Monday, June 28, 2010
Exponential Generating Functions
An exponential generation function (GF) representing the sequence $(a_n)$ is a GF of type $F(x) = \sum_n a_n \frac{x^n}{n!}$.
Sunday, June 27, 2010
Saturday, June 26, 2010
Cube
Is Cube (2000) a film about mathematics? Not like Pi. ( one of my favourite movies ). Cube is however based on mathematical ideas. People travel around in a 26x26x26 Rubik cube. Some rooms are safe, other rooms viciously kill upon entry. Safety depends upon the coordinates of the room being prime or not. Despite all that Cube is not about mathematics but about psychology and group dynamics. When seven strangers meet in the cube and one says "I'm a cop", the others immediately accept his authority and leadership. The person with the most impressive mathematical capabilities has some sort of mental disability, autism I guess. Well, some mathematicians simply are near autistic. Some merely act as if they were autistic. It is a great way to escape social pressure. While the autists are quiet the manics are rather noisy because they have to carry their colossal genius brains ( read: Ego ) around. Let's face it mathematicians are odd folk. I don't blame the director of Cube for showing that. ( OU trained mathematicians are entirely social and likeable of course! ) Considering the massive scale of conspiracy thinking since 9/11 I liked it when one of the developers of the Cube said: "There is no conspiracy. There is no control. It just happened." A thought I often have myself since the BP oil spill. What if governments only pretend to be in control?  Two more Cube movies were made. HyperCube (2002) and Cube Zero (2004). HyperCube is about a new 4D model of the Cube. Cube Zero goes back in time, it explains what happened before Cube 1. The main character of Cube 0 is the autistic mathematician of Cube 1. In this movie the purpose of the Cube is explained.
Tuesday, June 22, 2010
Saturday, June 19, 2010
10000000010000000010000000010000000010000000010000000010000000011
10000000010000000010000000010000000010000000010000000010000000011 is divisisble by 81. I calculated this number as an example in the process of finding a proof for the following proposition.
Every integer can be multiplied to a number consisting of only zeros and ones.
( No tricks, everything is in base 10. )
Doable with MS221 number theory, I suppose.
Every integer can be multiplied to a number consisting of only zeros and ones.
( No tricks, everything is in base 10. )
Doable with MS221 number theory, I suppose.
Friday, June 18, 2010
TIP: Aha! Solutions
From the preface of Aha! Solutions:
Every mathematician ( beginner, amateur, and professional alike ) thrills to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called "aha! solutions," a phrase popularized by mathematics and science writer Martin Gardner in his books Aha! Gotcha and Aha! Insight. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics. This book is a collection of problems whose aha! solutions I enjoy and hope you will enjoy too. The problems are at the level of the college mathematics student, but there should be something of interest for the high school student, the teacher of mathematics, the "math fan," and anyone else who loves mathematical challenges.
Tuesday, June 15, 2010
Difference male / female math student
There are quite a number of differences between the male and female humanoid.
Dressing outrageously: artificial smells, colourings on the face and the body, huge outfits on top of the head, aka: hair, high heels and always carrying around bags full of gadgets. Serious: women think different than men. When they are doing math for instance. Research shows that they do it with different parts of their brains. While they are working on a task they can do various things at the same time. Men feel discomforted when they have to do more than one thing at the time. Men like to zoom in, analyze, solve, fix and tick off, next issue. Men operate linear, women nonlinear. ( In math the nonlinear case is usually the difficult one. )
Anyway, I used that thought today while trying to fix some planning issues. The fact that was causing regular procrastion was that I was on two courses. I don't have much problems with M208 although it consists of at least three separate courses: Linear Algebra, Group Theory and Real Analysis. It is however neatly scheduled in a linear fashion. That was the key and I found it between the ears. I am now working on one ( virtual ) course called M208MT365. You can imagine the rest of the drill: I merged the plans, etc. Simply by changing perception I am much more at cause over my study.
Dressing outrageously: artificial smells, colourings on the face and the body, huge outfits on top of the head, aka: hair, high heels and always carrying around bags full of gadgets. Serious: women think different than men. When they are doing math for instance. Research shows that they do it with different parts of their brains. While they are working on a task they can do various things at the same time. Men feel discomforted when they have to do more than one thing at the time. Men like to zoom in, analyze, solve, fix and tick off, next issue. Men operate linear, women nonlinear. ( In math the nonlinear case is usually the difficult one. )
Anyway, I used that thought today while trying to fix some planning issues. The fact that was causing regular procrastion was that I was on two courses. I don't have much problems with M208 although it consists of at least three separate courses: Linear Algebra, Group Theory and Real Analysis. It is however neatly scheduled in a linear fashion. That was the key and I found it between the ears. I am now working on one ( virtual ) course called M208MT365. You can imagine the rest of the drill: I merged the plans, etc. Simply by changing perception I am much more at cause over my study.
MInd Manager or MindView (2)
MindView looks promising but unfortunately it is useless for my needs: it has only one calendar. Where corporations are compared to pyramids, the individual is a pyramid upside down. Tiny corporations with a sales departmant, finance department, and so on. ( Using that methaphore studying takes place in the R&D department. ) It is however a corporation with one staff member: unless we look at the hours of the week as staff...
I use mind manager to branch out ideas, thoughts, entirely free format. Some branches are mirrored in JVCGannt, MM's project management addin. In these branches I add concrete tasks to be executed. In the planner they are assigned a resource: work, study or personal. For these resources I have created a calendar. The STUDY calendar has the hours which I have reserved for study as work hours. The hours assigned for work and personal are nonworkable hours in that calendar (and so on). With MindView's one calendar limitation I can't use it to setup my plans. Other planning tools are out of the question because they don't have MindMap integration. So I'll stick with Mind Manager for a bit longer.  MindManager does have MS Project integration though. But it is of course completely over the top to maintain, what is in essence a to do list, in MS Project.
I use mind manager to branch out ideas, thoughts, entirely free format. Some branches are mirrored in JVCGannt, MM's project management addin. In these branches I add concrete tasks to be executed. In the planner they are assigned a resource: work, study or personal. For these resources I have created a calendar. The STUDY calendar has the hours which I have reserved for study as work hours. The hours assigned for work and personal are nonworkable hours in that calendar (and so on). With MindView's one calendar limitation I can't use it to setup my plans. Other planning tools are out of the question because they don't have MindMap integration. So I'll stick with Mind Manager for a bit longer.  MindManager does have MS Project integration though. But it is of course completely over the top to maintain, what is in essence a to do list, in MS Project.
MInd Manager or MindView (1)
Present Time. I failed to meet the MST365TMA02 deadline. I already informed the tutor. ALthough I have a valid explanation this should not have happened. ( I have to assign myself the condition of 'Danger' and apply its Formula. )
From the book Learning Strategies for College Success I learned that the components of academic selfmanagement are:
 motivation ( OK );
 time management (  );
 study methods ( ? );
 physical environment ( OK );
 social ( /? );
 monitoring ( this blog ).
I'll work on trying to improve timemanagement for a bit. I have used Mind Manager for brainstorm and planning purposes for ages. But Mind Manager has some issues as a planning tool actually ( i.e.: Gannt views through a 3rd party program JVC Gannt ). I am loyal to the programs that helped me but it is time to have a look at MindView.
From the book Learning Strategies for College Success I learned that the components of academic selfmanagement are:
 motivation ( OK );
 time management (  );
 study methods ( ? );
 physical environment ( OK );
 social ( /? );
 monitoring ( this blog ).
I'll work on trying to improve timemanagement for a bit. I have used Mind Manager for brainstorm and planning purposes for ages. But Mind Manager has some issues as a planning tool actually ( i.e.: Gannt views through a 3rd party program JVC Gannt ). I am loyal to the programs that helped me but it is time to have a look at MindView.
POLL3 > POLL3.1
I kindly ask those who voted on POLL3 to vote again. I had to delete and then add the poll again because a running POLL can't be modified in Blogger. Why the change? I forgot two rather important, open source, programs: SAGE and GAP. SAGE uses GAP as its Group Theory kernel. I have experimented a lot with GAP in the past. Currently I am still in a Mathematica phase. There are many other excellent programs around but I think that the list is fairly complete for what one might use when preparing a TMA.
Sunday, June 13, 2010
Zero friends paradox
(Dutch) mathematician Ionica Smeets explains why your friends ( very likely ) have more friends than you do. What if you have zero friends like me? Would that be a paradox? Ionica Smeets and one of her friends (...) have a very nice website about mathematics, unfortunately it is in Dutch. If you still want to have a look go here. They maintain a list of famous, yet still living mathematicians. Don Knuth, Ron Graham and Martin Aigner are not on that list. But Terence Tao is. ( ... )
( UPDATE: Corrected after comment received. )
Saturday, June 12, 2010
TeXnicCenter 2.0 Alpha 3 is available
A third Alpha version of the new TeXnicCenter 2.0 has been released. I have issued MT365TMA01 in handwritten format btw, but that's an exception.
UPDATE:
Tested with done TMA's and template for mathematics book Springer style. No bugs or issues found. Decided to use this version for the next M208 TMA.
UPDATE:
Tested with done TMA's and template for mathematics book Springer style. No bugs or issues found. Decided to use this version for the next M208 TMA.
Friday, June 11, 2010
Result  Poll 2
Again, thank you very much for replying! Here are the results of Poll2.
B14  Computing  3
B15  Mathematics for economics  2
B31  Pure mathematics  4
B34  Computing / Statisitics  0
B36  Statistics 1
B46  Mathematics and learning 2
Open Degree  1
With n=13.
Or grouped differently and including my own vote.
Math and Learning 2 = 15%
Applied Mathematics 7 = 50%
Pure Mathematics 5 = 35%
With n=14.
Thursday, June 10, 2010
M208 TMA03 Result is in
M208  TMA03 ( Linear Algebra ) result is in.. Result: 90%. Still four TMA's to go. Two on Real Analysis, one on Group Theory and a revision TMA just before the final exam. TMA results sofar were all in the distinction zone, and increasing: 85, 88, 90. Comparable to MS221 last year. That would mean I am heading for a grade 2 pass.
Wednesday, June 9, 2010
High school math
From the news.
Walton Middle School teacher Michelle Voekler has received the 2009 Presidential Award in Mathematics. “Mrs. Voekler’s classroom is amazing!” said WMS Principal Tripp Hope. “Every item in her classroom is used as a teaching school including the walls, the file cabinet, and the floor,” said Principal Hope. “Students are moving around using manipulatives and handson learning to understand how math is really is everywhere in our world.”We used to call our high school Colditz. A war camp we had to escape from. The school had forgotten one very important thing: learning us how to learn. My mathematics teacher taught straight from Euclid. A geometry based on the rules of logic. Very much considered passez in these days. We were 12,13 Ã½ear olds, he was teaching theorem / proof style. Way too early for us.
Monday, June 7, 2010
Another YouTube upload.
I made a step on the Mathematica gradient. I developed this program entirely using the Mathematica Workbench. ( Java developers recognize it as Eclipse. ) I need some practice using the Mathematica debugger though. It takes a while to learn Mathematica but it is worth it.  This program is a source of interesting mathematical problems. But more about that another time. The grid updates rather slow in this prototype. I think it was Don Knuth who said: postpone optimizing to when the program is functional correct ( something like that anyway ).
Friday, June 4, 2010
Result  Poll 1
I have closed poll 1. Thank you very much for replying! Here are the results.
Are you an OU: Student
Yes: Mathematics 100%
Yes: Other qualification 0%
Have been 0%
Thinking about it! 0%
No. 0%
With n=9.
An interesting result indeed. Replies from the group I would like to communicate with. (Open University) mathematics students. Next poll is about qualifications!
Are you an OU: Student
Yes: Mathematics 100%
Yes: Other qualification 0%
Have been 0%
Thinking about it! 0%
No. 0%
With n=9.
An interesting result indeed. Replies from the group I would like to communicate with. (Open University) mathematics students. Next poll is about qualifications!
MST365  CMA42 Feedback available
MST365  CMA42 result is in: 83%. Of 20 questions I had four errors. Not bad you would say. Well, compared to the other students I did rather poorly.
Score Students
0039 2
4054 10
5569 27
7084 78
85100 205
I basically come in with the last 25% or so. Nevertheless I am fairly happy with this result. Proud even. It's not a race.
Maybe students have been swapping results, which is simply not fair. On the other hand I think most MT365 students are extremely motivated. Others won't be on a 90 point load.
Looking at the results it seems the course is rather simple. Well, it is not. It's hard.
Score Students
0039 2
4054 10
5569 27
7084 78
85100 205
I basically come in with the last 25% or so. Nevertheless I am fairly happy with this result. Proud even. It's not a race.
Maybe students have been swapping results, which is simply not fair. On the other hand I think most MT365 students are extremely motivated. Others won't be on a 90 point load.
Looking at the results it seems the course is rather simple. Well, it is not. It's hard.
Tuesday, June 1, 2010
MT365  CMA42 Done
I was not sure at all if I was going to make it today. I even watched an action movie yesterday to get my mind off things, something I don't do too often. ( Resident Evil 1, not bad. ) When I woke up the CMA immediately entered my mind. As a sort of escapism I hadn't really read the CMA questions before today, I could no longer postpone. Postponing now would mean accepting the inevitable 0%.
Worked the entire day ( from 10am to over 6pm ) on MT365CMA42. Doing the questions after a revision or even a first study, as was the case with Designs 2.  The thought of actually dropping MT365, giving up, crossed my mind. I had visions of a score of 0% on this CMA42. Yesterday I was actually in the mood of accepting the 0% score and trying to recover from that low.
Considering this 'low', it wasn't too bad. I am fairly sure that I have at least half of the questions right. probably more. With 88, 79 as previous results and almost five months until the exam MT365 is recoverable. So the good news of the day is that I am not dropping MT365.
Still two TMAs to do this month. MT365TMA02, M208TMA04.
Worked the entire day ( from 10am to over 6pm ) on MT365CMA42. Doing the questions after a revision or even a first study, as was the case with Designs 2.  The thought of actually dropping MT365, giving up, crossed my mind. I had visions of a score of 0% on this CMA42. Yesterday I was actually in the mood of accepting the 0% score and trying to recover from that low.
Considering this 'low', it wasn't too bad. I am fairly sure that I have at least half of the questions right. probably more. With 88, 79 as previous results and almost five months until the exam MT365 is recoverable. So the good news of the day is that I am not dropping MT365.
Still two TMAs to do this month. MT365TMA02, M208TMA04.
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Welcome to The Bridge
Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)