DM527: Mathematical tools for computer science (5 ECTS)

STADS: 15002831

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.
2nd quarter.

Teacher responsible
Email: lenem@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Revison of timetable:
: S72 nedlagt og alle studerende sættes på S71 på 2.kvartal.

Comment:
Ubegrænset deltagerantal

Prerequisites:
None

Academic preconditions:
None.

Course introduction
The course should expose students to basic techniques for working with mathematical notions important within Computer Science. This is necessary for many more advanced courses in Computer Science.

Qualifications
The course mainly has two goals:

The students should learn how to formalize and work with abstract notions in a concise mathematical manner. The formulation of precise propositions as well as proofs for such propositions will play a major part. This will be done by covering a number of important topics from discrete mathematics relevant for Students from Computer Science. One further goal of the course is that students get used to mathematical reasoning which will be necessary for later courses in Computer Science.

More precisely, the participants will learn

• to formalize mathematical statements in a correct logical way;
• to prove propositions by means of different proof methods such as direct proofs, indirect proofs and induction proofs. The latter includes in particular applications to proofs of properties of recursively defined structures and algorithms;
• to understand the notions of a set and operations on sets, the notion of a function and basic properties such as injectivity, surjectivity and bijectivity. In particular, the students will learn how to argue that sets are (not) countable;
• to work with basic notions of number theory such as divisibility and greatest common divisor. They will understand how to compute a gcd of two numbers by the Euclidean algorithm and how to use the Chinese Remainder Theorem in order to solve systems of linear congruences; the RSA cryptosystem is addressed;
• elementary properties of matrices as they occur frequently in Computer Science applications;
• to work with relations, including representing relations, finding the closure of a relation and understanding the concept of equivalence relations.

Expected learning outcome


Subject overview
Propositional calculus, sets and functions, proof techniques, induction, numbers and their representation, Euclidean algorithm and Chinese remainder theorem, matrices, relations.

Literature

• Meddeles ved kursets start..

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
• A two hours written exam with textbook, notes, pocket calculator. External examiner, grades according to the 7-point marking scale. The evaluation accounts for 80% of the final grade for the course. A laptop is not allowed at the exam.
Re-exam after 4th quarter.
• A project assignment. The evaluation accounts for 20% of the final grade for the course. The project assignment can be counted only until the re-exam after the 4th quarter. It cannot be carried over to the following year.
• A number of mandatory assignments which account for 1 ECTS of the total 5 ECTS of the course (pass/fail, internal examiner). These assignments are not part of the first year test.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger, antal timer 21. Eksaminatorietimer/opgaveregning, antal timer 21.
Educational activities

Language
This course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.