MATH 3560: History of Mathematics (UNSW): Lecture 09

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 09 - Calculus

Calculus has its origins in the work of the ancient Greeks, particularly of Eudoxus and Archimedes. In the 17th century the subject was widely expanded and developed in an algebraic way using the coordinate geometry of Descartes. Calculus has two branches: the differential and integral calculus. The former arose from the study by Fermat of maxima and minima of functions via horizontal tangents. The integral calculus computes areas and volumes beyond the techniques of Archimedes. It was developed independently by Newton and Leibniz, but others contributed too.

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.)