Expected learning outcomes

After the course, the students should acquire:

1. understanding of the most important topics of abstract algebra
2. understanding of the most important topics of combinatorics, including fundamentals of graph theory.

Topic(s)

General concepts:
* Logic, proofs, sets, algorithms, combinatorics, discrete probabilities

Graphs:
* Connectivity, shortest path, coloring, (minimal) spanning trees

Modeling computation:
* Finite-state machines, Turing machines

Abstract algebra:
* Groups, rings, fields

Coding theory:
* Hamming distance, error correcting and decoding, BCH codes

Teaching Methods

Lectures
Exercises

Teaching Methods (additional text)

The course is given as a self reading course, where there is time for the students during lectures to raise questions on the theory and/or the exercises.

Form(s) of Assessment

Written exam, 3 hours

Grading Scale

Alphabetical Scale, A(best) – F (fail)

External/internal examiner

Evaluated by the lecturer.

Re-sit examination

The whole subject must be repeated.

Examination support

Ordinary calculator

Coursework Requirements

None.

Teaching Materials

- Kenneth H. Rosen:
Discrete Mathematics and its Applications, 6th ed.
McGraw-Hill International Edition (2007).
- William J. Gilbert and W. Keith Nicholson
Modern Algebra with Applications, 2nd ed.
Wiley (2004).

Additional information

In case there will be less than 5 students that will apply for the course, it will be at the discretion of Studieprogramansvarlig whether the course will be offered or not an if yes, in which form.