Classes & Timetable
Past courses
Fair Division and Voting Theory (26th June only):
The British electoral system is “First Past the Post”. In this system, many voters are voting strategically for one of the two most popular parties. Can there be a better voting system? One in which voters need not vote strategically, but can just vote according to their honest preferences? And what’s the best voting system, according to some mathematically precise definition of best? Come and find out in this course.
Heuristic Reasoning and the Art of Problem Solving (3rd July and 10th July):
Polya’s famous mathematical exposition ‘How to Solve It’ written in 1945 enumerates the following four stages of problem-solving:
Understand the problem
Devise a plan of attack to solve it
Execute the plan
Review your work to evaluate how it could be made better
He also states that for every difficult problem you can’t solve, there must exist an easier, more accessible related problem that you can solve: find it. While this might seem like elementary, obvious common sense, its utility in solving exciting mathematical problems of varying flavours is paramount and this is exactly what this course aims to demonstrate. In this course, we shall explore a selection of interesting conundrums and thought-provoking questions from a wide variety of topics to highlight the beauty, elegance and recreational pleasure they provide. As a skilled problem-solver, you can then employ these techniques of heuristic reasoning to unravel the magic of mathematics.
The Maths of Knots:
This course is an introduction to knots in mathematics and all the things we can do with them. We will approach this in a very intuitive and interactive way, with lots of pictures and examples!
Click here for course materials
Generating Functions:
This course will focus on generating functions, a technique in maths that provides a way to package an infinite sequence or string of data into a single function. We will discover ways to manipulate and combine these functions, leading us to interesting identities in combinatorics and number theory (for example, the proof of the Basel problem)