# Best mathematics courses to study in preparation for a tertiary degree in mathematics

Whilst this question can potentially be considered off topic I still believe that it is relevant and can benefit the site as a whole.

I've recently completed all of the mathematics courses in my school and still have a keen thirst for more knowledge as I really enjoy mathematics. I'm looking to pursue a dual degree of mathematics and computer science as an undergraduate degree for university, with a large focus on machine learning and it's applications. Whilst not entirely sure I think i'm leaning towards majoring in applied mathematics.

The topics that I've completed at school are:

Arithmetic and geometric sequences, functions and graphs, counting and probability, logarithmic and trigonometric functions

Calculus - Differentiation of continuous functions using the chain, product and quotient rule, Basic integration using U - substitutions. We've also covered basic applications in a 2 dimensional sense such as optimizing variables such as time.

Probability - Normal distributions, probability density functions, binomial distributions, sampling and estimation, confidence intervals.

Obviously my undergrad degree will be quite math intensive, but there is about 6 or so months until that starts and I don't think I can go that long without learning any new topics.

So, my question to all experienced mathematicians out there is: What are some math topics I should learn in preparation for studying mathematics and computer science at university?

• You will need linear algebra and multivariable calculus for machine learning. Besides that, do you have a solid foundation in reasoning and proof writing? That's probably the main difference between high school maths and university maths. Sep 1, 2021 at 12:15
• @Taladris My own curiosity has caused me to briefly explore methods such as proof by induction and direct proof Sep 1, 2021 at 12:18
• Math is a loooot of proving so "briefly" is good to start with, but probably there is a lot more to learn :D Sep 1, 2021 at 12:20
• Also important are new definitions and what they really mean. It's not like with a foreign language really, but one could phrase your question a bit like "best grammar and language courses to be prepared for the big literature in this new language". Well, take some basic grammar (math) book and start doing it! Fundamentals are calculus and linear algebra (used as often in mathematics as the English words "and" , "or", "because" in English literature....). Sep 1, 2021 at 12:41
• I've had a look at some of the questions you've asked to judge roughly where you are now. Also, something suggests to me that you're in the U.K. or Australia, where your first-year courses in math will be at a higher level than they would typically be in the U.S. I would suggest that you would benefit from: (1) reading an "introduction to proofs" book like Journey Into Mathematics by Rotman, (2) working through problem books (with solutions) on elementary material, where the problems might be a bit harder than the ones you've done. I'd suggest Problems in Calculus of One Variable by
– Mike
Sep 1, 2021 at 20:15