MM537: Introduction to Mathematical Methods

Study Board of Science

Teaching language: Danish or English depending on the teacher
EKA: N300005102, N300005112
Assessment: Second examiner: External, Second examiner: None
Grading: 7-point grading scale, Pass/Fail
Offered in: Odense
Offered in: Autumn
Level: Bachelor

STADS ID (UVA): N300005101
ECTS value: 5

Date of Approval: 03-04-2024


Duration: 1 semester

Version: Approved - active

Comment

The course is co-read with DM549 and DM547.

Entry requirements

The course can not be followed if passed: MM540, MM568, DM527, DM535, DM547 and DM549.

Academic preconditions

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

Course introduction

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.

Expected learning outcome

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.

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

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element b)

Timing

January

Tests

Written exam

EKA

N300005102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card

Language

Normally, the same as teaching language

Duration

3 hours

Examination aids

All common aids are allowed e.g. books, notes, computer programmes which do not use internet etc.  

Internet is not allowed during the exam. However, you may visit system DE-Digital Exam when answering the multiple-choice questions. If you wish to use course materials from itslearning, you must download the materials to your computer the day before the exam. During the exam itslearning is not allowed.

ECTS value

4

Exam element a)

Timing

Autumn

Tests

Mandatory assignments

EKA

N300005112

Assessment

Second examiner: None

Grading

Pass/Fail

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

1

Indicative number of lessons

58 hours per semester

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.

Teacher responsible

Name E-mail Department
Kevin Schewior kevs@sdu.dk Algoritmer

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.