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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.