How to memorize math theory

[u/Inevitable_Virus_403]

Im currently a first year student studying comp sci and im taking discrete math the issue is unlike any other faculty i have to learn actual theory behind math like whats C(n,k) selection and explain it with words and formulas.Ive got about 12 pages filled with 50 or 60 questions which if memorized gives me a passing grade and ive got 2 days to do it keep in mind the professor wants the questions answered exactly by his pdf. Ive youve had the same issues how should i go about tackling the problem and passing matu

[u/Etainn]

In school I was always to lazy too memorize stuff. That is why I loved mathematics, because here you could just understand it once and would never have to remember stupid formulas.

After university I would say that medium-term memorization techniques are not a good way to pass a math's test.

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[u/PuzzlingDad]

I would go back to the beginning of your notes where each formula is derived. I have to assume you started with learning the fundamental counting principle (if I have 4 pants and 3 shirts, then I can make 4×3=12 outfits).

Then from there you probably learned the ways to permute (arrange, order) a number of items, such as having 5 books, you have 5! = 5×4×3×2×1 = 120 ways to place them on a shelf. You have 5 choices for the first book you place, then 4, etc. It's an extension of the fundamental counting principle.

Next, let's say that you have some items that are identical, like 3 red books, 2 green books and 4 blue books. Then it's the way to arrange 9 books (9!) but then divided by the ways to arrange the 3 red books (3!), and the 2 green books (2!) and the 4 blue books (4!) because they would look identical and the 9! would overcount the permutations.

From there you get into having n items and needing to pick k of them, such as 10 students and you want to pick 6 of them to be a team. That's the C(n,k) formula which would start with arranging the n students (n!) taking the first k of them as part of the team and leaving the remaining n-k not as part of the team. But then divided by k! and (n-k)! because once they are categorized as on the team or not, their order in that group doesn't matter. Hence we divide by those factors. 

C(n,k) = n! / [k! (n-k)!]

tl;dr study each concept and formula in order, to understand how each one builds on the other and is derived from the earlier concepts.

[u/Inevitable_Virus_403 → u/PuzzlingDad]

thank you for this answer ill try it step by step

[u/BootyliciousURD]

In my experience, the best way to memorize something is to use it a bunch in more involved problems. And there's too much math for you to reasonably memorize everything and not forget it. Better to take good notes and keep them accessible so you can refer to them in order to quickly refresh your memory.

[u/StructuredChess]

First you have to understand it then you use it 100 times to solve problems.