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: - Mul

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.