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Here is this year's problem set, and my sample solution.
- John
Wednesday November 28th at 14.15 - 16.00 in auditorium 4, Vilhelm Bjerknes' hus:
- Section 51, Exercise 2
- Section 52, Exercises 1, 5
- Section 53, Exercises 1, 2, 3, 4, 6 (omit "completely regular").
A sample solution to the mandatory assignment is available under Canvas.
You can find exam problems from earlier years under "oppgaver" in the left margin of the course page. Of the more recent ones you might look at:
- MAT3500/4500 2017 (omit 2a(3), 2b(2), 4b)
- MAT3500/4500 2016 (omit 1a, 5)
- MAT3500/4500 2015 (omit 1, 3d, 4)
- MAT3500/4500 2014 (omit 3b, 4)
- MAT3500/450...
The syllabus (pensum) for the examination consists of the following sections of Munkres' textbook:
Chapter 1: Set Theory and Logic
1. Fundamental Concepts
2. Functions
3. Relations
5. Cartesian Products
6. Finite Sets
7. Countable and Uncountable Sets
Chapter 2: Topological Spaces and Continuous Functions
12. Topological Spaces
13. Basis for a Topology (omitting lower limit and K-topologies)
15. The Product Topology on X x Y
16. The Subspace Top...
The mandatory assignments have now been graded. Check Canvas to see your result. If the submitted paper was not accepted, you have the option to make a second (and final) attempt. The problem set is the same; the new deadline is November 15th.
Here is a summary of the student responses to the course evaluation. They will be kept in mind!
The mandatory assignment is now available, and should be handed in using Canvas before 2.30 p.m. on Thursday October 25th.
The student representative this semester is Are Aamot (aresaa@student.matnat.uio.no).
My lecture notes have been updated (November 21th), and are now close to their final form for this semester.
Various solutions to exercises in Munkres' book are freely available on the web. A search quickly leads to:
Se also:
- links to solutions (from 2011)
- handwritten solutions (from 2016)
Sections included in the syllabus (pensum) are emphasized in boldface.
Chapter 1: Set Theory and Logic
- Fundamental Concepts
- Functions
- Relations
- The Integers and the Real Numbers
- Cartesian Products
- Finite Sets
- Coun...
Until further notice, the information and lectures for MAT3500/4500 will be given in English.
"Topos" means "place", so "Topology" is the science of places, or the study of shapes, if you like. The main objects of study are shapes where we can make sense of limits, known as topological spaces. We can also make sense of what it means for a function from one such shape to another to be continuous. A large part of the course is about the properties of continuous functions, which we call maps. A second large part of the course is concerned with the properties of shapes that are invariant under invertible continuous transformations. For brief historical notes on the subject you may with to look at these excerpts from the Bourbaki v...
Here is the weekly MAT3500/4500 schedule:
- Mondays 10-12: Lectures (with John Rognes)
- Tuesdays 12-14: Exercises (with Gard Olav Helle)
- Wednesdays 14-16: Lectures (with John Rognes)
All lectures and exercise sessions take place in Auditorium 4 in Vilhelm Bjerknes' hus/building.
The following web page systems will be relevant to students taking MAT3500 or MAT4500:
- Vortex
- Canvas
- Studentweb
I will mostly use the MAT4500 semester page, which is part of the Vortex system. Here I will let you know what I plan to lecture about, so that you know what to read before the lectures, and I will summarize what I have gone through in the lectures, so that you will know what may be on the exam. The weekly problems for the exercise session will also be listed here.
The MAT3500 Canvas web page will be used to handle the announcement, submission and grading of the mandatory assignment.
I do not have access to Studentweb. This is where you register for this and other courses, but the ...
In case you are wondering, we will be using the same textbook this year as last year, namely "Topology, 2nd edition" by James Munkres:
- John