Entry requirements

Basic Course in Mathematics.

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 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.

Content

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.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course. Moreover, compulsory assignments during the course.