Final Post.

A final Farewell,

I can't believe it's already the end of the first semester, I remember the first time our class got this SLOG assignment, and even my first post, where I told the world I will not fall behind. I guess saying is a lot easier then actually doing.

Things just started to get confusing I guess, and I just believed asking for help was not a good option (In my mind I was just a bothersome person with all my questions)

Towards the end I really think I am finally started doing my hardest in this course, too bad I think it was a little bit late (I really should have started a lot earlier with the going to profs and asking for help, but at least I learned from my mistakes and acted on it right?)

Been studying for the final, and will continue to study for it really hard (I mean it!) and I hope all goes well in the future.

This class has truly been really interesting despite my dismal marks. Hopefully my new found ways of studying will help me in the future in terms of understanding everything.

Farewell and have a great winter break and happy holidays,
Amrutha Krishnan

Space Splicing Work.

Continuing my work from yesterday, here is the final bits of Space Splicing (in a neater format):

I can divide a sheet of paper into two regions with a single straight line. With two straight lines, I can divide a sheet of paper into two regions with a single straight line. With two straight lines, I can divide a sheet into 4 regions, and with three straight lines I can divide it into seven regions. 

If n is some positive whole number, what is the maximum number of regions I can divide a sheet of paper into with n straight lines?

Rough Work For SpaceSplicing.

Hey, after all of my assignments (not only 236 but 2 other classes as well) I can finally get back to my slog (Hence why it took till today). I think today will be my last update tomorrow is the day the slog's are due.

Question: SpaceSplicing.
Anyway. Here is a chart that I made up on photoshop after I cut up a square multiple times.

Now I guess the goal is to find a pattern for this. 

I kind of figured out a pattern...but I am not really sure at how to get a proof out of this. Every time the number of straight lines increases (Let n = Number of straight lines) then the number of max number of regions (let m = max number of regions) increases by the value of the difference of previous n values max number of regions plus one.

Below I have posted my rough work on getting a function that works for this problem. I used photoshop (since I tend to make a lot of changes during my rough work).

To make it more readable, I will probably post this up re-written on Latex tomorrow. For a full proof this function would need unwinding, to get a closed form. Then prove the closed form using induction.

Quick update.

As the title says this will be quicker then normal. I have been swarmed with assignments from all my courses this week so haven't had much time to update this slog. However after handing in the latest and final assignment I feel better about it.

First of all I started the assignment really early. Then worked on it for a really long time so all my answers seem well enough. However I did leave the 4th question for the day before it was due. So all of thursday night and friday I was trying to figure out how to write it. The program itself was hard for my to figure out because I have always had trouble with binary searches or any kind of searches and I guess it just takes a while for my brain to wrap around it. And when I finally found something that worked (after coding it multiple times in python and java) I realized just how long the actual proof was. All in all I was pretty happy with how I did on the assignment, but I doubt my question 4 is complete/detailed enough.

OH and after going through the proof from the wiki. The one about cutting paper from the previous post I finally realized what it was asking me. It was not how many regions in an arbitrary number of cuts x but the max number of regions you can obtain from a number of cuts x. I will update more after I work on it a bit more.

That's it for now. I will post more tomorrow. With more detail. (I always seem to skip a couple days when I say I will post but I do always get back :)

Peace for now...I have other assignments to work on.

Slog Assignment.

Note: I think I just did something stupid and forgot to public my "Working towards a goal. (4)" which I did Thursday night before I left for Rochester. Anyway that is why I havent posted in the last couple days. *(4) only talked about me going through the Slog Assignment topics. :/ I hope that is not too crucial. 

Today I worked on actually starting the Assignment/Mathematical portion of this slog. 

Below is my starting works on the first two problem solving questions:

1. Space Splicing: 

I can divide a sheet of paper into two regions with a single straight line. With two straight lines, I can divide a sheet into four regions, and with three straight lines I can divide it into seven regions.

If n is some positive whole number, what is the maximum number of regions I can divide a sheet of paper into with n straight lines?

2. Paper Folding: Grasp one end of a strip of paper between the thumb and index finger of your right hand, and grasp the other end between the thumb and index finger of your left hand. Fold the strip of paper once, so that the end of the strip that was in your left hand now is on top of the end that was in your right hand, and the thumb and finger of your left hand now grips the fold at what was the middle. If you were to unfold the strip of paper now, it would have a single crease in a direction you might want to call "down."

If you carry out the fold several times, always folding the strip so that the end of the strip that is in the left hand is placed over the end that is in the right hand, what pattern of "up" and "down" folds do you get? For example, if I make two folds, I get a left-to-right pattern of "up," "down," "down."

Note: This is mainly me pondering these questions. I shall post more tomorrow/day-after.

Working towards a goal.(3)

When I title this (if I havent mentioned this before) of "Working towards a goal" I am saying that my goal is: (Since I am always on the brick of just passing in this course) Is understanding and catching up, passing this course. (And till this SLOG is due I will update daily on my progress).

Problem Solving Episode:
I guess I finally understand what the mathematical portion of this slog is after bugging a bunch of upper years (who ended up not knowing much) then finally finding the prof. and asking him. Spending the rest of today and most of tomorrow going through the examples and questions given.

Preparing for Finals:
Today I saw my tutor again. She helped me understand and notice all the pieces I am missing from my proofs. (Things such as re stating the base case or the hypothesis to explaining why defining an n/k value i necessary (all of which I thought were obvious before)).

Note: I have always felt horrible for asking questions before usually because I feel like I am burdening everyone around me. Having a tutor that specifically wants to answer my questions, let's me ask my stupid questions without feeling really bad (so hopefully I will get really well prepared for this exam).

Working towards a goal.(2)

Class in general:
Been practising writing proofs. I met up with my tutor as I said before and I realized that the formatting and structure of my proofs are usually very off. After getting a few tips from her I have been trying to practise them and seeing if I am doing all right now.
Slog:
As for the mathematical problem, I am not really sure on what to work on yet. Trying to figure out a question is hard, and I am not sure I am approaching this right. I completely forgot to ask Danny about this on Monday and have been trying to find him to clarify the kind of question I should be trying to solve again all Tuesday. I will try again tomorrow, hopefully I can figure this out, so that the last 2 weeks before this slog is due is spent full on working towards (trying) to solve this mathematical episode.