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get out of jail free

Wednesday, 30 Nov 2011, 12:31

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I seem to have used this card.

Over two weeks ahead of schedule the M208 exam results came out today. I got a grade 2 with 65% for the exam and 93% for the continous assessment.

Given the stuff-up I made of the exam this is way beyond my expectations and, frankly, much more than I deserve.

Looking at the break-down of the results it looks like the mark bell curve has been shifted down [I should have required 70% for a grade 2]. Which is a bit odd, as I thought, despite my woeful efforts, that the exam was pretty fair.

On [another] plus side this should mean a good crop of distinctions for my tutorial mates.

Tags: m208

Permalink 11 comments (latest comment by ROSIE Rushton-Stone, Wednesday, 30 Nov 2011, 22:17)

at last

Friday, 28 Oct 2011, 18:46

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Edited by Neil Anderson, Friday, 28 Oct 2011, 18:48

My course review for M208 has been finished. Albeit with the wrong date.

Tags: m208

Permalink 3 comments (latest comment by Chris FInlay, Sunday, 30 Oct 2011, 09:48)

course review M208

Monday, 24 Oct 2011, 22:10

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I'm having trouble with this.

Usually I just write the thing. This time I have a problem; I've loved this course [M208 Pure Maths] but I'm going to get my worst mark ever. How should I slant it? [The review].

Just tell the truth? I learnt a long time ago that the truth isn't the truth. However hard I try I won't be able to tell the truth, ever, about anything.

So I'm going to do the review over a few nights, and I'm going to post the drafts. Democratic.

No. Just open, I'd pretend that anyhoo...so daraft #1

what’s involved here?

This is a sixty-point course, a wee bit more than my usual. I found it hard, really hard. I found it hard because of the workload, because of the content and because of me. Don’t let that put you off.

A sixty-pointer is always going to be harder, the ante is seriously upped compared to a thirty-pointer. We did seven, yes seven, TMAs and some of the material requires [at the very least] a second look. At times I felt that all life was a hellish series of TMA deadlines. This course requires a serious commitment; of your time, of your mind and of your mental stability. This course is something that you should think hard about.

Still, horrors aside, there are hearty morsels on offer here. More than enough to make skirting with failure and exhaustion more than worthwhile for the brave student. This was the first course where I really began to see what maths, pure maths, has to offer the mind. [Of which more later]

what’s involved?

This is a fairly stable course—things don’t change much. So you can be fairly confident that what follows will be much the same as what you will face.

There are six blocks, but four really. The introductory block doesn’t really count [except in the exam] it’s mostly a re-hash, the two Group theory blocks are co-joined [although not seemlessly], the Linear Algebra stands alone and the analysis blocks go together [again not seemlessly].

Hereis where we begin to realize that maths is all of a piece .

That’s what I really took from this course—I’m beginning to get why, “that curve” has something to say about prime numbers. I know now that I’ll never know why, but that isn’t the point. Next year I do topology, my shoddy understanding of Eigenspaces will come back to haunt me, I'm not sure how—but I’m certain that it will.

It wont be this way when I post it

Tags: pre, m208, trivia

Permalink 3 comments (latest comment by Neil Anderson, Tuesday, 25 Oct 2011, 18:38)

Elephants

Wednesday, 12 Oct 2011, 19:53

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And last M208 blog post.

Tags: m208

Permalink 9 comments (latest comment by Chris FInlay, Friday, 14 Oct 2011, 22:24)

Car

Tuesday, 11 Oct 2011, 21:03

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Crash.

Or how I messed up.

Tags: m208, exam

Permalink 4 comments (latest comment by Neil Anderson, Wednesday, 12 Oct 2011, 20:06)

nap

Saturday, 8 Oct 2011, 20:17

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Edited by Neil Anderson, Saturday, 8 Oct 2011, 20:21

I was utterly done in when I came home from work this afternoon. This business of working from 6am to 11pm and getting in for 8am the next day is something that's beginning to take its toll on the aging neil.

Anyway, after a [four hour] nap I did some maths. It wasn't too bad but I realized that it was time to be honest with myself—what grade am I aiming for here?

There's a bit of me that thinks that I can still get a distinction, the realist in me knows that I should ensure a grade 2. I'm going to go with my realist, and revise accordingly.

This is slightly gutting, but if I've learnt anything on the OU road it's to know yourself. It's way too easy to aim for the stars and end up with your nose buried and broken in the dust of some planet.

The trickiest of the things that we have to learn is the abilty to cross our own hopes, we can't always have what we want, can we accept that we aren't as special as we think we are?

Tomorrow we do maths...

Tags: trivia, m208

Permalink 2 comments (latest comment by Joyce Rae, Monday, 10 Oct 2011, 00:15)

Bad things

Friday, 7 Oct 2011, 22:16

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happen. But we will win. Or why I will pass my exam.

Tags: m208

Permalink 4 comments (latest comment by Susan Whelan, Sunday, 9 Oct 2011, 21:20)

october comes

Wednesday, 28 Sep 2011, 21:18

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What does an old man make of it?

Tags: m208, degree

Permalink 3 comments (latest comment by Neil Anderson, Thursday, 29 Sep 2011, 19:54)

i've failed

Tuesday, 27 Sep 2011, 20:39

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Edited by Neil Anderson, Tuesday, 27 Sep 2011, 23:24

So I plan for success.

Tags: m208, exam

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Where's neil?

Monday, 19 Sep 2011, 20:31

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Edited by Neil Anderson, Monday, 19 Sep 2011, 22:20

Every so often I read all of this rubbish that I write about a course [it's the main reason that I keep a blog]. Usually only before I write a course review, but sometimes at other times. And today I did so. What did I find?

[You have to realize that I am me, and my own words have a different effect on me than they will have on you.]

Aside from the usual moaning and the fact that I've always seem to have been scrambling on this one, something stands out: that I'm beginning to wonder if I'm up to maths. And that's not right.

Having got to the end of this course, except for the exam, I now know that not only do I love maths but I can grok it. There may come a time where it will get beyond me, that time is not yet. And that time may never come.

I don't say this to big myself up, I say this because the most serious problem that we face as students is to think that we can't do something.

The usual work/life overload occasions—they come with the territory, if you don't want them to visit, don't play here.

The idea that your mind isn't up to something is a far more sinister problem, it's all too easy to project this belief onto some other excuse—"the pace is too fast for me". Don't.

One of the best things about blogging is that you have to write around your own lies—and the worst lies that you can tell yourself are the excuses that you make to avoid doing something that you can do because you don't have the bottle to admit that you could.

Tags: trivia, m208

Permalink 3 comments (latest comment by Neil Anderson, Monday, 19 Sep 2011, 22:34)

A rather dodgy

Monday, 19 Sep 2011, 14:16

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revision plan is hatched.

Tags: m208, exam

Permalink 8 comments (latest comment by Neil Anderson, Monday, 19 Sep 2011, 20:41)

hhmmm

Wednesday, 14 Sep 2011, 21:24

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Got my marks for my penultimate TMA, got my ultimate TMA to submit by tomorrow. It's now down to the exam. [We aren't allowed to talk about our marks.]

I'm surpised by how much I've lost, and by how much I remember. But there are differences even in those categories.

Sometimes all it needs is a nudge, sometimes I need to work through the whole exercise again, sometimes the hand knows what to do.

I suspect we all feel this. Learning is hard.

But what else have we got?

Tags: m208

Permalink 5 comments (latest comment by Neil Anderson, Thursday, 15 Sep 2011, 14:58)

Wrong

Friday, 9 Sep 2011, 16:39

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Just wrong.

Tags: prime numbers, m208

Permalink 3 comments (latest comment by Neil Anderson, Friday, 9 Sep 2011, 20:47)

Strange stuff

Thursday, 8 Sep 2011, 21:24

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I want to understand it. Won't, won't stop my striving.

How stupid am I?

Tags: m208, revision

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Revision[2]

Monday, 5 Sep 2011, 19:53

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I've now looked through all the revision TMA questions, not happy, not happy with me. Too often I lack the knowledge and when I do have the knowledge I'm as slow as the snails that we re-housed from our garden to the canal recently.

I knew that this [my sloth] would come back to bite me. I haven't put enough effort into this course. Still I have a month or so...

One must never despair before the black-night is actually upon us. Until then we might escape the worst.

The worry is that I'm reliant on my own efforts to produce this Houdini-maneuver. That has never gone too well in the past.

Tags: m208

Permalink 4 comments (latest comment by Neil Anderson, Friday, 9 Sep 2011, 18:54)

Communication

Saturday, 3 Sep 2011, 11:52

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Problems

Tags: m208, revision

Permalink 2 comments (latest comment by Neil Anderson, Monday, 5 Sep 2011, 19:23)

Revision

Friday, 2 Sep 2011, 20:54

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Edited by Neil Anderson, Friday, 2 Sep 2011, 21:31

Us maths bods are fortunate in that we usually get a revision TMA. How helpful this is rather depends on how you are doing—can we afford to treat it as a true test, the sighter that it should be?

For now I'm tackling it using only the handbook [the one that we get to take into the exam]. But that may change; if I've stuffed up my last TMA then I may need the marks to give me a shot at a good result [a very real possibility].

Ideally this TMA would be a throw away for me and I could run rampent. Messing around with the assessment predictor has given me an idea as to how well I have to do for TMA06 to allow me to tackle TMA07 as an exercise. It isn't too bad, and hopefully I should be able to. But... until that result is in I'm in limbo.

exam

Having a few exams under my belt I think that I know what you have to achieve—be able to use what you know quickly. Time is the test. For maths much of your speed is down to your handbook and how well you understand it.

We're allowed to annotate said thing, I never do; the things there should spark what you know, what you know shouldn't be in there. It's a tool, not your brain.

At the end of a course you must stop learning and start strategizing [that is a Greek root?] for the exam. To be an OU student you have to be two people.

One who learns and one who can show that you've learned. Tough if you do one without the other.

Tags: m208, exam

Permalink 4 comments (latest comment by Neil Anderson, Tuesday, 6 Sep 2011, 16:44)

whoops

Wednesday, 31 Aug 2011, 20:29

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Post speaks for itself.

Tags: m208

Permalink 2 comments (latest comment by Neil Anderson, Thursday, 1 Sep 2011, 20:03)

TMA Avoidance

Tuesday, 30 Aug 2011, 20:32

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Angst

Tags: m208

Permalink 3 comments (latest comment by Neil Anderson, Wednesday, 31 Aug 2011, 20:38)

Taylor

Sunday, 28 Aug 2011, 13:52

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How I hate him

Tags: m208

Permalink 4 comments (latest comment by Neil Anderson, Wednesday, 31 Aug 2011, 20:56)

How

Sunday, 14 Aug 2011, 13:02

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History helps.

Tags: history of maths, analysis, m208

Permalink 2 comments (latest comment by Neil Anderson, Saturday, 20 Aug 2011, 14:08)

Got it I think

Wednesday, 10 Aug 2011, 15:19

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Edited by Neil Anderson, Wednesday, 10 Aug 2011, 15:20

It's a mess, needs optimized, I need to pseudo-overload it and tidy up my messes, but hey, I have a function that composes permutations!

<html>
<head>
<title>Permutation</title>
</head>
<body>
<script type="text/javascript">
/*
Signature:
Array [Array int || int] X int -->boolean
post:
true if the int is in the permutation
*/
function contains(arr, val){
var found = false, over = false, ret = false
var ix = 0;
while(!found && !over){
if(typeof arr[ix] == 'object'){    //a cycle
var subArr = contains(arr[ix], val);
ret = subArr;
found = subArr;
ix++;
}
else{
if(arr[ix] == val){
ret = true;
found = true;
}
else if(ix++ >= arr.length){
over = true;
}
}
}
return ret;
}

/*
Signature:
Array int X int --> int
Post:
the int after val
the first int in the array if val is the last member of the array
val if the array doesn't contain int
*/
function findNextInCycle(arr, val){
var len = arr.length;
for(var i = 0; i < len; i++){
if(arr[i] == val){ //we have the value
if(i == len - 1){ //end of the permutation return the first
return arr[0];
}
else{ //return the next value
return arr[i + 1];
}
}
}
return val; //val didn't exist in the permutation
}

/*
Signature:
Array [Array int || int] X int --> boolean
Pre:
Either an array of int representing a single cycle
or an array of array(int) with any fixed points excluded
ie [1,2,3] or [[1,3], [2,4]] but not [[1,2], 3, 4]
the last should be [1,2]
Post:
the int after val
the first int in the array if val is the last member of the array
val if the array doesn't contain int
*/
//uses findNextInCycle
function findNextInPerm(arr, val){
if(contains(arr, val)){
for(var i = 0; i < arr.length; i++){
if(typeof arr[i] == 'object'){ //an array hand it off to findNextInCycle
if(contains(arr[i], val)){
return findNextInCycle(arr[i], val);
} //otherwise we carry on through the cycles
}
else{ //hand the whole thing off to findNextInCycle
return findNextInCycle(arr, val);
}
}
}
else{
return val;
}
}

/*
Signature:
Array [Array int] --> Array int || Array [Array int]
Post:
If the argument contains only a single array it will return that
Otherwise it will return an array with all single length cycles removed
*/
function fixCycles(arr){
if(arr.length == 1){
return arr[0];
}
else{
var ret = [];
for (cycle in arr){
if(arr[cycle].length > 1){
ret.push(arr[cycle]);
}
}
return ret;
}
}

/*
Signature:
Array [Array int || int] X Array [Array int || int] --> Array Array int
Pre:
The arrays must be either of int representing single cycles
or arrays of array(int) with any fixed points excluded
ie for either array [1,2,3] or [[1,3], [2,4]] but not [[1,2], 3, 4]
the last should be [1,2]
Post:
a composition of permutations
Use the fixCycles function to change this into a single permutaion

Note:
We need len because we may not have all numbers may appear in the perms
*/
function composePerms(first, second, len){
var ret = [], cache = [];
for(var i = 1; i <= len; i++){
if(!contains(ret, i)){
var at = i;
while(!contains(cache, at)){
cache.push(at);
at = findNextInPerm(first, findNextInPerm(second, at));
}
ret.push(cache);
cache = []; //reset
}
}
return ret;
}

var x = fixCycles(composePerms([1,2,4,3,5], [1,2,3,5,4], 5));
for(i in x){
document.writeln(x[i]);
} //1 4 2 5 3

// -->
</script>
</body>
</html>

Now I need to write the unit tests, and a test suite.

Tags: group theory, javascript, m208, trivia

Permalink 2 comments (latest comment by Neil Anderson, Wednesday, 10 Aug 2011, 20:09)

failure

Tuesday, 9 Aug 2011, 19:27

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Edited by Neil Anderson, Tuesday, 9 Aug 2011, 19:27

Today I tried to write some Javascript that would allow me to compose permutations; I got an idea that I wanted to bulk test.

[I should be working on analysis but my mind and fingers itch for groups.]

It was surprisingly hard—because I tackled it stupidly, I didn't write a specification and I've lost my test harness somewhere along the road.

The beast is still in the myth stage.

I will manage this, but my uselessness, after all this study, annoys me hugely. And why do I rely on code [that I can't write] to confirm something that I should be able to prove?

Tags: group theory, javascript, m208, trivia

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More books

Monday, 8 Aug 2011, 18:09

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Edited by Neil Anderson, Monday, 8 Aug 2011, 18:11

I managed to acquire...

A concise history of mathematics Dirk J Struik
Real Analysis H L Royden
Mathematical Analysis T Apostol
Methods in Numerical Analysis Nielsen
The Philosophy of Mathematics S Körner

But best of all I got, A course of Pure Mathematics G H Hardy.

They sit next to me in a pile that I fondly glance at once a minute I guess. [Hardy I'm reading.]

Of all the things in this world, barring anything living, I do love books the best. I'm now old-fashioned but if books stop existing we will lose so much; we will have everything always available and nothing to hunt for. That is a truly sorry place for a human to be.

Tags: trivia, books, m208

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At some point

Wednesday, 3 Aug 2011, 20:13

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You may do what I have just done—make a stupid post that you can't retract. Here's how to react: scream a wee bit; strangely it helps.

For me I need to remember that I'm an idiot in a realm of giants; but we need idiots, I serve a point.

Tags: trivia, m208

Permalink 3 comments (latest comment by Wren Tyler, Thursday, 4 Aug 2011, 17:48)

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