The course Mathematical Logic focuses on the formalization of human reasoning by introducing students to the fundamental principles of logic, both in theory and practice. It begins with an introduction to the key objects of logic, emphasizing the distinction between syntax, which concerns the formal structure of statements, and semantics, which deals with their meaning. The study then advances to propositional logic, covering the formation and manipulation of propositions, logical connectives, substitution rules, truth tables, tautologies, contradictions, and normal forms such as conjunctive and disjunctive normal forms. Students also learn methods of resolution used in automated reasoning, including refutation and the propositional resolution rule. The course then extends to predicate logic, where learners explore terms, predicates, quantifiers, and the differentiation between free and bound variables, as well as the interpretation and satisfaction of logical formulas within structures. A solid understanding of basic mathematics and Boolean algebra is recommended. The evaluation is based on continuous assessment (40%) and a final exam (60%). Key references include Mathematical Logic by S.C. Kleene and Elements of Mathematical Logic by J.L. Krivine.
- Teach the student how to model problems using graphs
- Solve problems through algorithms like short path search, maximum flow.
- Understand the basic notions, knowledge and skills offered by graph theory.
This module introduces students to the fundamental principles and techniques of numerical methods essential for solving mathematical and scientific problems computationally. It begins with an overview of numerical analysis and scientific computing, including floating-point arithmetic, rounding errors, and stability concepts. Students then study direct methods for solving linear systems, such as Gaussian elimination and LU factorization, followed by iterative methods like Jacobi, Gauss-Seidel, and successive over-relaxation (SOR) techniques, along with their convergence analysis. The course also covers eigenvalue and eigenvector computations, including the power method, and concludes with a detailed study of matrix analysis, encompassing vector spaces, matrix operations, linear transformations, determinants, traces, and matrix norms. Evaluation is based on both continuous assessment (40%) and a final examination (60%).