I have now ploughed through the first two units of Analysis A; which is part of M208 Pure Mathematics, with the Open University. Now that I am off work sick, awaiting back surgery, I have managed to consume an entire Unit in two days (should take about 16hrs per unit); so things are going okay at the moment.
As I was studying, I picked up my wonderful copy of David Brannan's 'A First Course in Mathematical Analysis'. Now, the uninitiated may not actually know, but approximately 95% of the Analysis section of M208, is a direct lift from the pages of Brannan. Shock, horror, you say! I think that they have just left it mainly unaltered, because of the simple, sequential way that he expands on series and continuity, before launching into differentiation and integration, making the subject easier to follow.
This is not dissimilar to the way that Spivak, approaches the subject in his book, 'Calculus', the title of which may throw one a little, as the book actually covers much more than the simple mechanical aspects of calculus; as it weaves through series, limits, vectors, conics, planetary motion and plenty of rigour to whet the appetite of any purist. I have the third edition, and I thoroughly recommend owning it, even if it's for nothing else other than the beautiful way he explains the basic theories of numbers in chapter one; or the way he makes one chuckle, by entitling the seventh chapter 'Three Hard Theorems'. You certainly know what to expect from that chapter!
Now, one thing that struck me, about the M208 Units, whilst I was leafing through Brannan, is that each M208 unit is an A4 size booklet, of, say 40-60 pages of text. Each one, sometimes, feels, like a 'pamphlet', an easy read option, almost like lecture notes, purposely written to give a student an easy life. Yet, they are actually very deceiving!
It only took a few moments to realise, that just 8 of these 'pamphlets' actually cover the entire Brannan Analysis Textbook. I found this surprising, as when you look at Brannan, it looks pretty scary in size. So, maybe M208 isn't all that light on reading, after all. The only problem with that assertion, is that one of the tutors at day school (an insanely brilliant mathematician), recently described M208, as Pure Maths 'lite'. Well, it feels pretty 'full-fat' to me. Time will tell, as to whether it will provide enough background to cope with any future studies.
approximately 95% of the Analysis section of M208, is a direct lift from the pages of Brannan
ReplyDeleteThat's the wrong way round :) In fact, the book is based on M208 - see the Acknowledgements page xii. Brannan wrote some of the M208 units which he then turned into a book. He did the same for Geometry which was part of the predecessor course M203.
described M208, as Pure Maths 'lite'. Well, it feels pretty 'full-fat' to me.
It's the same at all levels of mathematics all the way up to research level. This year's course seems hard and is a lot of work but last year's is easy in comparison and next year's looks impossible. In the future you will look back at M208 and understand what the tutor meant.
Excellent, thank you Stevem.
ReplyDeleteWhen you come to the continuity, but Non differentiablity of the Blancmange Function you will see that Brannan covers the topic especially the Non differentiability in a lot more detail. The bit in M208 which discusses this is a bit hand wavy. So Brannan is a useful complement to M208 also you don't have those pesky audio tapes to interrupt the flow.
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