The dust has now settled following the completion of MST121 Using Mathematics, and I have now begun to put together my study for the interim period between MST121 and M208 Pure Maths in late January. The main theme that is going to run through this period of revision, reflection and breaking new ground; is the use of 'real world' text books.
The Open University study materials are written like a set of very good lecture notes which are quite different from the type of text's that one encounters in mathematics text books. The text books often gloss over algebraic manipulations, as they plough through the solutions. This can mean that if your algebra manipulation is not very good, then you will struggle to understand the text and will not get very much out of it.
I say that OU notes are easy to use, however, I do sometimes find them rather laboured which can actually be at the expense of clarity. I have encountered several topics that I have not really understood in the OU text, only to then glance at my copy of Brannan or Spivak, and they have explained in one paragraph, what the OU has tried to explain in a whole chapter.
Sometimes, brevity can mean clarity.
The reason that I am practising reading other textbooks, is two fold. Firstly, it makes sense to use two or three approaches to learning a subject, as one of them is bound to make sense. Secondly, postgraduate maths, requires the ability to sift through other people's work, because they are either used as the set book, or when you are required to write your dissertation, you need to be able to scan quickly, large amounts of the stuff and understand it.
I have found the Brannan books (Intro to analysis and the Geometry text), to be short, to the point and relatively easy to follow. I understand that large parts of the Brannan text, are used in courses such as M208 and I am sure I recognise parts of his Geometry text, in the course notes for M336 Groups and Geometry, which I browsed at the O.U library last month.
Even so, it is helpful to study the style and brevity of these texts, for future proofing my skills. The only worry that I have, is the horror stories that I have heard, where massive mathematics texts are riddled with errata. I can just imagine me banging my head off of a large brick wall after trying to understand a problem for hours, only to find out that the solution was written incorrectly in the appendix!
Anyway, here is my study for this week. Total hours 16.
Brannan: A First Course in Mathematical Analysis - Pages 1 - 9 Real numbers.
Brannan: Geometry - pages 1 - 10 Conic sections.
Gardner: Calculus Made Easy - Pages 184 - 209 Partial differentials / integration
Practice maths skills:
Advanced factorisation
Expansion of polynomial products
Review of Linear functions
Nice post, I am just about to embark on studying MST121 and MS221. Would you be able to recommend any books and resources that you have found fun / useful to use alongside the course material?
ReplyDeleteMy number one recommendation for a book to ease the flow of MST121 or indeed MS221, would be [Calculus Made Easy] by Thompson, Gardner.
ReplyDeleteISBN 0-333-77243-1
The calculus in these two courses can come as a shock, if you haven't done any before. They appear okay when you study them, but TMA4 and CMA42, for example, feature calculus questions that really test your fluid use of the rules of differentiation, integration and algebraic rearrangement.
I found that the Gardner book often explains very well in a few words, what the OU texts try to laboriously explain in a whole sub-unit.
My next post is actually going to feature an extract from this book, on this very topic.