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# SF1688 Discrete Mathematics 6.0 credits

## Information per course offering

Termin

### Information forAutumn 2024 Start 26 Aug 2024 programme students

Course location

KTH Campus

Duration
26 Aug 2024 - 27 Oct 2024
Periods
P1 (6.0 hp)
Pace of study

50%

Application code

51201

Form of study

Normal Daytime

Language of instruction

Swedish

Course memo
Course memo is not published
Number of places

Places are not limited

Target group
No information inserted
Planned modular schedule
[object Object]

### Contact

Examiner
No information inserted
Course coordinator
No information inserted
Teachers
No information inserted

### Course syllabus as PDF

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

Course syllabus SF1688 (Autumn 2019–)
Headings with content from the Course syllabus SF1688 (Autumn 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

Linear recursion with constant coefficients. The Master theorem.

Graphs. Euler circuits, Hamilton cycles. Trees. Graph coloring. Planar graphs. Euler’s polyhedron formula, Kuratowski's theorem. Bipartite graphs. Hall's marriage theorem. Augmenting alternating paths. Transversals.

Integer arithmetic. Modular arithmetic. Euler’s ɸ- and Möbius’ μ-function. Euler’s theorem and Fermat’s little theorem.

Permutations. Cycle notation. Conjugated permutations. Even and odd permutations.

Basic group theory. Order of group elements and group. Cyclic groups. The symmetric group. Subgroups, cosets. Lagrange’s theorem. Group actions on sets. Burnside’s lemma.

Rings and fields. Factorization of polynomials. Irreducible polynomials. Finite fields.

Error correcting linear binary codes. RSA cryptosystem. Primality tests.

### Intended learning outcomes

After the course the student should be able to

• formulate basic theorems and definitions of important concepts with discrete mathematics,
• apply theorems and methods in discrete mathematics,

in order to

• gain basic knowledge of discrete mathematics and elementary graph theory,
• acquire better problem solving abilities in elementary combinatorics,
• gain knowledge of how to use some abstract algebraic structures.

## Literature and preparations

### Specific prerequisites

Completed basic courses SF1671 Mathematics, Basic course, with Discrete Mathematics and SF1624 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 - Exam, 6.0 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.

Technology

First cycle