MM101: Analysis 1

Study Board of Science

Teaching language: Danish
EKA: N900000102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Professional Master

STADS ID (UVA): N900000101
ECTS value: 5

Date of Approval: 25-04-2019


Duration: 1 semester

Version: Archive

Comment

New course Autumn 2018.

Entry requirements

None besides entry requirements.

Academic preconditions

Students taking the course are expected to:

  • Have knowledge of basic theory about functions, continuity, differentiability, sequences and series as aquired in a typical calculus.
  • Be able to perform elementary mathematical reasoning and calculations.

Course introduction

The aim of the course is to provide the students with a solid introduction to the mathematical methods for dealing with limits and infinitesimal quantities. The course thus includes a rigorous treatment of e.g. continuous functions and the integral of such functions. Based on the course curriculum the student will obtain an advanced and solid starting point for the teaching of corresponding topics in high school.

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 probability theory, statistics and mathematical analysis 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 mathematical analysis in high school educations at a highly qualified level.
  • Give skills to formulate, structure and carry out mathematical results and reasoning concerning e.g. limits and infinitesimal quantities.
  • Give in depth knowledge and understanding of e.g. continuity, differentiability and integrals with a view towards teaching of these topics in the high school educations.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:
  1. define the notion of continuity precisely and account for the correspondence to more intuitive descriptions of that notion.
  2. formulate and provide detailed proofs of main results about continuous functions defined on closed and bounded intervals.
  3. define the notions of integrability and integral precisely and account visually for their intuitive interpretations.
  4. rigorously derive the fact that continuous functions on a closed and bounded interval are integrable.
  5. account for the interplay between integrals and differentiability.


Content

See Danish version

Literature

See Blackboard for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

January

Tests

Oral examination

EKA

N900000102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Additional information

The examination form for re-examination may be different from the exam form at the regular exam.

Indicative number of lessons

60 hours per semester

Teaching Method

See Danish version

Teacher responsible

Name E-mail Department
Steen Thorbjørnsen steenth@math.au.dk

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