5019.16 - Discrete mathematics
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, usage of the software LaTeX for writing projects, historical and teaching aspects of discrete mathematics.
Learning and teaching approaches
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 ◦ Work with recursive definitions and solve recurrences. Factorize polynomials and compute with complex numbers • Be familiar with the concept of 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 • Set a chosen mathematical topic from the course into a historical perspective • Use a chosen mathematical topic from the course for educational purposes in upper secondary school.
Compulsory activeties. The grade is based on written projects and multiple choice test during the course. Reexamination is 4 hours written exam with usual helping aids.
Kolman, Busby, and Ross: Discrete Mathematical Structures, 6th Ed., Pearson Education. Chapters 1-8, and weeklies and notes.