This page includes information about aim and learning outcomes, teachers, literature, examination, examination procedures, old exams and course evaluation. The program for all teaching sessions can be found on a separate page (Course syllabus).

Aim and learning outcomes

The aim and learning outcomes of the course can be found in the course plan.

Recorded lectures and lecture notes for 240917 and 240919

240917:

Video part 1

Warning: In the video for part 1, I forgot to share the screen. Hence you see me and you can listen to what I say but you need to open the corresponding lecture notes.

In the videos for the other parts you see what I type and you hear what I say but you might need to have a high volume.

Lecture notes part 1

Link to YouTube video about Brouwer's fixed point theorem:

https://www.youtube.com/watch?v=PwIDFSC1KzI&t=14s

240919:

Teachers

Examiner: Håkan Andréasson

Lecturer: Håkan Andréasson

Teaching assistants:

Lab supervisors:

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Course literature

[DM] L.Debnath/P.Mikusinski: Hilbert Spaces with Applications, 3rd ed, Chapters 1-5

[K] material not contained in the textbook together with additional exercises.

[S] Proof of the Banach-Steinhaus theorem by Sokal.

English-Swedish mathematical dictionary.

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Assignments

During the course there will be homework assignments. They are not mandatory but can result in bonus points on the written exam.

Please email me your solutions (hand at chalmers.se). I prefer a pdf-file but a handwritten solution is also fine.

Every homework assignment consists of 4 problems and a correct solution to a problem gives 1 point. The total number of points one can get is 12 points. This results in bonus points according to the following table:

4 bonus points if at least 11 points

3 bonus points if at least 8 points

2 bonus points if at least 5 points

1 bonus point if at least 3 points

Assignment 1

Assignment 2

Assignment 3

Examination

The course is examined by a written exam. This consists of 6 problems where 3 of them are of a more theoretical nature. For Chalmers students: To pass the exam you need to score 10 points (bonus points included) out of 25 points. To get the grades 4 and 5 you need to score 15 and 20 points respectively. For GU students: To pass the exam and get the grade G you need to score 10 points (bonus points included) and to get the grade VG you need 18 points.

You should be able to state and explain all definitions and state and prove the theorems given in the course and apply them in problem solving. The list of theorems from last year can be found here.

Below you find the October exams for the last three years.

Exam-2021-10-27 with solutions.

Exam-2022-10-26 with solutions.

Exam-2023-10-25 with solutions.

Exam-2024-10-30 with solutions.

The dates, times and places for the exams are in the student portal.

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Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply to exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at the University of Gothenburg.

Before the exam, it is important that you sign up for the examination. You sign up through Ladok.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

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Course evaluation

At the beginning of the course, at least two student representatives should have been appointed to carry out the course evaluation together with the teachers. The evaluation takes place through conversations between teachers and student representatives during the course and at a meeting after the end of the course when the survey result is discussed and a report is written.

Guidelines for Course evaluation in Chalmers student portal.

Student representatives

The following students have been appointed:

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Old exams

See above.

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Program

The program can be found on the Course syllabus.

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