Entry requirements

Algebra I

Learning outcomes

In order to pass the course (grade 3) the student should be able to

give an account of important concepts and definitions in propositional and predicate logic;

translate simple reasoning from natural language to propositional and first order predicate language, respectively, and exemplify and interpret important concepts in specific cases;

formulate important results and theorems covered by the course and describe the main features of the proofs of important theorems;

use the theory, methods and techniques of the course to solve problems;

present mathematical arguments to others.

Content

Language of propositional logic and of predicate logic. Functionally complete set of connectives. Formalisation of natural language. Induction over terms and formulas. Tautology, evaluation. Truth table. Disjunctive and conjunctive normal form. Structure for a given first order predicate language. Interpretation of a first order language in a structure. Model and counter model. Satisfiability. Axioms for a theory. Provability, natural deduction, consistency and independence. The concepts of soundness and completeness of a proof system. Incompleteness. Boolean algebra. Briefly about the difference between classical and intuitionistic logic.

Instruction

Lectures and problem solving sessions.

Assessment

Written or oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.