Google Docs

I've been told by my best partner that I should try this another interesting platform from Google, namely Google Docs. For people like myself who use mathematical symbols a lot. I mean really a lot. The famous word document such as LaTeX.is very powerful. For example, nowadays we can see that the transformation of using blogspot to wordpress for a blogger who need a friendly and fully integrated TeX medium (i.e. mathematical symbols) in the web has already been solved.

Now, with this features of Google Docs, we can make our quick or recall notes anytime without even using the LaTeX processor or medium to execute such file that we need. The best thing of Google Docs, is that for those who are used to LaTeX symbols or LaTeX documentation, the same ideas work very well in Google Docs. Plus also for those who doesn't really know about the LaTeX shortcut symbol, Google Docs had prepared an equation editor menu. So that as usual, one just need to just choose, click and insert the associated equation.

Thanks Google...

a new document

select the Equation editor on the insert menu

the TeX equation workbook

example of an output

No Short Cut

I've been preparing myself for the comprehensive exam in the specialized part which is physics. Which means, I have to 'cover' my previous undergraduates study on classical mechanics (CM), electrodynamics (~EM) and quantum mechanics (QM) at the same time. They provide the textbooks plus the selected chapters to focus on. It looks impossible to do and create pressure at the same time. But earlier student proved that it can be done.

Looking at the selected chapters, I try to be as positive as I can in terms of grabbing any facts, techniques, method and everything which are important. Believed me there are so many (sigh). Also to be honest, there are some chapters which I don't remember myself ever went through. For example the WKB approximation in QM. Then I thought to save time, I can try to talk to my SV (who also the question maker) so maybe that few chapters can be excluded.

But the response was just

"well, try to look at it first"

An answer which I've expected. So bring it on (in a positive way)

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

Measure Theory Demystified #1

The concept of measure is a generalization of the concept of "length", "area" and "volume". The famous theory of measure would be the Lebesgue measure which associated to the Lebesgue integration.

Every definition of an integral in based on a particular measure. I never learned such integration is integrated with a particular measure. I mean not in a normal integration.

For example,

1. Riemann integral is based on Jordan measure
2. Lebesgue (pronounced ləˈbɛg) integral is based on Lebesgue measure.

These two famous integrals usually encounter when study of analysis of functions (reals or complex). Lebesgue integral for example plays an important role in the branch of mathematics called real analysis and in many other fields in the mathematical sciences.

Remark: The study of measures and their application to integration is known as measure theory.

Second Lecture on Lie Groups

Last week, the teacher started his first lecture on Lie Groups in giving definitions on groups and stuff like that. I'm going to summarize later on (in my own words) basic important definitions that going to be understand when we learned about groups specifically the Lie Groups. Today is just the continuation from last week topics, but a little depth on the representation theory. Personally I need to work out on this one since I don't recall I have ever experienced this subject before.

It is a good practice for myself to be able to put some details on the web as my own personal (input) database which going to be useful in future. This is a mathematics class but I don't see any numbers and a common mathematical work being presented through out the lecture.

Note: I am so dense!