Discrete Mathematics

2018/2019

Prerequisite/Recommended prerequisite for participation in the module

The module builds on knowledge obtained in Linear Algebra.

Content, progress and pedagogy of the module

Learning objectives

Knowledge

  • Must understand set theory: sets, relations, functions, partial orderings, equivalence relations
  • Must understand fundamental number theory: modular arithmetic, Euclidean algorithm, the Chinese remainder theorem, Fermat’s little theorem and prime factorisation
  • Countability of the rational numbers
  • Must understand recursive/iterative algorithms
  • Must understand time complexity: asymptotic notation and Big-O notation
  • Must know about logarithm and exponential functions with base 2
  • Must know about combinatorics and the binomial formula
  • Must know about recursive functions and recurrence relations
  • Must know about proof techniques: weak and strong induction and proof by contradiction, contraposition and constructive
  • Must understand logic: propositional logics and quantifiers
  • Must understand graph theory: directed and undirected graphs, path, simple path and trees
  • Graph algorithms: search in graphs and shortest path

Skills

  • Must be able to construct proofs (using the proof techniques of the course) for results within the course
  • Must be able for formulate in writing mathematical results related to the course

Competences

  • Must have competencies in the use of concepts and techniques of discrete mathematics, including in connection with algorithms

Type of instruction

The teaching in Discrete Mathematics is a combination of sessions with lectures, exercises, and mini-projects.

Exam

Exams

Name of examDiscrete Mathematics
Type of exam
Written or oral exam
ECTS5
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentAs stated in the Joint Programme Regulations
http:/​/​www.tech.aau.dk/​uddannelse/​Studieadministration/​

Facts about the module

Danish titleDiskret matematik
Module codeESNITCOB2K3
Module typeCourse
Duration1 semester
SemesterSpring
ECTS5
Empty-place SchemeYes
Location of the lectureCampus Copenhagen
Responsible for the module

Organisation

Study BoardStudy Board of Electronics and IT
FacultyTechnical Faculty of IT and Design