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Could you share a type of math with 1 or 2 concepts that would be good for computer science or solving problems in general. Reference to something not too diff

Could you share a type of math with 1 or 2 concepts that would be good for computer science or solving problems in general. Reference to something not too difficult, but a "good to know" kind of thing. For example, something from upper division math. Let's say in undergraduate I would say: Calculus I - understand what is derivative. Calculus II - understand what is an integral. Math is broad, so maybe 1 or 2 takeaways from some topics in upper division math that I might find useful.

jules 5y ago
It's hard to capture an entire lecture series in one sentence, but one way you might categorise subjects by the type of problems they allow you to solve: - Multiple linear equations over the rationals/reals => linear algebra - Solve equations over the integers / integers mod p / factor numbers => number theory - Solve polynomial equations / factor polynomials => algebra - (Partial) differential equations => (partial) differential equations - Approximate solutions to various equations over the reals => numerical analysis - Counting the sizes of various finite sets => combinatorics - Integrate wild functions => measure theory - Formal understanding of real numbers => real analysis - General framework for differential equations => functional analysis - General framework for continuous functions and limits => point-set topology - Prove that two elastic shapes are different => algebraic topology - Prove that a knot in a circular piece of string cannot be untied without cutting the string => knot theory - Determine optimum strategy in a game with incomplete information => game theory - Describe very big sets / prove that certain things can't be proved => set theory - etc.
- jzer0cool 5y ago
  Appreciate the reply jules! Thank you for this list. Just picking the brains here for those who have Phds in this fields and sometimes providing retrospect helps us more junior's in math.
kovac 5y ago
If you had to pick one, I'd say the single most important high level math topic that'd be useful for computer science is Graph theory. There are so many applications of graphs in computer science. The thing about math is that regardless of which field you work in the treatment is the same. You start by stating a set of axioms. Based on these axioms you set up definitions and then prove lemmas, corrolaries and theorems. This approach isn't really necessary or directly useful for computer science though. But it is very beautiful. For example, if you truly want to appreciate, in it's full force, why a player playing a fair game against a casino will always eventually lose (theorem called Gambler's ruin) you can study stochastic processes with full rigour (this is also a very useful area). But that full rigour isn't necessary to not blow your savings on games of chance :)

jules 5y ago

It's hard to capture an entire lecture series in one sentence, but one way you might categorise subjects by the type of problems they allow you to solve: - Multiple linear equations over the rationals/reals => linear algebra - Solve equations over the integers / integers mod p / factor numbers => number theory - Solve polynomial equations / factor polynomials => algebra - (Partial) differential equations => (partial) differential equations - Approximate solutions to various equations over the reals => numerical analysis - Counting the sizes of various finite sets => combinatorics - Integrate wild functions => measure theory - Formal understanding of real numbers => real analysis - General framework for differential equations => functional analysis - General framework for continuous functions and limits => point-set topology - Prove that two elastic shapes are different => algebraic topology - Prove that a knot in a circular piece of string cannot be untied without cutting the string => knot theory - Determine optimum strategy in a game with incomplete information => game theory - Describe very big sets / prove that certain things can't be proved => set theory - etc.

jzer0cool 5y ago
Appreciate the reply jules! Thank you for this list. Just picking the brains here for those who have Phds in this fields and sometimes providing retrospect helps us more junior's in math.

kovac 5y ago

If you had to pick one, I'd say the single most important high level math topic that'd be useful for computer science is Graph theory. There are so many applications of graphs in computer science. The thing about math is that regardless of which field you work in the treatment is the same. You start by stating a set of axioms. Based on these axioms you set up definitions and then prove lemmas, corrolaries and theorems. This approach isn't really necessary or directly useful for computer science though. But it is very beautiful. For example, if you truly want to appreciate, in it's full force, why a player playing a fair game against a casino will always eventually lose (theorem called Gambler's ruin) you can study stochastic processes with full rigour (this is also a very useful area). But that full rigour isn't necessary to not blow your savings on games of chance :)