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# SF1610 Discrete Mathematics 7.5 credits

Basic course of discrete mathematics.

## Information per course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

Termin

### Course syllabus as PDF

Please note: all information from the Course syllabus is available on this page in an accessible format.

Course syllabus SF1610 (Spring 2020–)
Headings with content from the Course syllabus SF1610 (Spring 2020–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

The fundamental theorem of arithmetics, the Euclidian algorithm and a Diophantine equation. Modular arithmetics, Fermat's theorem and RSA. Sets, functions, relations, infinite sets and cardinal numbers. Proof by induction and recursions. Elementary group theory as the theorem of Lagrange and in particular the symmetrical group. Boolean algebra. Error correcting codes and in particular Hamming codes. Combinatorics, permutations, combinations, binomial and multinomial numbers, Stirling numbers, the sieve principle. Elementary graph theory, Eulerian and Hamiltonian graphs, matchings in bipartite graphs, planar graphs.

### Intended learning outcomes

After the course the student should be able to

• use concepts. theorems and methods to solve and present solutions to problems within the parts of discrete mathematics described by the course content,
• read and comprehend mathematical text.

## Literature and preparations

### Specific prerequisites

Active participation in SF1624 Algebra and Geometry or SF1684 Algebra and Geometry.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

Announced no later than 4 weeks before the start of the course on the course web page

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

### Main field of study

Mathematics, Technology

First cycle