teaching

Python programming for scientists

An introduction to Python for scientific computing and data science. Variables, data structures, flow control, functions, NumPy, Matplotlib. Hands-on labs and programming challenges.

AIMS South Africa AIMS Senegal AIMS Rwanda

Experimental mathematics with SageMath

Computational problem-solving through experimentation. Discrete mathematics, number theory, linear algebra, graph theory, combinatorics. Building SageMath notebooks for mathematical exploration.

AIMS South Africa

Ordinary differential equations

Existence and uniqueness theorems, first and second order equations, systems of ODEs, stability analysis, Laplace transforms. Applications to population dynamics and epidemiological models.

AIMS Senegal AIMS Rwanda

Topological data analysis

Persistent homology, simplicial complexes, Vietoris-Rips filtrations, Mapper algorithm, stability theorems. Implementation with GUDHI and Ripser in Python. Applications to health and financial data.

AIMS South Africa AIMS Senegal

Numerical methods with Python

Root finding, interpolation, numerical integration, linear systems, ODE solvers. Error analysis and convergence. All methods implemented from scratch and with NumPy/SciPy, with Jupyter notebooks.

AIMS Senegal AIMS Rwanda

Undergraduate

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

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

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

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

• Introduction to Data Science — Data wrangling, visualization, exploratory analysis (Python/R)
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• Machine Learning Foundations — Supervised & unsupervised learning, model evaluation, bias-variance
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• Programming for Scientists — Python, R, NumPy, Pandas, Matplotlib, scientific computing
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• Database Systems & SQL — Relational databases, queries, normalization, data pipelines
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• Data pre-processing — Missing data, outliers, encoding, feature engineering, text preprocessing, pipelines
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• Julia programming — Types, multiple dispatch, DataFrames, visualization, performance, scientific computing, ML
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Graduate / advanced

• Topological Data Analysis (TDA) — Persistent homology, simplicial complexes, Mapper, stability theorems
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• Geometric Deep Learning — Graph neural networks, manifold learning, equivariant architectures
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• Deep Reinforcement Learning — MDPs, policy gradients, DQN, actor-critic, multi-agent RL
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• Deep Learning — CNNs, RNNs, transformers, attention, generative models (GANs, VAEs, diffusion)
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• Natural Language Processing — Embeddings, sequence models, LLMs, fine-tuning, RAG
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• MLOps & Reproducible Research — Experiment tracking, model deployment, Docker, CI/CD for ML
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• Generative AI — Transformers, GPT, prompt engineering, fine-tuning (LoRA), RAG, diffusion models, agents
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• Data analysis for health specialists — Pandas, epidemiological measures, hypothesis testing, regression, ML for clinical prediction, geospatial health data
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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.