Friday, August 28, 2009
Video: Solving Cubic Equations
And more: Pythagoros theorem ( a^2 + b^2 = c^2 ) is not really by Pythagoras. Pythagoros is the probable leader of a cult called the Pythagoreans. There is an interesting formula for enumerating all the Pythogarian triples like (3,4,5) (5,12,13), etc.
In the next clip we learn that Fermat bought a translation from Greek to Latin of Diophantus' work and started his work on Number Theory from there on. It was also in Fermat's lifetime that Calculus was born. ( Fermat already worked on the currently very important Elliptic Curves which Andrew Wiles used to prove Fermat's famous last theorem. ) A method is shown to find rational points on elliptic curves. An elliptic curve is the graph of an equation of type y^2 = x^3 + px + q.
Then the video becomes less interesting. It seems that in academic talks it is custom to speak with great admiration of certain other scientists, mathematicians especially if you know them or are related to them. The speaker, professor Gross had John Tate as his thesis advisor. John Tate is a celebrity in a the Elliptic Curve branch of mathematics. So Gross shows a picture of him and Tate and all the other graduate students at that time. Then he mentiones all these students by name including the universities where they are now teaching as a mathematics professor.
( I suppose they had their euphoric moments too when they simply passed an exam. After a while more impressive results are needed to feel the same high, like being appointed as professor. )
See the rest for yourself if you are still interested...
Thursday, August 27, 2009
MS221 TMA03  Result
Lost a point due to a typo. This once again proves that you can literally save points by reviewing, QAing, checking whatever you call it. And check your results as much as possible by using a mathematics package like MathCad or your own preferred software, as long as it can do the math.
Friday, August 21, 2009
MST121  Overall Course Result ( Final )
Assignment Score
CMA 41 83
CMA 42 84
TMA 01 82
TMA 02 88
TMA 03 95
TMA 04 90
TMA 01 82 has been substituted to 87.7 giving a final score of 88.84 rounded to 89.
An 89 for this is course is much more than I deserve. Especially in the beginning of MST121 I did not study enough ( november and december last year ). During this period I also had a last minute approach towards TMA's. I definitely lost points there.
Anyway, I learned that in order to get high marks much more is expected of the student. TMA01 and TMA02 were quick and dirty jobs using pen and pencil. As from TMA03 I changed to LaTeX including several QA reviews using Mathematica ( if possible ).
Wednesday, August 19, 2009
Chinese Remainder Theorem
Solve systems of linear congruence equations using the Chinese Remainder Theorem.
Find a video lecture here ( Lecture #12 )
I was solving a problem from ' 104 Number Theory problems ' which required an application of the CRT. I had forgotten the algorithm. Instead of looking it up in a book I watched Song's lecture.
Tuesday, August 18, 2009
Sample MS221  Exam
I would say that anything is possible with regards to this exam. I could fail but I could just as well get a high score. It all depends on proper training from now till the exam. I am sure that a lot of exam training will pay off.
But first I have to finish MS221  TMA04.
How I spent some spare study time
I completely understand and am thus able to prove, ( now and in the future, I am sure ) the formula for the Sigma numbertheoric function. The sum of the dividers of a natural number. For example:
12 = 2^2 * 3
sigma(12)
= 1 + 2 + 3 + 4 + 6 + 12
= ( 1 + 2 + 4 ) + ( 3 + 6 + 12 )
= ( 1 + 2 + 4 ) * ( 1 + 3 )
= 7 * 4
= ( 2^3  1 ) / ( 2  1 ) * ( 3^2  1 ) / ( 3  1 )
= 28.
Furthermore, I am beginning to ger a practical understanding of Möbius inversion.
And I firmly consolidated knowlegde of and skills regarding
 Properties of integer division
 Euclidean algorithm for finding the GCD
 Linear diophantine equations
 Congruences
 etc.
Tuesday, August 11, 2009
How am I doing relatively ?
I mean how do my study results compare to other students? Do I actually care??! I read about people receiving TMA results of 99, 100 and so on. Than my average of 90 sofar seams low, very low as a matter of fact. On the other hand those who 'blog' 'brag' including me, I suppose. I wouldn't shout it around if I passed on 41/100, although it has exactly the same value to the overall degree result.  If a lot of students are scoring in the 80100 range then the TMA's are just too simple imho. Since the student can make the assignments at home that means they can be quite challenging.
Saturday, August 8, 2009
Studying mathematics with SuperMemo
I used to do a lot of selfstudying so a I used a lot of study time on tasks which aren't necessary when you do an OU course. I nevertheless got used to allocating time to studyimprovement on a regular basis. If I could only use SuperMemo then studying becomes a process which automatically produces a lot of statistical data about the studying process itself. But producing learning materials for SuperMemo can be timeconsuming in itself. That fact kept me from using SM thus far. But with the other tools I currently have like Mathematica, TeXnicCenter and so on I must be able to organize my way of studying, doing exercises etc. so that it will be fairly easy to document my work as a SM item/answer pair.
It is worth another try...
Thursday, August 6, 2009
MST121 overall course result
Overall course result
PassOverall continuous assessment score (OCAS) : 89
Overall assessment score (OAS) : 89
Substitution applied at : 87.7
Wednesday, August 5, 2009
Gödel, Escher, Bach
And now MIT made a series of six video lectures about the book. Haven't seen it yet but I expect them to be interesting. Gödel's incompleteness theorem is a topic in the course Number Theory and Logic which is part of my course plan.
Sunday, August 2, 2009
OU Courses for 2010
After MST121 and MS221, both M208 and MST209 are good options to do next. They can be done both but in that case you have to do one TMA per two weeks. That is a lot. Too much I can handle. Unfortunately.
Saturday, August 1, 2009
Graphs, networks and design
Formal grammars and languages
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Mathematics: is it the fabric of MEST?
This is my voyage
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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.)