Open University: TMA Cut-off date

As an OU student you have to make several TMAs for each course you do. TMA stands for Tutor Marked Assignment. A TMA consists of assignments covering all the booklets you studied in the period prior to the cut-off date of the TMA. The cut-off date is the latest date the work has to be received by your Tutor. This is a period of cut-off dates. Usually you'll find a lot of blog, forum, twitter or facebook posts about TMAs that have been done. Completing a TMA is just part of the study process but for an OU student it's somewhat of an event. Not like an exam, but sending it out gives a feeling of relief, achievement perhaps. Completing a TMA is not something most people do in a few hours, some TMAs take weeks if not months to complete.

The average result of the TMA ( after some formula has been applied to it ), is the maximum result you can get from the course because the final result of the course is the minimum of the exam result and the average TMA score. Also, a minimum TMA score is required to be eligible for taking the exam. For example.
TMA result: 15/100 not eligible for exam.
TMA result: 65/100. Exam result: 100/100. Course result 65/100.
TMA result: 100/100. Exam result: 15/100. Course result 15/100 and thus a FAIL.
Completing all the TMAs on time, requires regular study, and regular study enhances the chance on a good exam result significantly. I suppose that's the thought behind it all. The second example may seem rather undesirable, but it just is not a realistic scenario. A student with a 100% exam score usually has no problems with the TMAs.

Personally, the TMAs are no longer my 'major math challenge'. Slowly but steady I am working on my own mathematical projects. I still need to study, of course, but I am an OU student mainly to justify the time I spend on mathematics to the other stakeholders in my time. - When you say you study mathematics as a hobby, people accept it ( at best ), but explaining that, in fact, you are involved in your own mathematical research is worse than telling that you apply the tools of Scientology in your life. So... I am an OU Student, if you know what I mean. ;-)

OU exams more difficult than ever ( ... ) ?

I read a rumor on facebook that the Open University exams were harder than ever. No numbers were shown to substantiate the claim however. You may have been aware that the OU rates have been increased dramatically to align them with the rates of the "Brick Unis" ( = how normal universities are called in OU jargon ). Now one of the commenters said that they are doing the same thing with the exams. Suggesting that until now OU exams were much easier than Brick Uni exams. - To be honest I think it's the other way around. Often homework assignments ( for maths at least ) are part of the grade Brick Uni exams while at the OU you get the lowest grade of homework and exam.

The Big LaTeX discussion

Although it is perfectly acceptable to handwrite your TMAs at the beginning of every course someone starts the "Big Latex Discussion" again.

It's usually a nerd that starts off by listing the irrelevant but impressive specs of his ( not often her ) hardware, or bloats how much computing know how he has ( part-time math students often work in IT ). He then announces that he 'is going to make his TMAs in LaTeX.

Wow. Jaws dropping. Not.

Not often he also provides us with a list of software artefacts required, version numbers included. Nerdy but deep in the autistic spectrum.

I haven't decided how I'll produce my TMAs this time. I see three options. Hand-written, LaTeX typeset or (new!) handwritten but digitally stored in vector graphics format.

LaTeX became a problem ( pita ) for me in the past when I had to add drawings and stuff. Making and including mathematical drawings in LaTeX is not trivial. Besides it is a major distraction, while you should be thinking about math you are figuring out how some latex drawing package works. Serious waste of time.

Since you can draw on a tablet, store it in SVG and thus manipulate it any way you want, doing the formulas in LaTeX and the drawings 'by hand' is probably the route I take.

Since I do Android work Eclipse became more or less my IDE of (only) choice so I'll give TeXlipse with PDF4Eclipse a try.

Tilings resources

I am on a OU course again, ( more about that in posts to follow ). The course site opened today, that really kicks off the course for me.

For now some resources you might find interesting.

A tiling is a covering of the whole plane with non-overlapping tiles, each of which is a topological disc. The classic work on tilings is Tilings and Patterns by Grunbaum, Shephard. A list with other books on the subject can be found here.

M.C. Escher used tilings in his graphics work in an ingenious way. This book contains a nice collection of the work of Escher.

It's interesting to note that in Escher's time (1901-1972) there was hardly any mathematical theory about tilings. The foundational work on tilings was published five years after Escher died. Yet from Escher's work it is clear that he understood tilings, and the related line symmetries ( Frieze Patterns ), lattices and plane symmetries ( Wallpaper Patterns ) as no other.

If you are interested in puzzles at all it's likely that you came across Jaap's Puzzle Page, a vast resource of information regarding puzzles. The website is maintained by Jaap Scherphuis. You'll find his YouTube site here with many puzzle demonstrations.

To my astonishment Scherphuizen also maintains an impressive collection of tilings on a Tilings Page. His tilings demonstrations Java Applet is as impressive which you'll find on the same page.

'Pentagon Flower' ( background tiling is the [4,8,8] Laves tiling )
(c) nilo de roock 2012

Escher's imaginery workplace

#mathematics #art #Open University #m336 #Escher

The Scream by Edvard Munch was sold for USD 120 million. I didn't like it yesterday and I don't like it now that I know it's perceived value. My favourite artists are Escher, Kandinsky and Dali, their work inspires me, and I am truly impressed by what they have created, art needs beauty. M336 brings group theory and geometry together through visual symmetry, or the symmetry Escher used in a lot of his work. I browse a lot through work of Escher as a result of M336 studies. Recently I came across this sensational video. A must see, really.


( A short movie inspired on Escher's works and a free vision on how it could be his workplace. )

This is another video by Eterea.

( A short movie about numbers and geometry. )

What is a lattice? - Or lattices in M336

#openuniversity #m336

The Open University course M336 contains two booklets which are dedicated to lattices. One booklet about two-dimensional lattices (GE3) and one about three-dimensional lattices ( and polyhedra ) (GE6). To a layman I would explain lattice as some regular grid of points ( connected by thin lines ).

Click to enlarge

In the example above the lattice is defined by two vectors and consists of all points $n \mathbf{a} + m \mathbf{b}$ where $n,m$ are integers.

Fields which use lattice theory are crystallography, finance, game ( maze ) programming, group theory and number theory. When I dug a little bit deeper I discovered that the field of lattices is -ginormous-. Gabriele Nebe and Neil Sloan ( yes him ) maintain a catalog of lattices which now contains over 160,000 lattices. Mathematicians like to generalize over n-dimensions so yes, that database contains lattices in dimensions higher than 3. Like lattices in 40 dimensions for example. Forty.

A catologue of lattices.
Junkyard article about lattices and geometry of numbers.

The mathematical universe is expanding with tremendous speed.

hELP !

#openuniversity

Please help the Open University by signing this petition. It takes less than a minute of your time.

Stop the cuts in the Open University

Thank you very much.

( You must be a British citizen or normally live in the UK to create or sign e-petitions. )

Explorations beyond M336: the permutohedron

#maths #openuniversity

M336 is a two track level 3 Open University Mathematics Course with geometry track covering frieze- and wallpaper patterns, tilings and polyhedra, and a group theory track covering the Correspondence Theorem, the Sylow Theorems and the classification of Abelian groups. - When you are doing a course you are not only learning the course materials but it also broadens your view on the field. Well, I have seen quite a few new and ( fascinating ) topics lately.

Two short ones in this post and more to follow.

If you are into mathematics I bet that you have seen Inception, not that it is a mathematics movie per se but it is the type of movie math geeks love, I am sure. Anyway, do you remember the scene where Cobb and Ariadne walk on the Seine boulevard where she turns a mirror around and suddenly you see an infinite number of images. There is a name for the symmetry group of that pattern, it is a Dihedral Group with symbol $D_{\infty}$. Part of Group Theory is dedicated to studying that sort of groups, they are called Coxeter groups.

It took a while before I could dream the names of the five regular polyhedra: the tetrahedron, cube, octahedron, dodecahedron and isocahedron. But these are just the tip of the iceberg. There are enough familiar objects I don't know the name of. But there fascinating objects I never even heard of. Like the Permuatohedron for example: it is the n-dimensional generalization of a hexagon.

Permutohedron

Exploring new territory in mathematics can be quite fascinating. A library ( brick and / or online ) is a good place to start.

Mathematics and culture

#maths

Because I study mathematics at a British university I am starting to notice that the British insist on doing things their -own- way as much in mathematics as they do in general. I am not judging this, but it fits the pattern, i.e. traffic, currency, etc.

It is just that I thought mathematicians would be -wiser-. Wiser, how ignorant of me, how can I possibly understand the essence of 'being British'? I can't, of course.

Let me give two ( recent ) examples.

#1
An Open University forum moderator switching to UPPERCASE in reply to my mentioning that permutations are applied from left to right in default GAP while the only correct way is the British right-to-left. ( Going uppercase is about the rudest imaginable attitude known in internet etiquette and as you can imagine I was flabbergasted. )

#2
A note in a book published by the American Mathematical Society written by an English mathematician. I quote:

"Readers who prefer this convention should read this book upside down in a mirror."

He referred to a generally accepted style of notation in continental Europe. My jaws dropped. This wasn't meant as a joke.


P.S.
;-) !

Open University Library Services launches 2012 Student Survey

If you are a student at the Open University now is the time to give your opinion about the Library Services. What is your opinion about the fact that subscriptions on important journals can only be accessed with a delay of a year? I bet that this restriction is not applicable to academic staff. I know that the Technical University in Delft, Netherlands is subscribed to all Springer e-books. The OU does not. - Wasn't one of the motives for tripling the fees that an education at the OU is tantamount to one at any other university?

The Open University is interested in -your- opinion.

Get the most out of the Open University

A reminder and a tip. - While you are a student at the Open University you have access to the Open University ( on-line ) Library Services. To get the most out of this valuable resource it helps to take a few training sessions in how to use the Library Services. - Training starts today! - http://www8.open.ac.uk/library/training-and-events/online-training-sessions

2012, at last.

Fair is fair. The Open University gave me a call, registration is done. - It is now 2012. For me, anyway: that is how I feel about it.

About the Open University

Last year's problems seem simple with what I am going through now. What is going on? I have to withdray money from my student account which I hold with the Open University to pay for this year's courses, the procedure is simple and fast, really. First you call the course registration line, then you simply ask the student advisor to arrange it for you. But...

... I can't get through.

Not that I haven't been trying. Last week I gave up and wrote an e-mail asking for advice on how to establish contact. They say that it can take 'up to three working days before you get a reply'. It's past three working days already. But...

... no reply.

What's going on? Does it have to do with budget cuts? Queries about the new fees? I never had a problem to get through. The Open University is not just any university. They are =huge=. On a piece on the OU site I read that the OU is the biggest university in the UK with
- 250,000 students
- 7000 tutors ( Associate Lecturers )
- 1200 academic staff, and
- 3500 support staff
It is also an -international- university, they have 3500 students in Ireland, 9000 in the EU and another 7500 outside the EU.

In the meantime I am still waiting. I'll have to figure out something because I can't wait to start studying again. When everything is OK I do the reflection post first.

I haven't dropped the Fearless Symmetry series, on the contrary: I am styding algebra again. I have posted a question about Galois Theory here. Basically a course in Galois Theory makes you understand -why- polynomials with rational coefficients and degree five or higher can't be solved by radicals. At least not in general, if the corresponding Galois group of the polynomial is soluble however then there is a solutiuon. - Which you won't find in the textbooks. And that's what I find disappointing, to say the least. Maybe this is why a study in mathematics never seems to stop. A course answers a few of your questions but you'll have more questions after the course than you had before.

If Galois Theory is a blank for you, then this article ( pdf) might fill it, a bit. ;-)

Study Tip - 4 ( Plan, plan and plan )

It has been a while since my last study tip.

Learning style

I am not a type that can sit still for hours to read, think deep mathematics and make an occasional note in my virtual notepad in my memory. Although I would like to be like that it is not going to happen. They say Euler was like that. That's why he had no problem to continue with his mathematics after he became blind. Stephen Hawking also has this ability to do theoretical physics in his mind. In the Netherlands we have a former checkers World Champion, Ton Sijbrands, who can play and win or draw close to 30 games blind. It proves what the human brain is capable of, in principle. - I can't do it though because I have to be active, I must do something, better: create something. Otherwise I can literally doze off. A friend once said that I have a kinematic learning style. Different people have different learning styles. I can't sit in a lecture and listen to a lecturer either. It literally goes in one ear, leaves the other, without any storage or processing in between. I get extremely bored in lectures ( or courses ), days seem ages because I want to go home to -do- something.

Check-sheet

Over time I organized my style of studying into a series of to-do items. The first to do is always 'Make a detailed plan.' For example if I plan studying a booklet ( Open University study materials are delivered in booklets which often take two weeks to study, or something between 16 and 32 hours ) I create a check-sheet for it. ( If you have ever done a course in scientology, you know the concept. ) If you study from a check-sheet you won't have those blockages. They really work. The most important thing is that you create a plan that works for you. A plan helps you go through the materials and you know when to do what and no more. That way you won't fall in the 'I never have time-off trap'.

Statistic

Maybe you study to make a step on the career ladder, expect to make more money or maybe you simply want to be able to do your current job better. Or you study to get a(nother) job, or you finally want that degree. In any case you have a deep interest in the subject you study. Final study results come in after many years of study. They are hard to measure on a daily basis, even success on a module which usually takes a year is not a good measurement. TMA results? Yes, somewhat. But what if you got that 'good' result by cramming the TMA out in 48 hours of almost continuously cramming? You will have forgotten the materials on the exam. You have to set a study statistic you can measure on a daily basis. I make ( = do ) flash cards with the open source program Anki. For example when I study a definition, of a graph for example. I type in Anki Q: What is a graph. A. A graph G is a tuple [V,E] where V is a set of vertices. etc. Anki makes sure that I will never forget the definition by monitoring my recall on the question in a very efficient manner. But most of all, I am doing something while styding because I am alert and awake as to which questions I have to put in Anki. Naturally I try to formulate the answers in my own words. Anki then provides me a with a range of graphs and statistics about my progress.

Feedback

Have you ever made a plan which worked well for onze day but you threw away the next day because all the time unexpected things happen? I often made plans to study on times when I was not physically up to studying. I felt tired, spent too much time in traffic, got hold and so forth. That is very valuable information you can use when you make your next plan! And if you record the time spent on each topic your time-estimates will improve and improve.

That is what I mean by "plan, plan and plan".

Oh, I no longer think in time, my unit of doable work is the Pomodoro. More about pomos another time.

M381 - Challenge Exercise

In the Open University course Number Theory and Mathematical Logic the additional exercises sections of the workbooks are complemented with several 'challenge exercises'. This is one of them.

Let $n$ be an odd positive integer.
Prove that there are $\tau(n)$ ways of writing $n$ as a sum of consecutive positive integers.
For example, if $n=9$, $\tau(9)=3$ because $9$ has three divisors $1,3,9$ and the three sums are: $9$, $4+5$ and $2+3+4$.

To be continued.

M381 exam

Did M381 exam. All the questions were doable, easy as a matter of fact. Honestly. I am sure I have full marks for the first question I made. But when I was done and looked at the clock it was already past three o'clock. "Should I have been able to do that question in 10 minutes?", I thought. Maybe. I have a painful ear-infection at the moment, and I was drugged of course, prescription painkillers, doctor's order. And antibiotics, of course. I felt like walking on the moon, in an astronaut's suit. Whatever the outcome may be, I can set it right. More later on the exam, when I feel better.

Is M381 True or False ?

In facebook I have a photo album with mathematics related pictures. Sometime ago I added the picture below. I thought it was a joke...

... but I could not have been further from the truth. The picture could have been taken at any Open University M381 tutorial. This student is not clueless, on the contrary: he contemplates about some deep mathematics.

Anyway, if you have always wanted to give an answer to the layman's question: "But can you -prove- that 1+1 = 2?" then M381 is your course.

About mathematics at the Open University

There are of course many differences between studying ( mathematics ) at the Open University and studying math at a brick university. The main difference is of course the main method of delivering knowledge: course booklets versus lectures with accompanying lecture notes. A brick university course is often based upon some textbook. Homework includes reading assignments and exercises. An Open University booklet is a mix of theory, worked examples and exercises. If the method of presentation matches the way you like to learn math following a course is easy. - The way mathematics is presented in textbooks (at the advanced undergraduate or graduate level ) is however completely different. If you learn all your math from Open University booklets this may come as a shock, since the skill to read mathematics books hasn't been developed. Compare a graduate math book in your field of interest with one of the level 3 booklets to see what I mean. Or to put it differently: you have not been initiated in the ( secret ) protocols of how mathematicians communicate.

The challenge can best be met by attempting to solve the exercises without recourse to the hints. The density of information in the text is rather high; a newcomer may need one hour for one page. Make sure to have paper and pencil at hand when reading the text.

Wolfgang Rautenberg in "A Concise Introduction to Mathematical Logic 3rd edition, Springer 2010, preface"

The Code - Episode 3 - Prediction ( with Marcus du Sautoy )

Just like the orbits of the planets life follows a pattern. It can be reduced to cause and effect. Everything can be represented by numbers, and thus has mathematics at his heart. Strip everything away and mathematics remains.

The Code

Beautiful TV, the BBC at it's best. Series verdict 8.5/10. Not a 10 because given previous series with Marcus du Sautoy, and the promising title "The Code", my expectations were too high. I had the idea it was mostly about physics, ( of which some say is just another branch of mathematics ).

Episode 3 starts off with a tale about Columbus, lunar tables and the moon eclipse. Given the regular movement of the planets it is possible to forecast a moon eclipse.

"The Code is such a powerful thing that I entrust my life to it" says du Sautoy. He calculates the arc of a ball which is rolled off some ramp and takes a seat close by where the ball should land. Classical mechanics is predictable.

Denmark. Flocks of starlings. A single flock can contain a million birds. The Black Sun they call them. Suprisingly flocks can be modelled mathematically.

On to America. We meet a detective with a Ph.D in mathematics hunting for serial killers. ( I would rather consult Charlie Eppes though. Charlie is an expert in -all- branches of mathematics. ) This detective said that he studied the Jack the Ripper case and worked out the address of Jack the Ripper. Not bad for a case as old as 888. My prediction is that Jack the Ripper is dead by now.

Knowing the series is part of an Open University course I am not surprised that the logistic map made an appearance. If you intend to study math at the Open University be prepared. The logistic map is hard, very hard. The logistic map is what makes mathematicians modest, humble almost. - Suppose there is a God, a creator, who used mathematics as a language in the creation of the universe. Wouldn't he/ she/ it be so clever to -secure- the creation from having it cracked from creatures like us? If you assume that then the logistic map, chaos theory, the complexity of the primes, Goedel's theorems and all that could be just firewalls.

Anyway, du Sautoy shows that we can use the logistics map to understand the dynamics of ( lemming ) populations but we won't be able to predict populations with it. Weather systems ( and I suppose stress systems related to earthquakes ) are bound in a similar manner.

New York. Patterns everywhere, of course. ( Echoes of Max Cohen? ) There seems to be a 15% rule for cities. It says that when a city doubles in size everything gets better by 15%. Then I lost it:

You have 15% more restaurants to choose from, 15% more art galleries ( .... ).

Here the producers had to show off their class, I suppose. A bit insensitive in such harsh economic times. Not good in my opinion. - The evening The Code part 3 was broadcast a friendly between England and The Netherlands was canceled. Due to class related riots in London.

New mathematics documentary

The OU produced another mathematics series.

The Code is a three-part TV series about maths in the natural world, presented by Marcus du Sautoy. Why do bees make hexagonal honeycomb? Where's the best place to stand to get on a train first? How can dozens of wrong answers make a correct one? Join Marcus on an exciting journey to discover how maths shapes the world around us.

Starts on Wednesday 27th July, 9pm on BBC Two. - One day after copies will be all over the internet if you are in a place where you can't receive BBC Two.

Enjoy!