# Classes & Timetable

## Upcoming Courses

Introduction to Bayesian thinking (6th, 13th, 27th November and 4th December):

"If you toss a coin, the probability of getting heads is 0.5". Is this statement true? If you were to toss a coin 100 times and get 90 tails, would you still believe this statement? Or would the new data update your beliefs? And if so, how do we express this update mathematically? The Bayesian way of thinking is a formal process we use to update our beliefs about the world once we have observed some data. From the Monty Hall problem to alpha dog, Bayesian thinking is widely used not only in science but also in our everyday life. In this course we are going to learn about the basic logic behind Bayesian thinking through many interesting examples.

The course will run 5-7pm at Imperial College London.

Number Theory (6th, 13th, 27th November and 4th December):

Ever wondered why prime numbers are so special or how some diophantine equations have puzzled mathematicians for centuries? In this course, we’ll introduce you to the fascinating world of number theory, covering topics such as modular arithmetic, the quadratic reciprocity law, and more.

The course will run 5-7pm at Imperial College London.

Probability Theory (2nd, 9th, 16th, 23rd October):

We develop the necessary techniques to solve the following problem: Consider a square checkerboard where the tiles are randomly coloured black or white. Estimate the number of black and white regions just from knowing the size of the board. While we will rigorously study key concepts from probability theory, the main goal of this course is to showcase the trial-and-error nature of mathematical problem solving, the power of inequalities, and the importance of shifting perspectives.

The course will run 5-7pm at Imperial College London.

## Past courses

Fair Division and Voting Theory:

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:

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)