Mathematical Foundations of Everyday Life

Only very few people know how Mathematics is developed and how it is applied in all branches of science. A general aim of the course is to increase the number of such people. It is the easiest to explain the ideas of the course on an example.

Let's consider a modern mobile phone.  It heavily uses modern algebra for encrypting and decoding signals. This highly abstract algebra is still being developed. A modern phone very often has a satellite navigation.  In order to work properly, such a device has to apply rules of the relativity theory, which is a kind of geometry.  It is the aim of the course to explain these theories and how were they discovered, developed and applied.

The course will consist of twelve, more or less, independent modules. Each module will be devoted to a different branch of mathematics (e.g. probability) or a different type of applications (e.g. economy). The first two modules (Numbers and Formulae) are intended to be introductory and the other modules may depend on them. Topics covered are:

• Numbers (Jarek Kędra)
• Formulae (Jarek Kędra)
• Cryptography (Jarek Kędra)
• Controlling traffic (Marco Thiel)
• Probability (Assaf Libman)
• Biology (David Lusseau)
• Logic (David Pym)
• Special relativity (Jarek Kędra)
• Economy (Julian Williams)
• Computing Science (Matthew Collinson)
• Saving fuel of a spaceship (Jarek Kędra)
• Chaos (Marco Thiel)

Each module will consist of two hours of lectures and one hour of tutorial or discussion session in the following week.  It is our general aim to present easy examples, the basics of a theory, the historical background, applications and open problems for each topic.

There will be a weekly set of problems for each topic to be discussed in the following week.