Hello Folks,
I hope this message finds you well. I am currently participating in several programming contests and, in the process, have noticed that I often find myself facing challenges that seem rooted in mathematical concepts. Given that I have been professionally employed for two years now, I regret to admit that my engagement with mathematical exercises has been somewhat limited during this period. Nevertheless, I remain passionate about Competitive Programming (CP) and aspire to enhance my performance in upcoming contests. In light of this, I wanted to seek your perspectives on the importance of mathematics in this field.
During my high school years, I had a strong foundational knowledge of mathematics, having achieved an 'A' grade in my final examination. I had also pursued and excelled in Further Mathematics independently. While revisiting my Further Mathematics textbook (high school subject but actually content are somewhat similar to maths when I was in college (I did Electrical Engineering)) recently, I contemplated whether revisiting the topics from this advanced syllabus might be beneficial for my current endeavors.
For your reference, here is the syllabus from our Further Mathematics — Pure Mathematics Paper 1:
- Roots of Polynomial Equations
- Rational Functions and Graphs
- Summation of Series
- Matrices
- Polar Coordinates
- Vectors
- Proof by Induction
Second part:
- Hyperbolic Functions
- Advanced Matrices
- Differentiation
- Integration
- Complex Numbers
- Differential Equations
- Continued Differential Equations
In the context of CP, I am keen to understand which of these topics, or possibly others not listed here, you believe would be most beneficial to focus on. Additionally, if you have any specific recommendations on how to most effectively revise and apply these topics, I would greatly appreciate your insights.
Thank you for taking the time to read my message. I look forward to hearing your advice.
Personally I think whole second part is unnecessary for you, since these topics could only be useful for advanced algorithms which you won't need unless you want to reach a very high level in CP, and it'll probably take a while. Polar coordinates aren't useful at all in CP, i guess, it's just olympiad geometry, even in geometry problems in contests you will never find this
Graphs (i assume by graphs you mean theory about them and various techniques for solving graphs), vectors(for geometry), proof by induction and summation of series could be useful, although last two may only be required in a non-trivial combinatorics problem, and last one could probably only be used to solve problems like "compute a certain number", although if you say you studied further mathematics your amount of knowledge on this may be enough on these topics until a certain level, although these are not the most useful math topics in CP; for your level, you probably need smth easier.
This is just my opinion, i may misunderstand something or be wrong, although I mostly study math and believe my view on maths in CP is somewhat accurate. Hope that I helped you with choosing topics to revise!
Thanks for these, in summary, shall I just focus on vectors, mathematical induction, summation of series from above — sorry, I wanna ask how does induction could relate to our problem, can I have an example? what other topics you would think that is also important?
By the way, I did have study all of these in the past, but it has been many years ago, I still rememeber how intesne when I tried to solving the probelm in Further Maths, but now I nearly forgot most of them.
Thank you for your suggestion, I really appreciate it!
I've seen a problem that you need polar coordinate stuff so I wouldn't say it's useless, it's only VERY VERY VERY VERY rare, rarer than matroid intersection problems. To be specific, other than a couple of problems where things are given in polar coordinates and you can treat it as somewhat 2d coordinates directly, I've seen https://en.wikipedia.org/wiki/Great-circle_distance being asked, which is more spherical than polar but still kinda fits the bill.
You should add combinatorics,number theory and recurrences