SF1662 Discrete Mathematics 7.5 credits

Diskret matematik

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Course information

Content and learning outcomes

Course contents *

  • 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.

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.

Course Disposition

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Literature and preparations

Specific prerequisites *

Basic requirements. 

Recommended prerequisites

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Equipment

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Literature

Announced no later than 4 weeks before the start of the course on the course web page.

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.

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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Examiner

Maurice Duits

Further information

Course web

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 SF1662

Offered by

SCI/Mathematics

Main field of study *

Technology

Education cycle *

First cycle

Add-on studies

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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.