MATH31051/MATH41051 Home Page

Peter J Eccles

Announcements

The final lecture for this course will be on Monday 14 December.

There will be an opportunity to ask me questions about the course material on Friday 18 December at 4 p.m. in the Max Newman Lecture Room (Alan Turing G.107).

There will be a revision class on Friday 15 January at 11 a.m. in Humanities Bridgeford Street Lecture Theatre G.6.

Lecture times and places

The classes for this course unit are as follows:

Some of the Monday morning two hour session will be used for discussing the problem sheets.

Queries

Any queries about the course or comments can be emailed to me at pjeccles@manchester.ac.uk. I will try to reply within 48 hours.

Office Hours

Students are welcome to call on me in my office (1.111 in the Alan Turing Building) at any time. If I am busy I will ask you to come back another time and if possible arrange one. If I am not in my office then leave a note under my door or send me an email saying when you will return. I will try and make a point of being in my office available to students on Monday (1.00 - 2.00) and Friday (1.00 - 2.00) lunchtimes. However, sometimes I will have other commitments at these times.

Student Feedback

Week 3 Feedback Forms

Here is my report on the matters raised on the week 3 feedback forms. Thank you to the 54 students who took the trouble to complete and return one.

Books

There are very many books on the basic ideas of topology. The following are some that I have found useful in preparing this course. I do not know any book which includes the material on the classification of surfaces in the second half of this lecture course done in just the same way.

• M.A. Armstrong, Basic Topology. The first four chapters of this book covers the material in sections 1 to 7 of the course. Chapter 7 covers much of the material in the rest of the course but refers back to material in chapters 5 and 6 which is not in the course.


• Stephen Huggett and David Jordan, A Topological Aperitif. This book is a good introduction to topological ideas but does not include most of the course. The first two chapters contains the material on cut-points in section 1 of the course.Chapter 4 includes material on topological surfaces which is useful for section 8. The library catalogue provides access to an electronic copy of this book.


• W.A. Sutherland, Introduction to Metric and Topological Spaces. Chapters 3 to 6 cover most of the material in sections 2 to 7.

Background material

I have prepared a document summarizing the material on sets and functions (mainly from MATH10101/MATH10111) which will be used in this lecture course. I will go through these notes in the lectures but will refer to them from time to time. I suggest that students read through these notes as preparation for the course. If you have queries you can raise these when the material is used. The first section of the course uses the last section of these notes. I hope that this summary is useful.

• Background material on sets and functions

Lecture notes

These notes are not complete. They mainly list the definitions, theorems and examples discussed in the lectures. Some of the more complicated proofs are given in detail so that the lectures can concentrate on the ideas.

• 1. Introduction: Topological Equivalence (lectures 1 and 2)


• 2. Topological Spaces (lectures 3, 4 and 5)


• 3. Hausdorff Spaces (lectures 5 and 6)


• 4. Compactness (lectures 6, 7 and 8)


• 5. Quotient Spaces (lectures 9 and 10)


• 6. Subspaces (lecture 11)


• 7. Product Spaces (lectures 12 and 13)


• 8. Topological Surfaces (lectures 14 and 15)


• 9. Simplicial Surfaces (lectures 16, 17, 18 and 19)


• 10. Topological Invariants of Surfaces (lectures 20 and 21)

Supplementary reading for the level 4 MATH41051 course unit

The level 4 and MSc version of this course is rated at 15 credits rather than the 10 credits of the level 3 version. There are three sets of notes to provide supplementary reading for students taking this version of the course. The (three hour) examination for MATH41051 will be the same as the (two hour) examination for MATH31051 with an additional section based on this supplementary reading (with three questions: one question on each set of notes).

• A. Neighbourhoods, Interior and Closure


• B. Metrizability


• C. Symmetries of Surfaces

Problem sheets

• 1. Topological Equivalence


• 2. Topological Spaces


• 3. Hausdorff Spaces


• 4. Compactness


• 5. Quotient Spaces


• 6. Subspaces and Product Spaces


• 7. Topological Surfaces


• 8. Simplicial Surfaces


• 9. Topological Invariants of Surfaces

Solution sheets

• 1.


• 2.


• 3.


• 4.


• 5.


• 6.


• 7.


• 8.


• 9.

• A.


• B.


• C.

Assessment

Coursework

The coursework consisted of homework exercises due for handing in by 1 p.m. on Monday 9 November 2009. Here are some solutions and feedback on the coursework. The marked work was returned at the lecture on 30 November.

Examination

For MATH31051 the examination rubric is as follows: Answer ALL four questions in Section A (40 marks in all) and THREE of the four questions in Section B (15 marks each). The total number of marks on the paper is 85. A further 15 marks come from work during the semester making a total of 100. It is a two hour examination.

For MATH41051/MATH61051 the examination rubric is as follows: Answer ALL four questions in Section A (40 marks in all), THREE of the four questions in Section B (15 marks each) and ALL three questions in Section C (50 marks in all). The total number of marks on the paper is 135. A further 15 marks come from work during the semester making a total of 150. It is a three hour examination.

• MATH30009 January 2007


• MATH31051 January 2008


• MATH31051 January 2009 and some feedback


• MATH41009 January 2007


• MATH41051 January 2008


• MATH41051 January 2009and some feedback

The final section of the supplementary reading for MATH41009 in 2006-2007 was on different material to this year.

Diary of amendments to and additions to this webpage