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Teaching yourself pure mathematics

After 20 years of being a locksmith, I have decided that I want to get a university degree and I'll be starting next year! As part of my degree, I will be doing two mathematics courses - one in calculus and the other in linear algebra.

The problem? It has been two decades since I've touched any textbook, let alone a mathematics textbook! Also, I only know how to add, subtract, multiply and divide - and even that takes a while to do, yet I need to learn pure mathematics from basic arithmetic (preferably adding numbers in my head, adding fractions, finding percentages - those sort of things) to first year university calculus and linear algebra that is proof-based and rigorous.

If you were in my situation, what would your strategy be?
(edited 9 years ago)

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Original post by Lockie123
Imagine you're in your early 40's and it has been two decades since you've touched any textbook, let alone a mathematics textbook and you only know how to add, subtract, multiply and divide - and even that takes a while to do, yet you need to learn pure mathematics from basic arithmetic to first year university calculus and linear algebra that is proof-based and rigorous. What would your strategy be?


You want to go from pre-GCSE maths to Uni maths? How long have you got?
Reply 2
Original post by Lockie123
Imagine you're in your early 40's and it has been two decades since you've touched any textbook, let alone a mathematics textbook and you only know how to add, subtract, multiply and divide - and even that takes a while to do, yet you need to learn pure mathematics from basic arithmetic to first year university calculus and linear algebra that is proof-based and rigorous. What would your strategy be?



you have not told us why you are doing this.

Are you planning a degree or a new career?
personal pleasure or personal goal?
something else?


I am in a similar but not quite as bad situation.

I have not done any undergrad/postgrad stuff for 21 years, although I have been involved with mathematics teaching (at A level)during this time.

I started this summer revisiting slowly my old material.

my approach

Drew a plan for self teaching.
Got resources ready around me (in my case I dusted my very large books collection literally) and got myself a sensible Computer Algebra System.
Set realistic pace.
Did not put an upper limit on time (e.g I must be all done by then or else ...)
Looked for peers with similar interests.
Made allowances for my age so I do not get depressed when the going gets tough.
For motivation I am trying to share the material I am using/producing during my revision (that makes me work harder)


I started around July and although I am involved with a full time job (luckily self employed)
I have covered an awful lot of material and this is what I found.

brain is definitely slower (but still capable)
motivation is far higher.
experiencing mathematical maturity ( noticing things I never did first time round)

(Luckily I do not do pure! This gave a headache first time around!)

GOOD LUCK with whatever you are doing.
I hope it all works for you.
(edited 9 years ago)
Reply 3
Original post by Lockie123
Imagine you're in your early 40's and it has been two decades since you've touched any textbook, let alone a mathematics textbook and you only know how to add, subtract, multiply and divide - and even that takes a while to do, yet you need to learn pure mathematics from basic arithmetic to first year university calculus and linear algebra that is proof-based and rigorous. What would your strategy be?


I'm not a particular fan of the UK exam system in its current form, but exams do at least give you a benchmark and show how your level of knowledge compares to the expected knowledge of students going through the UK education at a "normal" pace.

If your knowledge is literally only the basic arithmetic operations, then you are at a sub-foundation level GCSE stage. Find some GCSE Foundation Tier papers online, see what makes sense and what doesn't and that will highlight the gaps in your knowledge! You may be able to fill in those gaps by following a GCSE course or textbook, or you may even have to go back a stage to texts for the Key Stages in schools.

I wouldn't even start worrying about concepts like "university calculus" and "linear algebra" until you've mastered the basics because you need to build up skills and confidence in all areas, and Maths is a subject that builds on firm foundations.
Reply 4
Original post by Wissenschaft
You want to go from pre-GCSE maths to Uni maths? How long have you got?


About a year.

Original post by TeeEm
you have not told us why you are doing this.

Are you planning a degree or a new career?
personal pleasure or personal goal?
something else?


I added more details to make it clearer, I thought no one would care but it seems like some people do!

Original post by davros
I'm not a particular fan of the UK exam system in its current form, but exams do at least give you a benchmark and show how your level of knowledge compares to the expected knowledge of students going through the UK education at a "normal" pace.


I've added more details so hopefully I can get more assistance now! What exam system do you like? Do you think I should focus on another exam system and not the UK's?
Reply 5
Original post by Lockie123
About a year.



I added more details to make it clearer, I thought no one would care but it seems like some people do!

I've added more details so hopefully I can get more assistance now! What exam system do you like? Do you think I should focus on another exam system and not the UK's?


I meant the "current UK system" (GCSEs, modular A levels etc) as opposed to the "old UK system" (O levels, proper A levels etc). :smile: The system is what it is, so in your position I would work through the progress levels as I suggested in my previous post.

Your plan sounds over-ambitious on the small evidence you've provided, but as I said you need to gauge where you are already compared to where you want to get to, Find a GCSE Foundation Tier exam paper, try answering the questions and see what happens. If you struggle with it then you've got a hell of a lot of catching up to do. If it seems like a piece of cake then you can look at GCSE Higher Tier topics involving algebra and trigonometry and see how you take to them.
Original post by Lockie123
After 20 years of being a locksmith, I have decided that I want to get a university degree and I'll be starting next year! As part of my degree, I will be doing two mathematics courses - one in calculus and the other in linear algebra.


I'm not going to lie, I think you may struggle to do this in a year. However, I think it is definitely worth doing. Good luck!
Reply 7
Original post by davros
I meant the "current UK system" (GCSEs, modular A levels etc) as opposed to the "old UK system" (O levels, proper A levels etc). :smile: The system is what it is, so in your position I would work through the progress levels as I suggested in my previous post.

Your plan sounds over-ambitious on the small evidence you've provided, but as I said you need to gauge where you are already compared to where you want to get to, Find a GCSE Foundation Tier exam paper, try answering the questions and see what happens. If you struggle with it then you've got a hell of a lot of catching up to do. If it seems like a piece of cake then you can look at GCSE Higher Tier topics involving algebra and trigonometry and see how you take to them.


Would you suggest I try to find the old UK system textbooks? Is there a reason why they are better?
Reply 8
Original post by Wissenschaft
I'm not going to lie, I think you may struggle to do this in a year. However, I think it is definitely worth doing. Good luck!


The way I see it, even if I don't finish it in a year, it's certainly better than doing absolutely nothing! :smile:
Reply 9
i am in the same situation as you however i am going on to todo engineering but i am learning mathematics outside of education and i would suggest that it is good to get the current textbooks and materials that are on offer and then compliment these with older textbooks and general mathematical publications as i have found that the older books have a lot more detail that can help explain some of the newer textbooks methods.
Reply 10
Original post by GRE60R
i am in the same situation as you however i am going on to todo engineering but i am learning mathematics outside of education and i would suggest that it is good to get the current textbooks and materials that are on offer and then compliment these with older textbooks and general mathematical publications as i have found that the older books have a lot more detail that can help explain some of the newer textbooks methods.


I would love it if I could get these older textbooks. Where can I get them from?

Also, in order, what are all the topics I should do?
Reply 11
Original post by Lockie123
I would love it if I could get these older textbooks. Where can I get them from?

Also, in order, what are all the topics I should do?


i would suggest the 'teach yourself books' series that were first published in 1950's and i find they are incredible in their explanations and their setting out.

it depends what exam board you are looking to complete
Reply 12
Original post by GRE60R
i would suggest the 'teach yourself books' series that were first published in 1950's and i find they are incredible in their explanations and their setting out.

it depends what exam board you are looking to complete


I'm not actually going to be sitting for the exams, I just need the knowledge :smile: Could you link me to the books you are talking about?
Original post by Lockie123
The way I see it, even if I don't finish it in a year, it's certainly better than doing absolutely nothing! :smile:


Absolutely! You'll find it challenging, but also extremely rewarding. If I were you, I'd buy edexcel A level textbooks for C1-4, M1 and S1.
Reply 14
Original post by Lockie123
After 20 years of being a locksmith, I have decided that I want to get a university degree and I'll be starting next year! As part of my degree, I will be doing two mathematics courses - one in calculus and the other in linear algebra.

The problem? It has been two decades since I've touched any textbook, let alone a mathematics textbook! Also, I only know how to add, subtract, multiply and divide - and even that takes a while to do, yet I need to learn pure mathematics from basic arithmetic (preferably adding numbers in my head, adding fractions, finding percentages - those sort of things) to first year university calculus and linear algebra that is proof-based and rigorous.

If you were in my situation, what would your strategy be?


I gave you a +rep for your post and aspirations :smile:

Also, your username is so fitting with your occupation! :biggrin:
Reply 15
Original post by Lockie123
Would you suggest I try to find the old UK system textbooks? Is there a reason why they are better?


It's not the textbooks particularly that I object to, it's the methods of examination and the culture of low expectations created by the GCSE and modular exam system :smile:

But for your purposes, you should just ignore my prejudices! Identify the areas where you have a skills gap and work on those areas, using the current exam specifications to work out what stage you're at compared to students progressing "normally" through the school system.

I'm a bit puzzled, however - you say you're starting a university course next year, but you're not planning on taking any maths exams before then! Do you actually hold an offer from a UK university and have you already met their entrance requirements?
Reply 16
Original post by Wissenschaft
Absolutely! You'll find it challenging, but also extremely rewarding. If I were you, I'd buy edexcel A level textbooks for C1-4, M1 and S1.


Do the books start from basic arithmetic and work towards first year calculus and linear algebra? I'm looking for books that are proof-based and rigorous :smile:

Original post by kka25
I gave you a +rep for your post and aspirations :smile:

Also, your username is so fitting with your occupation! :biggrin:


Thank you!

Original post by davros
It's not the textbooks particularly that I object to, it's the methods of examination and the culture of low expectations created by the GCSE and modular exam system :smile:

But for your purposes, you should just ignore my prejudices! Identify the areas where you have a skills gap and work on those areas, using the current exam specifications to work out what stage you're at compared to students progressing "normally" through the school system.

I'm a bit puzzled, however - you say you're starting a university course next year, but you're not planning on taking any maths exams before then! Do you actually hold an offer from a UK university and have you already met their entrance requirements?


I am moving to Australia next year as it has been years since I've seen them! I'm going to university there as well and yes I do have an offer. There are no prerequisites but there is assumed knowledge and after looking at the content, they said I should try to work up to and including A-Level Further Maths.

I heard that the old mathematics textbooks are a lot better than the newer textbooks and I'm not surprised at all! I would love to start from scratch using the old UK system and hopefully I can find the old UK system mathematics textbooks.

May I ask, after studying arithmetic (adding and subtracting, fractions, decimals, percentages, etc), did they go on to O levels, followed by A levels and then university?
(edited 9 years ago)
Original post by Lockie123
Do the books start from basic arithmetic and work towards first year calculus and linear algebra? I'm looking for books that are proof-based and rigorous :smile:


C1-C2 covers GCSE topics quickly. C3-C4 cover A level maths necessary for Uni. M1, FP1, and S1 will be very useful for you at degree.
Reply 18
I was looking at past threads and it seems that many people think that "The Core Course for A Level" and "Further Pure Mathematics" both by Bostock/Chandler are the best books to use for AS/A-Levels as they are rigorous and have excellent explanations. What do you all think?

However I did read a review of the books saying that these books assume that you have mastered the previous content. In your opinion, what topics do I need to have mastered before using these two books? Also, what textbooks (preferably also used in the 70's - 80's) can I learn those topics from?
Reply 19
Original post by Lockie123
I was looking at past threads and it seems that many people think that "The Core Course for A Level" and "Further Pure Mathematics" both by Bostock/Chandler are the best books to use for AS/A-Levels as they are rigorous and have excellent explanations. What do you all think?

However I did read a review of the books saying that these books assume that you have mastered the previous content. In your opinion, what topics do I need to have mastered before using these two books? Also, what textbooks (preferably also used in the 70's - 80's) can I learn those topics from?


Bostock and Chandler are brilliant books to cover the Pure content of the A level and FM syllabi, but they do assume that you have covered things like algebra and trigonometry (the level taught at GCSE should be sufficient for this, although even the best GCSE students seem to forget these topics over the summer after their GCSE exams which is the biggest challenge when they come to do A Level!).

As I said earlier, don't try to jump ahead yet. Have a look at some GCSE papers and make sure that you are comfortable with the topics examined. Once you're confident in answering questions at that level, then you can start on B&C :smile:

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