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, 23 April 2014
- 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. Error correcting codes. Graphs, trees and graphcolouring.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.