I still have the plague (man flu) and I am having to take some heavy duty painkillers for a chest infection. This has caused a certain haziness which has made any mathematics study difficult, but not impossible.
I have continued to try and refine my study methods that I will deploy when M208 begins in January 2012. The books should arrive at the end of December, around xmas time, but I have managed to find enough of the unit materials, to not only get a small head start, but also to allow me to prime any areas that I may find difficult next year.
If I were to say which are my favourite areas of M208 mathematics, they would probably be, in the following order, (favourite first):
Group Theory
Analysis
Linear Algebra
I find all the groups stuff very interesting and with such amazing applications from discovering new particles to solving the Rubik's cube.
Just a general note about M208. I fear that if one were to stumble across the OU website and take the 'Are You Ready for M208' diagnostic knowledge check; then one could very easily get caught in an elephant trap, if one then assumed that the test is a fair representation of the mathematical maturity required, to study the course.
It is true that you can start the course with the knowledge from a good A level, but having looked at all the M208 study material in detail, last month; there are some very challenging topics and it goes into wonderful depth and breadth, around these topics.
I am not sure I would have coped, had I not started reading Brannan et al, last month and therefore turning a 9 month course into a 12 month course by getting a head start.
The rough list of main topics covered is as followed:
Real functions and graphs
Graph sketching
Hybrid functions
Curves from parameters
Sets
Functions
Proof
Binomial theorem
Geometric series identity
Number systems
complex numbers
Modular numbers
Equivalence relations
Symmetry in R^2
Representing symmetries
Group Axioms
Proofs in group theory
Symmetry in R^3
Groups and subgroups
cyclic groups
isomorphisms
groups and modular arithmetic
Permutations
Conjugacy
Subgroups
Cayleys theorem
Cosets and Lagrange's theorem
Vectors and conics
Matrices and vectors
Vector Space etc
Linear transformations
Eigenvectors
Conics and Quadrics
Inequalities
Bounds upper and lower etc
Sequences
Series
Continuity
Conjugacy
Homomorphisms
Kernels and images etc
Group actions
Orbits and stabilisers etc
Limits and continuity
Differentiation
Integration
Power series
Wow, all that in 9 months, 7 coursework assignments and one 3hr exam.
I can't wait!
Monday, 31 October 2011
Monday, 24 October 2011
Dicta-phones and highlighter pens!
I'm currently in bed sick, after 5 days of glandular fever, which is not pleasant. As such, I have only managed a few hours of study this week and I have concentrated further on honing my study method, rather than worrying about what to study.
Last week I decided to ditch the idea of recording study material and then playing it back to myself. However, I have further expanded that idea and this week I have used the dicta-phone again, but I have recorded short questions, based on the material, followed by a recorded answer.
I have found that listening to the question, retrieving the information, and then answering the question, has been a useful memory tool. It has allowed me to effectively learn some of the 'filler' material in a unit, that isn't necessarily directly tested by doing practise exercises, yet is important to know.
I have also used the highlighter to clearly define what I need to remember, and then strictly, only re-read the highlighted areas, when I have revised the unit. This seems to be working well and is cutting down revision times.
Anyway, I'm too sick to do much else this week. Hopefully I'll be better soon.
Last week I decided to ditch the idea of recording study material and then playing it back to myself. However, I have further expanded that idea and this week I have used the dicta-phone again, but I have recorded short questions, based on the material, followed by a recorded answer.
I have found that listening to the question, retrieving the information, and then answering the question, has been a useful memory tool. It has allowed me to effectively learn some of the 'filler' material in a unit, that isn't necessarily directly tested by doing practise exercises, yet is important to know.
I have also used the highlighter to clearly define what I need to remember, and then strictly, only re-read the highlighted areas, when I have revised the unit. This seems to be working well and is cutting down revision times.
Anyway, I'm too sick to do much else this week. Hopefully I'll be better soon.
Tuesday, 18 October 2011
Study Methods (Mathematics)
Alrighty,
This past week or so, I have been testing out some different approaches to studying mathematics. I hope to find a groove that I can develop and then duplicate for future mathematics courses over the next 3 years. I have tried a couple of minor tweaks, whilst I have been studying Brannan's Analysis. Some examples are below:
Test 1 (4 days of study time)
Chapter 1, p.1- 29
2 x skim read (to gain overall structure of chapter)
2 x detailed read, no examples attempted (to become used to new terminology and start to embed the flow of the subject material)
1 x recording on dictaphone, all rules, theorems and definitions.
1 x playback of recording
Selected 1 x example for each type of new problem introduced.
Attempting selected problems (6 in total), repeated each day, at the start of a study session.
1 x video lecture on topic (Notts University Analysis series on U tube)
Test 2 (4 days of study time)
GTA1 Symmetry M208 (Pure Mathematics)
2 x skim read
1 x detailed read, with highlighter pen, in hand
4 x detailed read of highlighted text only
Selection of 1x examples for each different type of problem
Attempting selected problems (12 in total), repeated each day, periodically throughout the day
I haven't done a scientific test of which aspects of these two test periods is the most effective. I have simply gone on feel. I want to develop a personal set of tactics that fit my current lifestyle and work / life balance; whilst maximising the amount of information retention.
The early results are thus:
Recording and playing back a dicta-phone, didn't really work for me. I will probably ditch that.
The skim read was good and stopped me getting bogged down with examples, whilst giving me an overall picture of the chapter.
The detailed read was good, but it was difficult to stop my self getting tied up with examples. That discipline will come though with practise.
Selecting one example for each area was a good idea. It allowed me to repeat each one, eventually from memory. This will help with later exams, allowing me to memorize problem structures, rather than relying on an annotated handbook, which will save time on the day.
The Notts University year 2 Analysis lectures, are a real find. They are clear, concise and presented by a lecturer who is clearly a very good teacher, rather than just an academic who is begrudgingly forced to teach undergraduates. No clouds of chalk dust here.
I have also started to experiment with some new software that I am trialling. It is called MindGenius and is some very advanced and intuitive mind-mapping software. It allows for rapid creation of mind-maps of study chapters, almost as quick as you can type. As a dyslexic, I have needed to study using mind-maps, for years, as they suit my non linear way of thinking and aid my memory recall.
I will report more on MindGenius next week.
ps: I've put the link here for ease of finding it, I don't earn any money from it.
Other maths studied this week
Factor theorem
Remainder theorem
Graphing quadratics
Proof of identities
Total time spent: 36hrs
This past week or so, I have been testing out some different approaches to studying mathematics. I hope to find a groove that I can develop and then duplicate for future mathematics courses over the next 3 years. I have tried a couple of minor tweaks, whilst I have been studying Brannan's Analysis. Some examples are below:
Test 1 (4 days of study time)
Chapter 1, p.1- 29
2 x skim read (to gain overall structure of chapter)
2 x detailed read, no examples attempted (to become used to new terminology and start to embed the flow of the subject material)
1 x recording on dictaphone, all rules, theorems and definitions.
1 x playback of recording
Selected 1 x example for each type of new problem introduced.
Attempting selected problems (6 in total), repeated each day, at the start of a study session.
1 x video lecture on topic (Notts University Analysis series on U tube)
Test 2 (4 days of study time)
GTA1 Symmetry M208 (Pure Mathematics)
2 x skim read
1 x detailed read, with highlighter pen, in hand
4 x detailed read of highlighted text only
Selection of 1x examples for each different type of problem
Attempting selected problems (12 in total), repeated each day, periodically throughout the day
I haven't done a scientific test of which aspects of these two test periods is the most effective. I have simply gone on feel. I want to develop a personal set of tactics that fit my current lifestyle and work / life balance; whilst maximising the amount of information retention.
The early results are thus:
Recording and playing back a dicta-phone, didn't really work for me. I will probably ditch that.
The skim read was good and stopped me getting bogged down with examples, whilst giving me an overall picture of the chapter.
The detailed read was good, but it was difficult to stop my self getting tied up with examples. That discipline will come though with practise.
Selecting one example for each area was a good idea. It allowed me to repeat each one, eventually from memory. This will help with later exams, allowing me to memorize problem structures, rather than relying on an annotated handbook, which will save time on the day.
The Notts University year 2 Analysis lectures, are a real find. They are clear, concise and presented by a lecturer who is clearly a very good teacher, rather than just an academic who is begrudgingly forced to teach undergraduates. No clouds of chalk dust here.
I have also started to experiment with some new software that I am trialling. It is called MindGenius and is some very advanced and intuitive mind-mapping software. It allows for rapid creation of mind-maps of study chapters, almost as quick as you can type. As a dyslexic, I have needed to study using mind-maps, for years, as they suit my non linear way of thinking and aid my memory recall.
I will report more on MindGenius next week.
ps: I've put the link here for ease of finding it, I don't earn any money from it.
Other maths studied this week
Factor theorem
Remainder theorem
Graphing quadratics
Proof of identities
Total time spent: 36hrs
Wednesday, 12 October 2011
A Mathematical Interlude...
I have composed a quick test that can be used, to determine whether you been studying maths with the O.U , for too long:
1. Read the following joke. If you laugh, then you have done too much studying. I recommend that you take 6 weeks off.
Joke:
Q: What's a rectangular bear?
A: A polar bear after a coordinate transform!
That is all.
1. Read the following joke. If you laugh, then you have done too much studying. I recommend that you take 6 weeks off.
Joke:
Q: What's a rectangular bear?
A: A polar bear after a coordinate transform!
That is all.
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