)

LECTURE Two. The greatest Egyptian pyramid

  1. Inducing the volume of a truncated square pyramid (ca. 1850 B.C.)

LECTURE THREE. From the laboratory into the study

  1. Introduction of deductive procedures into mathematics (ca. 600 B.C.)

LECTURE FOUR. The first great theorem

  1. The Pythagorean theorem (ca. 540 B.C.)

LECTURE FIVE. Precipitation of the first crisis

  1. The discovery of irrational magnitudes (ca. 540 B.C.)

LECTURE six. Resolution of the first crisis

  1. The Eudoxian theory of proportion (ca. 370 B.C.)

LECTURE SEVEN. First steps in organizing mathematics

  1. Material axiomatics (ca. 350 B.C.)

LECTURE EIGHT. The mathematicians'bible

  1. Euclid's Elements (ca. 300 B.C.)

LECTURE NINE. The thinker and the thug

  1. Archimedes on the sphere (ca. 240 B.C.)

LECTURE TEN. A boost from astronomy

  1. Ptolemy's construction of a table of chords (ca. 130)

LECTURE ELEVEN. The first great number theorist

  1. Diophantus and his Arithmetica (ca. 250)

LECTURE TWELVE. The syncopation of algebra

  1. The first steps toward algebraic symbolism (ca. 250)

LECTURE THIRTEEN. Two early computing inventions

  1. The abacus (uncertain, but early)
  2. The Hindu-Arabic numeral system (before 800)

LECTURE FOURTEEN. The poet-mathematician of Khorasan

  1. Omar Khayyam's geometrical solution of cubic equations (ca. 1090)

LECTURE FIFTEEN. The blockhead

  1. Fibonacci and his Liber abaci (1202)

LECTURE SIXTEEN. An extraordinary and bizarre story

  1. The algebraic solution of cubic equations (1554)
  2. The algebraic solution of quartic equations (1554)

LECTURE SEVENTEEN. Doubling the life of the astronomer

  1. Napier's invention of logarithms (1614)

LECTURE EIGHTEEN. The stimulation of science

  1. Galileo and the science of dynamics (1589ff)
  2. Kepler's laws of planetary motion (1619)

LECTURE NINETEEN. Slicing it thin

  1. Cavalieri's method of indivisibles (1635)

LECTURE TWENTY. The transform-solve-invert technique

  1. The invention of analytic geometry (1637)

Hints for the solution of some of the exercises

Index

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