Course Topics Overview

A tour of the semester: what each topic is, and why it is worth your time. One level up from the lecture schedule, one level down from the syllabus.

How the course works. Each topic arrives as a pre-recorded lecture you watch before class, with a short knowledge check due before the session starts. Class time is a ≤30-minute recap with cold-call Q&A, then a hands-on group activity — that is where the technique becomes something you can do rather than something you have heard of. Weekly theory homework exercises the foundations and prepares you for the three in-class quizzes. The layers are deliberate: lectures introduce, activities deepen, homework consolidates. If a topic below feels briefly treated in lecture, look for its depth in the activity and homework attached to it.

Orientation

What is Data Science? — Before any technique: what the field is, the taxonomy of questions data can answer (descriptive through causal), how real projects run, and what the job landscape looks like. Ends with the techniques map — a one-table index of this course that we revisit in the final session. Why: most failed analyses fail by answering the wrong kind of question; learning to classify the question is the cheapest skill with the highest payoff.

Foundations

Distances and similarity — What “alike” means, made precise: Euclidean, cosine, and friends, and how the choice changes every downstream conclusion. Linear-algebra essentials (vectors, norms, inner products) are refreshed here, where they are first needed. Why: half the techniques this semester — clustering, k-NN, recommenders, embeddings — are built directly on a distance; choose it badly and everything above it wobbles.

Finding structure without labels

k-means clustering — The workhorse grouping algorithm: an objective, an iteration, and surprisingly deep behavior from three lines of math. Why: your first end-to-end unsupervised method, and the cleanest place to learn how optimization-by-iteration thinks. The practice of clustering — choosing k, evaluating quality, coping with messy data — is taught where you will actually learn it: in this unit’s in-class activities and homework.

Hierarchical clustering — Groups nested inside groups, dendrograms, and when you genuinely do not know how many clusters exist. Why: many real taxonomies (customers, documents, genes) are trees, not flat partitions.

Mixture models and EM — Soft membership: every point belongs to every cluster, with probabilities. The EM algorithm that fits such models appears across machine learning. Why: your first fully probabilistic model — the bridge between “algorithms” and “statistical modeling,” with the probability refresher woven in where it pays off.

Learning from labels

Learning from data — What it means to learn: generalization, overfitting, bias and variance, and why performance on data you trained on proves nothing. Why: the conceptual contract every supervised method signs; the shortest lecture with the longest reach.

Decision trees and random forests — Interpretable if/then models, and then the ensemble trick — many noisy trees voting — that turns them into one of the most reliable predictors available. Why: random forests are frequently the strongest thing you can run in an afternoon on tabular data, and the bagging/ensembling idea recurs across modern ML.

k-NN and Naive Bayes — Predict by proximity; predict by probability. Plus the curse of dimensionality — why “nearby” stops meaning much in high dimensions. Why: two completely different inductive biases in one session, and the baselines any fancier model must beat.

Linear regression — Fitting lines, reading coefficients, least squares as projection. Why: still the most-used model in the world, the vocabulary of quantitative fields, and the foundation the causal sessions stand on.

Logistic regression and regularization — Classification done with regression machinery, and penalties that trade bias for variance on purpose. Why: logistic regression remains the default industrial classifier, and regularization is the general answer to “my model memorized the data.”

Representation

SVD and low-rank approximation — Every matrix hides a ranked list of its own most important patterns; SVD extracts them. Why: the single most useful matrix fact in data science — compression, de-noising, and the engine inside both PCA and the recommender session.

PCA and t-SNE — Projecting high-dimensional data down to the few directions that matter, and nonlinear maps for seeing cluster structure. Why: you cannot plot 300 dimensions; dimensionality reduction is how high-dimensional data becomes visible, and its caveats (what t-SNE plots do not mean) protect you from confident misreadings.

Cause and effect

Causal inference I: correlation, causation, counterfactuals — Why the regressions you just fit describe association, not causation; confounding, selection bias, and the counterfactual way of asking “what if we had acted differently?” Why: almost every decision your employer will ask about — pricing, treatment, policy — is a causal question, and prediction-grade evidence quietly fails it.

Causal inference II: causal graphs and estimating effects — Drawing assumptions as a graph, reading off what to control for, and estimating effects from observational data. Why: the practical toolkit — the difference between “our users who got the discount churned less” and “the discount reduced churn.”

Modern toolkits

Neural networks (two sessions) — From a single neuron to trained networks: gradient descent, backpropagation, and the practical craft of making training work. Why: the technology behind the current AI wave, taught from mechanisms up so it is understanding rather than incantation.

Natural language processing — Text as data: tokenization, embeddings, and the pipeline from raw language to features a model can use. Why: most of the world’s data is text; even in the LLM era, the representations here are how you reason about what language models do.

Recommender systems — Predicting preferences from sparse user–item data via matrix factorization — SVD’s ideas, deployed commercially. Why: recommenders drive a remarkable share of online commerce and content, and the session shows a “pure math” tool becoming a billion-dollar mechanism.

Graphs I & II — Networks: representing connected data, then centrality (who matters — closeness, betweenness, eigenvector, and PageRank as its web-scale cousin, met in the activity), and spectral partitioning as a route to community structure. Why: social networks, citations, supply chains, and the web are graphs; some of the most valuable questions — influence, fraud rings, bottlenecks — only exist once you model the connections.

Synthesis

The techniques map, revisited — After the last quiz, the course closes with a class exercise that returns to the map from week one: given a fresh problem, which question type is it, which technique fits, and why — this time answered from your own experience rather than the syllabus. Why: this is the interview question, and the job.

Optional modules

Recorded material beyond the required sequence, for projects and curiosity: time series analysis (forecasting, temporal structure), anomaly detection (finding the points that don’t belong), and CNN/RNN deep dives behind the neural network sessions. The reference appendices cover Python, Git, Pandas, and scikit-learn tooling.