There will be two sessions of short 30 minute talks at **11.30**, **13.15** and **14.00**. Each talk will be given three times

*Probability in Financial Markets,*Dr Darren Banfield*The mathematics of matches,*Professor Simon Blackburn*Mathematics at University,*Professor Stefanie Gerke*Omg, we have the same birthday!*Erin Hales*Traffic Jams*, Dr Alastair Kay*Pi,*Professor James McKee*The shape of space,*Professor Brita Nucinkis*Puzzles and Problem solving**The MU Puzzle*, Professor Rüdiger Schack

*Transition from School to University (teachers only and only one session)*

The abstracts (i.e. short summaries of the talks) are below:

*Probability in Financial Markets,* Dr Darren Banfield

An understanding of probability is key to the pricing of financial instruments. We illustrate some concepts by looking at a simple game of tossing coins. We also introduce a financial instrument called a credit default swap. We show that its pricing is similar to the coin-tossing game, but also has complications which makes the mathematics more difficult.

*The mathematics of matches*, Professor Simon Blackburn

Who wins when two good players play a game? What is the winning tactic? There is often some beautiful and surprising mathematics behind these questions. This session explores one particular game (often played with piles of matches) to illustrate some of the mathematics involved.

*Mathematics at University, Professor *Stefanie Gerke

Are you interested in studying Mathematics at University? This session will deal with the types of course available and the qualifications required, the ways in which university mathematics is different from or similar to mathematics at A-level, and the careers available.

*Omg, we have the same birthday!* Erin Hales

How likely is it that you will share a birthday with someone else in the room? Not very, right? After all, there are 365 days in a year… In this talk, we will explore how likely it really is, and take a journey through probability and its applications.

*Traffic Jams*, Dr Alastair Kay

Have you ever been sat in a really long traffic jam and then, when you get to the front of the queue, there’s no apparent reason for why it took so long? This talk will attempt to explain how that happens.

*PI*, Professor James McKee

When one divides the circumference of a circle by its diameter one gets the number 3.141592653589793 . . ., regardless of the size of the circle. Somewhat surprisingly the same number appears when one divides the area of a circle by the square of its radius, as Archimedes showed about 2300 years ago. This “circle number” is called Pi. This number Pi keeps cropping up in mathematics, even if we don’t see any circles. For instance, the infinite alternating sum of the reciprocals of all odd positive integers 1−1/3+1/5−1/7+ 1/9−. . . yields Pi/4; or the infinite sum of the reciprocals of all squares 1+1/4+1/9+1/16+. . . is PI^2/6; the probability that two positive integers are relatively prime is 6/PI^2. We’ll ex- plore a few interesting facts about PI and how little we actually know about one of the most fundamental constants in mathematics.

*The shape of space,* Professor Brita Nucinkis

How big is the universe? Is it finite or infinite? Does it have a boundary? These and other questions lead us to an area of mathematics called Topology. We will explore these topics, first in dimension 2, and will then see how to extend this to higher dimensions.

*Puzzles and Problem Solving*

This is a hands-on workshop where students can experience a variety of problems individually or in small groups. There will be the opportunity to demonstrate maths, logic, communication and teamwork skills as different tasks covering a variety of topics are tackled. Some of the problems are from the NRICH roadshow.

*The MU Puzzle, *Professor Rüdiger Schack

Starting from a given sequence of letters and four simple rules, can one arrive at the word MU? We will show that this simple mathematical puzzle leads to surprising insights into the nature of mathematical proof and the limitations of computers. And, of course, we will also solve the puzzle.

*The Transition from School to University *

This session is for teachers only. We will discuss what we do to help the students in their first year or foundation year to ease the transition from school to university and how schools can help prepare their students for mathematics at university.