Probability Theory and Discrete Mathematics
Sannolikhetsteori och diskret matematik

FMSF40, 7.5 credits, G2 (First Cycle)

Valid for: 2024/25
Faculty: Faculty of Engineering LTH
Decided by: PLED I
Date of Decision: 2024-04-16
Effective: 2024-05-08

General Information

Depth of study relative to the degree requirements: First cycle, in-depth level of the course cannot be classified
Mandatory for: IDA2, IEA2
Language of instruction: The course will be given in Swedish

Aim

The course has two main aims:

1) to present the basics of discrete mathematics, with particular emphasis on concepts which are important in computer science

2) to give a general introduction to probability theory.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

• have good knowledge of how to carry through a proof in an (informal but) logically correct way
• in practical situations be able to identify and do computations on different combinatorial ways of selection
• have good knowledge of and understanding of functions and relations, as well as related concepts
• have a good understanding of the basic concepts in probability theory: independent events, probability, discrete and continuous distributions, expectation and variance
• have knowledge about how to compute, from a specific distribution, the probability of an event and the expectation and variance, and be able to show capability to carry out the computations essentially correctly.

Competences and skills
For a passing grade the student must

• be able to show good computational ability within the scope of the course
• in connection with problem solving be able to demonstrate an ability to integrate methods from different parts of the course
• be able to demonstrate an ability to explain a mathematical reasoning in a well-structured and logically clear way.

Judgement and approach
For a passing grade the student must

Contents

Sets. Logic. Proof techniques. Combinatorics. Recursion. Relations. Functions.

The probability axioms. Conditional probability. Independent events. Stochastic variables. Expectation and variance. The normal distribution, the binomial distribution and other important distributions. Functions of stochastic variables.

Examination details

Grading scale: TH - (U, 3, 4, 5) - (Fail, Three, Four, Five)
Assessment: Written test comprising theory and problem solving.

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.

Modules
Code: 0117. Name: Probability Theory and Discrete Mathematics.
Credits: 7.5. Grading scale: TH - (U, 3, 4, 5). Assessment: Written exam

Admission

Assumed prior knowledge: Basic courses in single variable calculus and linear algebra.
The number of participants is limited to: No
Kursen överlappar följande kurser: FMSF32 FMSF20 FMSF30 FMSF35 FMSF45 FMSF50 FMSF55 FMSF70 FMSF75 FMA661 FMAA25 FMSF80

Reading list

• Vännman K, Jonsson A: Matematisk statistik - 3:e upplagan. Studentlitteratur, 2020, ISBN: 9789144133249.
• Eriksson, K & Gavel, H: Diskret matematik och diskreta modeller. Studentlitteratur, 2013, ISBN: 9789144089997.

Contact

Director of studies: Johan Lindström, studierektor@matstat.lu.se
Course administrator: Susann Nordqvist, expedition@matstat.lu.se
Course homepage: https://maths.lu.se/utbildning/hoegskoleingenjoersutbildning/