# Course syllabus - Discrete Mathematics 7.5 credits

### Diskret matematik

 Course code: MMA122 Valid from: Autumn semester13 Autumn semester17 Level of education: First cycle Subject: Mathematics Main Field(s) of Study: Mathematics/Applied Mathematics, In-Depth Level: G1N (First cycle, has only upper-secondary level entry requirements), School: UKK Ratification date: 2013-02-01

## Objectives

The aim of the course is to introduce the basic concepts and methods in discrete mathematics, and to give improved proficiency in mathematical modeling, problem solving and reasoning, as a basis for further studies in mathematics and computer science.

## Learning outcomes

At the end of the course the student is expected to be able to
- explain, in a way adapted to the mathematical level of the reader/listener, the concepts presented in this course,
- describe some application of each of the subareas of the course content,
- use properly the set algebraic operations and set up models to solve problems by set algebraic means, and describe the relation between propositional logic and boolean algebra
- formulate and interpret statements written in the notation of predicate logic,
- give an account of the concepts of prime numbers and divisors, and apply Euclid's algorithm to problems such as linear modular equations,
- prove theorems by induction, and solve problems that rely on recursion,
- describe and apply the fundamental methods and principles of combinatorics and probability theory,
- use basic graph theoretic terminology and set up models to solve problems by graph theoretic means,
- construct and interpret automata, and describe the relation between automata and regular languages.

## Course content

Set theory. Arithmetic. Recursion and induction. Combinatorics and probability. Graph theory. Logic. Automata and formal languages.

## Teaching methods

Lectures and group work sessions.

## Specific entry requirements

Mathematics C or Mathematics 3c.

## Examination

Oral examination (TEN1), 4.5 credits, marks 3, 4 or 5
Exercise, 3 credits (ÖVN2), marks 3, 4 or 5

A student who has a certificate from MDH regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2016/0601). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

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## Enviromental aspects

This course does not include any specific environmental considerations.

Course literature is preliminary until 3 weeks before the course starts. Literature may be valid over several terms.

Valid from: Autumn semester13

Decision date: 2013-07-18

Last update: 2013-07-18

## Books

Diskret matematik och diskreta modeller.

ISBN: 91-44-02465-7 : 493:00 LIBRIS-ID: 8604379

ix, [1], 355 s.

NOTERA: Valfri utgåva kan användas