MATH 3560 - History of Mathematics

MATH 3560: History of Mathematics (UNSW). Taught by Professor N. J. Wildberger, this course provides an overview of the history of mathematics, in 17 lectures; meant for a broad audience, not necessarily mathematics majors. Starting with Greek mathematics, Professor N. J. Wildberger discusses Hindu, Chinese and Arabic influences on algebra; the development of coordinate geometry, calculus and mechanics; the course of geometry from projective to non-Euclidean in the 19th century; complex numbers and algebra; differential geometry; and topology. This course roughly follows John Stillwell's book 'Mathematics and its History' (Springer, 3rd ed).

Lecture 06a - Polynomial Equations

We now move to the Golden age of European mathematics: the period 1500-1900. We discuss hurdles that the Europeans faced before this time and how they emerged, with the help of Arab algebra and translations of Greek works, to harness the Hindu-Arabic number system and a host of novel symbols including Vieta's new use of letters to represent unknowns to tackle new problems. Quadratic equations had been solved by almost all earlier mathematical civilizations; cubic equations was a natural step, taken by Tartaglia and Cardano and others.

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Lecture 1a - Pythagoras' Theorem
Lecture 1b - Pythagoras' Theorem (cont.)
Lecture 2a - Greek Geometry
Lecture 2b - Greek Geometry (cont.)
Lecture 3a - Greek Number Theory
Lecture 3b - Greek Number Theory (cont.)
Lecture 04 - Infinity in Greek Mathematics
Lecture 5a - Number Theory and Algebra in Asia
Lecture 5b - Number Theory and Algebra in Asia (cont.)
Lecture 6a - Polynomial Equations
Lecture 6b - Polynomial Equations (cont.)
Lecture 7a - Analytic Geometry and the Continuum
Lecture 7b - Analytic Geometry and the Continuum (cont.)
Lecture 08 - Projective Geometry
Lecture 09 - Calculus
Lecture 10 - Infinite Series
Lecture 11 - Mechanics and the Solar System
Lecture 12 - Non-Euclidean Geometry
Lecture 13 - The Number Theory Revival
Lecture 14 - Mechanics and Curves
Lecture 15 - Complex Numbers and Algebra
Lecture 16 - Differential Geometry
Lecture 17 - Topology