In order to pass the course (grade 3) the student should be able to
give an account of important concepts and definitions in the area of the course;
exemplify and interpret important concepts in specific cases;
formulate important results and theorems covered by the course;
describe the main features of the proofs of important theorems;
express problems from relevant areas of applications in a mathematical form suitable for further analysis;
use the theory, methods and techniques of the course to solve mathematical problems;
present mathematical arguments to others.
Elementary logic and set theory. Functions and relations. Equivalence relations. Natural numbers and integers: induction, divisibility, primes, Euclid's algorithm, congruences, representation of numbers in different bases. Diophantine equations. Rational and irrational numbers. Denumerability. Polynomials over R and C: factorisation, Euclid's algorithm, multiple roots, rational roots of polynomials with integer coefficients.
Lectures and problem solving sessions.
Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.