Advanced topics in artificial intelligence I (CK0261)

The course overviews the elementary mathematical foundations and tools necessary to understand, define and implement standard machine learning and artificial intelligence methods.
  1. Geometry: Linear algebra and analytical geometry;
  2. Calculus: Differentiation and vector fields;
  3. (Probability, series and sequences): Probability measures, distributions, sequences and series.
Stuff from the past: Previous version of the course are available for 2017.1, 2016.2 and 2015.2



Instructor ♞: Francesco Corona (FC), francesco döt corona ät ufc döt br

Physical location ♜: Tuesdays and Thursdays 16:00-18:00, Bloco 915, Sala 1064 A ([Was: B]).
Internet location ♖: Here! Or, here (CK0146) for mambojumbo related to administration.

Evaluation ✍: Each student gets to give four lectures to the class as and participates to six lectures as opponent. The combination of two (2) given lecture plus three (3) opposed lectures will be treated as a single partial evaluation (AP). The final score is given by the average of the two APs. If needed a final evaluation (AF) will be arranged.

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Lectures and schedule

  1. About this course

    A About this course (FC)
    • About this course

  2. Linear algebra, geometry and matrix decompositions

    A Linear algebra (I, II and II)
    1. A+B versus C+D+E (March 07 and March 12)
    2. C+D versus A+B+E (March 14 and March 21)
    3. A+E versus B+C+D (March 26 and April 02)
    1. Systems of linear equations and matrices (Ch. 2: Intro, 2.1, 2.2 and 2.3)
    2. Vector spaces and basis (Ch. 2: 2.4, 2.5 and 2.6)
    3. Linear mappings and affine spaces (Ch. 2: Ch. 2.7 and 2.8)
    B Analytical geometry (I, II and III)
    1. B+C versus A+D+E (April 09 and April 11)
    2. D+E versus A+B+C (April 16 and April 30)
    3. A+C versus B+D+E (May 02)
    1. Normed vector spaces, length, distances and angles (Ch. 3: Intro, 3.1, 3.2, 3.3, 3.4 and 3.5)
    2. Orthogonal projections and rotations (Ch. 3: 3.6 and 3.7)
    3. Rotations (Ch. 3: 3.8)
    C Matrix decompositions (I and II)
    1. B+D versus A+C+E (May 21 and May 23)
    2. C+E versus A+B+D (May 28 and May 30)
    1. Deteminant and traces, eigenvalues and eigenvectors, Cholesky decomposition (Ch. 4: Intro, 4.1, 4.2 and 4.3)
    2. Eigendecomposition and singular value decomposition, diagonalisation (Ch 4: 4.4, 4.5 and 4.6)

  3. Vector calculus I and II

    A Scalar and vector differentiation (I and II)
    1. A+D versus B+C+E (June 04 and June 06)
    2. B+E versus A+C+D (June 11 and June 13)
    1. Scalar and vector differentiation, vector fields (Ch. 5: Intro, 5.1, 5.2, 5.3 and 5.4)
    2. Gradient of matrices and automatic differentiation (Ch. 5: 5.5, 5.6, 5.7 and 5.8)

  4. Other topics

    B Sequences and series (FC)
    • Convergence, sandwich theorem and ratio tests for sequences
    • Geometric, harmonic, power and other common series
    A Probability measures and distributions (FC)
    • Probability spaces and random variables
    • Sequences and series
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