First Impressions

Well,  I think I like my new courses.  Number Theory isn't as heavy on content, as I first thought, and I have been able to manage to stay on track for my first 1.5 weeks of study.  The main thrust of the material, is the mastery of Mathematical Induction as a way of providing simple proofs for integer problems.

I struggled with induction, when I studied M208 Pure Maths; but I think this was because I didn't allow enough time to complete practice problems, on the subject.  However, I have taken head of the warning in the material for the number theory course, which states that Induction must be mastered, asap.

So, I have spent hours doing problems and redoing them, until the method started to stick.  Having said that, I have pretty much struggled with the algebraic step in the last part of all of these proofs.  Now, I considered myself to be at an advanced intermediate level, when it comes to algebraic manipulation; but these examples in the texts, make huge jumps in the algebraic reasoning, that I have struggled to follow or replicate (even by punching the expressions into Wolfram Alpha).

I definitely need to ask my tutor for some advice, about that.  I do hope that I have not reached a natural ability ceiling, that hinders my progress on the course.

The groups course has been quite heavy on material volume, in the first book.  You only get 1.5 weeks per book, where as, you get 2 weeks for a similar amount of material in number theory.  Most of the material introduced, was basic concepts and language, that will be needed for the course; however, there was a cheeky little chapter on Affine geometry, which I started off hating, but then when I got all the examples right, without referring to the answers; I started to love it.  How fickle!

Also, I have to say, that I find it soothing, rather than boring, to manipulate tiling's.  I know that people who previously took the course, felt that it was all a bit dull.  I find that they are all so geometrically neat and satisfyingly symmetrical; just the right amount of order needed, after a torturous and chaotic day at work!

I am adopting a new strategy for my studies this year.  That is, I have decided to complete all of the practice examples in the books, having a good go at them, before referring to the answers.  In my last few courses, I had started to get into the habit of skimming the examples, kidding myself that I was saving time, or leaving myself extra practise examples for exam time.  I think it was a false economy and harmed my understanding of some of the more difficult concepts in analysis and linear algebra.

Lets see if it does me any good, this year.