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: exam period

  • (past) Monday 21 October 11am-1pm in Peter Hall room 166
  • (past) Tuesday 29 October 11am-12:30pm in Peter Hall room 166
  • (past) Thursday 31 October 12:30pm-2pm in Peter Hall room 166
  • (past) Wednesday 6 November 1pm-2pm in Peter Hall room 166
  • (past) Friday 8 November 11:30am-1:30pm in Peter Hall room G03 (Evan Williams) NOTE CHANGE IN LOCATION!!!

There may be some changes to this schedule, either in terms of time or location. Please check this page in advance if you plan to attend.

Lecture notes

Here are the latest version of the lecture notes (updated: 18 October) and the latest version of the exercises (updated: 18 October). You may consider these versions to be definitive; I will only update them further if I become aware of errors.

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.

Assignments

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

Assignment 1

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.

Solutions for the first assignment.

Assignment 2

Here is the pdf file for the second assignment, due 9 October at 20:00. If you want to write your solutions in LaTeX, here is a macros file and the template file for the second assignment.

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

Solutions for the second assignment.

Special consideration

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

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

Everything you need to prepare for the exam is contained in the lecture notes, in the exercise booklet, in the tutorial sheets, and in the two assignments. I have marked with a star (*) the sections in the lecture notes, and the questions in the exercise booklet, tutorial sheets, and assignments that can be considered highly optional (aka can be ignored) for the purposes of review of the material and the preparation for the exam.

Caveat: when looking at past exams, remember that "past performance is not indicative of future results".

Here is the 2023 final exam: questions and solutions.

Here are the 2022 exam paper and 2010 exam paper.

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.