Longest Verification

I've been doing this calculation of group multiplication from a 'new' group representation theory for about two weeks now. Last weekend saw me doing it over and over again. Which at the end, showed that no resolution is covered. Last week also during my discussion, me and my advisor are somehow 'fighting' each other to show which formula really works and how to solve it.

There are two things which I need to prove. The first part is using the group multiplication one needs to show that the group representation is correct. And the second part is to get the correct matrix form from the group representation. I sense that this is not as simple as the 2x2 or 3x3 matrices. So I start with 4x4 and all my matrix multiplication so far show a NO go. One of the terms which I got is not correct. I just manage to get only three terms correct out of four. Which is not correct at all. It has to be a unique solution.

Owh I feel so so tired. But I need to keep it up and try other ways plus trying to look for if there is meaning comes out of it. The multiplication and groups. Aarrgghh...

First Day of Class

Today is the first day of the Quantum Mechanics II (QM II) course. It will be carry on during this semester for every Wednesday afternoon from 2pm until 4.45pm. I was so excited to attend this course since the lecture will be given by my supervisor. Plus also on how would he made quantum mechanics to be lovable. That is the first thing he did, when he first started his lecture. He said exactly

"this would be a very fun course. It contains the story of the love of my life which is quantum mechanics"

I do have a bit of uneasy on how I would perform in his class, but the way he gave lecture effected me even more.

As I imagined, the student who took this courses are mostly male students. The fact that I'm trying to be as early as possible to the class, so that I can sit in front was not working that well. I'm competing myself with a few other tough guys which also taller than myself. And in the end I only secure myself for the second row. Maybe next time I can try to squeeze more to get a better view.

Today's topic touched on the historical of quantum mechanics and later on trying to generate concepts from the classical mechanics towards quantum mechanics. This is by doing the most famous example such as the pendulum and harmonic oscillator. I can safely say that I enjoyed this first lecture and also understand most of the topic which have been discussed.

good luck...

Redo and Redo

Up until this post is written, I had spent the whole morning and the afternoon working on the construction of the group multiplication related to the Stockwell transform. I am quite sure that I have work out the computational method in a right way. According to the journal I'd refer. But at the end my final answer was not correct.

The next piece of paper will mark the eight (rough) paper for the computation alone. And there's more to come.

Lets do it all over again...

Reckless About Proof

Until now, the whole picture which I'm sure every student in this department has very well-verse in is at proving theorems, corollaries or a proposition. I, on the other side, are trying to find my individual internal personal connection with the idea of prove and satisfaction of proving. And I had to say that the chemistry is still not there.

I spoke to one of my friend and he mentioned that you need at least a year to comprehend yourself with the skills of proof. One cannot by any chance grab it instantly. Its more about getting attached to the whole idea of any particular concepts where later on your proof is well-defined (logically). Which I failed to feel it in the first place. I cannot start my proof, not until I read some of the hints. Meaning, I don't even know where to start. I've talked to my SV about my reckless about proof, and he did gave me notes on mathematical thinking. I looked at them, study, listing out important things and try to work out the exercises. It seems OK.

Then everything went wrong. Again. When I came back to reality, facing subject like measures, I feel dumb. The things I've learned is hardly applied to this part of subject. OK, this will not stop me. So I made a second move, to speed up my pace. What I did was to learn from any individuals who willing to show some of the skills/techniques. But yet as they spoke the same language (of maths), I feel terribly sorry for myself. So I think I need to go back to the canonical way. A book.

At the end I found that I have no basic in analysis at all. Supposed, I should have taken any functional analysis back then. Whoops, there's no point to mention it now.

Feels Like ...

It's been almost seven months now, I've been struggling hard to catch up everything which I feel left behind. I am speaking of my studies. This is due to my 1st qualifying exam which is due this coming June. The topics involved are general maths. But believed me, general doesn't mean easy. Since the question may varies. There are five topics to be covered (sigh). And right now I feel like I am becoming a math's student rather that a physics student. I can safely said that in my department, I am the only student who finished my degree in physics. Fortunate for me that I did some maths subject during my degree which help me to speed some of the understanding. But I don't think it's enough. Most whom I met (the students) have a pure maths background. And there's only one so far who did her bachelor in mathematical physics. Which I cannot compare myself with her since her grasp in fundamental of maths were gigantic as well. Lucky that when I have discussion with this student and when I cleared myself that I came from physics background, they being really reasonable. They treated me like I was in my first level of high school. Which is cool.

There's one thing that I've learned from these maths student is the way they play around with notations and indices. They can make easy generalization out from a very specific problem and apply them to a particular problem. They write equations a lot and tell a 'story' out of them. Numbers are hardly notice in our everyday life but variables are. Proof is normal thing to do and honestly, I don't really like to proof. One more thing is they like to discuss and presents ideas. Always. Right now, I am trying my best to be if not equal but at least not that far from them.

Note: My Chinese friend is more helpful than the whites (pure). If I asked only some idea to solve, she simply solved everything towards the end. thanks a lot. I may need to absorb everything from these people just to make sure that I am fully apprehended with the techniques before the coming of the exam.

Journey towards PhD

From "A PhD Thesis Without Tears", John Creedy, 2007 (research paper)

During your preliminary reading, ...in describing what you want to investigate, you should be able to frame a clear question. One should prepare to answer questions like

1. 1. What was the question motivating this paper?

   2. What are the author’s major results?

   3. What do you regard as the main limitations of the approach?

   4. In what ways do you expect your research to extend existing literature?

Note: a very useful standard materials

Finally... A Real Task

As usual I have a weekly discussion with my supervisor for the subject on the group theory, topics on Hilbert space and Lebesgue measure. Those three topics are the ultimate goal for the rest of 24/7 days of my life so far. However, for this week, after preparing myself for whole week on my presentation, I didn't managed to present a thing. Since my supervisor has taken the whole time to explain me the general idea of the matter discussed. And I found myself happy with it. I must say that this is the shortest discussion that I've ever had.

Before we end, I suggest few things on my preparation for the comprehensive exam plus continuing on the problems for modern analysis and group theory. He mentioned that in the mean time, he will hand over some journals and group theory problem for me to work on with because later on I may end up working on such problems. Better start now or then.

So I guest this is the beginning of my research work. It doesn't have to wait until I finished all my courses though. But first thing first, I need to pass the comprehensive test. Good luck.

Ph.D Thesis Proposal

I went to the scariest talk ever this afternoon. The talk was meant for the Ph.D thesis proposal (see below title). This is the first time I've had a chance to joint this kind of a talk. To make this talk even scarier is the audience is a number theorist which make the talk is dense with an unfamiliar notations and terminologies. I think I picked the wrong slots. The topic is not really for me. Well, it is not like I ever want to try to understand the contents but the main idea of joining would be to have some kind of a motivation. I would love to see and feel how's it like to present your thesis proposal because eventually I will do same as this is part of the comprehensive exam. But on the other hand, I do found some familiar concepts like the group homomorphism and irreducible representation being mention in his early talk.

From my observation,

1. There are five audience, which includes the advisor, two co-advisors and two audience (count me in).
2. The advisor and the co are empty handed. No papers at hand and don't even note down a single thing while the speaker is presenting.
3. The speaker used a blackboard for his presentation and not once he ever refer to any reference while he's presenting.
4. The speaker is well known of those of the notations he used, and matters that he was saying.
5. When the speaker get lost or cannot answer some question, his advisor took in charged.
6. When the speaker was not known to an answer, he can definitely say I have no idea...

The thing that I learned would be

1. Be precise (always) what you are explaining. Give examples, perhaps a definition and so on up to every notations that you used. Don't aspect audience is well-aware to what you are presenting even though they really an expert.
2. A general organized talk would be to have a motivations of research, reviews from previous works, thesis problem and expected output.

Note: Apart from the above two things, I need to work on more in the first part. My former supervisor used to remind me of this...

Title of the talk:
Constructing Special Types of Fontaine Sheaves: Comparison Isomorphism Theorems

Pretty Bad

I received an email later today from our graduate assistant. She mentioned that she has to withdraw my name from the course that I have registered for the Winter term, Mathematical Quantum Mechanics due to the low enrollmment. There are only two of us. I was sad about the news since the teacher for the course is my supervisor. During our first lecture, I was kind of excited to listen to his lecture.

It was more than just a lecture. He inspired us with a very nice starting through intuitive examples of quantum mechanics. In my early days, it is far well-known that subject on quantum mechanics is less interesting to students due to its depth abstract mathematical usage which is unreachable from any ordinary imagination. But believe me. Once when we get to its roots and terminologies, it was really interesting. There are many to relate to the physical world but of coz there's more open question about its existence.

I really hope that I can still have a chance to take this course. I have more years to go. This is something that I really needs as to practice myself to become a good QM teacher one day.

Totally Paranoid

OK...I am totally paranoid because of nothing!

It turns out that I'm not doing so so bad at all for my midterm. I am so relieved. It was more than half of the total. Which is OK for me. All my furious and other bad feelings have gone now. Nothing to regret for being left out from the 'discussion' during the running of the exam. I have actually tried to answer everything towards the end and believed it that it is lucky that some of them is actually correct.

However I learn it here that when you are trying to answer a mathematical problem. Please please make sure everything is written up. Don't left any tiny single idea that you had in mind. NEVER. Justified everything...

My level of courage is up now.
Thanks

Paranoid

OK, lets face it. Am I being paranoid or what. Is it just my feeling or it's nothing to do with anything. It's happened that exams over here is nothing the same like with exams we had in our country.

1. We can bring in formula (in only one piece front and back of a paper). So I wrote exactly the formula needed. But towards the day of the exams. I found out everyone wrote not only formula but also notes. Of coz in a very tiny little handwriting just to fit in both sided of the paper.

2. While exam is running, we usually don't discuss any of the question. Thus we don't even talked loud. Yeah maybe we can asked if the question really really confuses us. However in my midterm, everyone keep questioning the lecturer until they get to the answer.

But what really pissed me off is, the lecturer actually go one by one asking if they have came to point of question 2 for an answer. AND AND she didn't even asked me. Nope...she didn't stop at my place. You will never imagine that the class was actually were having a discussion instead of an exam. And it worst that I've just been left out. Totally left out.

There were just 9 of us in the class and to me its pretty small. I can hear a student and the lecturer was discussing the question in a very loud sound. For e.g.
Dialogue 1:
the lect - "Have you solved question 2 part 2?
student-"Not yet I've just finished part 1 (and she showed the lecturer her answer sheet)"
the lect-"Owh you actually has already the answer. Just write it in the form of Psi(s) and Phi(s). Now for part 2 you need to...bla..bla"
I can't help to hear again since time is running and I have another 2 parts of the question to answer. The the lecturer just went around the table asking everyone if they have come to answer question 2 part 2.

I was so confused and at the same time feel terrible about it (that shed didn't asked me) but I still want to make an effort and I just raised my hand and asked. And guess what, the lecturer just told me that "you need to make a change of variables" then she left. The discussion just continued. the lecturer even used the board to show everyone the idea. And I was so 'like terkapai-kapai', running towards time and in the same time stretching my brain to get an idea for solving the two parts. I again raised a hand to ask the lecturer, again the lecturer was just pointed very tiny ideas which don't really helps. Or maybe I asked in a wrong way. I'm not sure. But the lecturer never border to see how am I doing like the way she did it to the other student.

I just give up and wait for a stop sign to hand the paper in. I don't even bother to ask again. I am lost. So lost and mad.

So, am I being paranoid?

Welcome To Real Stuffs

Today I had a meeting with my supervisor at around 10.30 am. He was asking of how I'm doing so far in Montreal and how's my classes which. I just tell him the truth regarding my approximation theory class which I found most difficult to absorb if compared to my PDE class. Though I can follow during classes, however when it comes to proof a theorem I am totally stuck. I told P. Ali regarding my lack of mathematical proving stuffs and he gave me a notes call mathematical thinking. It is a very straight forward notes which meant to be for the undergraduate level (college to be exact) as a preparation for them to take mathematics in university level. I got a chance to view a bit of the notes while I'm sitting in the metro on my way back to Verdun and I found out that there's a lot of stuff especially techniques to learn when you're dealing with maths. It tells you how exactly all the questions of why, what is maths doing.

OK...just forget about that coz I'm going to be stuck myself to that notes for the rest of my next week. So during my meeting with P. Ali also, we've decided that we will have a weekly meeting together every Friday morning and that will be the time for me to ask, reporting and what ever it is that I found appropriate to say to him. Its like it will be the time for us to get along with. Meaning also that, I need to be all set before getting into his room on that particular Friday.

Another thing is that I finally or officially get my core subject to focus on as part of a mathematical physics acquire. For instance I need to have some expertise on group theory, differential geometry, functional analyses and hilbert space. Together with this the quantum theory stuff will also be included. Or its more to quantum mechanics.

The mystery of my overall core research area is finally announced. I hope that I am capable to learn the above topics and lets the hard time begin...

A Well Planned Writing #1

7 Writing Principles

Introduction What did you do? Why?
Materials & Methods How did you do it
Results What did you find
Discussions Your interpretation of results
Summary Statement of main findings
Acknowledgements Who helped
References Details of reference cited

Source: SCIENTIST MUST WRITES: A GUIDE TO BETTER WRITING FOR SCIENTIST, ENGINEERS AND STUDENTS, Robert Barrass, 1978 (old edition), Chapman & Hall.

I found that I need to upgrade my writing skills especially when sometime I felt that I am OK with my writing and most of the time I felt that I’m doing it the wrong way. First I must read and try to analyze any interested papers/journals and later divide its contents into those 7 principles. I believed theoretical papers would probably cause me more than 2 weeks or months for extracting the contents.