Just finished Highschool and I am starting my degree in math after the summer, but in the mean time what subjects should I try and study?

Question

Hi I just finished Highschool, I'm starting a degree in math when the summer is over but I want to do a bit of self-studying just for fun. As you might expect I am not very knowledgeable of college level mathematics and do not know what subjects I should study. To give you a better idea of my level I have in my free time finished going through Calculus Early Trancendentals By James Stewart. This is (I think) Calc 1 2 and 3 (they did however start omitting alot of proofs at the calc 3 section). This book wasn't insanely difficult for me but it also wasn't a walk in the park (which is to be expected when learing something new). I have also completed highschool mathematics with a 9.8 (we here use grades from 1 to 10 where 10 is perfect and 1 is nothing correct).

What subjects should I now study, could you also explain in short what the subject studies and do you have any good book recommendations?

Thanks in advance!

Answer 1

Did you got the curriculum of your major(/track if your college have) and know what you must study to get the degree? Anyway, I believe Cal 3 (as you mentioned, inc. partial derivatives, line integrals, vector fields, Green's/Stokes' Thm, etc), linear algebra (sth like eigenvalues/vectors, span, rank, etc) and analysis (more proper/vigorous definitions on calculus, infinite sequences, metric spaces, etc) are a must.

So for these 3 areas of study, Stewart's multi-cal textbook or Paul's online math notes would still be a feasible choice for Cal 3. As for lin alg and analysis, I relied on lecture notes pretty much and don't have a good idea for the course materials. Maybe you can find the past exams papers and have a peek on what you will be tested.

Answer 2

I think you should read something fun, something you're not likely to see in the undergraduate curriculum. Ian Stewart, Another Fine Math You've Got Me Into, or Albert Beiler, Recreations in the Theory of Numbers, or pretty nearly anything by Martin Gardner. Or Imre Lakatos, Proofs and Refutations.

Answer 3

Not exactly a reference for study but I highly recommend that you take time to organize your day and take time for self care; exercising, meal planning, taking time for yourself. I am very happy you are excited for college, but understand it is a marathon and not just a sprint. You want to build healthy habits now as a freshman because you will struggle in upper level courses. When you struggle, it is important that you have set up strong and good habits to take a break from work before trying again. College takes a lot of work, recovering between challenges is super important to your long term success.

But if you really want something to play with I recommend Linear Algebra and its Applications (https://www.amazon.com/Linear-Algebra-Its-Applications-5th/dp/032198238X)