# Discrete Mathematics, MSc SD (Autumn 2022)

#### Official course description:

##### Course info

##### Programme

##### Staff

##### Course semester

##### Exam

##### Abstract

The course is an introduction to discrete mathematics as a foundation to work within the fields of computer science, information technologies, and software development.##### Description

Mathematics and logic are our key tools for both understanding computers and for modelling the world around us. Abstractions from mathematics pervade computer science, and to truly excel at both programming computers and model aspects of the real world in computers, one must understand the core vocabulary of mathematics provided in this course.

The course aims at providing the basics of the mathematical foundations of computer science.

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

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.

##### Formal prerequisites

There are no formal prerequisites. However, we expect that you remember how to do basic high school algebra (solving linear and quadratic equations; simplifying arithmetic expressions; working with fractions, exponentiations, and logarithms; inequalities). The course starts with a*very*quick refresher on these topics in the first week. But we recommend the

*Algebra 1*course on khanacademy.org if you need a more thorough refresher.

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.

##### Intended learning outcomes

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 state machines
- Use models of computation and specification
- Use combinatorial reasoning
- Assess probabilities of events
- Use basic modular arithmetic

##### Learning activities

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.

##### Mandatory activities

There are twelve weekly mandatory activities: six hand-ins that have to be handed in through a peer-grading system, and six corresponding peer-feedback sessions where each student has to give written feedback to three hand-ins of their peers. To be admitted to the exam, the student has to complete and pass five hand-ins and five peer-feedback sessions.If a student does not pass a mandatory activity, they will receive a second chance one week after they have received the feedback for the original activity.

The purpose of the mandatory activities is to practice both to write in a mathematically precise manner and to critically read mathematical arguments.

The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

##### Course literature

Susanna S. Epp, *Discrete Mathematics with Applications*, Metric Edition, BROOKS/COLE Cengage Learning, 5th edition, ISBN: 9780357114087

##### Student Activity Budget

Estimated distribution of learning activities for the typical student- Preparation for lectures and exercises: 20%
- Lectures: 15%
- Exercises: 25%
- Assignments: 20%
- Exam with preparation: 20%

##### Ordinary exam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A33: Written exam on premises on paper with restrictions

**Exam duration:**

4 hours

**Aids allowed for the exam:**

Calculator

##### reexam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A33: Written exam on premises on paper with restrictions

**Exam duration:**

4 hours

**Aids allowed for the exam:**

Calculator