Small Group Sessions

There will be two sessions of short 30 minute talks at 11.30 and 13.15. Each talk will be given twice

 

  • Mathematics and the Laws of Nature: A Variation on the Theme of Wigner, Professor Jens Bolte
  • Big Numbers and Securing the Internet, Mr Benjamin Curtis
  • Prime Numbers, Perfect Numbers and Amicable Numbers, Professor Rainer Dietmann
  • The Birthday Paradox and its applications, Ashley Fraser
  • Beyond the Third Dimension, Further Mathematics Support Programme, Mr Mark Hughes
  • Exploring Mathematics with MATLAB, Dr Alexey Koloydenko
  • The shape of space, Professor Brita Nucinkis
  • Fun Maths Roadshow and Problem Solving, Further Mathematics Support Programme, Mr Steve Collins
  • The MU Puzzle, Professor Rüdiger Schack
  • The Liar Game, Dr Mark Wildon
  • Further Mathematics for Teachers, Mr Steve Collins. For teachers only, from 12.30 to 13.00

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

Mathematics and the Laws of Nature: a Variation on the Theme of Wigner, Professor Jens Bolte

At least since Galileo Galilei, the laws of nature have been formulated in mathematical language. The mathematical physicist E. P. Wigner once gave a talk on this subject, under the title “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, in which he elaborates on “why the success of mathematics in its role in physics appears so baffling”. In this talk I shall explain Wigner’s ideas in examples, from the very simple ones to some of the more “baffling” ones. Among the latter is P. A. M. Dirac’s prediction of anti-matter, solely based on the mathematical consistency of the (Dirac-) equation that he developed in 1928.

 

Big Numbers and Securing the Internet, Mr Benjamin Curtis

Big numbers keep the internet safe. In this talk we will begin with a discussion about large numbers, and how we can put them into context. For example we can understand how large the number 10 is, but it is much more difficult to understand how large 13,700,000,000 is. We will then discuss exactly how large numbers need to be in order to secure the internet, as well as how these numbers are used. We will consider a simple example of how some mathematical problems get ‘harder’ as the numbers get bigger. Finally, we will look at how future developments in computers will mean that we need a different way to secure the internet in the future.

 

Prime Numbers, Perfect Numbers and Amicable Numbers, Professor Rainer Dietmann

Primes are amongst the most fascinating objects in mathematics. In this session we want to discuss some of their basic properties such as the fact that there are infinitely many prime numbers. This can for example be demonstrated by using so-called Fermat numbers, which were conjectured to be all prime until Euler found a counterexample in 1732. Another interesting class of primes, Mersenne primes, are closely connected to so-called perfect numbers which are subject to many interesting unresolved conjectures and are related to so-called amicable numbers.

 

The Birthday Paradox and its applications, Ms Ashley Fraser

How many people do you have to invite to a party so that there is a 80% chance that there are at least 2 that have the same birthday? The number is surprisingly small and this is known and the “birthday paradox”. Today the birthday paradox is used to compromise passwords and we will discuss how these attacks work and how to prevent them.

 

Beyond the Third Dimension, Further Mathematics Support Programme, Mr Mark Hughes

Have you ever wondered what lies beyond the third dimension? In this journey through the dimensions, we will be exploring a branch of mathematics called topology (sometimes playfully referred to as ‘geometry on a rubber sheet’). We will explore some shapes that can’t exist unless you add more dimensions. We will discover that transitioning from the third to the fourth dimension is not much harder than transitioning from the second to the third dimension. We will also find that time isn’t necessarily the fourth dimension, despite physicists’ claims.

 

Exploring Mathematics with MATLAB, Dr Alexey Koloydenko

MATLAB is a powerful package for scientific computing, typical of the facilities available in mathematical laboratories. We make considerable use of such packages, both in teaching and in research. Algebra and calculus can nearly all be done ‘automatically’ on the computer rather than by hand, thereby avoiding ‘getting the sign wrong’ or ‘forgetting the factor of 2’ that plague all of us at times. This is particularly important in applications where the equations can spread over several pages at a time. In this introduction, you will be guided through some basic algebra and calculus examples, including 2D and 3D graphs and a demonstration of solving a real life problem.

 

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.

Fun Maths Roadshow and Problem Solving, Further Mathematics Support Programme, Ms Cath Moore

This is a hands-on workshop where students can experience a variety of problems 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. This workshop is ideal for any student in the first year of A level Maths or Further Maths.

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 Liar Game, Dr Mark Wildon

Ask a friend to think of a secret number between 1 and 15. How many questions with yes/no answers do you need to discover your friend’s number? How many questions would you need if your friend is permitted to lie in one answer? We will answer these questions and learn how to play these games optimally, using the mathematics of coding theory to detect lies.

Further Mathematics for Teachers, Mr Steve Collins

This is an informal opportunity for current or potential teachers of Further Maths to share ideas and to find out how the Further Maths Network can support them. It will also provide an opportunity for teachers to get together and discuss different aspects of Further Maths teaching.