MM537: Introduction to Mathematical Methods

Students taking the course are expected to have A-level mathematics from high school.

The course gives the foundation for further studies in mathematics,
since the students learn about logic and how to reason in mathematics.
Moreover they are introduced to fundamental concepts such as sets,
relations and functions.

The course forms the basis for all
courses in the BA-degree in mathematics and applied mathematics as the
students here learn the basic methods of proving in mathematics. The
course also interrelates with the courses MM536 Calculus for mathematics
as the students learn about the set theoretic definitions of core
concepts used in analysis, and MM5xx Algebra 1, as they learn about
equivalence relations which is a fundamental concept in algebra.

In relation to the competence profile of the degree it is the explicit focus of the course to:

• 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.

As listed in the educations competency profile the course has explicit
focus to give the students ability to formulate, go through and present
mathematical arguments, as well as giving the ability to:

• 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.

The following main topics are contained in the course:

• Logic
• Sets and cardinality
• Functions
• Proof techniques
• Number theory, prime numbers and congruence
• Relations, order and equivalence relations.

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.

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.