Course syllabus
Foundations of Analysis, 7.5 credits
| Course code: | MA158G | Credits: | 7.5 |
|---|---|---|---|
| Main field of study: | Mathematics | Progression: | G1F |
| Last revised: | 14/09/2023 | ||
| Education cycle: | First cycle | Approved by: | Head of school |
| Established: | 02/12/2019 | Reading list approved: | 14/09/2023 |
| Valid from: | Spring semester 2024 | Revision: | 2 |
Learning outcomes
Knowledge and comprehension
After having completed the course the student shall be able to
- discriminate between a mathematical proof and a general reasoning.
Proficiency and ability
After having completed the course the student shall be able to
- prove mathematical propositions within the scope of the present course using standard techniques and known theorems, and
- propose mathematical proofs with good structure and stringent notation.
Values and attitude
After having completed the course the student shall be able to
- give written and oral presentations of mathematical proofs which emphasize the crucial parts and are easy to follow.
Content
Real numbers. Number sequences and convergence, subsequences, Cauchy sequences and series. Topology and the Heine-Borel theorem. Continuous functions, compact functions and supremum. Uniform continuity. Differentiable functions, Riemann integrals, mean value theorems. Sequences of functions, absolute convergence and power series. Metric spaces.
Examinations and grades
Examination, 7.5 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).
According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).
In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.
The grades used on this course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).
Modes of assessment
- Examination (code A001): Written assignment and oral examination
For students with a documented disability, the university may approve applications for adapted or other modes of assessment.
For further information, see the university's local examination regulations.
Specific entry requirements
Multivariable Calculus, 9 Credits.
For further information, see the university's admission regulations.
Other provisions
All or part of the course may be given in English. The teaching methods may be altered, should only a few students take the course.
Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.