History of Complex Numbers and Curves 
History of Complex Numbers and Curves
by UNSW / N.J. Wildberger
Video Lecture 25 of 32
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Date Added: January 19, 2015

Lecture Description

In the 19th century, the study of algebraic curves entered a new era with the introduction of homogeneous coordinates and ideas from projective geometry, the use of complex numbers both on the curve and at infinity, and the discovery by the great German mathematician B. Riemann that topological aspects of complex curves were intimately connected with the arithmetic of the curves.In this lecture we look at the use of homogeneous coordinates, stereographic projection and the Riemann sphere, circular points at infinity, Laguerre's projective description of angle, curves over the complex numbers and the genus of Riemann surfaces.This meeting of projective geometry, algebra and topology led the way to modern algebraic geometry.

Course Index

Course Description

In this course, Prof. N.J. Wildberger from UNSW provides a great overview of the history of the development of mathematics. The course roughly follows John Stillwell's book 'Mathematics and its History' (Springer, 3rd ed)Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology and hyperbolic geometry.  This course is meant for a broad audience, not necessarily mathematics majors. All backgrounds are welcome to take the course and enjoy learning about the origins of mathematical ideas. Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. At UNSW, this is MATH3560 and GENS2005. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.

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