(Created 2011-09-01.)
 PROBABILITY THEORY AND DISCRETE MATHEMATICS FMA661
Credits: 7,5. Grading scale: TH. Cycle: G2 (First Cycle). Main field: Technology. Language of instruction: The course will be given in Swedish. FMA661 overlaps following cours/es: FMA091. Compulsory for: IDA2. Course coordinator: Director of Studies, Anders Holst, Anders.Holst@math.lth.se, Mathematics. Recommended prerequisits: Basic courses in single variable calculus and linear algebra. Assessment: Written test comprising theory and problem solving. Home page: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

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.

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.

Skills and abilities
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.

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.

Literature
Vännman, K: Matematisk statistik. Studentlitteratur 2 uppl 2002. ISBN: 9789144016900.
Eriksson, K & Gavel, H: Diskret matematik och diskreta modeller. Studentlitteratur 2002. ISBN: 9789144024653.