Course syllabus

Diskret matematik
Discrete Mathematics

FMAB75, 7,5 credits, G1 (First Cycle)

Valid for: 2020/21
Decided by: PLED F/Pi
Date of Decision: 2020-04-01

General Information

Elective for: BME4, C4-pv, D4-pv, E4, F1, Pi1
Language of instruction: The course will be given in English on demand

Aim

The aim of the course is to treat some basic parts of discrete mathematics, of importance in computer science, information theory, signal processing, physics and many other subjects in technology and science. The aim is also to develop the students' ability to solve problems and to assimilate mathematical text. The course should also provide general mathematical education.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must

Contents

Number theory: Divisibility. Prime numbers. The Euclidean algorithm. Chinese remainder theorem. Modular arithmetic.

Sets, functions and relations: Injective, surjective and bijective functions. Inverse function. Equivalence relations.

Combinatorics: The four cases of counting with or without repetition and with or without regard to order. Binomial coefficients. The principle of inclusion and exclusion. The method of generating functions.

Recursion: Recursion formulae and difference equations.

Rings and fields: Definition. Applications to coding.

Graph theory: Terminology and basic concepts. Eulerian and Hamiltonian graphs.

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written exam followed by an oral exam for those who pass the written exam.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Admission

Assumed prior knowledge: Elementary linear algebra and analysis (FMAA01/05 and FMAB20).
The number of participants is limited to: No
The course overlaps following course/s: MATB13, FMA091, FMA661, FMAA15, FMAA25

Reading list

Contact and other information

Course coordinator: Anders Holst, studierektor@math.lth.se
Course administrator: Studerandeexpeditionen, expedition@math.lth.se
Teacher: Anna Torstensson, annat@maths.lth.se
Course homepage: http://www.maths.lth.se/course/fmab75discrete/