A New Mathematics for the Million?

So I have to admit that I didn't take "A-level" Maths (plural in the UK, but over time I have come to better appreciate it being singular in the US like "sheep") and so I never really had a great preparation in mathematics. Over the years I tried various books to learn calculus and failed numerous times, but eventually succeeded finding it wonderful and basically fun at Khan Academy!. I am now forcing my way through the Linear Algebra with less success - but I think that might be as much about the subject matter being just a little harder to apply. I also found a book hanging around the house by Lancelot Hogben - Mathematics for the Million -  which is quite good, but I am not sure that I recommend it. It is easier to learn calculus from youtube videos than from this book, but in general it has an infectiousness that is pleasing.

This has had me thinking for a long time what the mathematics the everyman should want to know. Practical things, useful things, a better understanding of finance, how machines are now making decisions for us. I think this list of things that everyone needs to know - although perhaps they don't need to know how to do - has changed dramatically in the last two decades, and is rapidly changing now - to the point where perhaps someone who doesn't want to be a mathematician maybe doesn't care about the proofs. It is also best taught via applied mathematics - i.e. the course should be a set of fascinating problems - so you never hear the question - "Why is this interesting again?"

So what is the list:

  • Python, NumPy, Pandas ect - this is the new place to do math
  • Calculus - just the basic stuff to realize that it is fun.
  • The fun parts of differential equations - making model equations and differentiating to get insight
  • Bayesian stats - which I think are now best learned as part of machine learning
  •  Linear algebra as a part of machine learning
  • Modelling - how everything is being made aerodynamic now
  • Finite element analysis?

What do you think should be on the list?

I want to gradually improve this post by adding the links to where to lear about these things.