2
$\begingroup$

So, I am a high school student and my original plan was to major in Computer Science and Minor in mathematics. I have recently discovered an intense interest in mathematics and am contemplating a double major in Computer Science and Mathematics. I am currently taking Algebra 2 and plan to take pre-calculus over the summer so that I can be on track to take all the math courses my school offers. Besides that I have been approved to self-study discrete mathematics next year and am currently taking an online introductory course in Combinatorics. I'm pretty sure I will be finished with the Combinatorics course within the next month or so, which leads me to my question: What should I study next that would help complement knowledge in Combinatorics? Am I studying things in a non-beneficial order?

$\endgroup$
  • 1
    $\begingroup$ This is a bit short for an answer, but I recommend you take a look at "Introductory Mathematics: Algebra and Analysis" by Geoff Smith. $\endgroup$ – Harambe May 5 '18 at 3:29
  • $\begingroup$ Will do. I'm always looking for a good study book. $\endgroup$ – CaptainAmerica16 May 5 '18 at 3:31
  • $\begingroup$ It's one of my favourite maths books because it taught me that maths isn't just computations - it starts by teaching you some basic logic, then proof techniques, and finally a few different specific mathematical objects. $\endgroup$ – Harambe May 5 '18 at 3:33
  • $\begingroup$ I'm actually glad to hear that. I've only discovered recently that there is a theoretical side to mathematics outside of the computational things I'd been taught in school. That's what drew me in so heavily. $\endgroup$ – CaptainAmerica16 May 5 '18 at 3:35
  • $\begingroup$ You might be interested in the book "An Introduction to the Analysis of Algorithms" by Sedgewick and Flajolet. This book would extend your knowledge of combinatorics, with applications to computer science. $\endgroup$ – awkward May 5 '18 at 15:39
3
$\begingroup$

This is how I went through my Stats&Probability course in A-level (Class of 2017, H2 Math + H2 FMath, Singapore) which I think has a really nice flow to it:

  1. Intro to combinatorics
  2. Intro to probability
  3. Discrete RV (Intro, Binom, Geo, Poisson)
  4. Continuous RV (Intro, Normal, Uniform, Expo)
  5. Poisson process (Poisson+Expo)
  6. Hypothesis testing + Confidence Intervals (Z, T, Chi-squared)

You might want to master from the pure math side:

Before (3): Series & Sequence; Summation techniques; Recurrence Relations (1st&2nd order linear)

Before (4): Single-variable Calculus

Good to have but not really needed: Intro Linear Algebra

$\endgroup$
  • $\begingroup$ Thank you for this! It looks like I've already started a logical flow. So, I'll probably look into studying probability this summer after I finish Combinatorics. $\endgroup$ – CaptainAmerica16 May 5 '18 at 3:25
  • $\begingroup$ I decided to just ask this here since it it's related to my question: Would it be beneficial to study Set Theory at some point? The use of its notation has become prevalent in my Combinatorial studies and, while I understand it in relation to Combinatorics, I don't really understand what "Set Theory" is itself. Do you think it may be beyond my understanding based on what I've studied so far? $\endgroup$ – CaptainAmerica16 May 7 '18 at 0:44
  • $\begingroup$ @CaptainAmerica16 Intro is enough imo. I didn't formally study set theory either. I just learn how to read the notation and use it without too much inaccuracy haha $\endgroup$ – Karn Watcharasupat May 7 '18 at 6:23
  • $\begingroup$ Lol, ok. I may just have it as an aside, although it does sound a bit cool. $\endgroup$ – CaptainAmerica16 May 7 '18 at 12:57
1
$\begingroup$

First of all make sure that you got combinatorics on 100% because combinatorics itself is widely used in programming and is essential to learn probability which is also widely used in programming. So the best choice after combinatorics is definately probability. Probability is usualluy the topic that is taught after combinatorics in most textbooks. After probability, it would be really handful to learn Sequences and analysis. And if you are interested in neural networks Jump in Calculus.

$\endgroup$
0
$\begingroup$

If you want to augment what you have learned in combinatorics then I would recommend:

  1. Graph theory
  2. Number theory
  3. Probability
  4. More advanced combinatorics.

For the last suggestion, I would recommend the book “Enumerative Combinatorics volume 1” by Richard P. Stanley. You can get it for free on the web.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.