Elementary and Middle School Math

Arithmetic: Basic operations like addition, subtraction, multiplication, and division.
Fractions and Decimals: Working with parts of wholes, ratios, and simple percentages.
Pre-Algebra: Introduction to negative numbers, basic formulas, and simple unknown variables.

High School Math

Algebra 1: Solving equations with variables, graph plotting, and linear functions.
Geometry: Studying shapes, angles, area, perimeter, and proofs.
Algebra 2: Expanding into quadratic functions, polynomials, and logarithms.
Pre-Calculus & Trigonometry: Studying triangles, wave functions, and vectors to prepare for calculus.
Calculus (Introductory): Introduction to limits, derivatives, and rates of change.

College and Undergraduate Math

Calculus I–III: Single-variable and multi-variable calculus, exploring continuous change and spatial integration.
Linear Algebra: Matrix theory, vector spaces, and linear transformations.
Differential Equations: Equations involving rates of change used in physics and engineering.
Discrete Mathematics: Logic, set theory, graph theory, and combinatorics for computer science.
Intro to Proofs: Learning how to rigorously prove mathematical statements rather than just compute answers.

Graduate Level and Advanced Research

Real and Complex Analysis: Rigorous study of the real number line and complex functions.
Abstract Algebra: Study of algebraic structures like groups, rings, and fields.
Topology and Differential Geometry: Study of space, shapes, and properties preserved through continuous deformations.