Discrete Mathematics, MSc SD
AbstractThe course is an introduction to discrete mathematics as a foundation to work within the fields of computer science, information technologies, and software development.
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 prerequisitesBasic arithmetic.
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
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 activitiesThere are six mandatory assignments that have to be handed in though a peer-grading system. For each assignment it is mandatory that the student gives peer-feedback at a satisfactory level.
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.
Susanna S. Epp, Discrete Mathematics with Applications, Metric Edition, BROOKS/COLE Cengage Learning, 5th edition, ISBN: 9780357114087
Student Activity BudgetEstimated 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 examExam type:
A: Written exam on premises, External (7-point scale)
A33: Written exam on premises on paper with restrictions