Discrete Mathematics

5 credits

Syllabus, Bachelor's level, 1MA012

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MA012
Education cycle: First cycle
Main field(s) of study and in-depth level: Mathematics G1F
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

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 number theoretic concepts and definitions;

give an account of the concepts of binary relation, lattice and finite fields;

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;

solve simple number theoretic problems and problems about relations and lattices;

do computations with polynomials and solve systems of equations with coefficients in a finite field;

present mathematical arguments to others.

Content

Number theory: divisibility, congruences, the Chinese remainder theorem, Euler's phi-function, Fermat's little theorem, the RSA algorithm.

Binary relations: partial orderings and equivalence relations. Lattices. Finite fields. Vector spaces, systems of equations and polynomials over finite fields.

Instruction

Lectures and problem solving sessions.

Assessment

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