Explore groups, rings, and fields to understand the algebraic structures underlying modern mathematics and cryptography.
Learn to write rigorous mathematical proofs using direct proof, contradiction, induction, and formal logic.
Master linear programming, convex optimization, and numerical methods for solving optimization problems in engineering and economics.
Explore continuity, compactness, and connectedness in abstract topological and metric spaces.
Master fundamental calculus concepts including limits, continuity, derivatives, and their applications to real-world problems.
Study graphs, networks, and their applications to computer science, social networks, and optimization problems.
Study prime numbers, modular arithmetic, and their applications to modern encryption and cybersecurity.
Extend calculus to functions of several variables, covering partial derivatives, multiple integrals, and vector calculus.
Learn vectors, matrices, eigenvalues, and transformations with a focus on applications in data science and AI.
Deep dive into probability axioms, random variables, expectation, and limit theorems for rigorous statistical reasoning.
Rigorous study of sequences, series, limits, continuity, differentiation, and integration on the real line.
Master probability distributions, hypothesis testing, regression analysis, and statistical inference for data-driven decision making.
Study logic, set theory, graph theory, and combinatorics essential for algorithm design and software development.
Explore integration techniques, infinite series, and applications of definite integrals to area, volume, and more.
Solve ordinary and partial differential equations and apply them to model physical, biological, and engineering systems.