What do teachers recommend for self study?

Foundation Maths by Anthony Croft and Robert Davison is very helpful; it starts at a very basic level and is easy to follow. It has nothing to do with the foundation GCSE level!

I feel almost embarrassed posting this given my age but I've finally decided to learn maths but at school I was learning it because I had to, now it's different because I want to and so I think I'll progress much faster.

I'm looking for a good AS/A-Level level book to get me started. I already have this book http://www.amazon.co.uk/Basic-Mathematics-Serge-Lang/dp/0387967877 Basic Math - Serge Lang and I'm sure this will be fine for GCSE level stuff as it does go quite indepth and covers many topics like quadratics, inequalities, sets, geometry, complex numbers, logarithms and many other things so I'll be using this as a refresher for GCSE level material.

The problem is there are so many books out there it's hard to chose. I'm doing this more as a hobby and won't be taking any actual tests so I'm looking specifically for a book that focuses on self teaching and not a book that supplements school work.

I hope to learn calculus at some point but this will be impossible if I don't develop a strong understanding of the basic mathematics

To be perfectly honest, if you really want to teach yourself mathematics, I'd go with the AS Mathematics textbooks. Our school does Edexcel and their own textbooks are really excellent in general. They're very clear and I taught myself C1 and C2 from them in Year 10 (http://www.amazon.co.uk/Edexcel-AS-Level-Modular-Mathematics/dp/0435519107)

Whilst there are a books focusing more on the holistic side of maths (i.e. the deeper, more logical and creative sides), in my experience it's not a good idea to turn to them if you're not already experienced at mathematics. You need to have a high level of mathematical maturity to understand the deeper underlying logical concepts and the only way you achieve this is through practice. So, if I were you, I'd get hold of textbooks for some of the core modules (start with C1 and C2) and from then on you can go in whatever direction you want. If you enjoy the textbook style of learning (which I do), you can go on to do further pure modules (like C3/4, FP1-3) or you can try applied modules (M1-5, S1-3, D1-2).

This modular A Level style approach is really good in my opinion because it provides you with the tools you need to do proper mathematics. I think it's much more sensible going down this easier (albeit more artificial) learning curve than diving directly into the real pure mathematics. Alternatively, you can go down the more uni-style maths route if you're brave enough. I had an excellent book to recommend but a friend borrowed/stole it and I can't remember the title for the life of me although I can try to find it out.

This book looks excellent too. It covers slightly different topics as the other book but I guess with it being a book by an academic body it's specifically geared for the content likely to be in a real exam. The problem I hope I don't run into is that the book only teaches you the very basics of each topic. Would you say that if I worked through C1,C2 and C3 this would be enough to start a calculus book?

I'm just worried that the book only covers the basics of each topic.

Calculus is taught in C1-4. Polynomial differentiation and integration is introduced in C1 as well as its application of being used to find tangents, normals etc. C2 introduces integration as a method to find the area under graphs and differentiation as a method to find maximums, minimums, turning points as well as some real life applications. I haven't finished C3 or 4 so I can't tell you what exactly the calculus element is, but you can see the specification here: http://www.edexcel.com/migrationdocuments/GCE%20New%20GCE/UA035243_GCE_Lin_Maths_Issue_3.pdf

Whilst I understand your concern about the books 'only introducing the basics', it's very important that you're not over-ambitious. A Level Maths is excellent in terms of the fact that it provides a very structured framework that is easy to follow. If you find the core A Level modules easy then yeah, I'd go ahead and start reading some more advanced books but I doubt that someone without a mathematical background would find them easy (apart from C1 which is really easy).

Thanks I think I'm going to purchase C1 to get me started

I am self learning maths and FM. May I recommend the book Core Maths by Bostock and Chandler? (Make sure you buy the latest edition) It is absolutely top notch and is one of very few books Cambridge suggest for Pre U maths. The problem with module text books is that the expense rapidly begins to mount up.

I also use the web site Worked Solution : ExamSolutions Maths Revision Video Tutorials which is a stunningly useful resource and one which has completely changed my approach to self learning (and my results)

Could you link the exact book you're talking about? There seem to be quite a few different names such as advanced maths, a level maths ect. It's a shame I can't preview the books contents.

http://www.amazon.co.uk/Core-Maths-Advanced-Level-3rd/dp/0748755098

May I suggest you "read up" on the book and check the reviews before u buy iy. It is very highly regarded. Not sure of the latest edition but you can find out. Second hand ones are sometimes on sale too. I found it has real academic rigour allied to very simple clear and mercifully brief explanations. Supported by cracking exercises, multiple choices tests and a plethora of A level questions all in one book. Incidentally the authors (two women I think) do other similar books for Applied stuff.

The book which changed my life though and set me on my path is Teach Yourself Calculus. It is donkeys years old, has been upgraded since, but IMHO never surpassed. Taking short cuts in Calculus as per the examining boards module books never pays in the long run.

Finally this university maths professor in the USA has his whole course online, and much of it is in our A level syllabus:

http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

Hope this helps.