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.