PREFACE
LECTURE ONE. Scratches and grunts
- Keeping count by a one-to-one correspondence (many millennia ago)
LECTURE Two. The greatest Egyptian pyramid
- Inducing the volume of a truncated square pyramid (ca. 1850 B.C.)
LECTURE THREE. From the laboratory into the study
- Introduction of deductive procedures into mathematics (ca. 600 B.C.)
LECTURE FOUR. The first great theorem
- The Pythagorean theorem (ca. 540 B.C.)
LECTURE FIVE. Precipitation of the first crisis
- The discovery of irrational magnitudes (ca. 540 B.C.)
LECTURE six. Resolution of the first crisis
- The Eudoxian theory of proportion (ca. 370 B.C.)
LECTURE SEVEN. First steps in organizing mathematics
- Material axiomatics (ca. 350 B.C.)
LECTURE EIGHT. The mathematicians'bible
- Euclid's Elements (ca. 300 B.C.)
LECTURE NINE. The thinker and the thug
- Archimedes on the sphere (ca. 240 B.C.)
LECTURE TEN. A boost from astronomy
- Ptolemy's construction of a table of chords (ca. 130)
LECTURE ELEVEN. The first great number theorist
- Diophantus and his Arithmetica (ca. 250)
LECTURE TWELVE. The syncopation of algebra
- The first steps toward algebraic symbolism (ca. 250)
LECTURE THIRTEEN. Two early computing inventions
- The abacus (uncertain, but early)
- The Hindu-Arabic numeral system (before 800)
LECTURE FOURTEEN. The poet-mathematician of Khorasan
- Omar Khayyam's geometrical solution of cubic equations (ca. 1090)
LECTURE FIFTEEN. The blockhead
- Fibonacci and his Liber abaci (1202)
LECTURE SIXTEEN. An extraordinary and bizarre story
- The algebraic solution of cubic equations (1554)
- The algebraic solution of quartic equations (1554)
LECTURE SEVENTEEN. Doubling the life of the astronomer
- Napier's invention of logarithms (1614)
LECTURE EIGHTEEN. The stimulation of science
- Galileo and the science of dynamics (1589ff)
- Kepler's laws of planetary motion (1619)
LECTURE NINETEEN. Slicing it thin
- Cavalieri's method of indivisibles (1635)
LECTURE TWENTY. The transform-solve-invert technique
- The invention of analytic geometry (1637)
Hints for the solution of some of the exercises
Index
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