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# Expanding my maths... watch

1. Hi all,
I'm intending to study mathematics at university, and wondered if anyone had any good ideas on how to expand your mathematical knowledge past that of the A-level syllabus?

Thank you!
2. Study Linear Algebra, Regression Theory (OLS, GLS, anything in econometrics), Optimisation (simplex method, non linear optimisation)
3. Linear algebra, vector calculus, integral transforms, operator methods

Fourier series and Sturm Liouville theory are pretty interesting topics that are quite general

Set theory tends to be a good one that some read up on during A-Levels

I'm not a mathematician, I'm talking from a scientist's point of view, so I wouldn't know how to expand your knowledge other than to just keep reading
4. Read Disquisitiones Arithmeticae by Carl Friedrich Gauss
5. Thank you so much!
6. I would recommend going through Andrew Wiles' proof of Fermat's last theorem and trying to understand it best you can.
7. (Original post by B_9710)
I would recommend going through Andrew Wiles' proof of Fermat's last theorem and trying to understand it best you can.
Isn't it like the most confusing proof ever though?! Hahaha
8. Well, if you know
-the terms "theorem", "lemma", "corollary", "proposition" and "conjecture"
-the different types of proof (direct, induction, contraposition, contradiction etc.)
-the "blackboard bold" symbols used to represent sets of numbers (ℕ ℤ ℚ ℝ ℂ)
You're pretty much ready for degree-level maths

btw if you have a specific career in mind after you leave uni, plan for that well in advance - you might find that you don't need to know Fermat's last theorem in your career
9. (Original post by shawn_o1)
Well, if you know
-the terms "theorem", "lemma", "corollary", "proposition" and "conjecture"
-the different types of proof (direct, induction, contraposition, contradiction etc.)
-the "blackboard bold" symbols used to represent sets of numbers (ℕ ℤ ℚ ℝ ℂ)
You're pretty much ready for degree-level maths

btw if you have a specific career in mind after you leave uni, plan for that well in advance - you might find that you don't need to know Fermat's last theorem in your career
Hahaha thank you!

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