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.
SF1679 Discrete Mathematics 7.5 credits
Information per course offering
Information for Spring 2025 Start 14 Jan 2025 programme students
- Course location
KTH Campus
- Duration
- 14 Jan 2025 - 16 Mar 2025
- Periods
- P3 (7.5 hp)
- Pace of study
50%
- Application code
60177
- 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 SF1679 (Autumn 2019–)Content and learning outcomes
Course contents
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
Equipment
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 - 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
Opportunity to raise an approved grade via renewed examination
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.