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 12 - Non-Euclidean Geometry

The development of non-Euclidean geometry is often presented as a high point of 19th century mathematics. The real story is more complicated. The important insights of Gauss, Lobachevsky and Bolyai, along with later work of Beltrami, were the end result of a long and circuitous study of Euclid's parallel postulate. But an honest assessment must reveal that in fact non-Euclidean geometry had been well studied from two thousand years ago, since the geometry of the sphere had been a main concern for all astronomers.

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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