MM103: Algebra I

Study Board of Science

Teaching language: Danish
EKA: N900003102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Professional Master

STADS ID (UVA): N900003101
ECTS value: 5

Date of Approval: 04-10-2021


Duration: 1 semester

Version: Approved - active

Entry requirements

None

Academic preconditions

Students taking the course are expected to:

  • Have knowledge of the basic numbersystems and associated compositions
  • Be able to use and perform elementary mathematical reasoning and calculations.

Course introduction

In abstract algebra the fundamental objects of study are sets with one or more compositions. A composition is a mapping that associates to any two elements of the set a third element. For example the set of integers and the set of polynomials both have two compositions: addition and multiplication. Sets with compositions appear everywhere in mathematics. The algebraic theory for such sets has many applications both within pure mathematics and in applications of mathematics. The goal of the course is to make the students feel acquainted with the basic algebraic concepts through important examples like the integers and polynomials, and with applications in e.g. cryptology. The participants will learn how an abstract theory can be constructed based on axioms, and how it can be applied in concrete cases. 

The course builds on the knowledge acquired in courses in calculus and linear algebra, which are mandatory prerequisites for students entering the masters studies in mathematics with focus on teaching in high school educations.

The course gives an academic basis for studying e.g. the topics geometry and algebra 2 that are part of the degree.

 In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give the competence to teach topics related to algebra in high school educations at a highly qualified level.
  • Give skills in applying the algebraic techniques, results and concepts on concrete examples in e.g. number theory, rings and polynomials.
  • Give knowledge and understanding of the basic structure of the number systems and their compositions. 

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:
  • Apply algebraic algorithms on concrete problems. Examples could be Euclids algorithm and division of polynomials.
  • Argue for the various steps in algebraic problems with reference to the relevant theory.
  • Perform calculations modulo an integer and in rings of polynomials over a field.

Content

The following main topics are contained in the course:

  • The basic number systems
  • Elements of group theory, rings and polynomials.
  • Primenumbers, primefactorization of integers, cryptology, quadratic remainders.
  • Introductory group theory, rings, polynomials and finite fields.

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

June

Tests

Written exam

EKA

N900003102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card

Language

Normally, the same as teaching language

Examination aids

The exam is without aids. However, standard build in calculator in Windows/MAC are allowed. It is also allowed to use Maple, Mathematica, Mathcad, MathLab, GeoGebra Apps, R, R-Studio, CAS TI-Nspire, Ms Excel og LibreOffice Calc. WordMat is allowed but not recommended. Use of WordMat is at your own risk and no support is provided for errors caused by the program. 

Internet is not allowed during the exam. However, you may visit system "DE-Digital Exam".

ECTS value

5

Indicative number of lessons

supervision hours are coordinated with the supervisor

Teaching Method

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

The introductory lessons/training phase lessons take place as traditional lectures/practice lessons for the collections. The rest will be organised with electronic means, e.g. via online videos and electronic material for the assignments.

Teacher responsible

Name E-mail Department
Peter Jørgensen pjor@imada.sdu.dk Institut for Matematik og Datalogi

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

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.