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SF1679 Discrete Mathematics 7.5 credits

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


For course offering

Spring 2025 Start 14 Jan 2025 programme students

Application code


Headings with content from the Course syllabus SF1679 (Autumn 2019–) are denoted with an asterisk ( )

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.

Literature and preparations

Specific prerequisites

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

Recommended prerequisites

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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.

Grading scale

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


  • TEN1 - Exam, 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

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Opportunity to raise an approved grade via renewed examination

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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.

Offered by

Main field of study


Education cycle

First cycle

Add-on studies

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