IX1500 Discrete Mathematics 7.5 credits

Diskret matematik

  • Education cycle

    First cycle
  • Main field of study

    Mathematics
    Technology
  • Grading scale

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

Course offerings

Autumn 19 for programme students

Autumn 18 for programme students

Intended learning outcomes

General Objectives

After course completion the student should be able to:

  • formulate, analyze and solve problems in discrete mathematics significant to in the ICT sphere.
  • apply and develop discrete models with the aid of mathematical programming language.
  • review and comment a given solution to a problem.
  • comment a discrete model and propose improvements.
  • make presentations of solutions of a discrete problem.

Detailed Objectives

After course completion the student should be able to:

  • compute the number of possibilities with simple selection principles (order/recurrence).
  • compute permutations and combinations.
  • use set notations and Venn Diagrams.
  • use and refer to the Inclusion-Exclusion Principle.
  • refer to the Induction Axiom and apply it in simple recursion examples.
  • decide whether a function is surjective, injective or bijective.
  • characterize relations in important classes, e.g. equivalence relation and partial order.
  • decide whether an algebraic structure is a group, a ring or a field.
  • determine sub groups and ideal.
  • use Euler's and Fermat's theorems concerning element's order in a group.
  • use the Chinese Remainder Theorem in certain problems.
  • determine the minimum spanning tree.
  • determine shortest path in graphs.
  • set up graph models in problem solving (e.g. optimization and coloring).

Course main content

Combinatorics and setsInclusion-Exclusion Principleintegers, divisibilityinduction and recursionfunctions and relations Introduction to groups, rings and fieldsFermat's and Euler's theoremsChinese Remainder Theorem  Graph theoryisomorphism trees, walks and searchesEulerian graphs, Hamiltonian graphsplanar graphscoloring, chromatic number.

Disposition

The teaching method is problem oriented and computer aided. The education time is evenly distributed among the three main topics:

  • conceptual understanding and modelling
  • algorithms
  • conclusions and synthesis.

Eligibility

Entance qualifications: 

  • IX1303 - Algebra and Geometry
  • IX1304 - Calculus

Literature

Examination

  • INL1 - Problem Assignments, 4.0, grading scale: A, B, C, D, E, FX, F
  • TEN1 - Examination, 3.5, grading scale: A, B, C, D, E, FX, F

Requirements for final grade

  • Written exam (TEN1; 3, 5 credits)
  • Problem assignments (INL1; 4,0 credits)

Offered by

EECS/Communication

Examiner

Anders Västberg <vastberg@kth.se>

Version

Course syllabus valid from: Spring 2019.
Examination information valid from: Spring 2019.