M338
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Can one knot untie another? |
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M338
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Written by Ines
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Thursday, 24 June 2010 14:20 |
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This was the title of a great lecture held by Gareth Williams two days ago. The lecture was held using Elluminate and about 60 students attended. In my opinion this is a large number of students, since this lecture was not part of the course or so ... it was held for those who were interested in why we need topology. ;)
But is the question "Can one knot untie the other?" important at all? Is it only theoretical or even practical?
Assume we are given a piece of string with a knot tied in it. Can we then tie another knot which will combine with the first knot to produce an unknotted piece of string? Answering this question is not only interesting it is of practical interest for sailors, biologists (DNA), bungee-jumpers etc. as well.
After considering Seifert's surfaces, adding some knots we then came to the conclusion that one knot cannot be tied after another in such a way as to make the result equivalent to the trivial knot, and so, one knot does not untie another. :)
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Preparation for Topology course |
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M338
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Written by Ines
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Tuesday, 09 February 2010 20:23 |
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I just noticed that a good preparation for the topology course is the booklet AA4 (Continuity) from the 2nd level course M208. Unit A1 of the topology course starts with continuity. But on the other hand the explaination of the sequential definition of continuity and the  definition of continuity are very well explained in Unit A1 of the Topology course.
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Starting with the Introduction on DVD |
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M338
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Written by Ines
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Thursday, 04 February 2010 10:55 |
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I started the topology course by watching the DVD. The DVD gave a brief introduction into the ideas of topology. Firstly, the film introduced properties of different surfaces. For example, we need only 4 colours to paint a map on a surface without a whole (like a sphere), but if you want to paint a map on a torus you need more than four colours. Also, the fixed point property and the edge identifications were outlined. Then the film explained what continuous transformations are and therefore introduced open sets.
And finally, the film showed whether two surfaces are equivialent or not.
This afternoon I will start unit A1: Distance and continuity.
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M338
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Written by Ines
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Wednesday, 03 February 2010 15:55 |
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The contents of the box are:
- Units A1 - A4
- Assignment Book 1
- Study calendar (on A4 paper)
- Course Guide
- Stop Press
- Exercise Booklet I
- Handbook
- Computer Guide
- DVD
- Software
- TMA Form
The StudentHome says that another material delivery is scheduled for mid February. Also, I have to submit my TMAs on paper ... no eTMAs are allowed. :-/
The course is divided into 3 blocks of all in all 13 units, whereas Block A and B consist of 4 units each, whereas Block C consists of 5 units. The Blocks A and C are based on the idea of continuity (from the course M208), while Block B studies the properties of surfaces such as the Möbius band or a torus. Like, M381 only the handbook (but without annotations) is allowed in the exam.This means that I'll also work with flashcards in M338.
BTW, this is another course with shiny booklets and DVDs in this material dispatch. :o)
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