Pure Mathematics
Real Analysis
Sequences, series, continuity, differentiation, and Riemann integration
Linear Algebra
Vector spaces, linear maps, eigenvalues, and canonical forms
Discrete Mathematics
Combinatorics, graph theory, logic, and proof techniques
Abstract Algebra
Groups, rings, fields, and Galois theory
General Topology
Open sets, continuity, compactness, and connectedness
Number Theory
Divisibility, primes, congruences, and quadratic reciprocity
L2-L3
First and second order equations, systems, and stability
Complex Analysis
Holomorphic functions, Cauchy's theorem, and residues
Measure & Integration
Lebesgue measure, Lp spaces, and Radon-Nikodym theorem
Riemannian Geometry
Connections, curvature, geodesics, and comparison theorems
Algebraic Topology
Fundamental group, homology, cohomology, and Poincaré duality
Differential Topology
Smooth manifolds, transversality, Morse theory, and degree
Functional Analysis
Banach and Hilbert spaces, spectral theory, and duality
Category Theory
Functors, adjunctions, Yoneda lemma, and derived categories
Fixed Point Theory
Banach, Brouwer, Schauder, and Caristi theorems with applications
Advanced Point-set Topology
Quasi-metrics, sober spaces, Scott topology, and locales
Applied Mathematics & Statistics
Scientific Programming
Python, NumPy, Pandas, Matplotlib, and R fundamentals
Probability Theory
Probability spaces, distributions, law of large numbers, and CLT
Database Systems
Relational algebra, SQL, normalization, transactions, and NoSQL
Numerical Analysis
Root finding, interpolation, numerical integration, and ODEs
Mathematical Statistics
Estimation, hypothesis testing, regression, and nonparametric methods
Mathematical Modelling
Population dynamics, epidemiology, diffusion, and chaos
Operations Research
Linear programming, simplex, graphs, and network flows
Heat, wave, and Laplace equations with Fourier and Sobolev methods
Convex Optimization
Convex sets, duality, gradient descent, and interior-point methods
Stochastic Processes
Markov chains, martingales, Brownian motion, and Itô calculus
Time Series Analysis
ARIMA, GARCH, spectral analysis, and state-space models
Bayesian Statistics
Conjugate families, MCMC, hierarchical models, and variational inference
Dynamical Systems & Chaos
Stability, bifurcations, Lyapunov exponents, and strange attractors
Quantitative Finance
Black-Scholes, stochastic calculus, portfolio optimization, and risk
Data Science & ML
Intro to Data Science
Data wrangling, visualization, EDA, and introductory ML
Machine Learning
Regression, classification, SVM, ensembles, and Bayesian ML
M1-M2
Embeddings, attention, transformers, LLMs, and RAG pipelines
Deep Learning
CNNs, RNNs, transformers, GANs, VAEs, and diffusion models
Topological Data Analysis
Persistent homology, simplicial complexes, Mapper, and stability
Deep RL
MDPs, DQN, policy gradients, actor-critic, and multi-agent RL
Geometric Deep Learning
Graph neural networks, equivariant architectures, and TDA