Course 2024-2025 a.y.

• Complex Numbers
• Vectors
• Linear Systems and Matrices
• Vector Spaces

• Linear Maps and their Matrix Representation

• Invertible Linear Maps and Isomorphism

• Norms and Inner Products
• Eigenvalues and Eigenvectors

• Change of Basis
• Spectral Theorem
• Positive Definite and Semidefinite Matrices
• Experiments, Probability, Events, Probability in Experiments with equally likely outcomes

• Permutations, Sampling with Replacement, Sampling without Replacement
• Binomial Coefficient, Multinomial Coefficient
• Probability Space, Axioms of Probability
• Conditional Probability and Independence of Events
• Bayes' Theorem and Law of Total Probability
• Discrete Random Variables
• Expectation, Linearity of Expectation
• Variance and Standard Deviation
• Independent Random Variables
• Markov Inequality
• Chebychev's Inequality
• Continuous Random Variables

Demonstrate basic knowledge of linear algebra and probability theory.
In particular, the linear algebra part of the course covers the following topics: vectors, vector spaces, matrices, linear maps, eigenvalues and eigenvectors, spectral theorem, and singular value decomposition. The probability part of the course covers the following topics: probability spaces, random variables, Markov Inequality and Chebychef inequality.

Understand the fundamental concepts of linear algebra and probability theory, and solve basic exercises.

• Lectures
• Practical Exercises

Classes are taken online, with a set of prerecorded video lectures.

The course has no exams.

Suggested textbooks:

• Sheldon Axler, Linear Algebra Done Right
• Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, Mathematics for Machine Learning
• Gilbert Strang, Introduction to Linear Algebra
• Sheldon Ross, A First Course in Probability
• Michael Mitzenmacher, Eli Upfal, Probability and Computing