MT365 - First Impression

MT365 has three more or less self contained tracks:
- Graphs
- Networks
- Designs.
I am currently reading the Introductory Lesson and the ( additional ) book on Graph Theory. An important skill is recognizing / classifying the type of a problem: problem classification. There are four major categories.
- Existence ( i.e. Is there a ... ? )
- Connection ( i.e. Describe the connection ... )
- Enumeration ( i.e. List all ... )
- Optimization ( i.e. What is the fastest / cheapest ... ? )
For each of these categories there are a sort of 'reference problems' that have been studied in depth. The solutions of these problems can be used as a start in solving your own problem.

MT365 seems harder than I thought although there is hardly any mathematics ( calculus / linear algebra / any ) required. The style is not mathematical either. Not the typical theorem, proof, example style. I don't know how many students are assigned to one teacher but from a list I saw that there are approx. 30 MT365 groups. In the book I am reading I read that there are about 500 students taking MT365 every year. Partly due to the T in MT365 I suppose. The course is a so-called applied mathematics course and must therefore be accessible to for example students in computer science or physics.

I read through some CMA questions and before I can answer these I have to quite some studying. MT365 is certainly not a give-away.

MT365 - Introductory Chapter online

I was unfair to the course coordinator. He managed to scan and upload the first chapter of MT365. Still, the book is a nice complement to the course. Graph Theory started with a paper of Euler about the bridges in Konigsberg. That fact is mentioned in practically all books on graph theory and discrete mathematics I have seen sofar but I hadn't seen the actual article written by Euler yet. Well, there is translation of that article added to the introductory chapter of MT365 as an appendix. The more I learn and hear about Euler his statue grows. I am beginning to understand why he is considered ( one of ) the greatest mathematicians of all time.

Fibonacci introduced his famous series 1,1,2,3,5,8,13,21,34, etc. in 1202, Binet published his formula around 1850 or so. A problem that was unsolved for more than six hundred years. Today, I learned that Binet's formula was known to Euler ( ... ) , de Moivre and Bernouilli over a hundred years earlier. I can prove Binet's formula using a technique in Linear Algebra called 'change of basis'. I wonder how Euler found the solution because that particular technique was not yet known when Euler still lived.

MT365 Textbook

I haven't received the materials yet and since there are no pdf's for this course ( yet? ) i proactively searched for something on Graph Theory on the level of MT365. I found that there is actually a Springer textbook for MT365: Graph Theory and Applications by Aldous / Wilson. I now have the e-book version of the book. It's a start on MT365.

I suppose it takes a while to get 'into' graph theory. In the beginning once the overall concept is clear it is a matter of learning new words, words and words. ( In a study course I once did this is called clearing MU's ( misunderstoods). I distinguish between misunderstoods, undefineds, defineds and owned concepts. )

Software TIPS

I made two software 'discoveries' today. Must have stuff, really.
- 1. Asymptote. A graphics programming language really, directly includable in Latex. Sort of a steep learning curve but so has Latex and that was an investment that paid off for everyone who learned it. That is I never heard of someone who regrets to have learned Latex.
- 2. Dropbox. The definitive solution for sharing data between your computers ( desktop(s), laptop and phone ). Free up to 2GB. It creates an extra folder on all your systems. I am setting it up right now.

External Links:
http://asymptote.sourceforge.net/,
http://www.dropbox.com/

Dropbox is ideal for syncing your iTunes Library file over your PC, Laptop and iPhone.

Received M208 course materials

Received a DHL shipment with M208 course materials. I1,I2,I3 and GTA1,2,3,4 books, but I already had access to these as PDF. More important: got the CD and two DVD's and very important: the course handbook. Have to 'live in it' until the exam. I have learned from my MS221 exam experience that the handbook is very important indeed. I am going to buy past exams this time, that is something I did not do for MS221, I thought one trial exam was 'enough'.

Google tools at the Open University

On the StudentHomepage the following message is displayed:

... "The University will be deploying Google Apps for Education to run alongside other learning systems, with services that include: email, instant messaging, contact management, calendar, space for shared documents, and online document creation. There is the potential for more services to be added in the future.

These additional services are being provided to students to enable them to network and collaborate more effectively with each other. The default email provision for students will be with Google, but existing preferred email options will be maintained.

Google Apps will provide students with an area in which to store and share documents. They will also be able to create content without having to have an office application residing on their desktop – all carried out using a web browser on a range of platforms and devices." ...

It looks as though Office-type-of tools will become commodities available on the net. Leaving Office for the desktop for a limited group of power users. Typing homework can simply be done from within the browser although since I have a tablet PC Microsoft OneNote became one of my favourite programs of all times.

Bad news about TeXnicCenter 2.0 alpha

I compiled some TMA's and the result was -not- as expected. Problems with /figure. The included graphics files were not included. I created a new document and included a figure with the wizard, which is a new feature in version 2. The file was included but major problems this time with the size of the pic. Since it is an alpha release I decided to let go. Hopefully better next time. TeXnicCenter has an Office 2007 look and feel. ( Would they have seen the again new l&f of office 2010? Even better than 2007 imho ). - So it remains version 1 for me, I suppose. Does not matter. It did the job, the marks came back home.

Starting on M208 / TMA01

M208/TMA01 consists of 7 questions.
To be delivered in 2 parts.

Part 1 Cut-off 12/2 ship 5/2
1. 25p ( Graph sketch )
2a-b. 10p ( Graphs of hybrid functions )

Part 2 Cut-off 5/3 ship 26/2
3a-b. 10p ( Sets )
4a-d. 15p ( Functions )
5a-b. 10p ( Induction )
6a-b 15p ( Complex numbers )
7a-b 15p ( Equivalence relations )

120 OU points per year ?

Can it be done? 120 OU points per year ? I just read this in the MT365 forum.

"I've opted for MT365, M343 (Probability), MS325 (Chaos and stuff), and MS324 (Waves, etc.)..."

I suppose the hardest is the fact that there are 4 exams to prepare for in october. - The OU estimates an average workload of 8 hours / week for 30 points. So, technically it can be done. - Just contemplating on my own schedule, in fact, of only 90 points.

Are programmers double happy?

Just came across this quote...:

"People who [program] have double happiness. First of all they experience the sheer beauty of elegant mathematical patterns that surround elegant computational procedures. Then they receive a practical payoff when their theories make it possible to get other jobs done more quickly and more economically.'' - Donald Knuth

So programmers are 'double happy' people?! I would like to hear that from one of the programmers Knuth ever worked with. It shows that typical scholars like Knuth have no idea of what's going on in a profit driven enterprise.

M208 - February 2010

Week 0 30 January
Course text: Introduction; 1 Real functions and graphs
CD title: Graphs of basic functions

Week 1 6 February
Assignment number: TMA01 part 1
Assignment cut-off date: Feb-12

Week 2 13 February
Course text: Introduction; 2 Mathematical language and proof

Week 3 20 February
Course text: Introduction; 3 Number systems

Week 4 27 February
Assignment number: TMA01 part 2
Assignment cut-off date: Mar-05

TMAs / CMAs - 2010

By course:

M208 ( Pure Mathematics ) - 60 points
TMA01/pt1 12 Feb
TMA01/pt2 5 Mar
TMA02 9 Apr
TMA03 21 May
TMA04 25 Jun
TMA05 30 Jul
TMA06 3 Sep
TMA07 17 Sep

MT365 ( Graph Theory ) - 30 points
CMA41 7 Apr
CMA42 29 May
CMA43 21 Jul
CMA44 27 Sep
-
TMA01 26 Apr
TMA02 14 Jun
TMA03 31 Jul
TMA04 13 Sep

or by month:

Feb
12: 208/TMA01 Pt 1

Mar
5: 208/TMA01 Pt 2

Apr
7: 365/CMA41
9: 208/TMA02
26: 365/TMA01

May
21: 208/TMA03
29: 365/CMA42

Jun
14: 365/TMA02
25: 208/TMA04

Jul
21: 365/CMA43
30: 208/TMA05
31: 365/TMA03

Aug
-.

Sep
3: 208/TMA06
13: 365/TMA04
17: 208/TMA07
27: 365/CMA44

That's quite a load. Well, it is what you can expect from a 90 point schedule, I suppose.

Let's get busy!

Registration M208, MT365 - revisited

I can't wait to start on M208 and MT365!

( I like programming and mathematics but I can't seem to find the ideal synergy between math and programming. It bothers me... )

Last year, my then employer, arranged the registration of the course. This time I had to do it myself. Well, I suppose the best thing is to do just register by phone using a credit-card. That's how I will do it next year. I did it by bank transfer. I sent the money last week, it takes three days max for a transfer from the Netherlands to the UK so the money arrived Monday, latest. I sent an enquiry e-mail. The reply was that it could take up to 4 days to expect an answer. I can understand that, I suppose it is rather busy at the beginning of a new study year.

What's odd that when I called there was zero waiting time, which is truly excellent for such a huge organization as the Open University with thousands of students. It turned out that the money was received in my 'Student Ledger'. The person who handled my call 'Joanne', effectively handled the matter and if everything goes well my courses should show registration status by tomorrow.

Abacus

A fascinating device, forever.

Side effects of an activity ( i.e. studying mathematics )

I want to document the (side-)effects studying ( mathematics ) at the Open University has on life ( as well ). This is therefore the first post in the category 'Personal'. What is to be expected on beforehand? The study can have a positive or negative influence on your personal and / or worklife. I haven't measured it but I have spent at least 20 hours / week on mathematics related activities. There must be some measurable effect. I suppose there is. It is of course impossible to put everything in a blog entry so I'll just make a note of certain things. - I have worked in IT for many years in various roles. So that is what I am, I suppose, an IT consultant. Although when asked about my profession I simply can't say that I -am- an IT consultant. I -do- ( for example ) programming, that's it. I suppose that a doctor will say, "I -am- a doctor". There is a difference. Now onto the first fact I want to document.

Last year approximately around this time I was spending more time on learning Adobe Flex ( which has been renamed to Flash Builder I just found out, which triggered this blog-entry in a way ) with various back-ends like PHP / MySQL and BlazeDS / Oracle than I was spending on learning MST121 stuff and technologies required for the project I was working on at that time ( Oracle ADF / Struts ). - I started in september 2008 with MST121. I seriously committed myself to a number of years of mathematics study next to my job. Becayse I studied a lot of math in the years prior to 2008 as an amateur student I felt that MST121 was rather easy. Back to last year. MST121 was not easy. And MS221 was coming on top of it. The project I was working on needed more time and dedication of me. Something had to be done. I discussed matters with a colleague on the project and decided to take a week off to finish TMA02 of MST121. I worked extremely hard and managed an 88 / 100 for TMA02. So only after four months I experienced some of the impact the study had. I implemented quite a few changes by then.

I started to make my TMA's using TeXnicCenter which costs more time but definitely leads to higher marks. I also started to work on the TMA's asap. I just started and figured things out while working on the TMA. That gives a feeling of progress all along. I had to learn, re-learn Latex which I don't regret btw. Anyway. From february until june I was very busy on MST121 and MS221. Producing TMA after TMA. - My work on Flex crashed which I regret very much. I deeply like the ActionScript language. - I no longer work on the project I was working on early 2009. ( More about that in another blog-entry ).

I have always been  and always will be attracted to computer programming. I decided that this is one of my 'advantages' in math and that I should develop it further. Although I can work very well with Mathematica as a mathematics tool, and can even write small functions in it, I knew that the language had many secrets I hadn't discovered yet. I started to study the book  Introduction to Programming with Mathematica which eventually led to cognition after cognition and somehow brought me back to early 2009. Mathematica is a functional language, much like Lisp which is extremely powerful. It is called the 'programmable programming language' where code is as easily changed as data. Since my main skills are in Java I was delighted to find Clojure which has everything Java has and is also basically a Lisp dialect.

Sofar.

As far as studying is concerned I am awaiting the payments to show up at my Student Fee Account and the subseqyent shipment of the M208 and MT364 materials. I can't wait actually, I am ready. Until then I'll spend some more time on Clojure. - I am somehow hoping to find a way / define a project so that I can use Clojure preferably with Flash Builder to the benefit of my study.

Costs of studying at the Open University

What does it cost *money-wise* to study at the Open University? For residents of the UK the costs are highly subsidized. I don't complain that non-UK residents have to pay three or four times the amount UK students must pay. On the contrary, I am glad we get the opportunity to study at the OU. There is an Open University in The Netherlands as well. The courses are -probably- OK but the courses they offer are limited. They don't offer mathematics. The Dutch attitude is "no second-chance for mathematics". What they offer is economics and law.

To the point. I just paid the full cost of a years study ( 90 points ) at the OU UK, that is M280 ( pure mathematics ) and MT365 ( graph theory ) : the total amount was GBP 2625 or approx. Euro 2750 which is tax-deductable. This includes everything: books, DVD's, teacher support, TMA revisions and exam fee. It's OK. Although if you have a family to support and money is tight it could be expensive. Thank G_d, I can afford it.

I am very grateful I can do this. Nobody is telling me I should. I simply want to. It feels like a great adventure.

Mathematics Subject Classification 2000

Over the years I collected a lot of (e-)books on mathematics for which it is my intention to develop a database system made entirely to my requirements and wishes. Key functions of such a system are of course searching and browsing. In order to meaningful browse categories ( and sub-categories ) are required. While thinking about categories for my ebooks database I stumbled upon the Mathematics Subject Classification 2000 ( pdf ). The MSC 2000 is a 69 page pdf document with thousands (!) of categories.

( ( IT ) projects ( which the development of my ebook database in a sense is ) -always- have some sort of problem to solve. I suppose that is why they are called projects. Projects, unlike processes which can be optimized slowly over time, are unique and are done one time only. )

Adopting the MSC 2000 would mean that there would be more categories than books in my system. That wouldn't help browsing a bit. Classifying by the toplevel categories would mean I would have to check the classification in each book and categorize accordingly. Clever programmers would say: "You could write code for that. Yes. But not for all of them. Some books are merely a collection of scan images.

I guess this justifies a list of categories of my own. I could make it in such a way that I could gradually enhance the categories. - ( More thinking to do. )

P.S.
A manager I once had told me that studying is by definition frustrating. Once you have mastered a subject you discover all you mastered is just a tiny introduction to a bigger ( or deeper ) subject. There is no end to it. - I suppose it's not about understanding everything it is moving to the boundaries of the field so that you understand how the field is developing by reading the journals.

Some correspondence at the OpenLearn forum

I'm going to be doing M208 and MST209 next year. I must be mad! I was wondering if anyone else if doing these courses next year. Would be good to get a study group online or something going?

(Christina)

I replied as follows:

Mad? No. 120 points / year is still in the do-able range. I have thought about doing M208 and MST209 together in one year very carefully. It simply means you will have to pump out a TMA every two weeks from february to september. It will work if you can spend all your time on math. I can't because I would like to do some other things as well like watching football since it's a World Cup year. I decided to go for M208 and MT365 this year. If it all goes well, I'll do MST209 next year.

Mind Manager SP2

I upgraded to MindManager 8 SP2 or 8.2.319. This release solved the very annoying issue of a slow start during which several 'Server busy' error messages had to be OKed or Canceled. I use MindManager to plan and control the progress of my Open University courses. - Before that I successfully used Mind Manager for a zillion other things since 2001 or so. It is a wonderful tool.

Mathematica is a functional language

Mathematica is a functional language. A program that calculates n!, n factorial looks like this:

f[n_] := Apply[Times, Range[n]]

The function f[5] yields 120 = 5!

Explanation of the code:
- Range[5] by itself yields {1, 2, 3, 4, 5}
- Times[a,b] yields a*b.
- Apply[Times, {1,2,3,4,5}] yields Times[Times[Times[Times[1, 2], 3], 4], 5]

Functional programming goes back to the 1950's when the programming language Lisp was developed. Since then Lisp has always been in use ( in some dialect ) for the development of highly complicated systems like Artificial Intelligence (AI) systems. But unexpectedly for the time the first Yahoo Store web application has been built in Lisp also.

Personal Statements

I found this site where mathematicians / students explain their choice for mathematics. ( Elsewhere on the site statements form students in other fields ) Very readable and interesting life-stories of young people.

Snippet :
"  Mathematics can, at times, be the single most frustrating subject I have ever studied, yet I love it. The euphoria of completing a particularly hard puzzle, or the sudden realisation of a particular topic clicking into place, makes the challenge and the hard work all the more worthwhile. "

From Lisp to Mathematics

I was watching one of the video lectures from the course 6.001 Structure and Interpretation of Computer Programs from MIT OpenCourseWare. Although the course is even for Computer Science standards up-to-date the lectures were recorded in 1986 at an HP company course. It looks rather outdated, pre-historic even when he demos the Lisp editor / interpreter. But is it really?

I entered the same commands in Eclipse ( using the Cusp Lisp plugin ) and Lisp wise there hasn't changed a thing.

I suppose that there is a difference between old and 'still around'. I could name numerous so-called 4th generation languages invented in the 80's and 90's which are dead and forgotten. The fact that Lisp which dates back to the 50's(!) keeps popping up and is taught at MIT today must make it a very special language.

Single variable calculus dates back to the second half of the 17th century. And we all know what an extremely powerful toolset calculus in fact is. The 'advanced' topics in an undergraduate program date back to the 19th century or before that. Except for maybe graph theory which was developed in the 20th century. To become 'current', knowledgeable of the -state-of-the-art- developments in any topic is difficult but I believe that it is even harder for a science like mathematics. Simply because it has been around for so many years and the field becomes more advanced by the day.

Looking back on 2010 - (1)

The number of readers of this blog has been more or less constant during the first two years of collecting stats. Somewhere in October both the number of unique visitors and pages viewed doubled. ( Visits were high in the exam-period. ) Visitors stabilized on this new level in November and December. I don't think there is one explanation for the doubling but attributing factors might be regular 'on-topic' posting and tweets about new posts. It is nice to know that someone is reading your scribblings.

Somewhere during 2010 I implemented MathJax ( LaTeX for HTML ). Because Blogger does not officially support MathJax ( yet, I hope ), I am leeching resources elsewhere. This slows down MathJax somewhat. Recently I installed the AMS extensions which further slowed down MathJax performance. One way or the other I'll fix this issue.

More pageviews per visitor in 2009

Happy 2010 to all my readers. I hope for a good math year for all of us.

Site statistics 2009:


The left axis shows the number of visitors, pageviews. The right axis shows the ratio views / visitors. The number of visitors fluctuates by month but the trend seems flat. There is however an increasing trend in the views / visitor ratio which might mean that there are less hit and run visits ( Google 'misses' ) and that visitors are actually reading my notes.

I don't want to change the focus of this blog. It will remain a set of logs, diary entries if you wish about a mathematics study at the Open University and the influence it has on my perception of mathematics. I may however decide to use other software than the default Blogger facilities. ( It's on my list, but there are other priorities at the moment. )

Lecture 24 of Abstract Algebra E-222

Lecture 23 was difficult but it was the last lecture in E-222 on group theory. The remaining lectures will be on rings which are also ( abelian ) groups but with an additional operation ( multiplication ).  Purpose of the first lecture on rings was mainly to establish some definitions and show analogies between group theory and ring theory. I expect a lot of stuff on ideals in the forthcoming lectures.

Definition.
A ring is an abelian group with an additional operation * such that:
- * is closed.
- * is associative
- 1 * a = a.
This makes the ring a monoid with respect to *.
( Gross defined it slightly different in the lecture ).

Gross showed an interesting way to construct rings from abelian rings. The endomorphisms of an abelian group End(A) form a ring if an element f_a in the ring is constructed from an element a in A by taking the map f(1) = a.

Some furter topics which were introduced:


( Ideal )


( Quotient ring )


( Unit )


( Examples of groups of units )