Basic course of discrete mathematics.
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Content and learning outcomes
The fundamental theorem of arithmetics, the Euclidian algorithm and a Diophantine equation. Modular arithmetics, Fermat's theorem and RSA. Sets, functions, relations, infinite sets and cardinal numbers. Proof by induction and recursions. Elementary group theory as the theorem of Lagrange and in particular the symmetrical group. Boolean algebra. Error correcting codes and in particular Hamming codes. Combinatorics, permutations, combinations, binomial and multinomial numbers, Stirling numbers, the sieve principle. Elementary graph theory, Eulerian and Hamiltonian graphs, matchings in bipartite graphs, planar 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.
Literature and preparations
Active participation in SF1624 Algebra and Geometry or SF1684 Algebra and Geometry.
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.
- 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.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- 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 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 SF1610