Discrete Mathematics
2011-2012 - IMT3511 - 10 ECTS

Expected learning outcomes

Knowledge:

• The candidate possesses knowledge of important topics within abstract algebra.
• The candidate possesses knowlegde of important topics within combinatorics.
• The candidate possesses knowlegde of fundamental topics within graph theory.

Skills:

• The candidate knows relevant methods and terminology in discrete mathematics.
• The candidate is capable of applying his/her knowledge in different courses.

General competence:

• The candidate is capable of understanding and analyzing problems related to abstract algebra, combinatorics and graph theory.

Objectives:  
After the course, the students should acquire:

• Understanding of the most important topics of abstract algebra
• Understanding of the most important topics of combinatorics, including fundamentals of graph theory.

Topic(s)

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

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

Modeling computation:
* Finite-state machines, Turing machines

Abstract algebra:
* Groups, rings, fields

Teaching Methods

Lectures
Exercises
Tutoring

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

Oral exam, individually

Form(s) of Assessment (additional text)

Candidates will get an oral exam (max 30 minutes) with written preparation (max 60 minutes). Candidates will be given a number of assignments within the topics of the course and 60 minutes to prepare written answers. After this the candidates will be questioned about their answer in the oral part.

If the number of students is too high, then the oral exam is replaced by a 3 hour written exam. The students will be notified about this one month prior to the exam at the latest.

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 and dictionary

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.