20933  MATHEMATICS FOR AI  PREPARATORY COURSE
Department of Computing Sciences
ISABELLA ZICCARDI
Suggested background knowledge
Mission & Content Summary
MISSION
CONTENT SUMMARY
Lecture 1 (28/08/23):
 Complex Numbers
 Vectors and Matrices
 Linear Systems
 Gaussian Elimination
Lecture 2 (29/08/23):
 Linear Combination of Vectors
 Vector Spaces
 Basis and Dimension of a Vector Space
Lecture 3 (30/08/23):
 Matrix Multiplication, Rank of a Matrix, Inverse Matrix, Trace of a Matrix
 Linear Maps and their Matrix Representation
 Kernel and Image of a Linear Map and the RankNullity Theorem
 Injective and Surjective Linear Maps
Lecture 4 (31/08/23):
 Invertible Linear Maps and Isomorphism
 Computing an Inverse Matrix with the Gaussian Elimination
 The Rank of a Matrix (equivalent definitions)
 Determinant, Computing the Determinant with the Gaussian Elimination
 Norms and Inner Products
 Eigenvalues and Eigenvectors
Lecture 5 (01/09/23):
 Change of Basis
 Diagonalize a Matrix
 Spectral Theorem
 Positive Definite and Semidefinite Matrices
 Singular Value Decomposition
Lecture 6 (04/09/23):
I forgot to record the first part of Lecture 6. You can find a scan of my notes attached.
 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
Lecture 7 (05/09/23):
 Discrete Random Variables
 Expectation, Linearity of Expectation
 Jensen's Inequality
 Variance and Standard Deviation
 Independent Random Variables
 Examples of Discrete Random Variables: Uniform, Bernoulli, Binomial, Poisson, Geometric
 Conditional Expectation
 Markov Inequality
 Covariance and properties of Covariance and Variance of two independent random variables
 Chebychev's Inequality
 Continuous Random Variables
 Examples of Continuous Random Variables: Uniform, Exponential
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
At the end of the course, the student will have 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
By the end of the course, students will know how to understand and solve basic exercises in linear algebra and probability theory.
Teaching methods
 Facetoface lectures
 Online lectures
 Exercises (exercises, database, software etc.)
DETAILS
Classes are taken in person with the possibility of being taken online. In addition, all lectures are recorded.
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
 Fabrizio Iozzi, Lecture Notes
 Sheldon Ross, A First Course in Probability
 Michael Mitzenmacher, Eli Upfal, Probability and Computing