SF1662 Discrete Mathematics 7.5 credits

Diskret matematik

Please note

The information on this page is based on a course syllabus that is not yet valid.

  • Education cycle

    First cycle
  • Main field of study

    Technology
  • Grading scale

    A, B, C, D, E, FX, F

Course offerings

Spring 19 for programme students

Spring 20 for programme students

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 main content

  • 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.

Eligibility

Basic requirements. 

Literature

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

Examination

  • TEN1 - Examination, 7.5, grading scale: A, B, C, D, E, FX, F

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.

Offered by

SCI/Mathematics

Examiner

Maurice Duits <duits@kth.se>

Version

Course syllabus valid from: Autumn 2019.
Examination information valid from: Autumn 2011.