Mathematics for Artificial Intelligence I

The course comprises three modules and covers areas of mathematics relevant to artificial intelligence. Module 1: Discrete mathematics and logic (2.5 credits) The module covers combinatorics, sets and relations, propositional logic, real and complex numbers. Key concepts include permutations, combinations, propositions, implication, equivalence, intersection, union, relation, and the concept of numbers. Module 2: Analysis (5 credits) The module covers function theory and differential and integral calculus in one and several dimensions. Key concepts include functions, injective and surjective functions, limits and continuity, derivatives, and integrals. Relevant methods include limit calculations, differentiation and integration techniques. Module 3: Linear algebra with computations (7.5 credits) The module covers the following key concepts: vectors, systems of linear equations, linear transformations, matrices, determinants, vector spaces, bases and change of bases, eigenvalues and eigenvectors, inner products, orthogonal sets, and quadratic forms. Relevant methods include vector computations, Gaussian elimination, matrix factorisations, determinant and eigenvalue calculations, the least squares method, and Gram-Schmidt orthogonalisation.