Computational Foundations of Artificial Intelligence

Course Policies

Course Format

Students are expected to listen to pre-recorded lectures before coming to class. The class hours will be utilized for a recap and answering any questions.

Course Topics

  • Linear Algebra
    • Vector Space
    • Basis and Dimension
    • Direct Sum
    • Linear Maps, Kernel, Range
    • Matrices
    • Invertible Maps and Matrices
    • Transpose
    • Change of Basis
    • Rank of a Matrix
    • Determinant
    • Eigenvalues
    • Characteristic Polynomial
    • Trace of Matrix
    • Diagonalization; Triangular Matrices
    • Metric Spaces
    • Normed Spaces; p-norms
    • Norms on $\mathbb{R}^d$ are Equivalent
    • Convex Set Induces a Norm
    • Spaces of continuous and differentiable functions
    • Inner Product and Hilbert Spaces
    • Orthogonal Vectors and Basis
    • Orthogonal Matrices
    • Symmetric Matrices
    • Spectral Theorem for Symmetric Matrices
    • Positive Definite Matrices
    • Variational Characterization of Eigenvalues
    • Singular Value Decomposition
    • Matric Norms; Rank-K Approximation;
    • Pseudo-Inverse of a Matrix
  • Calculus
    • Sequences and Convergence
    • Continuity
    • Sequence of Functions, Pointwise and Uniform Convergence
    • Differentiation on $\mathbb{R}$
    • Riemann Integral on $\mathbb{R}$
    • Fundamental Theorem of Calculus on $\mathbb{R}$
    • Power Series
    • Taylor Series
    • Differentiation on $\mathbb{R}^n$; partial derivatives
    • Differentiation on $\mathbb{R}^n$; total derivative
    • Differentiation on $\mathbb{R}^n$; directional derivative
    • Differentiation on $\mathbb{R}^n$; higher-order derivatives
    • Minima, maxima, saddle
    • Matrix Calculus
  • Probability Theory
  • Probability spaces and axioms
  • Discrete distributions and density functions
    • Cumulative distribution function
    • Random variables
    • Conditional probabilities
    • Bayes Theorem
    • Independence
    • Expectation (discrete case)
    • Variance, covariance, correlation (discrete case)
    • Expectation and covariance (general case)
    • Markov and Chebyshev’s Inequality
    • Example distributions; binomial, Poisson, multivariate normal
    • Convergence of Random Variables
    • Borel-Cantelli
    • Law of Large Numbers; Central Limit Theorem
    • Concentration Inequalities
  • Glivenko-Cantelli Theorem
  • Joint distributions
  • Marginal distributions
  • Conditional distributions
  • Conditional expectation

Grading

  • In-class multiple-choice quiz: 10%
  • Mid-term exam: 35%
  • Final exam: 35%

  • Concept Demo: 20%

    • Each team of two or three students must build one interactive HTML and JavaScript demo that teaches one concept from the course. Examples include orthogonal projection, eigenvalue decomposition, the union bound, and convergence in probability. The Concept Demo Guidelines page gives the full requirements, grading rubric, and a worked example.
    • The demo is team work in teams of two or three students. Students may use generative AI tools, but AI use is not required. The team remains responsible for the mathematics, code, explanation, and final submission, and every member must be able to explain the whole demo. Each submission must include the AI use and verification record and the contribution statement described in the guidelines.
    • Demos are due within one week after the lecture that covers the concept. A late demo loses 10 percent of the demo grade for each day it is late, and a demo more than ten days late receives no credit.
    • The 2026 concept sign up sheet will be posted here before sign ups open. Do not use a sign up sheet from an earlier course offering.
    • Accepted demos will be published on the course website, credited to the student.

    Homeworks (optional)

    • Optional assignment will be provided.
    • These are for self-study, they do not need to be turned in.
    • The assignments will not be graded.

Grading Rubric

Range Grade
90+ 4.0
60 $<$ score $\leq$ 90 3.5
25 $<$ score $\leq$ 60 3.0
0 $<$ score $\leq$ 25 0.0

Plagiarism

This course has adopted the Chegg and Similar Sites policy. Submission of student work (e.g., assignments and/or exam solutions) based on those found on Chegg, Brainly, Quizlet, and other similar websites will result in an Academic Dishonesty Report (ADR) and an automatic failing grade of zero (0.0) for the course. The ADR for students personally posting questions from assignments or exams to these sites will request additional sanctions.