THE SHEER JOY OF MATHEMATICS

Introduction

This is a course for those with a healthy curiosity and the cognoscenti. To educate for a purpose is not the intent. Rather, it is to provide a loosely structured mode of engagement to appreciate the ubiquity of mathematics as a human endeavour. The topics listed below have been selected to convey a sense of diversity and harmony. While some of them are taught to some degree, the emphasis here will be on moving beyond existing curricula by retrieving and highlighting lesser-known insights into their structure.The course will be accessible to students (undergraduate and above) and teachers in any science/math program.

Topics

Unit 1 : Polynomials: Equations of degree 3, 4 and 5. Chebyshev polynomials, Geometry of polynomials.

Unit 2 :  Excursions in Geometry: Inversive geometry and applications, the Hexlet, Conic sections, topics in Euclidean Geometry.

Unit 3 : Differential Equations: Examples from mechanics, Continuum models (heat flow, fluid flow, vibrations and waves), discussion on some topics from Newton’s Principia.

Unit 4 : Using a 3D printer for math visualization – possibilities and challenges.