teaching

Undergraduate

• General Topology — Open/closed sets, continuity, compactness, connectedness, product & quotient spaces
• Real Analysis I & II — Sequences, series, limits, continuity, differentiation, Riemann integration, metric spaces
• Abstract Algebra I & II — Groups, rings, fields, homomorphisms, quotient structures, Galois theory
• Linear Algebra — Vector spaces, linear maps, eigenvalues, inner product spaces, canonical forms
• Complex Analysis — Analytic functions, Cauchy's theorem, residues, conformal mappings
• Differential Equations (ODE) — First & second order equations, systems, Laplace transforms, stability
• Number Theory — Divisibility, congruences, primes, quadratic reciprocity, arithmetic functions
• Discrete Mathematics — Combinatorics, graph theory, logic, proof techniques

Graduate

• Algebraic Topology — Fundamental group, covering spaces, singular homology, cohomology, exact sequences
• Differential Topology — Smooth manifolds, tangent bundles, transversality, Morse theory
• Point-Set Topology (Advanced) — Quasi-metric spaces, asymmetric topology, T₀-spaces, bitopological spaces
• Fixed Point Theory — Banach contraction principle, Brouwer & Schauder theorems, generalized metric spaces
• Functional Analysis — Banach & Hilbert spaces, bounded operators, spectral theory, Hahn-Banach theorem
• Measure Theory & Integration — σ-algebras, Lebesgue measure, Lp spaces, Radon-Nikodym theorem
• Riemannian Geometry — Connections, curvature, geodesics, comparison theorems
• Category Theory — Functors, natural transformations, limits, adjunctions, Yoneda lemma

Undergraduate

• Probability Theory — Sample spaces, random variables, distributions, expectation, law of large numbers
• Mathematical Statistics — Estimation, hypothesis testing, confidence intervals, regression
• Numerical Analysis — Root finding, interpolation, numerical integration, error analysis
• Partial Differential Equations — Heat, wave & Laplace equations, separation of variables, Fourier series
• Operations Research — Linear programming, optimization, simplex method, duality, network flows
• Mathematical Modelling — Formulation, dimensional analysis, dynamical systems, epidemiological models

Graduate

• Stochastic Processes — Markov chains, Poisson processes, Brownian motion, martingales
• Convex Optimization — Convex sets & functions, duality, gradient descent, interior-point methods
• Dynamical Systems & Chaos — Stability, bifurcation, Lyapunov exponents, strange attractors
• Quantitative Finance — Black-Scholes, stochastic calculus, portfolio optimization, risk measures
• Time Series Analysis — ARIMA, GARCH, spectral analysis, state-space models, forecasting
• Bayesian Statistics — Prior/posterior, MCMC, hierarchical models, Bayesian inference

Undergraduate / introductory

• Introduction to Data Science — Data wrangling, visualization, exploratory analysis (Python/R)
• Machine Learning Foundations — Supervised & unsupervised learning, model evaluation, bias-variance
• Programming for Scientists — Python, R, NumPy, Pandas, Matplotlib, scientific computing
• Database Systems & SQL — Relational databases, queries, normalization, data pipelines

Graduate / advanced

• Topological Data Analysis (TDA) — Persistent homology, simplicial complexes, Mapper, stability theorems
• Geometric Deep Learning — Graph neural networks, manifold learning, equivariant architectures
• Deep Reinforcement Learning — MDPs, policy gradients, DQN, actor-critic, multi-agent RL
• Deep Learning — CNNs, RNNs, transformers, attention, generative models (GANs, VAEs, diffusion)
• Natural Language Processing — Embeddings, sequence models, LLMs, fine-tuning, RAG
• MLOps & Reproducible Research — Experiment tracking, model deployment, Docker, CI/CD for ML

Introduction to generative AI & LLMs

3 days — Prompt engineering, fine-tuning, Retrieval-Augmented Generation (RAG), deployment. Hands-on with OpenAI API and open-source models.

Data science for decision-makers

3 days — Non-technical training for managers and executives: understanding AI, identifying use cases, steering data projects, evaluating ROI.

MLOps in practice

4 days — From notebook to production: Docker, CI/CD pipelines, model monitoring, experiment tracking (MLflow), versioning (DVC).

Reinforcement learning: from theory to practice

5 days — MDPs, Q-learning, DQN, policy gradients, actor-critic methods. Applications in resource allocation, game playing, and optimization.

Geometric Deep Learning

4 days — Graph neural networks, learning on manifolds, equivariant architectures. Applications in molecular science, social networks, and point clouds.

Applied Bayesian statistics

4 days — Bayesian modelling, MCMC, Stan/PyMC, hierarchical models. Applications in health, finance, and social science.

Python for data science

5 days — From zero to analysis: Pandas, data visualization, cleaning, exploratory analysis, and first ML models with scikit-learn.

R for statistical analysis

4 days — Tidyverse, ggplot2, statistical modelling, reproducible reports with R Markdown. Companion to The Shape of Data.

Scientific writing with LaTeX, Overleaf & Prism

3 days — Writing articles, theses, and dissertations with LaTeX. Collaborative editing on Overleaf and AI-assisted scientific writing with OpenAI Prism.