PREFACE LECTURE TWENTY-ONE. Order within disorder - The birth of mathematical probability (1654)
LECTURE TWENTY-wo. Moving pictures versus still pictures - The invention of the differential calculus (1629-1680s)
LECTURE TWENTY-THREE. Like opening and closing a door - The fundamental theorem of the calculus (1669-1690s)
LECTURE TWENTY-FOUR. Power(ful) series - Taylor and Maclaurin series (1715, 1742)
LECTURE TWENTY-FIVE. Yea + Yea + Yea + Yea - Fourier series (1807)
LECTURE TWENTY-six. The liberation of geometry, I - The discovery of non-Euclidean geometry (1829)
LECTURE TWENTY-SEVEN. The liberation of geometry, II - The discovery of non-Euclidean geometry (1829)-continued
LECTURE TWENTY-EIGHT. The liberation of algebra, I - The discovery of a noncommutative algebra (1843)
LECTURE TWENTY-NINE. The liberation of algebra, II - The discovery of a noncommutative algebra (1843)-continued
LECTURE THIRTY. An important atomic structure - The group structure (1830-1860)
LECTURE THIRTY-ONE. A remarkable codification - The Erlanger Programm (1872)
LECTURE THIRTY-TWO. Pythagoras justified - The arithmetization of analysis; the natural number system as a foundation of mathematics (end of the nineteenth century)
LECTURE THIRTY-THREE. Digging deeper - Set theory as a foundation of mathematics (end of the nineteenth century)
- Abstract spaces (1906)
- The function concept refined by set theory (beginning of the twentieth century)
LECTURE THIRTY-FOUR. Beyond the finite - Transfinite numbers (1874-1895)
LECTURE THIRTY-FIVE. Some remarkable definitions - Formal axiomatics (early twentieth century)
- A definition of mathematics (early twentieth century)
LECTURE THIRTY-SIX. Some clarifying examples - A definition of mathematics (early twentieth century)continued
LECTURE THIRTY-SEVEN. The third level - Metamathematics (1899-1920)
LECTURE THIRTY-EIGHT. Mathematics as a branch of theology - Godel's incompleteness theorem (1931)
LECTURE THIRTY-NINE. The dream that came true - The modern electronic computing machines (1944)
- Resolution of the four-color conjecture (1976)
LECTURE FORTY. Apology and regrets HINTS FOR THE SOLUTION OF SOMIE OF THE EXERCISES INDEX |Contact| |Front page| |Contents| |Books| Copyright © 1996-2018 Alexander Bogomolny 71763641 |