The hangover of a TMA completion

Just completed TMA01 for MS221. This was a hard one, it took me many hours to complete all six questions. TMA01 is all about recurrence equations and transformations of conics. I'll take some more review time later this week, the cut-off for this TMA is April 8th. This is my fourth TMA completion since I am doing OU courses and I can't say that I ever felt of having completed a task. It takes at least four weeks before the grading gets done ( by then I am most likely up to my ears in making the next TMA anyway ) so there is no relation getting the results and the effort. So now there is a sort of a void of being just in between TMA's. Sort of a hangover. I hope keeping a blog helps to create some perspective so that this empty feeling doesn't lead to procrastinating the next TMA only to avoid the next void. - Better get started right away on part B, TMA02.

The euphoria of solving a mathematics exercise.

The first part of exercise 1.10 in 'A Course in Enumeration' by Martin Aigner asks to evaluate the sum below by counting configurations of dots.

Although the answer can be simply taken from Pascal's Triangle as

C(n+1,2)+2C(n+1,3)

the challenge of the exercise was to deduce the same answer by setting up a particular configuration of dots.

To make a long story short... that's how I spent my entire free Saturday. By not finding the answer that is. I did this ( Sunday ) morning though with great relief. I was close right away but I -sort of- forgot to finish it correctly, instead I kept searching for other, better dot configurations. In the rush of having solved another 'difficult' exercise I remembered an article with the title 'Addicted To Knowledge' which explains the feeling I had.

Aigner says in the preface: 'It is commonplace to stress the importance of exercises. To learn enumerative combinatorics one simply must do as many exercises as possible.' An exercise is only an exercise if it was a challenging exercise, I would like to add. And harder means deeper in the context of exercises.

Hint to the answer: find a dot-configuration for the sum of 1,2,3,...,n first.

Conics ( MS221 - A2 )

 

A conic is the intersection between a double cone and a plane. In the image we see from left to right an ellipse, a parabola and the hyperbola.

The math teacher and his chalk

I don't like to sit through math lessons. It's because of the lecturers of course. Every teacher is different but there sure is a pattern. Like when he/she turns around and starts talking to the blackboard instead of the people in the class. He isn't interested in people anyway otherwise he wouldn't have been interested in math in the first place. Then he usually starts to write a theorem on the board. The same which is already in the book! But in the book it's usually written complete and in a nice readable font. It takes ages before the theorem is on the board but still sort of incomplete. Mathematics should be beautiful at all times.

Math teachers should do what they are good at. Writing mathematics in books, correcting papers, exams and that kind of stuff. The process of learning and understanding math is usually not done in a classroom anyway. And if there is some form of knowledge transfer going on then it can't be to all students involved. For most of them it will be either too slow or too fast. Math should be read and not listened to.

WolframAlpha

Stephen Wolfram is a very ambitious person. As the inventor of Mathematica he already made it to the history books of software. But that is not enough for Stephen Wolfram, it seems. He wants his name in the ranks of the Great Scientists. Until SAGE ( The Open Source alternative for Mathematica, Maple etc. ) is on par with Mathematica we have to pay too much for Mathematica. I now know why: to fund Wolfram's obsession of becoming the Greatest Scientist of all times. It seems he is on to something huge though and is probably dreaming of Wolfram competing heads on with Google.

If someone can do it it is Stephen Wolfram. What he brought the world so far ( Mathematica, MathWorld, NKS ) is truly beautiful. Maybe his Next Big Thing is worth waiting for. It is called WolframAlpha.

Proving the existence of higher dimensions

In this Newsweek article I read that one of the goals of the Large Hadron Collider in Geneva is to prove the existence of higher dimensions. That would be fascinating indeed.

MST121 - TMA03 done

Today I finished MST121 - TMA03, the calculus stuff of MST121, books C1,C2 and C3. The algebraic workout videos for this book are excellent. There are three of them and in these videos they show all the tricks required for doing the TMA03 exercises.

I prepared TMA01 and TMA02 with pen and paper. For this TMA I have used LaTeX. It's a tool with a rather steep learning curve and several required software packages but it's all free and there are zillions of tutorials on internet as well as a lot of examples. LaTeX is what the publishers use for typesetting mathematics books. LaTeX is based on TeX, which started as a one-man project by Don Knuth, one of the great mathematicians born in the previous century. I used TeXnic centre a free IDE for LaTeX. On the TeXnic website you'll find stuff to get started.

At least preparing TMA03 wasn't a last-minute job. That's a major, major ( epic ) win for me. Actually finishing something on time. A self-confidence booster. I have learned that having a good place to do studywork is an important resource. I went beyond that and have been experimenting with brainwave entrainment which is a technique to stimulate concentration and focus. It requires a good headphone and the right software. I currently use Atmosphere de Luxe in which you can 'hide' the brainwaves in nice atmospheric sounds. I use a sennheiser headphone with Active Noise reduction to cancel out noise elsewhere in the room.

I'll work this month on MS221 book A.

One more issue, although the Open University materials are excellent I wasn't really happy with MathCad. I am sure it cost me points already. At least with Vista it is a buggy mess. I upgraded to MathCad 14 which is a different experience altogether. Sufficient for coursework. It is still far from Mathematica which is now at version 7. Besides using Mathematica for my own research I use it as a final check on my TMA work before I send it in.

Hopf fibration

Hopf fibration is a topic I encountered while studying the book Naive Lie Theory. I would not know in which branch of mathematics Hopf fibration is studied. From what I understood sofar it has to do with mappings from the 4th to 3rd dimension.

The World Within

( More later ... )

MST121 - TMA02

Score: 88. Much better than expected.

Next Saturday, the 14th of february I am starting on the MS221 course: 'Exploring Mathematics'.

A book I am reading at the moment is Naive Lie Theory. It's an introduction to Lie Theory at the undergraduate level. NLT starts with a chapter on quaternions and how they can be utilized in the calculation of rotations in R3.

MS221 Exploring Mathematics

I registered for the course MS221 starting at the 14th of february. This is a course which I am very excited about. I am still working on MST121 but MS221 is designed to be studied next to MST121 or just after it.

This course is intended for study with or immediately after Using mathematics (MST121). It builds on the concepts and techniques in Using mathematics and uses the same mathematical software. It also looks at questions underlying some of those techniques, such as why particular patterns occur in mathematical solutions and how you can be confident that a result is true. It introduces the role of reasoning in mathematics and offers opportunities to investigate mathematical problems. This course and Using mathematics will together give you a good foundation for higher-level mathematics and physics courses.

Welcome

Thanks for visiting this blog. If you are studying math then you will find this text on "Tips for Success in Undergraduate Math Courses" interesting.