I'm recently going to be, hopefully, starting a PhD in Artificial Intelligence which requires me to urgently brush up my maths skills, which haven't been used since high school 7 years ago.

Can anyone recommend a book to help me get 'back in the game'. Ideally, I am interested in one that starts from the point that you completed high school maths, but haven't been using it for sometime. Hopefully one exists that dusts off your essential skills, then introduces you to various interesting ideas and fields without going into too much depth, so I know better the overall landscape and so can guide myself deeper through the topics I want.

Otherwise, I'd look for one that focused more on helping you along with probability / information theory without assuming too much.

I know it is a wishy washy question, but currently I am having to do a 'top down' approach when I come across something (often just as equations), and work out what it means so I can work out what I need to know to understand it, then learn each of those elements, some of which requries something else, etc. etc.

Many thanks!

Any textbook on Precalculus or on College Algebra and Trigonometry will do. The one I own is so old that I was not able to find it on the internet. But I am sure all of them are good.

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"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran

I think a smart thing to do would be to do a bridging course at your nearest uni. Its about 1-2 weeks (depending on the uni), 5 days a week, generally about 4-8 hours depending again on the uni, and it covers all year 12 HSC (you live in the cayman islands so I take it you've heard of the HSC, but if you hadn't its the test taken in NSW for Year 12).

It'll bring you up to scratch on all preuni maths. There's 2 unit (advanced), 3 unit (Extension 1), and 4 unit (extension 2). Don't be fooled by the 2 unit advanced tag, its nowhere near advanced. Extension 1 is probably the basics, teaching you calculus, parametrics, binomial theorem, probability, 3D trig, etc. 4 unit introduces complex numbers, integration by parts, etc (still pretty basic). If your gonna be going for a phD I recommend 3 unit and 4 unit bridging courses, and then get some 1st, 2nd and 3rd year undergraduate textbooks in your area of study (what will you be using? There's differential calculus, integration, Linear Algebra, Statistics, etc. If you focus on the maths you'll need [definitely calculus, and maybe linear algebra, i.e. vectors, matrices, eigenvalues and vectors, etc])

If all else fails go to the head of whatever faculty your getting your phD in (prob science or engineering) and set up an interview. They'll put you on the right track, pointing you towards people you can talk to who are doing the same area of study (very precise AOS, that is those in AI).

Not heard of the HSC, no. However, the concept of a bridging course had occured to me and is something I've been investigating. I'll be studying in the UK, so hopefully there will be something available.

For my PhD I would be using information theory primarily, so I dived right in with a book on Information Theory, but it assumes a lot of knowledge that I don't have or have forgotten. I have an A-Level (High School) Statistics textbook which I find easy to follow and helps fill in some of the blanks. Otherwise, it is a case of working 'top down' like I said to fill in the gaps in my knowledge; so I'm just looking to lay a better foundation I can build from.

I'll continue to look into courses I can take and stumble on like I am for the moment.

Thanks, theperfecthacker, for your book topic suggestions - I'm going to have a look into those too.

Unfortunately, it was only after I'd left school I realised how fun maths can be.