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jackLast night, I decided I definitely *was* pining for maths, and came home and looked out my numbers and sets example sheets. I was pleased that my storage of maths notes, while not anal, was labelled enough that I could find it, though I couldn't find the lecture notes.
(Numbers and Sets was a course in the very first term, taught by Doctor Leader, notorious for requiring no prerequisites, but being a good introduction to how to think about pure maths, and the example sheet questions graduating from "show you can use the theorems taught" to "no-one solves this ever, apart from a few of the supervisors and professors".)
I've gone through the first half. I could do everything fairly easily that I did fairly easily seven years ago.
Amazingly, I can remember the relevant theorems from the first part of the course after all this time and even how to prove them -- no doubt being the first things, and the first interesting things, they sank in more than everything else[1].
I admit, solving the questions would be basically impossible without remembering them -- you'd basically have to deduce them from the whole cloth, which is possible, but requiring a great leap of intuition. This is something to remember for later courses: often becoming lost was due to not grokking that Blah Theorem was the fundamental part of this section of the course.
My logic is, I need some recreational puzzles, and these are perfect for it: based on knowledge I have, and designed to be solvable by a bright person. And that you can work towards solving, requiring a mix of knowledge, perseverance and insight (well, ok, not much so far). Neither requiring application of only a limited set of skills, nor just the right leap of insight (as eg. soduku or riddles do).
If anyone wants to join me, feel free; I can post the questions and the solutions I do work out :) (I would expect someone bright and interested in maths but without a maths background to be able to make a start, though people may disagree in either direction.)
[1] There are only three: (1) That 1,2...(p-1) all have inverses mod p (2) Fermat's Little Theorem, ap-1=1 mod p and (3) Wilson's Theorem, (p-1)!=(p-1) mod p.
(Numbers and Sets was a course in the very first term, taught by Doctor Leader, notorious for requiring no prerequisites, but being a good introduction to how to think about pure maths, and the example sheet questions graduating from "show you can use the theorems taught" to "no-one solves this ever, apart from a few of the supervisors and professors".)
I've gone through the first half. I could do everything fairly easily that I did fairly easily seven years ago.
Amazingly, I can remember the relevant theorems from the first part of the course after all this time and even how to prove them -- no doubt being the first things, and the first interesting things, they sank in more than everything else[1].
I admit, solving the questions would be basically impossible without remembering them -- you'd basically have to deduce them from the whole cloth, which is possible, but requiring a great leap of intuition. This is something to remember for later courses: often becoming lost was due to not grokking that Blah Theorem was the fundamental part of this section of the course.
My logic is, I need some recreational puzzles, and these are perfect for it: based on knowledge I have, and designed to be solvable by a bright person. And that you can work towards solving, requiring a mix of knowledge, perseverance and insight (well, ok, not much so far). Neither requiring application of only a limited set of skills, nor just the right leap of insight (as eg. soduku or riddles do).
If anyone wants to join me, feel free; I can post the questions and the solutions I do work out :) (I would expect someone bright and interested in maths but without a maths background to be able to make a start, though people may disagree in either direction.)
[1] There are only three: (1) That 1,2...(p-1) all have inverses mod p (2) Fermat's Little Theorem, ap-1=1 mod p and (3) Wilson's Theorem, (p-1)!=(p-1) mod p.
no subject
Date: 2007-07-21 01:23 am (UTC)no subject
Date: 2007-07-21 01:27 am (UTC)My invitation to graduation dinner said we should say if we wanted to see if our old tutor or dos was able to come and see us, but it didn't seem worth it, since we're both around and I can just drop into the CMS to say hi. Though if I'm doing N&S example sheets again I *may* end up talking to him...
BTW, do you know about the picnic tomorrow? I thought I couldn't come, but my parents may not be able to be here, in which case I would like to see you all. But Risa's email didn't actually say when or where. Is there a plan, or should I ring someone tomorrow? I have the mobile telephone numbers you had four years ago, but don't know if they are still current.
no subject
Date: 2007-07-21 02:34 pm (UTC)It's at 6.30 at Ashleigh's. I don't think the phone number I have for you is up to date either, heh. Mine ends in 037...
no subject
Date: 2007-07-21 02:50 pm (UTC)