Taking Notes

In this post I want to share some ways of working with course notes that I am currently using. As you all know taking notes is one of the most basic parts of studying. While it is possible to do well without it, it usually only means that you are borrowing somebody else notes (or downloading them). However, taking notes and using them are two totally different things. Firstly, handwritten notes tend to differ greatly in quality due to people handwriting and the lecturer. In my case my notes are close to being unreadable for anyone except for me (for some reason I can read what I wrote easily enough, but I have problems reading other people notes). Also, if the lecturer speaks in a disorganized way the notes become difficult to read and understand.
Obviously handwriting and organization of notes is not much of a problem - it is after all perfectly possible to take notes on a computer. Actually, if I were studying a subject that don't have formulas I would use a computer to take notes myself. Since I study math, I do not believe that I should try to take notes on a computer, although I know people who do just that.

However, the really difficult part comes when you need to go over your notes. In the first and second year the lecturers tend to give you all the material in a very detailed way, but with time they stop doing this. Instead you are now supposed to figure all the extra stuff yourself. As a result, you basically need to add to your notes on your own. So how do you do this, while still keeping the notes organized and in a format that allows you go over them easily?

At this point of time I cannot honestly say that I found a real solution to this question. But I managed to come to the conclusion that I need two things. The first thing is to make sure that I have the notes made in an organized way. To do this I make a second (also handwritten) copy of my course notes. In this copy I write all the definitions and theorems (with their proofs) with as much details as I need to understand them. This copy is later used when I need to prepare for the exams.
The second thing is basically a reference list. The idea is to make a list of all the definitions and theorems, as well as links to any useful source of extra information on the topic. It is obvious that such a list should be done on a computer. The end result is basically another version of your notes, but instead of being detailed and organized it is easily to search. This makes it easy to check any general fact you are unsure of. It is especially useful if you want to check some specific definition of the wording of a theorem. Obviously you can do the same thing just by searching on Wikipedia, but using such a reference list makes it much easier - you are able to see what you look for by just taking a glance on it, instead of searching a whole site. Also, making such a list on the computer allows (depending on what software you use) to add extra notes and to modify them easily. Since I do not want to type math formulas myself I ended using Google notebook to clip content (mainly from Wikipedia) and then edit and categorize it the way I want. Unfortunately, Google notebook is the only service I managed to find that had all the features that I wanted.

If you follow all this you will end with three different sets of notes (plus, if available, a textbook). Obviously this is a lot of work, but I feel that this approach allows me to understand the material as well as I can.

I wonder if I am pushing myself too hard...

Despite my best efforts I barely manage to finish all of my homework in time. Partially it is due to the fact that I was ill for a couple of days which caused me to slightly fall behind, but it seems that getting ahead is more hard that I thought. I also spent half a day yesterday fixing things in the new apartment. As it looks now I will finish all the exercises (of this week) on time, but this will require studying all day long (for the next three days). I don't mind doing so, but after a certain number of hours my head just stop working (and I get a headache). I also think that I am not getting enough sleep...

I was told once that the workload for math students raises with every year (unlike for biology students, who on fourth year can work on two part time jobs). It certainly seems true.
I am also planning on tutoring a bit, it seems line I have an hour or two once a week that can be used for such a purpose. It probably would be better to study during this time, but I am rather sure that I wouldn't manage to do this anyway - my homework requires much more energy to do that I have at that time of week, tutoring somebody will surely be simpler so I hope to manage.

As of now, my main concern is to manage to get ahead in doing homework, so that I will be able to read my notes and to look the material ahead. I really hope to mange to d0 it this week (I hoped the same the last week,so wish me luck.. ).

Now to brighten the mood a bit - a little math fun fact ( the link goes to wikipedia, and the explanation there is not very good, it is too difficult to read. I will try to find something better or to write it myself).

Politics

The only good thing in politics, in my opinion, is that most of the time it doesn't influence you directly. Unfortunately, this is not the case for me now. The rest of the post is my complains, so feel free not to read it.
First of all, there are elections to the mayor office at Jerusalem at the middle of next month. As of now, I don't even intend to vote because I don't have the time nor the desire to check the information available on the candidates. Also, I will probably be too busy studying anyways. What annoys my most is that for some reason I got a call asking me to help with the election process - to take attendance notes. I have no idea why they called me with this..

Secondly, next week I suppose to start a new semester. However the university already sent letters telling all the students that the semester will not open because the government doesn't give them the money they need. They even included a long list of emails in the letter to where we can send complains. I really doubt that anything will happen to the semester, but who knows...

Thirdly, due to government policies and economical crisis the apartments in Jerusalem are rather expensive now, and my family and I are currently looking for a new apartment. Horrible timing... I certainly hope that we will find something soon.

On a somewhat brighter note, here are link to some political jokes I found:

Two political candidates were having a hot debate. Finally one of
them jumped up and yelled at the other: "What about the powerful
interests that control you?"

The other guy screamed back, "You leave my wife out of this."

Found this one here, follow the link for more.
Also check the Circle vs. Square webcomic, its author did an excellent job making fun of politics without insulting anybody.

University vs the Government

I received an email from the university today, as expected it was an official statement that unless the government will provide the necessary funds the upcoming semester will be canceled. The previous year the situation was the same, and in the last moment the government decided to give the necessary funds. I wonder what will happen this year...
The letter also contained a call for students to join the fight with the government. While I am not going to participate in such activities, I am sure there will be enough people who will.
I just hope that the semester will open in time and in an orderly fashion..

I am back

I didn't post anything for a lot of time, but I am still here. Sorry for suddenly stopping posting, I was busy with exams so I had to stop posting for some time. I already got all the exam results, I did good in all except two (but this was expected from the start, so this is not much of a problem).
Originally I planned to stop posting only for a few days, maximum a week, but for some reason not posting anything was so relaxing that I just couldn't force myself to write anything. I even didn't read my rss :).

The next semester will start only next month, so I still have a lot of time to prepare for it. I already have some books for next year, and I intend to buy more. Hopefully I will be able to prepare well - learning seven courses in one semester is not a nice thing...

Overload

As you probably noticed, I didn't post for a few days. The reason for this is that I have to prepare to exams. Next week, the posting will continue as usual. Meanwhile, you are welcomed to use the skribit suggestion widget to suggest topics for me to write about.

The Department Quilt

Today I decided to do something I do very rarely - to look on the recommended feeds in Google Reader. I usually don't look on them, because I have almost 100 subscriptions already, and I don't want to add any extra feeds. However, today I decided to look on those feeds. In one of the feeds I suddenly saw a very familiar image:





These two images are the front and back sides of a quilt that can be found on the second floor of the mathematics department of Hebrew University Jerusalem. At first I thought that the blog author whose rss feed I was reading visited HUJI, and took those photos, but then I noticed that the post is called Our Department’s Quilt.

This is how because of a Quilt a found the blog of Gil Kalai - Combinatorics and more. He is a professor of mathematics in Huji. His main areas of interest are Combinatorics and convexity, so if you are interested in anyone of them, it is probably a good idea to visit his blog.

What a good exam

Today I did my first exam of this semester, and I am very pleased of how it went. There is a tradition on this course to give on exam questions which are not very solvable. Those who write the exams must of course make sure that the material that will appear in the exam is what was learned during the semester, but they always try to give tricky questions. Instead of making questions that just test your knowledge of the material, they give questions that require you to think about some trick.
However, this semester one of the lecturers on this course is new and he decided to break this tradition. I know about this because he told the class himself. Near the end of the semester he came to class and said that he will make sure that the questions in the final exam will be solvable, unlike what was in the previous years. He told that he looked on the exams from the previous years and concluded that even a person who knew all the course material might not be able to solve the questions. He later told us that the other lecturer and other people who have influence on the questions that will go into the exam, say that this is the course tradition to give such tricky questions.

The exam was today, and as it looks he won the fight (and my guess that it was indeed a fight). Some of the questions were more difficult than others, but overall the exam was very straightforward and even simple.

The semester has finally ended

It was a long year... While officially there were only two semesters, we actually did three because the professors where on strike during the first one. I still have exams to do, but the last lecture was today.
Well, it was a fun year. I hope the next one will be even better.
I am sorry for not posting for a few days, I was extremely tired and busy. Hopefully I will be able to continue posting as usual during the exam season. I am sure that while I would be revising I would get a lot of ideas for things to write about on Math pages.

Also, it is a sad day to the math blogger community today. Craig Laughton, the author of Gooseania, wrote his last post today. He finished his math Phd, but decieded that he doesn't want to be a mathematician. His blog was created to document the process of doing a Phd, and it contains a lot of information. It is clearly visible how his enthusiasm for math slowly gets way to depression. He decided not to continue posting on the blog in the future. Hope he will find his place in this world....

The weirdest "Hello" ever

Today in the morning I was just entering the Einstein Institute Building in the Hebrew University when another student was going outside. I talked with him a few time before, he is also studying mathematics, and is a really nice person. We both were in a hurry, because it was almost the time for our lectures to begin, so we just said "Hello" and went on. Well, almost. I just said "hello". He said" Oh! Hello professor, how are you doing?". I am not a professor, and nobody was standing behind me. Since it was totally unexpected, and I was in a hurry I even didn't react in any way to this. That was a weird morning... While I want to do an advanced degree in math, I am sure I never told him about it, so I really fail to see why he would joke like this.. Well, it might be prophetic. :)

On a more serious note, the semester ends on 4/9. Oh should I say, the exam month begins on 4/9. Anyway you put it, it is good news actually. I feel that I really want to start learning new courses, that is I want to start the next semester. I need to study a lot for two of the exams, I don't feel that I know these courses material well enough. But I am sure I will manage.

Have you ever saw the photo of Pythagoras?

This was a question asked on a lecture today - by the professor. After not getting an answer, he concluded that we didn't see the photo, so he told us he will draw it. I thought about photographing it, but my cell phone camera is not very good. The drawing you see below is my recreation of his drawing:



I am starting to think that this particular professor has a special love to Pythagoras theorem.. Not so long ago he told the class a story about a graduate student, who was asked on a final test for M.S. what do you know about Pythagoras theorem (in Hebrew theorem and trial is the same word), and he answered I think the jury decided he is not guilty...

Learning History of Mathematics

The title of this post is a bit misleading - I am not going to write about History of Mathematics in this post. This I plan to do in another post.

I am now doing a short introductory course about History of Mathematics. When I took it I though it is going to be a simple and easy course. However, it turned out to be problematic. The course itself is only two hours a week, but we are also supposed to read books about History of Mathematics. The professor recommended History of Mathematics by Boyer (very good book), and also some other books. I was reading this book in the library for some time, but somebody took it so I can no longer use this copy. When I found out the Boyer was taken, I took another book - Development of Mathematics by Bell. I cannot say I like it, he is very critical and he is also jumping a lot. One of the purposes of this book was to show to students what areas are now alive in math and what areas are of no interest now, however this goal makes it more difficult to read. Unfortunately, the part of the library where this book is, was closed today and will be closed for the following month.
I requested Boyer and will get it for 3 weeks on 9/7, so this is not a problem. I also have two books on my computer - A History of Mathematics From Mesopotamia to Modernity by Luke Hodgkin and History of Mathematics An Introduction 6th Edition by David M. Burton. I don't like to read from the computer screen, but the books are very good. Another resource that the professor recommended is MacTutor. It is a very good site with a lot of articles about math history and it also has a lot of mathematicians biographies.

However, after doing this course for six weeks it is obvious that reading one book is not enough. I feel that to really understand and learn this subject I need to search for extra information to feel the gaps which are not filled by the books I have. This means that I will have to "research" on the net the topics that are not clear to me.
Since I will be doing this research anyway, I will write about these topics on Math Pages. I have a post about faster than light travel and another one about definite integrals to write, but after finishing them, I will write about math history. Probably I will start with solving the cubic equation.

Web Apps for the student?

I just stumbled on this post - Must Have Web Apps for the Hi-Tech College Student. I must say I am totally confused. The post begins with a claim that "There are tons of new web apps that have been created with the college student in mind." I suppose it is so, but it is hard to believe that some of the apps mentioned in the post were created for students. For example Netvibes. I don't use it, so I don't know much about it. But when I visited it I didn't notice anything that would suggest that it was created for students. Meebo is another example. While it is useful for communication, it is even better for wasting time. If someone did it especially for students he clearly did them a bad thing.

The other apps mentioned also don't look like especially useful for a student. Google Docs is a nice application, but unless you tend to write your homework in groups (and for some reason prefer to do it while sitting at different computers) , I see no reason to use it instead of OpenOffice.
The online calculators mentioned can be replaced by your own calculator and by Google calculator for unit conversion. If you are using Gnome-do you can even do conversions without visiting Google.

Perhaps I am seeing it this way because I am a math student and the only program that I find useful for me as a student is Latex...
What do you think about it? Are those lists about apps for students just an attempt to get some traffic or do they offer any solid advice?

A summer place

Our world is a unique place... even if there are millions of other planets with intelligent lifeforms on them, the planet we live on is still unique - because any other place will be different. We have a lot of conflicts and difficulties but there is also rest and beauty of nature. The video below was made by my friend CRISSANCA67. For me the important part in it is the images - I never liked music and I don't listen to it. The images however manage to tell an interesting story - they manage to capture a lot of unique moments.

In other news I clearly managed to find myself a lot of problems. I decided to study History of Mathematics this semester, hoping that it will be an easy and simple course. Unfortunately, it turned out that I am supposed to do a lot of extra reading for the course. I have to read the whole History of Mathematics by Boyer. Normally this wouldn't be a problem, but it is a 700 pages book and I have to read it in the library. The book is well written, and it is interesting to read - if you happen to take a course in this subject it is a good choice. It begins with what is known about mathematics in ancient Egypt, then jumps to Mesopotamia and Greece. I thought about buying it, but it would mean ordering it from Amazon or eBay, which even with its relatively cheap price I don't want to do. I managed to get a copy of History of Mathematics by David M. Burton, but since the exam will be based on Boyer there is not much reason to read Burton. Hopefully I will manage to read Boyer enough each week. I read it for only about an hour last week because I had to go to a restaurant with some friends of mine, whom I didn't see for a long time... It seems that I will have more time this week. I should probably try to read half of it by the end of next week.

Back to University

Finally, the winter break is over... Thats good news for me. I really missed studying. I can study at home, but it is just not the same. Besides, it is usually more funny at the lectures. I don't have a lot of courses this semester, but as it looks now I will have a lot of homework to do. On a less brighter side, one of my new professors has a "weak connection to reality" - I don't know how to describe it... During the second hour of the first lecture, he just set down for a few minutes in a corner and read his notes for 3-4 minutes. After this he stood up, turn to the board and asked: "What I did here?". Overall he managed to make a rather strange impression. Despite this, he explains well.

Since I will be busier now, I will post less to this blog. I will try my best to post as much as possible, but I simply have less time now.
During the last week I did one post per day - from now on I will try to do one post per two days. I did this during the previous semester, so it shouldn't be too difficult to continue.
If you want a specific topic to be covered you can use the Skribit widget in the sidebar to suggest it (or to vote for suggestion already there).

New semester old semester

As I already wrote there was a long strike in all of the Universities in Israel. This was the longest such strike ever - 89 days. It ended this week. Also this week is the last week of the first semester..
I suppose Israel is the only place where after such strike the semester is not canceled and no compensation is payed to the students. Moreover, we still have to do our exams, on the courses that were taught despite the strike, while studying other courses. The semesters will be shortened also, so we will have to learn in 11 weeks what is normally taught 14 weeks. It was also announced today that due to financial problems there will be no TA classes for one of the courses next week.
For me this is good actually. It looks like I will be able to add a course to this semester, and overall I don't have too much to study. So I am not complaining.
There is no timetable for now but I will probably will have less than 20 hours per week.

For the blog this is bad news unfortunately - I will have much less time to work on it especially during the 2-3 next weeks. I hope that I will manage to use all the time I have wisely.

Geometry trick

As I already wrote once, I like strange theories and paradoxes, but I believe that there is always some underlaying logic. For example look at this image:
Do you see the reason for this? There is nothing wrong with this picture. Moreover this is exactly what you will get if you will make your own triangle.

The explanation is very simple. The area of all of the smaller triangles is equal, in both pictures, to the original one. But if you will look carefully you will see that that the slope, of the second figure, is different.
Update: This wasn't clear to some of the readers, so I wrote a more detailed explanation.

Such things are the reason why in math everything must be proven. We cannot just trust our intuition. It was relatively easy to spot the reason in this case, but it is not always easy. Geometry we can at least visualize, and even make pictures. When the question is totally abstract it is much more difficult to understand it - especially if our intuition is wrong about it.

A few days ago I overheard two students talking about their linear algebra exam. There was a question in the exam to find a basis for some vector space. The student found it, but didn't prove it is indeed a basis. He didn't get any points for the question naturally. And he was angry about it...
But without proof there is nothing. Even if the answer is correct, without proof it is worthless. Such approach is the only way in which paradoxes can be solved and mistakes can be avoided

Strike in the University

You probably don't know about this but all the universities in Israel (there are seven) are partially close for about two month now. The professors are on strike so they just don't show up.
They have a serious disagreement with the treasury. In Israel the professors salary is payed by the universities, but all the agreements about it are done with the government. Or more precisely are not done at all. The last contract they had ended a few years ago and the government simply refused to do a new contract. It lasted in this way for a few years and all went well - except for the inflation. Because of inflation the professors lost about 35% of their salary. At the end of last year they tried to begin talks with government officials about this but without any success.
This year they decided not to show up to classes until their demands are met. It didn't help. As far as I know the government refused to acknowledge the problem and they even said they don't care if the semester will be canceled because of this.
The students are the main victims in all of this, but for different reasons they prefer to wait and see what happens. Officially they support the professors, but many of them a very angry.
Personally I support the professors. I didn't go to any of the demonstrations and I don't plan to go. Partially it is because half of my courses are taught despite the strike but mainly because I simply don't see any point in such demonstrations. The government already showed clearly what they want. Their plan is to modify the universities so that they will bring immediate profit. It was already stated in a public enough way. As a side note there is even a poster near the entrance to the Hebrew University - "We want education not education ltd." So what is needed is a change of policy. And for this to happen ... only God knows what can cause this.
I hope the strike will end soon and that the professors will get what they want.