5019.23 - Discrete Mathematics

5019.23

Discrete Mathematics

7.5

Upper secondary school with mathematics at the level B

To give the students an introduction to discrete mathematics with respect to applications in computer science with the purpose to give a good theoretical foundation for further work both with computer sciences and mathematical sciences.

Basic mathematical methods, logic, counting problems, relations, functions, order, l'Hospital´s rule, trees, graphs, usage of the software Maple, and usage of the software LaTeX for writing projects.

Lectures, exercise sessions and independent/individual work.

By the end of the course the student is expected to be able to: • Determine the correctness of mathematical reasoning using logical inference rules. • Formulate simple mathematical arguments, in particular by use of mathematical induction and proof by contradiction. • Carry out calculations and use algorithms within the subject matter of the course, especially ◦ Perform formal logical operations on mathematical assertions ◦ Recognize different types of relations and make use of them ◦ Analyze combinatorial problems using counting arguments as well as algebraic manipulations ◦ Recognize different simple types of graphs and apply certain algorithms associated with graphs ◦ Set up recursive definitions and solve recurrences. Factorize polynomials and compute with complex numbers • Specify the growth rate of a function and to make use of O-notation. And to be able to use l'Hospitals rule in connection with this • Relate the mathematical content of the course to problems in computer science. • Use the software Maple to illustrate and to solve certain problems in both mathematics and in computer science - especially as part of the projects • Use the software LaTeX for writing project

One compulsory activety. The grade is based on written projects and multiple choice test during the course. Reexamination is 3 hours written exam with usual helping aids.

External

7-

Kolman, Busby, and Ross: Discrete Mathematical Structures, 6th Ed., Pearson Education. Chapters 1-7, and weeklies and notes.

Mortan Janusarson Thomsen