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I am about to start an undergraduate course in Computer Science at UCL this autumn. Since seventh grade i had this lasting passion for mathematics, and I still want to find out more than - let's say - basic highschool maths. I am curious if this course would satisfy my thirst for more advanced math, or if I - in the worst case - will have time to teach myself some of that, besides my regular courses.

How would you start going about it? Do you have any advice?

I do not wish to get answers like "You should have opted for a Mathematics course.". I have not explained the reasons for my choice, and I believe they are irrelevant in the context of the question. I wish you would not state the obvious, since if it was Math i had chosen, this very question would not have existed. Thank you.

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    $\begingroup$ I would not lean towards attempting to teach yourself advanced mathematics unless you are very self-motivated and have a good chunk of free time. One of the many benefits of going to a great school like UCL is the excellent teaching staff - use them. Upper level undergraduate math can be quite beautiful, and learning happens much more quickly and enjoyably with a good lecturer. You could even shadow/audit classes without having to enroll. $\endgroup$ – D. W. Aug 8 '16 at 20:35
  • $\begingroup$ I absolutely agree. I tried to learn some things by myself, but it's much more efficient when you look up to someone who know a lot of stuff. Will i get the opportunity to join such "upper level" classes? $\endgroup$ – Hemispherr Aug 8 '16 at 20:37
  • $\begingroup$ You'll learn lots of discrete mathematics, but you'll be missing abstract algebra and topology $\endgroup$ – Jorge Fernández Hidalgo Aug 8 '16 at 20:41
  • $\begingroup$ That is exactly what i fear. I loved things like Group theory in highschool and i feel as though we bearly touched and outlined it all. I still don't see the clear picture in my mind with the symmetry being described by groups, we never talked about fundamental grops, nor group actions or equivalence classes.. i hoped i could find out more by going to university. $\endgroup$ – Hemispherr Aug 8 '16 at 20:45
  • $\begingroup$ As someone said check the books of Knuth, not only the Concrete mathematics, check the trilogy related to computational maths. And it will be interesting to learn too some book about numerical methods applied in computers. $\endgroup$ – Masacroso Aug 8 '16 at 22:16
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Read through (and work many exercises in!) "Concrete Mathematics" by Graham, Knuth, and Patashkin. This is a wonderful book on discrete math with a slight slant toward matters applicable to computer science. It should definitely satisfy your thirst for more advanced math, and will come in handy if you ever have to consider analyzing algorithms. Plus it is fun (at least if you love math).

Knuth, BTW, is a BIG NAME in computer science.

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  • $\begingroup$ Thank you for your book suggestion, i have a lot of spare time this summer. Wonder if i could find it on local libraries, although chances are pretty small, living in Romania. $\endgroup$ – Hemispherr Aug 8 '16 at 20:41
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    $\begingroup$ I was wondering why you had seen group theory in highschool, i guess it makes sense since you are from romania. In my country we didn't even learn calculus :( $\endgroup$ – Jorge Fernández Hidalgo Aug 8 '16 at 20:49
  • $\begingroup$ Allways thought i'm lucky in this respect. The education here did a great job at making me curious. Hope it wasn't a big obstacle for you. $\endgroup$ – Hemispherr Aug 8 '16 at 20:52
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During your CS degree, you will probably do three semesters of Calculus and one or two of Linear Algebra as well as some probability. You will learn some discrete mathematics; in particular, logic, propositional and predicate calculus, and most likely some combinatorics. However, you probably won't encounter any of: Real Analysis, Abstract Algebra, or Topology. These three areas are probably the main milestones of the undergraduate Math curriculum. You will probably have some electives though, so you'd most likely be able to take some of these if you are really interested in them. It's really hard to say at this point whether or not these would interest you.

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  • $\begingroup$ They certainly would, topology is a branch of mathematics that i was keen to understand for a long time now. Given the chance, i'd opt for these courses. $\endgroup$ – Hemispherr Aug 8 '16 at 20:39
  • $\begingroup$ That's great! Also, it's never too early to start. If you are interested in topology, Munkres' textbook is a great starting point. It's especially nice since the first chapter explains elementary set theory and logic. If you completely new to proofs, however, you might want to look through the book "Mathematical Proofs: A transition to Advanced Mathematics." $\endgroup$ – ervx Aug 8 '16 at 20:44
  • $\begingroup$ I should really make a list of the books recomended here, i never know where to start from. Thank you. It's kinda hard when you got no one to point you in a direction. $\endgroup$ – Hemispherr Aug 8 '16 at 20:47
  • $\begingroup$ Topology g.co/kgs/EpN7bs is it this one? $\endgroup$ – Hemispherr Aug 8 '16 at 20:53
  • $\begingroup$ Yes. And here's the other one: amazon.com/dp/0321797094/ref=pd_lpo_sbs_dp_ss_1/… $\endgroup$ – ervx Aug 8 '16 at 20:55
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You should talk to an advisor at your university. In a good computer science program it should be possible to take a lot of math courses, especially if you specialize in "theoretical" computer science.

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