20933  MATHEMATICS FOR AI  PREPARATORY COURSE
Department of Computing Sciences
Course taught in English
Go to class group/s: 1
Course Director:
ISABELLA ZICCARDI
ISABELLA ZICCARDI
Suggested background knowledge
No background is required, other than basic mathematical knowledge.
Mission & Content Summary
MISSION
This preparatory course introduces the basis of linear algebra and probability theory.
In the first part of the course, we will cover some basic topics of linear algebra, including vectors, matrices, linear systems, vector spaces, linear maps, eigenvalues and eigenvectors, the spectral theorem, and the singular value decomposition.
In the second part of the course, we will cover basic topics of probability theory, introducing discrete and continuous random variables, expectation, variance, Markov's Inequality and Chebyshev's Inequality.
CONTENT SUMMARY
 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
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
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.
APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
Understand the fundamental concepts of linear algebra and probability theory, and solve basic exercises.
Teaching methods
 Lectures
 Practical Exercises
DETAILS
Classes are taken online, with a set of prerecorded video lectures.
Assessment methods
Continuous assessment  Partial exams  General exam  


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ATTENDING AND NOT ATTENDING STUDENTS
The course has no exams.
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
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
Last change 24/07/2024 10:20