### Choose semester and course offering

Choose semester and course offering to see information from the correct course syllabus and course offering.

## Content and learning outcomes

### Course contents

The fundamental theorem of arithmetic, the Euclidian algorithm and a Diophantine equation. Modular arithmetic, the Chinese remainder theorem, Fermat’s little theorem and RSA. Equivalence relations, partial orders, induction and recursion. Functions, infinite sets and cardinality. Elementary group theory, the theorem of Langrange, the symmetrical group and the lemma of Burnside. Error correcting codes, Hamming codes. Generating functions and partitions of integers. Combinatorics, multinomial numbers, Stirling numbers, the sieve principle and the Möbius inversion formula. Elementary graph theory, planar graphs, coloring problems, matchings in bipartite 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

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,
• practice in conducting stringent mathematical reasoning and construction of mathematical proofs.

### Course Disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Completed basic course SF1672 Linear Algebra or SF1624 Algebra and Geometry.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

No information inserted

## 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, 7,5 hp, betygsskala: 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 web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF1679

SCI/Mathematics

Technology

First cycle