# Depth first search in mathematics

I have been studying mathematical stuff like combinatorics, probability, number theory etc from various books . Thier is one book on Enumerative Combinatorics by Richard p Stanley which consists of approx 300 pages and topics it contains are counting and posets ,I haven’t read it completely but similarly Thier are books for the other topics as well.
I just want to understand that do I really need to go in such depth in mathematics for being able to solve the problems in competitive programming and it is not only for combinatorics but for every mathematical topic. Last time in June long challenge I saw a problem which was on forbenius number I have never heard of such thing before so I want to know I do people recognise such things

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You don’t need too much mathematics for competitive programming. Even the combinatorics is basic in my opinion. Depends on where you get questions from though.

Neither had I heard of such a thing but I still solved it. You just need good observarions and use very standard algorithms to solve most ‘math heavy’ problems (At least the ones I’ve seen).
Also, knowing what a Frobenius number is wouldn’t even have helped you.

1. There was no use in knowing the largest number you cannot express as a sum or those numbers. You needed the number of such numbers.
2. There is no polynomial time algorithm for calculating the Frobenius number for arbitrary values (source: some Vsauce2 video). You’d have to solve this for the special case in the problem yourself.
3. Whoever told you reading up on Frobenius numbers will help has no idea what they are talking about. I imagine such people to just look at a problem, immediately Google and find some semi-related concept.

If you need a book for CP related maths, I would suggest Concrete Mathematics. I haven’t read it but have seen many people recommending it.

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