- The Euclidian algorithm and Diophantine equations. The Euclidean algorithm for polynomials and Gaussian integers. The Fundamental theorem of arithmetic. Modular arithmetic. Fermat's theorem and RSA.
- Recursion and proof by induction. Sets, functions, infinite sets and cardinal numbers. Elementary boolean algebra.
- Combinatorics and probabilities. The addition and multiplication principles, the pigeonhole principle, binomial and multinomial numbers, Stirling numbers, the sieve principle.
- Elementary group theory, cyclic groups, subgroups and cosets, the theorem of Lagrange. Permutations, the symmetric group.
- Elementary graph theory, Eulerian and Hamiltonian graphs, trees, planar graphs, vertex colorings, matchings in bipartite graphs.
SF1662 Discrete Mathematics 7.5 credits

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.
Information for Autumn 2025 Start 27 Oct 2025 programme students
- Course location
KTH Campus
- Duration
- 27 Oct 2025 - 13 Mar 2026
- Periods
Autumn 2025: P2 (4.0 hp)
Spring 2026: P3 (3.5 hp)
- Pace of study
25%
- Application code
51107
- 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]
- Schedule
- Schedule is not published
Contact
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus SF1662 (Autumn 2019–)Content and learning outcomes
Course contents
Intended learning outcomes
Efter the course the student is expected to be able
- Apply definitions, theorems and methods, to solve, och present solutions to, problems within areas of Discrete Mathematics that are part of the course content.
- To read and understand mathematical texts.
Literature and preparations
Specific prerequisites
Basic requirements.
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.
Grading scale
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.
Examiner
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.