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Original post by .matt
You met any measure theory yet? It gets more fun the more you learn, seriously 
I think we have touched it just, in probability we have done up to the distributions, pdf, joint and CLT and so far that was very quite engaging as well!
Markov processes next semester tis!!! Sounds interesting to say the least!
Original post by the greatest
I think we have touched it just, in probability we have done up to the distributions, pdf, joint and CLT and so far that was very quite engaging as well!
Markov processes next semester tis!!! Sounds interesting to say the least!
Markov processes next semester tis!!! Sounds interesting to say the least!
Markov stuff is very interesting, probably one of the most fun courses i've done, and very elegant.
Original post by ForGreatJustice
Markov stuff is very interesting, probably one of the most fun courses i've done, and very elegant.
Added Bonus, the lecturer himself, has done vasts amount of research on MC, stochastic processes and applied SP and an editor for springer queueing theory!
Should be a treat!
Have you finished ur degree or in your last year at cambridge?
K guys. Trying to learn algebraic top for an exam next friday. Didn't go to lectures. This was a mistake.
Can someone give me a clarification of the difference between a simplical complex and a CW complex and what my idea of a singular complex is.
CW Complex.
I think of this as a collection of points with edges drawn on and then sides added to the edges, then just imagine that it would continue... (with the sides which are being attached homemorphic to .)
Simplicial complex
I think of it as basically the same object only the actual "complex" is the set of maps taking to it's respective place in the complex.
Singular complex
So given a space X (which I'll take here to be something akin to what I've just described), I imagine a singular complex on X to be the set of every possible map from into the space X. So for any non-discrete space the set C_1(X) is uncountably infinite, as for each point on an edge joining two verticies there are uncountably many points which I can map to.
Now, can someone clarify my picture of these and give me some distinction between the first two. Is there any real difference between attaching maps from n-cells and from delta complexes?
I'm also finding that although I understand a lot of the material (such as the exact sequences) I'm pretty much useless at any calculations.
As a final note, can someone explain how to attach 2-cells by words.
e.g. in Hatcher, pg 142, "Let X be obtained from S^1vS^1 by attaching two 2-cells by the words and "
Is a an oriented loop around the first circle then b the same around the second? How would I visualise this?
Sorry for the long post, I thought this would be the best place to ask.
Can someone give me a clarification of the difference between a simplical complex and a CW complex and what my idea of a singular complex is.
CW Complex.
I think of this as a collection of points with edges drawn on and then sides added to the edges, then just imagine that it would continue... (with the sides which are being attached homemorphic to .)
Simplicial complex
I think of it as basically the same object only the actual "complex" is the set of maps taking to it's respective place in the complex.
Singular complex
So given a space X (which I'll take here to be something akin to what I've just described), I imagine a singular complex on X to be the set of every possible map from into the space X. So for any non-discrete space the set C_1(X) is uncountably infinite, as for each point on an edge joining two verticies there are uncountably many points which I can map to.
Now, can someone clarify my picture of these and give me some distinction between the first two. Is there any real difference between attaching maps from n-cells and from delta complexes?
I'm also finding that although I understand a lot of the material (such as the exact sequences) I'm pretty much useless at any calculations.
As a final note, can someone explain how to attach 2-cells by words.
e.g. in Hatcher, pg 142, "Let X be obtained from S^1vS^1 by attaching two 2-cells by the words and "
Is a an oriented loop around the first circle then b the same around the second? How would I visualise this?
Sorry for the long post, I thought this would be the best place to ask.
(edited 12 years ago)
Has someone got a digital copy of the Cambridge IB Variational Principles notes that used to be on the Archimedeans site? I printed these out, but think I've lost them!
I can offer various digital nice maths goodies in return!
I can offer various digital nice maths goodies in return!
Original post by Totally Tom
As a final note, can someone explain how to attach 2-cells by words.
e.g. in Hatcher, pg 142, "Let X be obtained from S^1vS^1 by attaching two 2-cells by the words and "
Is a an oriented loop around the first circle then b the same around the second? How would I visualise this?
Sorry for the long post, I thought this would be the best place to ask.
As a final note, can someone explain how to attach 2-cells by words.
e.g. in Hatcher, pg 142, "Let X be obtained from S^1vS^1 by attaching two 2-cells by the words and "
Is a an oriented loop around the first circle then b the same around the second? How would I visualise this?
Sorry for the long post, I thought this would be the best place to ask.
You can visualise the loops a and b by drawing a basepoint and then drawing two oriented edges starting and ending at the chosen basepoint. Then simply label one a and one b. Then, to glue the 2-cell, you orient the boundary and divide it into (e.g. eight for a^5b^{-3}) sectors and attach each sector according to the corresponding letter in the word. If you like, draw the two cell and write the word you are attaching by onto the boundary in this fashion.
If you are worrying about orientations then note the following - the choice of orientations for a and b is really just a choice of generators for the copies of Z in the fundamental group of the S^1s so as long as you fix orientations and stick to them - everything is consistent.
Example. Take X = S^1 v S^1 and attach a two cell by the word aba^{-1}b{-1}. Then we get a torus. How to see this? Simply draw your 2-cell as a square and then form the identification space of the square. This is the same as attaching it via the indicated word since the S^1 v S^1 is embedded in there as the corners of the square and the a and b sides.
Tbh... this is the kind of question where it is really much more handy to discuss in front of a blackboard but HTH anyway.
Also, if nobody else answers the first part, I'll say something later about that too.
(edited 12 years ago)
Just did a mock paper. Was violently sick several times and had a horrific headache. That's a bad sign right?
Original post by SimonM
Just did a mock paper. Was violently sick several times and had a horrific headache. That's a bad sign right?
Were you sick because you were ill or because you were nervous?
Original post by IrrationalNumber
Were you sick because you were ill or because you were nervous?
Presumably ill. I'm working so hard to screw up my exams this term that I don't deserve to be nervous
Just ****ed up my analysis exam beyond all recognition. Gonna struggle to hit 40%. Why do I bother? I learned so much, but I just had a bad draw with the questions. 
That's really unlucky Hedgeman, hopefully you'll get a nice examiner? 
Anyone have notes or worked examples on using the comparison test on integrals with a discontinuity? I have a hundred million examples of integrals from x = 1 to x = infinity, but almost nothing for using the comparison test when the integrand isn't defined at a specific point. Would really appreciate it!
Anyone have notes or worked examples on using the comparison test on integrals with a discontinuity? I have a hundred million examples of integrals from x = 1 to x = infinity, but almost nothing for using the comparison test when the integrand isn't defined at a specific point. Would really appreciate it!
Original post by Swayum
That's really unlucky Hedgeman, hopefully you'll get a nice examiner?
Anyone have notes or worked examples on using the comparison test on integrals with a discontinuity? I have a hundred million examples of integrals from x = 1 to x = infinity, but almost nothing for using the comparison test when the integrand isn't defined at a specific point. Would really appreciate it!
Anyone have notes or worked examples on using the comparison test on integrals with a discontinuity? I have a hundred million examples of integrals from x = 1 to x = infinity, but almost nothing for using the comparison test when the integrand isn't defined at a specific point. Would really appreciate it!
Yeah hope so, maybe I'll get lucky with some curving. If not then I'll just have to do well in the rest of my exams to soften the blow.
Original post by Jake22
Original post by Jake22
You can visualise the loops a and b by drawing a basepoint and then drawing two oriented edges starting and ending at the chosen basepoint. Then simply label one a and one b. Then, to glue the 2-cell, you orient the boundary and divide it into (e.g. eight for a^5b^{-3}) sectors and attach each sector according to the corresponding letter in the word. If you like, draw the two cell and write the word you are attaching by onto the boundary in this fashion.
If you are worrying about orientations then note the following - the choice of orientations for a and b is really just a choice of generators for the copies of Z in the fundamental group of the S^1s so as long as you fix orientations and stick to them - everything is consistent.
Example. Take X = S^1 v S^1 and attach a two cell by the word aba^{-1}b{-1}. Then we get a torus. How to see this? Simply draw your 2-cell as a square and then form the identification space of the square. This is the same as attaching it via the indicated word since the S^1 v S^1 is embedded in there as the corners of the square and the a and b sides.
Tbh... this is the kind of question where it is really much more handy to discuss in front of a blackboard but HTH anyway.
Also, if nobody else answers the first part, I'll say something later about that too.
If you are worrying about orientations then note the following - the choice of orientations for a and b is really just a choice of generators for the copies of Z in the fundamental group of the S^1s so as long as you fix orientations and stick to them - everything is consistent.
Example. Take X = S^1 v S^1 and attach a two cell by the word aba^{-1}b{-1}. Then we get a torus. How to see this? Simply draw your 2-cell as a square and then form the identification space of the square. This is the same as attaching it via the indicated word since the S^1 v S^1 is embedded in there as the corners of the square and the a and b sides.
Tbh... this is the kind of question where it is really much more handy to discuss in front of a blackboard but HTH anyway.
Also, if nobody else answers the first part, I'll say something later about that too.
thanks a lot, very useful.
I feel very sick. Too much exercise and not enough rest.
When does everyones exams finish? 7th of June can't come sooner.
When does everyones exams finish? 7th of June can't come sooner.
Mine finish this monday, but they've been going a while and rather relentlessly. Feel my will to revise flagging 
Mine are 2nd-7th June. I don't feel very prepared, but I'm probably just worrying too much. I know enough to be able to attempt a reasonable number of questions on each paper.
I've probably put more effort into revision this year than ever in my life (possibly with some years combined even), but I don't think I'm going to get the grades that I want unless good questions come up =/
I have linear algebra at 1pm, feeling mostly alright about it as long as the questions that have come up in the past two years come up again.
I hate exams. I can't wait for them all to be gone.
I was wrong, finish wednesday. Only QM left though
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