Math Topics

Teaches operations like addition, subtraction, multiplication, and division

The first appearance of variables and graphs

First appearance of proofs

Discovery is disputed between two famous mathematicians

While its predecessor studied derivatives and integrals of y = f(x), it studies z = f(x, y)

Vital for information theory; studies elements of Rⁿ

Study of how things change with one independent variable

First true introduction to analysis and set theory

Rigorously analyzes local theory, holomorphic functions, residue theorem, and more

Study of how things change with multiple independent variables

Rigorously studies functions as objects in infinite dimensional vector space

Rigorously defines "size," "area," "volume," "probability," and more.

Rigorous study of operations and their rules, covering symmetry, algebraic structure, invariants, and more

Studies properties of space that are preserved under continuous deformations (i.e. stretching, bending twisting)

Study of integers and their properties (asking questions like: which numbers are prime? how do numbers divide each other?)

Study of algebraic structures (sets equipped with operations) that satisfy specific axioms

Discrete and structural, focusing on networks and relationships rather than change or continuous space

Basis of all other mathematics; determines properties such as countability, cartesian products, unions, and intersections.

A way to generalize vectors and matrices so differentiation and integration can make sense independent of coordinates

A "container" of the above, studies smooth manifolds, the basis of general relativity

Study of angles, periodicity, and geometric relationships (especially in circles and triangles)

Study of how functions can be decomposed into basic oscillatory components (extension of the above into infinite-dimensional analysis)

Studies distinct, separate objects, rather than continuous quantities. Foundational to computer science, algorithms, and combinatorial structure.

Formal study of uncertainty, randomness, and stochastic behavior

Study of learning from data: differs from the above by focusing on inference, figuring out unknowns from finite, noisy observations.