Mgccl's Ivory Towerso tired

There are many different websites running on different themes.
Some websites have the same kind of sections, but presented in a different way.
For example, the navigation is on the right instead of left. Recent comment bar is showing on the bottom instead of top or w/e.
Each time I go on a website I have to get used to the interface.
If I'm only going to use this website once, it still take time to find information I need.

Semantic web is nice. Because I can ignore all the web design, and apply my own set of templates on all of them.

Semantic web NOW!

I have to complain because I have nothing better to do. Now I'm happy and going back to study for the midterm.

I wish I can get paid for complaining.

I like to record the problems so I can use them in the future.
I like data to be portable. I should create some standard so I and possibility someone else can use to store problems for really easy manipulation later.(Minimal migration required).

Currently I haven't developed the system I need to manipulate those data. There will be some function map each JSON file to a directory of files.(each resource is a file) Someone going to write it, likely me.
Problems can be recorded with JSON or XML. I prefer JSON.

top level there are the field id, name, output and resources
where id is a unique string(here I use a 64bit integer in hex form).(btw I have this 64bit integer in hex script that generate it for you)
name is the name for the problem. In English or Romanization/translation of the name of the problem.

Output is an array of objects, each have 4 fields: type, format, language, and out. Type can be "problem_statement, sample_in, sample_out, input, output" and others I can't think of.
format include any possible plain text output format that might be useful. I think "latex, html" are pretty much it for now. out is either a string or an array of strings.
Language is the language it is in. Seems reasonable.

Resource field is there to store binary files. It's an dictionary of binary files. Currently I don't need it. It is possible to use it for the future.

BTW JSON is a context free language.

{
    "id": "7455689cc5d35040",
    "name": "Putnam and Beyond Problem 12",
    "output": [
        {
            "type": "problem_statement",
            "format": "latex",
            "language": "English",
            "out": [
                "Prove that $|\\sin nx| \\leq n |\\sin x|$ for any real number $x$ and positive integer $n$."
            ] 
        },
        {
            "type": "citation",
            "format": "plain",
            "language": "English",
            "out": [
                "Putnam and Beyond ISBN:9780387257655 p.6"
            ] 
        } 
    ]
}

Nice.
Of course, it can be XML files.

This will become useful later.
I'm keeping set of problems in some database. So I can keep a queue of problems I didn't figure out the first time by just record their ID's somewhere.

I found it boring to only solving problems by myself.

Only a few classes I have attended have interactive problem solving sessions, those classes ROCKED.

---List of problem solving sessions I had on campus--- ignore if you don't care---
CSE 150, I think this is the best course I have taken in my entire life. I assume this class is somewhat like classes in AwesomeMath or other math camps. Students engaged and anticipated in solving the problems.
CSE 350, especially the recitation, is similar to CSE 150.

There are two other classes related to problem solving, but not that interactive.
CSE 392. Most of the thinking for the problems are done outside classroom. The class is basically explaining how someone solved it.
MAT 160. I been to the class only twice. It seems to be like: Do the hw, discuss how it is done. Instead of doing it in class. What's good about the class, is there are people who are enthusiastic about solving the problems.

I expect to try MAT 260 and see how it works.

Other than courses, there are 2 other places I had done some problem solving.
Math club. Last semester the preparation for Putnam, the clubbers have done some problems.
ACM practice was also similar.
--------------------end list---------------------

I feel it's not enough. There is a lack of interactive problem solving sessions on campus. Won't it be nice if there is some club that meet sometimes every week and work on some problem collaboratively. Problems of math, computer science and physics nature. i.e. Union of math/cs/physics club and intersect it with problem solving.

Some possible format.
ARML/HMMT team competition like.
People can organize them into smaller groups, working on a set of problems at a time.
Then people explain their ideas.

Seminar like. Someone pick out some set of problem, and direct the flow of the solvers, ask for participation, until the problem get solved.(Similar to last semester's math club)

Just putting the idea out there. I would totally come to events like this.

Instead of using cvs, svn, git just for large open source projects. It can be used as a personal system for backups of text files.(that include source codes to essays)

Github gave each free user 300MB of space. Pretty nice. That should be enough for just storing texts, right?
It might be abusing the ToS a little. Github free should be used for free and open source projects. All the files one commit are open to everyone. Make sure only to back up things you allow others to see.

Let's assume one doesn't store the end product the first time they commit their work. And each commit should only create a small change in the work. To be safe, let all the revisions of a file 2 times the size of the original file. Then we have 100MB of space.

For some people, they use only ascii, thus 1 byte per characters. That would be 100 million characters.
I envy people who only know English, because they will never need to use any other language, thus live in ascii world happily. They never have to worry about charset, input method and some software might not support what ever they are going to type.
I digress.
Suppose someone use UTF in some of them. Then it need 50 million characters. Let's not consider them, just consider English and source codes.

Is it possible to write 100 million characters in one's life time?
Sure.
If one type at the speed of one character per second on average over a period of 3 years, it will surpass the limit.

Likely, that's not going to happen, especially if one use their brains before writing down anything. I use lots and lots of scrap papers. My notebooks are scrap papers. I only store information on the computer in electronic format.

The source of all the hw I have done from last semester to now is 0.2MB. All the source I submitted to any online judge this semester is 0.025MB. Certainly I have written other stuff, like my blog posts. Those doesn't require back up because it's in my blog. Suppose those do require backup, I would believe it is less than 0.25MB.
Thus a total of around 0.5MB of original data was generated for a period of around 6 months.

That means I can use github for backup for 100 years if my productivity stays the same.

The amount of keystrokes I had was "6163302", last updated 2010/01/23.(I don't have a linux version yet :() It was on the computer that I use less often after college, but I would believe it contained at least 6 months of keystrokes. Even if all those keystrokes are realized, it is only a 6MB file.
Github is at least good enough for 10 years. At least I can use it until I start to earn money to pay for extra storage. COOL.

If I got a new laptop, or I need to do something on someone else's computer. All I have to
do to sync is a few command line code. Nice.

Some people did all their work in Word or w/e, where do they back them up? Google Docs. LaTeX gave me more freedom because LaTeX codes are plain texts. WIN. That's why I stopped using word. Except I dislike how kile don't have automatic spell check function yet.

It should be in future tense, I was right on almost all problems on the last hw I submitted. Those are some classical counting problems.

I'm dying from AMS 311 hw no.2(due tomorrow). I'm getting almost every single question wrong during the first attempt and require extensive amount of time to correct them in a period of 8 hours with help of various people(#math in freenode). I need to find a systematic way to deal with this when I find some time.

It's still possible there are errors in my extensively corrected hw.

What's the probability of being dealt one pair from poker?(a,a,b,c,d. where a,b,c,d are distinct values)

Seven balls randomly withdraw from an urn, find the probability that 3 red, 2 blue, and 2 green balls are withdrawn.

Suppose that n balls are randomly distributed into N compartments. Find the probability that m balls will fall into the first compartment. Assume that all N^n arrangements are equally likely.

I got all those question wrong the first time I tried(and these just tip of the iceberg).

They are suppose to be easy problems, it's hw problem from a introductory probability text.

How can I not get it? I have no problem doing CSE 555 problems(although hard, but at least I don't get wrong answers). I can do MAT 160 problems(btw, they are interesting) with a reasonable amount of confidence. In my opinion those problems suppose to be way harder than the ones in AMS 311.

There is something wrong with my counting skills. I can't count correctly. Inclusion exclusion principle and other counting principles are not what I didn't master. I always have stupid reasoning during counting.

For example, for the balls and urn problem. I thought, there are 12 ways to chose the first red ball, 11 for 2nd red ball, 10 for 3rd red ball and etc. The probability would be . At the moment I found it perfectly reasonable, then I did a calculation. WRONG, it's greater than 1.

Then I realized it's
Interesting how I got the question just before the balls one correct the first attempt.

A forest contain 20 elks, 5 are captured, tagged then released. Then 4 of the 20 elks are captured, what's the probability that 2 of these 4 have been tagged?

That question is almost isomorphic to the balls one. Why do I have a complete different set of reasoning for the 2 problems?

I don't get it.
Do I not understand counting?

What if when I did some probability wrong, but it is something smaller than 1? I will get the problem wrong and only realize it when I get my hw back.

I feel like I will fail the first midterm.
Oh well, seems like I have to do every single problem in the textbook.