Teaching yourself pure mathematics

The you will have to choose your applied units, which means that I don't know which exactly which books to recommend. I do know that Edexcel release a series of books for each unit that will definitely serve as good AS/A2 material.

The books are not proof-based because GCSE-level and A-level work is not proof-based. You will learn one method of formal proof in A-Level - proof by induction - that's it. Undergraduate work is when you learn more about mathematical proof.

As for "informal" proof - where you simply show that something is the case, not prove that it is the case, the more difficult questions in B&C, but particularly B&H will give you a great deal of practice.

Could you link me to the B&H books so I know which ones to buy? Also, do they cover all of the AS/A-Level maths and further maths content or are there a few topics missing?

Excellent, at least I'll be on the same level as everyone when I get to university! How do they normally introduce mathematical proof at university and what textbooks do they use?

Can't really recommend any undergraduate textbooks because I'm yet to get them myself! I did A-Level Further Mathematics, though, and a lot of the stuff in FP2 and FP3 is part of the first year degree course under the heading of "Analysis". Things such as mathematical proof at that level are beyond my current knowledge.

Do they cover AS/A-Level maths and further maths? Does it skip any topics in the current syllabus?

If you go to any exam board website you can download their Maths Syllabi and check what topics are covered

Can I just confirm that you are talking about these books:
http://www.amazon.co.uk/Pure-Mathematics-Book-First-Course/dp/0582353866/ref=sr_1_2?s=books&ie=UTF8&qid=1414238356&sr=1-2

http://www.amazon.co.uk/Pure-Mathematics-Course-Backhouse-Paperback/dp/B00HK37GXY/ref=sr_1_4?s=books&ie=UTF8&qid=1414238356&sr=1-4

Do they cover AS/A-Level maths and further maths? Does it skip any topics in the current syllabus?

Yes, those books. Got both of them sitting on my desk.

They cover AS/A-Level maths and further maths, as in units C1-4 and FP1-3. The applied units are not covered at all. As for syllabus coverage, they cover about 95% of the current syllabus, with the other 5% of the book being things that are left to undergraduate nowadays.

You should also note that they style of questions in these books is very different to the modern standard, so you will need modern books as well for questions practice. These books are good for teaching you the subject and expanding your knowledge and skill, but not quite in the way that is expected today.

Do B&H have textbooks for the applied units? Are you saying that they cover more advanced content that the current syllabus then? Perhaps that's why the old syllabus is seen as better.

Could you tell me what you mean by that last paragraph? How are the questions different? How do they teach differently?

B&H only have textbooks for Pure Mathematics. The closest equivalent for applied stuff is B&C. Whatever books you get, make sure that you download a copy of the syllabus, and only learn what is on it, since B&C are also likely to make digressions from the modern syllabus.

I was shying away from politics there. What I mean is is that these books have harder questions (some of them are of STEP and AEA standard), and much more clear and succinct explanations of the subject. The modern approach is to ease you into the subject more gently, which is great if you're struggling a little. These books come from a time when A-Levels were not something everyone did and cater only for people that can keep up. They will say things well, and they will say it once.

Overall, the modern expectations are lower than the standard of these books, and you need to find the balance that's best for you between meeting the current requirements and striving for excellence in the subject.

Dear Lockie123,

I realise that this reply is a bit late but I hope that you will read it.

I was in a similar situation to you. I am 27 and I have recently taken up A-Levels in Mathematics. I studied History at University, so I have not touched maths in just over 10 years.

I think that a lot of the replies here are wonderful and well meaning. However, I think that it is extremely important that you are reminded how difficult Mathematics is. I would argue that most of the students here have probably gone straight from GCSE into A-Level. There will be many processes that they are therefore extremely familiar.

BIDMAS – for example. This tells us the order in which we must complete an equation.

This means that:

(-2)^2 = 4.

But…
-2^2 = -4.

When you are dealing with difficult problems, it is extremely important that your basic skills are very good. Lengthy equations that take a few minutes to work out, might be wrong because you used an incorrect sign earlier on.
At the beginning, this can be extremely disheartening.

Having studied A-Level Mathematics as a mature student, I have a much greater appreciation of its complexity and to an extent, its beauty! It is my opinion that developing an aptitude in Mathematics is similar to playing a musical instrument. A-Level Maths can not be learned in a binary fashion and then just regurgitated at a later date. You have to practise it, A LOT! Mathematics is a skill and you will have to be prepared to work extremely hard at it.

I think that if you have gone straight from GCSE to A-Level, it is a little easier. Your brain has a better ability to understand numbers. Going from a non-mathematical profession and then studying a Mathematical subject at University will be hard. Really hard.

I do not believe the average person could develop the skills necessary for University level Maths within a year. You might be extremely intelligent or have a savantish ability for Mathematics. In which case you may pick it up very quickly.

As a mature student myself, I found it extremely challenging and extremely humbling studying Maths.

My advice:
Try out different Mathematics tutors. Different tutors will articulate problems in different ways. It would be wise to find a tutor that works well with you.

You are going to have to work hard. I would try to consider it a job and aim to do a minimum of 4-6 hours a day.

I am sure that users here will disagree with me, but I wanted to offer my opinion. I wish you the best of luck and I hope that you are able to do well at University. I just wanted to kindly inform you that you might be in for a bit of a shock. If you would like to discuss this privately or would like any more assistance then please let me know and I will send you my email address.

Good Luck!