This was my last post of my Mathematics Plugged Blog. I will continue here, but concentrate more on the methodology and technology aspects.
A numbers or a symbols person?
I really enjoy meeting Paul Wilmott from tie to time, and he once asked his readers in a blog post: are you a numbers or a symbols person? Expecting hard-sciemce people to be symbols and, say, accountants to be numbers people.
This is important for the maths education, but even within the mathematical disciplines it is not so clear.
IMO, it starts with the question: axiomatic or algorithmic mathematics? In axiomatic maths two functions are defined "identical" if they have the identical I/O relation. In algorithmic maths you need to take care of the economics (resources usage, performance, ..).
As a former algebraist I worked in axiomatic maths. But in my business life I combined.
Dance with symbols
In symbolic computation programs shall be able to manipulate symbols that can be mathematical expressions, geometrical objects, molecule structures … or even programs.
We describe problems in the language of mathematics and try to solve with symbolic computation methods (exact, by closed form solutions). But the world of closed form solutions is usually a small world. Just think of the Black Scholes formula in quantitative finance (restricted to constant volatility).
It's all numbers
Many problems cannot be transformed into closed form solutions. You need numerical schemes (in most of the real world cases). You need them to solve models of material flows, chemical reactors, conservation of energy, financial risk management …
Good numerical schemes fit perfect along sub-domains where closed form solutions are available and do not lose accuracy or robustness "in between".
So, applied mathematics is symbols and numbers. Asymptotic maths is about the decomposition of a domain into sub-domains where exact solutions are available and their reintegration into one solution.
This is really critical. If you understand the power of the combination your complex systems will add values. You usually add value, if you do the most difficult work. It's valued and scarce because it is difficult.
Use the future technology
And luckily there is technology that leverages your problem solving power: Wolfram Technology.
At uni software plus we developed know-how packages and conducted projects for major players and innovators in various industry sectors from metallurgy to quant finance.
Uni software plus is a comparatively small outfit. But it is amazing, what complex systems we could and can build - by knowledge-based programming, with built-in algorithms combining symbols and numbers.
You can too. We will be pleased to show you how.