## Timetable

**09.00**Registration and refreshments**09.40**Welcome from the Principal, Professor Paul Layzell**09.45**Quick quiz with prizes, Mr Laurence O’Toole**10.20**The Music in a 2000 year old proof, Professor Rüdiger Schack**11.30**Small Group Talks**12.00**Lunch**12.30**Tours of campus from outside the Windsor Building**12.30—13.00**Further Mathematics (for teachers only), Mr Steve Collins**13.15—13.45**Small Group Talks**14.00**Mathematics at University, Professor James McKee**14.45**Juggling—Theory and Practice, Dr Colin Wright**15.45**Close and questionnaires

## Main Talks

### Professor Rüdiger Schack: *The* *Music in a 2000 year old proof*

Are all quantities in mathematics ratios of integers, such as 5/7? The ancient Pythagoreans thought so. For them, mathematics, cosmology, and music were firmly based on the integers. The Pythagorean world view was thrown into crisis in the 5th century BC when it was discovered that some distances, and by implication some musical intervals, cannot be expressed as ratios of integers, that is, they are “irrational”. It took more than 2000 years for mathematicians and musicians to fully come to terms with the discovery of irrational numbers. This talk will present a simple and beautiful proof that the square root of 2 is irrational, and through it explore connections between music and mathematics.

*Professor Rüdiger Schack has been teaching at Royal Holloway’s Mathematics Department for more than 20 years, including 5 years as Head of Department. He has made numerous research contributions in the field of quantum theory ranging from foundations to optics and cryptography. Recently he was a panelist at the World Science Festival in New York. His musical interests include singing in a choir and playing piano and harpsichord.*

### Dr Colin Wright: *Juggling: Theory and Practice*

Juggling has fascinated people for centuries. The skilled practitioner will keep several objects in the air at one time, and weave complex patterns that seem to defy both gravity and analysis. In this talk we develop a simple method to describe and annotate juggling patterns. We see how simple mathematics can be used to classify them, to describe those patterns that are known already, and discover a technique for creating new ones.

*While earning his Ph.D from Cambridge University in the 1980s, Colin also learned how to fire-breathe, unicycle, juggle and ballroom dance. He has worked as a research mathematician, a computer programmer, and an electronics hardware designer, and takes time to give talks all over the world on various mathematical topics.*

### Professor James McKee: *Mathematics at University*

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.

*Professor James McKee is the Head of the Department of Mathematics. He works at the interface of number theory and combinatorics, with computational leanings. His recent work has mostly been connected with associating algebraic numbers with certain combinatorial objects.*