- 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
This course will be discontinued.
Decision to discontinue this course:
Decision made by the Faculty Board for the School of Engineering Sciences PA-2025-0019
Date of decision: 2025-09-25
Last semester the course is given: autumn 2025
Last semester with an examination in the course: autumn 2027
Background: The course is being discontinued and will be replaced with a new course. All affected programs are informed.
Information per course offering
Course offerings are missing for current or upcoming semesters.
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 2026–)Headings with content from the Course syllabus SF1662 (Autumn 2026–) are denoted with an asterisk ( )
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
You can find information about course literature either in the course memo for the course offering or in the course room in Canvas.
Examination and completion
Grading scale
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.
If the course is discontinued, students may request to be examined during the following two academic years.
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.
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
Technology
Education cycle
First cycle