Mathematics for computer science

Responsible: Leon van der Torre

Assistant: Mathijs de Boer

Note: homework assignments must be put in the mailbox of the assistant on Monday before the following lecture. The homework assignments will be taken into account for the scores of the tests.

Objectives: This is a foundational course, in the sense that the student acquires various abilities he or she will use in the remainder of his education. After the course, the students should:

• understand basic discrete mathematics about logic, sets, relations and graphs
• be able to prove statements in discrete mathematics, using various proof techniques including induction
• be able to apply discrete mathematics about logic, sets, relations and graphs to model phenomena in computer science
• understand some concepts about state transition systems
• have a feeling for the role of (discrete) mathematics in computer science

Course materials:

The book we use for this course is available both in english and in german.

Rod Haggarty, Discrete Mathematics for Computing (Diskrete Mathematik für Informatiker)

Course schedule:
20.02 LT: Haggarty chapter 1+2: Logic and proofs 1 slides ppt homework
27.02 LT: Haggarty chapter 1+2: Logic and proofs 2 slides ppt handout homework
05.03 LT: Haggarty chapter 1+2: Logic and proofs 3 slides ppt homework
12.03 EW: Haggarty chapter 1+2: Logic and proofs 4
19.03 LT: Haggarty chapter 1+2: Logic and proofs test (exercises test06 test06fr test07 test07fr test07sol test07sol
test08sol)
26.03 Easter break
02:04 LT: Haggarty chapter 3: Set Theory slides homework
09:04 LT: Haggarty chapter 4: Relations slides homework
16:04 LT: Haggarty chapter 5: Functions slides homework
23.02 EW: Haggarty chapter 6: Combinatorics
30.04 LT: Haggarty chapter 3-6: Sets, relations, functions and combinatorics test in room A12 (solution exercise 4: By the pidgeonhole principle, at least two of the 150 numbers are equal. Since all the (a-i)s are distinct and all the (a-i+24)s are distinct, it follows that a-i=a-j+24 for some i>j. Thus, in the period from the (j+1)st to the i-th hour, there are exactly 24 matches.)
07.05 MB: Haggarty chapter 7-8: Graphs 1 (slides homework)
14.05 MB: Haggarty chapter 7-8: Graphs 2 (slides homework)
21.05 MB: Haggarty chapter 7-8: Trees (slides homework)
28.05 MB: Haggarty chapter ---: FSAs (slides)

Contents:

• propositional and first order logic
• proofs and induction
• set theory, functions, relations
• graphs
• trees

Aims of qualification

• This course aims at introducing students to discrete mathematics such as proofs, sets, relations, graphs and state transition systems.

Form of the classes: 1.5 hours; mix of lectures and practicals.

Lectures are in English.

Workload: 2 ECTS Points = 30 hours lectures / exercises

Form of the Exams: Written, grades follow ECTS

There are two ways to pass the exam. There is a written exam in January, at the end of the winter semester, and the obtained grade will be the final grade.

Moreover, there are two intermediate exams held during the summer semester, which is a prerequisite to participate in the final exam at the end of the summer semester. The final grade will be 30% for each of the intermediate exams, and 40% for the final exam.

Here are the final results: web_grades.pdf

For students who followed the MFCS course in earlier years, there is also the option to do a written exam at the end of the summer semester which counts as the final grade.

Requirements: none

Length: 1 Semester = 14 Weeks

Frequency: Every Summer semester

Last years course: You might want to take a look at last years course, slides and tests are still up at Mathematics for computer science 2007.

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