MATH 3560: History of Mathematics (UNSW): Lecture 15

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 15 - Complex Numbers and Algebra

Complex numbers of the form a+bi are mostly introduced these days in the context of quadratic equations, but according to Stillwell cubic equations are closer to their historical roots. We show how the cubic equation formula of del Ferro, Tartaglia and Cardano requires some understanding of complex numbers even when only real zeros appear to be involved. The use of imaginary numbers in calculus manipulations and the geometrical planar representation of complex numbers are illustrated.

Go to the Course Home or watch other lectures:

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.)