Two parts. The written exam on graphs & trees, relations and counting techniques gives 4 hp. A project on recurrence relations and cellular automata gives 3,5 hp. For the project problems you use Mathematica and your answers are presented in a written report.
Discrete mathematics is according to the mathematical dictionary a collection of a number of mathematical subjects that have the following in common: Only finite processes (no limit arguments) and they take mainly place in the set of integers. The subject can be said to play the same role for computer science as analysis do for physics. Topics that are generally included into discrete mathematics are theory of sets, combinatorics, graph theory and algorithm theory.
Book:Selected parts of Kenneth H. Rosen's book Discrete Mathematics and Its Applications. I use 8:th edition ISBN 978-1-260-09199-1. But you can also use 7:th edition ( a sunflower on the front) , ISBN 978-0-07-131501-2. Even the sixth edition works fine, ISBN 978-0-07-124474-9. The chapters and sections are the same in the 7:th and 8:th editions but the numbers of the exercises can differ somewhat.
Plan for lectures: The two first weeks we give an introduction to graphs, prepare you for the project and finally mention some things from chapter 1-6.Then we dig into chapters 8-11 for 6 weeks. This is the new stuff that will be exmined. Schedule 1ma462. We finish by looking at old exams. Plan and exercises are here.
My notes and comments: I made these a couple of years ago when I used 6th edition. So the numbers for chapters don't match 8th edition. Advanced Counting Tecniques was chapter 7 and is now chapter 8 in 8th edition, Relations 8->9, Graphs 9->10 and Trees 10->11. Sometimes I expand beyond what is needed for exam. More recent recordings from 2020-2021 can be found on Moodle.Introduction to graphs:
Five lectures with background material. Covers chapters 1 to 6 in 8:th edition:Logic and Proofs.(text) (sound).
Sets and Functions (text) (sound). Algorithms, Integers and Matrices (text) (sound). Induction and Recursion (text) (sound). Counting (text) (sound). Three lectures related to the project:Advanced Counting Techniques, part I (text) (sound).
Logistic map (text) (sound). Cellular Automata (text) (sound). Combinatorics:Advanced Counting Techniques, part II (text) (sound).
Relations:Relations, part I (text) (sound).
Relations, part II (text) (sound). Five lectures about graphs and trees:Graphs & Trees, part I (text) (sound).
Graphs & Trees, part II (text) (sound). Graphs & Trees, part III (text) (sound). Graphs & Trees, part IV (text) (sound). Graphs & Trees, part V (text) (sound).Examination:Written exam 25/5. Next try 10/6 and the last will take place 17/6. The exam consists of 10 problems, On average 5 points on each, and 20 points is needed for passing . A project on recurrence relations and cellular automata is also part of the examination. Will be delivered 7:th of April. The final grade is a weighted average of the grades on the two parts. Limits for written exam: E 20 points, D 23 p, C 26 p, B 30 p and A 35 p.
Latest exams: Note: A sheet with formulas at exam.
Lectures with Hans Frisk and Efraim Laksman. Mondays in Kalmar 13-17. In Växjö Tuesdays 13-15, Thursdays 13-15 and Zoom-meetings Wednesdays 15-17 . Distance students meet Wednesdays 6pm at Zoom.
Exercises: Look here.
FAQ: Here I collect the questions I get and my answers to them. Some in Swedish. First chapters, Advanced counting technique,
Relations, Graphs and Trees.
Extra material (some in Swedish):
Some problems from a math competition. (13-15 y old)
About the RSA-crypto.
Something about non-linear recurrence relations.
A nice introduction to Cellular Automata .
A beautiful proof of Fermat's little theorem. by coloring of necklaces.
Sarada Herke's graph theory lectures
Back to Hans Frisk's homepage.
Latest update the 28/3 2022