Physics and Maths, Studied this Week.

This week, I have broken new ground by studying some of the course units of M208.  I have also been recapping and filling in some gaps in my knowledge, so that I don't falter because of a lack of basic manipulation skills.

With M208, Pure Mathematics, I have started to study the Unit GTA (Group Theory A).  I have not really studied Group Theory in any depth before, other than some fun in the summer with my Rubik's Cube, and applying some group theory to its solution.

The method of study that I am using for these 'pre'-read topics that I am looking at, is somewhere in between a light touch scan, and a full exploration of the material and examples.  My aim is to have lightly read each M208 Unit, before the module begins in January.  I am reading through once and then checking my understanding by doing one worked example, followed by one or two questions on my own.

The purpose of this style of studying, is to briefly understand the new concepts and then for them to quietly mature over the winter, followed by detailed practise in an attempt at mastery, when I study the unit proper, next year.

Just a quick word on the act of reading through a mathematics text.  I have decided to experiment over the winter with a few different methods of reading.  The first that I am applying to Group Theory A and Analysis A and B, will be the Feynman method.

Richard Feynman used a simple but effective method when approaching graduate texts for the first time.  He would start at the beginning and read until he got an example wrong or lost the thread of the text.  At that point, he would then go all the way back to the beginning of the text and read through again until he hit the next area of difficulty.  Each stopping point would be slightly further on than the previous one.

I am testing this method out, as I want to see how much time it takes to keep rereading a text and whether this saves revision time later on.  I presume that after five or six passes over the whole text in this way, most of the structure and concepts of the mathematics being studied, will be like an old pair of slippers by the end of the course.

In the meantime, I am also researching other methods of study and will perhaps attempt one or two more, before comparing the efficacy of these approaches.

Anyway, here is this week's completed study:

Time spent 14hrs.

Group Theory A
Intuitive ideas of symmetry
Formalising symmetry
Symmetries of a plane figure

Analysis - Brannan
Convergent sequences and the squeeze rule. Most exercises attempted. P.48 - 61

Other Maths Exercises (60 exercises completed, in total)
Remainder Theorem
Factor Theorem
Proving inequalities
Binomial Expansion

Next week, I will fully implement the Feynman method and look at some more Group Theory.