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Books to read to prepare for maths at university

Books to read to go beyond A-Level

I’m thinking of taking a gap year to reapply for maths/trying to switch the course at my firm university, please can anyone recommend good books to work through that are on the level of BSc maths/stats?

Also some problem solving book recommendations are appreciated as if I take a gap year I’ll be taking MAT, STEP etc

My current level of maths is A-Level Further Maths for context

I would also appreciate any tips on how to self-study this type of maths

Thanks
Original post by yzven
Books to read to go beyond A-Level
I’m thinking of taking a gap year to reapply for maths/trying to switch the course at my firm university, please can anyone recommend good books to work through that are on the level of BSc maths/stats?
Also some problem solving book recommendations are appreciated as if I take a gap year I’ll be taking MAT, STEP etc
My current level of maths is A-Level Further Maths for context
I would also appreciate any tips on how to self-study this type of maths
Thanks

You'll need probably, Real Analysis and Linear Algebra books with some probability I guess if you're interested in stats.

Real Analysis wise it is very personal which book will suit you. I've always found the Springer undergraduate books ok. Obviously there are classics like Spivak's Calculus which is a nice introduction and Principles of Mathematical Analysis by Rudin which is very much like being thrown in at the deep end. Terry Tao has some books out on it and I've heard they are quite good though haven't gone through them personally.

Linear Algebra wise I have no idea as I've never used a book for it, though I think Axler's Linear Algebra Done Right is viewed quite highly.

For probability/stats there is a book called All of Statistics which I find quite good.

In terms of how to self study, you will need to go through a chapter making your own notes, explaining examples and try to come up with a few other examples. Then you just need to do all the questions at the end of each chapter. Once you have seriously attempted each question if you are unsure about an answer, either it will be online to look up, or you can ask how to complete it on the maths stack exchange (only do this if you also explain your answer so far and what you don't quite get). From there it is just rinse and repeat.

Self studying from a book can be quite a big task especially if you haven't done any sort of university mathematics yet. If you are struggling, there are plenty of full lecture courses available on Youtube for free. Obviously you won't have the problem sheets for the class but you can just answer the questions in the book you get on the topic that is being covered in the lectures.
Reply 2
Original post by yzven
Books to read to go beyond A-Level
I’m thinking of taking a gap year to reapply for maths/trying to switch the course at my firm university, please can anyone recommend good books to work through that are on the level of BSc maths/stats?
Also some problem solving book recommendations are appreciated as if I take a gap year I’ll be taking MAT, STEP etc
My current level of maths is A-Level Further Maths for context
I would also appreciate any tips on how to self-study this type of maths
Thanks
There a myriad of transition to uni maths books you can take a look at, i thought richard earls was good but never really worked through it and more skimmed it.

If you're taking a gap year and planning on reapplying then i don't really recommend studying uni texts, the style is completely different and wont be helpful for entrance exams like mat/step. You'll have plenty of time to study them whilst at uni.

That said, if you do want to here are a few recommendations:
For real analysis i'd start with M. Hart, Guide to Analysis Macmillan, its a "soft" book compared to a lot of the others that get recommended but personally its a great starting point.
Linear Algebra, i'd just use google to find a random unis lecture notes and take a look.
Abstract Algebra/Basic set theory, A.F.Beardon, Algebra and Geometry, CUP, 2005 This is a great book.
If you want something closer to A-levels that will be really helpful throughout your degree then take a look at Multivariable Calculus by James Stewart.
(edited 3 weeks ago)
Reply 3
Original post by zetamcfc
You'll need probably, Real Analysis and Linear Algebra books with some probability I guess if you're interested in stats.
Real Analysis wise it is very personal which book will suit you. I've always found the Springer undergraduate books ok. Obviously there are classics like Spivak's Calculus which is a nice introduction and Principles of Mathematical Analysis by Rudin which is very much like being thrown in at the deep end. Terry Tao has some books out on it and I've heard they are quite good though haven't gone through them personally.
Linear Algebra wise I have no idea as I've never used a book for it, though I think Axler's Linear Algebra Done Right is viewed quite highly.
For probability/stats there is a book called All of Statistics which I find quite good.
In terms of how to self study, you will need to go through a chapter making your own notes, explaining examples and try to come up with a few other examples. Then you just need to do all the questions at the end of each chapter. Once you have seriously attempted each question if you are unsure about an answer, either it will be online to look up, or you can ask how to complete it on the maths stack exchange (only do this if you also explain your answer so far and what you don't quite get). From there it is just rinse and repeat.
Self studying from a book can be quite a big task especially if you haven't done any sort of university mathematics yet. If you are struggling, there are plenty of full lecture courses available on Youtube for free. Obviously you won't have the problem sheets for the class but you can just answer the questions in the book you get on the topic that is being covered in the lectures.
+1 on tao, those are excellent imo.
Never gone through Spivaks first calculus book, but ive worked through parts of calculus on manifolds and it was pretty good so i'd assume the first would be decent too.
Rudin💀
Reply 4
Original post by zetamcfc
You'll need probably, Real Analysis and Linear Algebra books with some probability I guess if you're interested in stats.
Real Analysis wise it is very personal which book will suit you. I've always found the Springer undergraduate books ok. Obviously there are classics like Spivak's Calculus which is a nice introduction and Principles of Mathematical Analysis by Rudin which is very much like being thrown in at the deep end. Terry Tao has some books out on it and I've heard they are quite good though haven't gone through them personally.
Linear Algebra wise I have no idea as I've never used a book for it, though I think Axler's Linear Algebra Done Right is viewed quite highly.
For probability/stats there is a book called All of Statistics which I find quite good.
In terms of how to self study, you will need to go through a chapter making your own notes, explaining examples and try to come up with a few other examples. Then you just need to do all the questions at the end of each chapter. Once you have seriously attempted each question if you are unsure about an answer, either it will be online to look up, or you can ask how to complete it on the maths stack exchange (only do this if you also explain your answer so far and what you don't quite get). From there it is just rinse and repeat.
Self studying from a book can be quite a big task especially if you haven't done any sort of university mathematics yet. If you are struggling, there are plenty of full lecture courses available on Youtube for free. Obviously you won't have the problem sheets for the class but you can just answer the questions in the book you get on the topic that is being covered in the lectures.

thanks a lot
Original post by yzven
Books to read to go beyond A-Level
I’m thinking of taking a gap year to reapply for maths/trying to switch the course at my firm university, please can anyone recommend good books to work through that are on the level of BSc maths/stats?
Also some problem solving book recommendations are appreciated as if I take a gap year I’ll be taking MAT, STEP etc
My current level of maths is A-Level Further Maths for context
I would also appreciate any tips on how to self-study this type of maths
Thanks


Try Hall and Knight’s higher algebra I haven’t started my GCSEs yet but I’ve started that book and it’s good my frnds in India who are preparing for their uni JEE ADV exam suggested me that book
Original post by yzven
Books to read to go beyond A-Level
I’m thinking of taking a gap year to reapply for maths/trying to switch the course at my firm university, please can anyone recommend good books to work through that are on the level of BSc maths/stats?
Also some problem solving book recommendations are appreciated as if I take a gap year I’ll be taking MAT, STEP etc
My current level of maths is A-Level Further Maths for context
I would also appreciate any tips on how to self-study this type of maths
Thanks

Hi!

I am studying maths and recommend reading Lara Alcock's book How to Study for a Mathematics Degree. I found it useful to help me prepare for the difference in how to study going from school to university and generally give me an idea of what to expect. She also has a book on real analysis (How to Think About Analysis) if you are interested in reading ahead!

I hope that helps and good luck with your studies! 🙂
Florence (Lancaster University student ambassador)
Original post by yzven
Books to read to go beyond A-Level
I’m thinking of taking a gap year to reapply for maths/trying to switch the course at my firm university, please can anyone recommend good books to work through that are on the level of BSc maths/stats?
Also some problem solving book recommendations are appreciated as if I take a gap year I’ll be taking MAT, STEP etc
My current level of maths is A-Level Further Maths for context
I would also appreciate any tips on how to self-study this type of maths
Thanks

There are some Oxford lectures by Vicky Neale [RIP] which are good.

https://people.maths.ox.ac.uk/neale/WhyStudyMathematics.html

https://www.youtube.com/watch?v=VSw5RUy9W5E

https://www.youtube.com/watch?v=ahbJk5d6F18

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