Please note that this course is not open to bachelor-students. Instead bachelor students can take the SWU Bachelor course: Foundations of Computing - Discrete Mathematics BSc.

Læringsmål:

After the course the student should be able to:

* Describe and apply formal definitions

* Conduct and explain basic formal proofs

* Work with regular languages and finite and infinite state machines

* Use models of computation and specification

* Use combinatorial reasoning

* Assess probabilities of events

* Use basic modular arithmetic

Fagligt indhold:

The course is an introduction to discrete mathematics as a foundation to work within the fields of computer science, information technologies, and software development. The course develops the necessary terminology and conceptual tools needed for later courses. This includes:

* formal reasoning, induction, set theory, relations and functions

* models of computation, such as finite state machines and grammars

* basic graph theory, language theory

* combinatorics, probability and number theory

The course aims at providing a basic understanding of the mathematical foundations of computer science.

Central terms and concepts: Logic, specifications, sets and sequences, functions, sums, induction and recursion, number theory, permutations and combinations, discrete probability, relations, graphs, trees, finite state machines, grammars and theory of computation.

Læringsaktiviteter:

14 ugers undervisning bestående af forelæsninger og øvelser

The course consists of 14 weeks of lectures and exercises.
• The lectures will provide the theory and examples of formal definitions, formal proofs, regular languages, state machines, models of computations, combinatorics, discrete probabilities and modular arithmetic (c.f. ILO).
• The weekly exercises are written exercises that train the students in working with and apply the theory introduced in the lectures. The problems that the students solve in the weekly exercises will prepare the students for the written exam, as the exam will contain problems of similar nature.

NB!! Course restriction I!!
Please note that there is a course restriction between this course and the SDT course Modelling and Design.
If you have already taken Modeling and Design you need to register for the course Foundations of Computing - Algorithms and Data Structures.

Obligatoriske aktivititer:

Der er ingen obligatoriske aktiviteter. Vær venlig KUN at ændre denne tekst når der er obligatoriske aktiviteter./
There are no mandatory activities. Please, change this text ONLY when there are mandatory activities.

4 hours written exam with no aids.
There is no access to advanced electronic tools such as computers, e-Readers or tablets.
Only old-fashioned pocket calculators and standard tools for writing on paper are allowed (pen, pencil, eraser, etc.).
Only use of pen is allowed for the final exam hand-in.

Form of re-exam is the same as the ordinairy exam.

Litteratur udover forskningsartikler:

Susanna S. Epp, Discrete Mathematics with Applications, International Edition, 4 edition, Brooks Cole, ISBN 978-0495826163