Mathematics for Data Analysis

1

Vectors, matrices, and data geometry

Foundations of linear algebra for data analysis: vectors, matrices, and the geometry behind the numbers.

2

Similarity, distances, and linear transformations

Similarity metrics, metric spaces, and how linear transformations shape data.

Prerequisites: 1

3

Probability: axioms, events, conditioning

Probability fundamentals: from the three axioms to Bayes' theorem, with analytical applications.

Prerequisites: 1

4

Distributions, expectation, variance, and covariance

Random variables, probability distributions, and the three fundamental statistics.

Prerequisites: 1

5

Bayes' Theorem and Belief Updating

How Bayes' theorem formalizes learning from data in every analytical decision.

Prerequisites: 1

6

Hypothesis testing: logic, not ritual

The logic of hypothesis testing beyond the mechanics of the p-value.

Prerequisites: 1

7

Estimation, standard error, and confidence intervals

How to estimate parameters from data and quantify the uncertainty of the estimate.

Prerequisites: 1

8

Law of Large Numbers and Central Limit Theorem

The two fundamental theorems that justify all statistical inference.

Prerequisites: 1

9

Regression as geometry + intuitive optimization

Regression seen as geometric projection and minimization problem.

Prerequisites: 1

10

Final math problem set with guided solutions

Integrated exercises on the entire math module for data analysis.

Prerequisites: 1