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Expanding my maths...

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!
Reply 1
Avatar for fg45344
fg45344
2
Study Linear Algebra, Regression Theory (OLS, GLS, anything in econometrics), Optimisation (simplex method, non linear optimisation)
Reply 2
Avatar for fg45344
fg45344
2
https://www.youtube.com/playlist?list=PLwJRxp3blEvaxmHgI2iOzNP6KGLSyd4dz

https://www.youtube.com/watch?v=a2QgdDk4Xjw&list=PLAD23E7AEFE221F70

https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD91010BC51F8
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
(edited 7 years ago)
Read Disquisitiones Arithmeticae by Carl Friedrich Gauss
Original post by fg45344


Thank you so much!
Reply 6
Avatar for B_9710
B_9710
18
I would recommend going through Andrew Wiles' proof of Fermat's last theorem and trying to understand it best you can.
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
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 :biggrin:

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 :wink:
(edited 7 years ago)
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 :biggrin:

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 :wink:


Hahaha thank you!

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