This week-long course equips engineers, managers, and technical decisionmakers with an intuitive understanding of the mathematical and modeling foundations underlying modern AI and machine learning. We will focus on the essential structures shared by supervised, unsupervised, and generative models, demystifying how they are constructed, why they succeed or fail, and how to use principles from optimization and statistics to guide data collection and training.
Starting from accessible refreshers in calculus, linear algebra, and probability, we will build the vocabulary and mental models needed to evaluate AI methods, communicate with technical teams, and recognize when custom modeling is required. Hands-on case studies will build skill in translating messy, real-world problems into the abstract language of modern AI pipelines.
By the end of the week, participants will have a practical, under-the-hood grasp of AI foundations and modeling that enables faster adoption, smarter technical oversight, and more creative problem-solving with this emerging toolset.
Participants will leave the course understanding the mathematical, computational, and modeling foundations that underpin modern AI systems. They will gain fluency in the concepts and terminology needed to evaluate model capabilities, collaborate with or lead AI/ML teams, and design AI solutions. By practicing how to distill messy, application-driven questions into precise mathematical formulations, participants will strengthen their ability to scope AI projects, select appropriate methods and architectures, and identify valuable tools within the vast and rapidly-evolving landscape of AI technologies.
Course outline:
Day 1: Linear algebra and parametric modeling
Theme: Representing data and models with vectors, matrices, and transformations
Math concepts: Vector spaces, linear maps, dimensionality, features, latent variables
AI concepts: Multilayer perceptrons, embeddings, autoencoders
Activities: Visualizing layers and feature maps of a pre-trained neural network
Day 2: Calculus and optimization
Theme: Loss functions and gradient-based learning
Math concepts: Multivariate derivatives, chain rule, gradient descent, backpropagation
AI concepts: Training of machine learning models, stochastic gradient descent, Adam, learning curves, hyperparameters, differentiable programming
Activities: Training a neural network end-to-end
Day 3: Probability and generative modeling
Theme: Randomness as a modeling tool, learning and sampling from distributions
Math concepts: Probability distributions and densities, likelihoods, noise processes
AI concepts: Diffusion models, VAEs, score-based methods
Activities: Training a simple diffusion model
Day 4: Modeling for AI
Theme: Turning messy problems into structured mathematical ones
Math concepts: Constrained and unconstrained optimization, regularization, invariance/equivariance
AI concepts: Inductive bias, specialized architectures (CNNs, GNNs, attention), loss function design, evaluation metrics
Activities: Comparing model choices for a graph learning task
Day 5: Evaluating AI models
Theme: Generalization, reliability, and making informed decisions about AI performance
Math concepts: Basic statistics, bias-variance tradeoff, overfitting, validation, uncertainty
AI concepts: Dataset selection, adversarial/out-of-distribution examples, generalization
Activities: Comparing models under dataset shifts
