MM537: Introduction to Mathematical Methods
Comment
Entry requirements
Academic preconditions
Course introduction
- Give skills to formulate mathematical arguments
- Give knowledge and understanding of various core concepts from the foundations of mathematics such as sets and from number theory.
Expected learning outcome
- formulate a statement in a logical correct way
- express yourself clearly and accurately
- prove mathematical statements by various proof methods such as a direct proof, indirect proof, use induction.
- use known concepts, results and techniques on known as well as new problems
- argue sufficiently for your solutions.
Content
The following main topics are contained in the course:
- Logic
- Proof techniques: Direct proof, proof by contraposition, proof by contradiction, and proof by induction
- Sets and cardinality
- Functions
- Recursive definitions and strong induction
- Relations, including various representations of relations, closures, partial orders and equivalence relations
Literature
Examination regulations
Exam element b)
Timing
January
Tests
Written exam
EKA
Assessment
Grading
Identification
Language
Duration
Examination aids
ECTS value
Exam element a)
Timing
Tests
Mandatory assignments
EKA
Assessment
Grading
Identification
Language
Examination aids
ECTS value
Indicative number of lessons
Teaching Method
At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.
In order to enable students to achieve the learning objectives for the course, the teaching is organised in such a way that there are 58 lectures, class lessons, etc. on a semester.
These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:
- Intro phase (lectures, class lessons) - 24 hours
- Training phase: 24 hours
- Study phase: 10
In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours or the training phase hours.
Activities during the study phase: Students work in their study groups with fundamental concepts and techniques from the course.