The Champagne integral
Mathematics for Radar Research
Dr Robert Tough has developed a series of courses on the applied mathematics required for Radar Research. Bespoke courses have been developed for particular audiences and have been given at:
- The Defence Evaluation and Research Agency
- University College London
- The University of Cape Town
- Electromagnetic Scattering Theory
- Kalman Filters
- Detection Theory
Motivation
Mathematics provides a remarkably compact, precise and powerful tool for the analysis of the physical world. Furthermore a little bit of mathematical know-how can be made to go a very long way. So, by becoming acquainted with a few new tricks, chosen for their relevance to radar research, you can access a large literature that would otherwise be rather impenetrable.
Having done that you, at the very least, have a good idea of what all that squiggly stuff means. You will find that the techniques we cover are widely applicable and will stand you in good stead in your research; they provide a useful complement to simulation and data analysis studies.
Maths is a common language for scientists and engineers, some proficiency in which enables you to cross cultural, interdisciplinary and linguistic barriers with ease. The ‘applied maths’ of the sort we will cover here can be great fun; identifying, correctly posing and solving a practical problem is most gratifying. So the material covered in this course will help you enjoy your work and provide an extra element of job satisfaction. In many situations a little maths adds a veneer of intellectual credibility to an otherwise quite ordinary product. With this course under your belt you have instant added value at your fingertips. The same applies to you, of course, as you present your way through life. A black belt in sums can come in very useful.
These and other reasons for studying maths are echoed in the opinions of the good and the great, of which a few are:
- ‘The analytical method I followed was no longer a bookish dogma, it was put to the test every day, it could be refined, made to conform to our aims, by a subtle play of reason, of trial and error. To make a mistake was no longer a vaguely comic accident that spoils an exam for you or affects your marks: to make a mistake was similar to when you went climbing - a contest, an act of attention, a step up that makes you more worthy and fit.’ Primo Levi (1975)
- ‘We construct and keep on constructing, yet intuition is still a good thing. You can do a good deal without it, but not everything. Where intuition is combined with exact research it speeds up the progress of research. Exactitude winged by intuition is at times best. But because exact research is exact research, it gets ahead without intuition. It can be logical; it can construct. It can build bridges boldly from one thing to another. It can maintain order in the midst of turmoil.’ Paul Klee (1928)