2024 MAST30026 Metric and Hilbert Spaces

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Many administrative details about the organisation of the subject can (as always) be found in the subject handbook entry.

Consultation hours

I will have consultation hours on Tuesdays 10am-11am and Fridays 11am-1pm in Peter Hall room 166.

Lecture notes

Here are the latest version of the lecture notes (updated: 6 September) and the latest version of the exercises (updated: 6 September).

Tutorials

Tutorial classes start in week 2 of the semester. The tutorial sheets appear here at the start of the corresponding week, and solutions appear at the end of the week.

Week 2: tut02 and solutions
Week 3: tut03 and solutions
Week 4: tut04 and solutions
Week 5: tut05 and solutions
Week 6: tut06 and solutions
Week 7: tut07 and solutions
Week 7: tut08

Assignments

The two assignments will be posted both here and on the subject's Canvas page. Your solutions should be submitted via Canvas and Gradescope.

Here is the pdf file for the first assignment, due 4 September at 20:00. If you want to write your solutions in LaTeX, here is a macros file and the template file for the first assignment.

Ed Discussion post with instructions/FAQ/errata for the first assignment.

I am planning to release the second assignment on 11 September (due 9 October).

Stay tuned for the upcoming sermon on the quality of work expected on the assignment submissions.

Special consideration

Special consideration procedures are undergoing changes at the level of the Faculty of Science. For the current semester and subject, this means:

Any request for a short extension for one of the assignments that is made before the due date of the assignment should be sent to me.
In all other cases the request must be lodged via the special consideration portal.

The definition of short is ⩽ 10 business days. However, unless the circumstances are extreme, the longest "short" extension I am willing to give is 5 business days. This helps ensure that proper assignment feedback (solutions) can be made available to the students in a timely manner, and that the student who needs the extension does not fall too much out of rhythm with the rest of the class.

Exam preparation

TBA

Ed discussion board

Please see the subject's Canvas page for access to the discussion board.

Lecture recordings

Please see the subject's Canvas page for access to the lecture recordings.

Other references: prerequisite knowledge

The main prerequisites for the subject are the University of Melbourne's MAST20022 Group Theory and Linear Algebra and MAST20026 Real Analysis (or some equivalent subject, see the handbook entry for details).

For those of you arriving with a different background, this means a solid understanding of linear algebra and previous exposure to abstract algebra concepts like groups, group actions, fields; also required is a firm grasp of analysis of functions on the real line.

There are many excellent abstract algebra and real analysis texts out there, so feel free to grab some to use as a reference while working on this subject.

Here are some suggestions:

Other references: metric and Hilbert spaces

There are also many excellent analysis texts out there covering various of the topics we are studying. I'll list here any that I refer to.

Note: Many of these references may be accessible via the library system either as electronic resources or physical tomes.