Colourful Diagrams; Skipping the Proofs
For whatever reason, the majority of the engineering students do not enjoy the maths courses, and retain little of the necessary material after 1 year. We can justify this assertion by the spot tests we give at the start of EC3 or Fields and Waves (in the 3rd year) or Advanced Control (in the 4th year).
Traditionally Advanced Engineering Mathematics texts (such as Kreyszig) contained proofs for the general cases and discussed issues such as existence and uniqueness of solutions to ODEs etc. Mathematically trained engineers (and mathematicians) who typically delivered these courses considered these, and related skills necessary. However those consultants, engineers and technicians that solve industrial problems rarely use these skills, but do require a highly developed set of corresponding skills that are not addressed in the typical final-year engineering maths paper. What they is the ability to construct a flexible and reliable numerical algorithm to solve a given problem and, most importantly, the ability to interpret and critique the results, and keep a watchful eye out for typical problems such as numerical round-off, poor scaling with problem size, extreme parameter sensitivity. Again, we can justify these statements because of the extensive consulting work that my research group (Industrial Information and Control Centre) does with industry over the last 5 years, the numerous industrial short-courses I deliver to industry, academia and commercial sector (Reserve Bank, Deutsche Bank) in Australia and New Zealand, and the large international take up of our optimisation toolkit, Opti. I make the hypothesis that by teaching certain elements of engineering maths in a more visual manner using careful use of colour, extensive use of diagrams and giving the overview of the algorithm (as opposed to the details of the proof that it is correct) is more useful for the practising engineer. It was pointed out in a recent department meeting that the use of colour is problematic with those people who are colour blind. Currently I use colour-blind friendly pallets, but this needs further research. There are some simple and obvious consequences such as the mathematical textbook must be printed in full colour, the students also must use colour in assignments and exams. The lecture must be able to present ideas schematically in a natural manner, (hence the relation to the first project). It could even be that the text should be hand-written (which could be interpreted as an extension to Knuth’s “Concrete Roman” font or Octave Levenspiel’s handwritten The chemical reactor omnibook1)
- A/Prof David Wilson (project leader) – re-writing my two textbooks (Advanced Control and Numerical Analysis) in the above manner.
- Dr Roy Nates – critical review of the colour
Project leader – A/Prof David Wilson email@example.com
1 Book available from: http://www.amazon.com/chemical-reactor-omnibook-Octave-Levenspiel/dp/0882460676