DM527: Mathematical tools for computer science (5 ECTS)

STADS: 15007011

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.
1st. quarter.

Teacher responsible
Email: lenem@imada.sdu.dk

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

Revison of timetable:
: Større lokale onsdag

Comment:
Ubegrænset deltagerantal. Kurset kører i 1. kvartal. Fælles undervisning med MM524 - Matematiske redskaber.

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.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a) Project assignment which goes across the three courses in 1st quarter. Pass/fail, internal evaluation (1 ECTS). The deadline for handing in the assignment will be announced in the beginning of the course.
b) Evaluated on the basis of a final 3 hour written examination and continuous assignment throughout the course. 7-point grading scale. External examiner. The assignments count for 30 % of the final grade (4 ECTS).

The assignment are valid until the reexamination after 2nd quarter and cannot be carried through to the following year.

Note: You do not have to hand in the first assignment (a) if you attend this class for the second time or if it is part of your programme's second or third year. You still will be attributed 5 ECTS for the whole course.

Re-examination after 2nd quarter.

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 or English, depending on the lecturer.

Remarks


Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.