# Sympy Core

It was good seminar. It was more of a philosophical discussion for me because I knew broad outline of the code. It’s not present in a state where I can model mathematical structures because he is often change the logic layer of the code. So, at least for the time being, I have decided that I will a pursue a new project. Actually it’s not a new one, I have thought about it for a while. I wanted to translate Sympy’s core from Python to Haskell. I thought I should begin this somewhere in August. I can’t do it now because I haven’t learned Haskell yet. Actually I am little afraid that it may give a hard time while learning it.
So, I am going to switch Haskell with Scala for now.  But in future, I am definitely going to rewrite the code in Haskell.

Coming to the main thing, that is to translate Sympy core in Scala. The core has evolved like crazy, over the years, I guess. I presently have two points from where I can try to understand the core. The first start point is try to understand the code of the first version of sympy i.e, version 0.2 (as per google code). The other is ready the current core. I think, present core of is almost impossible to understand from the ground level because it’s too vast and complex. So, I will start with sympy-0.2 core and try to build a reasonably working interface. Once it starts working, I will try to read the new code base and change the core or I will write core module in different way.  Any way, my first goal is to write sympy-0.2 core.

I am thinking than writing a summary at the end of week I will keep writing on a post and I’ll update it till the week-end. And as the new week starts, I will start with a new post. Yosh! Ikuzo…

# Working with Scala

This summer I am going to work on Proving Ground, an automated theorem prover, written in Scala by professor Siddhartha Gadgil. I am mostly going to model mathematical objects starting with algebraic objects like groups. I’ll post weekly summary of my work.

As of now, my Scala skills are poor. I seriously need to improve them to write to good code and good amount of code. I had plans of reading Complex Analysis – T. Gamelin. But now, I don’t think it’s possible now because I just want to concentrate on the project heavily.

Today there is seminar on Automated reasoning by professor in which he will explain the current code base of Proving Ground and have some general discussion on using computers in mathematics. In the evening, I’ll write a short summary of the seminar. That’s all for now.

# Life at IISc

It has been nearly 18 days I have started my life at IISc. I am quite comfortable. Math Lectures are absolutely brilliant. I have found some good classmates. I am kind of enjoying my life. I haven’t yet started studying rigorously I have to start it as soon as possible. And I am the administrator for the IISc UG web site. I have to upload lecture notes, post announcements, homework assignments etc. I am enjoying my job. That’s all for now….

# Mathematics vs IIT Coaching Schools

I happen to hail from a country India. Here the school education system in recent years is getting  totally ruined due to an examination called IIT-JEE, most of the Indians know this fact. This kind of situation is particularly prevalent in towns and cities. The thing which disturbs me sometimes is the title I have put here.  I have also studied in an IIT coaching school so I know what it is. But when I was a student there, the practices were different.  My friends and I used to go library read books because we used to have the freedom and time. But now a day’s the situation is entirely different, the students are experiencing a lot of unnecessary burden due to tests, assignments, exercises, home-works so that no student has time to go to the library and read books even. Now coming to Mathematics (my favorite subject due to its elegance) I find myself very unhappy at its situation now a days due to these practices. I’ll explain how. Mathematics in schools is just taught as something as in which one has to prove something or solve a problem to get a solution (either in terms of numerals or variables). I don’t think that’s what mathematics is. Problem solving is only a part of mathematics. A student has to be taught logic which is the basic essence of mathematics because mathematical theorems are derived only by the application of rigorous logic on a set of axioms. It is sad that high school math textbooks give less or no emphasis on mathematical logic. Math teachers also play a major role in learning math in the sense that the kind of training they received to teach math, the teaching methods they follow in the classroom, their interest attitude towards math etc. Mathematics is always incomplete without that rigorous logic so the  teachers should inculcate the habit of looking things in a rigorous way to the students in math.

Now-a-days teaching calculus to high school students has become a fashion (fancy thing).  I don’t think that high school students have that maturity to understand the elegance and importance of the theorems in the calculus. I don’t think they have the necessity to find the limit of a function, to solve differential equations, either integrate or differentiate a function etc., At the most, they are asked to solve a quadratic equation and for analyzing the properties of a quadratic equation. I don’t think one has to learn integration or differentiation to do this job. This doesn’t stop at this point (due to stiff competitions among schools for students) even vector algebra  has been introduced. I think these ridiculous things have to stop at one point or the other. According to me, a high school student must solve good geometry and algebra problems. After solving them one should develop the attitude to look into the solution for improving the present solution to a more elegant solution, try to connect the problems by observing common things between the present solved and unsolved to the past problems draw some parallel lines etc., this will improve the observation skills and intuition. If this is just a brief description of the situation of math in the schools, just think about the other science subjects like physics and chemistry they are in much worse situation (may be). Only the degree of worseness changes from school to school but that worseness is present everywhere. More over what’s condition of languages god only should know.

One of the reason which caused these ridiculous activities is that physics people also started teaching some Senior High school  concepts for which they needed the mathematical concepts like Vector Algebra and Calculus etc., to high school  students. Here I am writing a few examples to show those physics people, that you can actually avoid calculus and produce more elegant solutions using the basic math theorems.

Ex.1 We will consider a simple kinematics problem. If the position of a particle (x) varies with time (t) as $\sqrt{2x-1}= t-3$. Find the acceleration.

Sol: This a high school problem which just requires a simple observation. For this problem if a high school student starts applying calculus on this, then one will end up with a solution like this. Here’s the solution.

$\sqrt{2x-1}=t-3$
Differentiating on both sides and rearranging the terms,
$v=\sqrt{2x-1}$
Squaring on both sides,
$v^{2}=2x-1$
Again differentiating on both sides,
$2va=2v$
$a=1$

One can take pains like that or can simply get the solution like this.

$\sqrt{2x-1}=t-3$
Squaring and rearranging terms on both sides,
$x=\frac{1}{2}t^{2}-3t+5$
Compare the coefficients of equation with $\Delta s= ut +\frac{1}{2}at^{2}$,
We can easily see that $a=1$

Now just think which method is better.Okay If you are not satisfied with this example lets take another example.

Ex.2 Now I will take a classic example I am sure most of you have seen this. In a given circuit with resistor R and non ideal battery of emf E with internal resistance r, then prove that if that if the power dissipation through R is maximum when R=r.

Sol: I am not writing the solution using calculus cause it looks tedious to me. I’ll try to write some what simple solution here it goes.

The Power dissipated through the resistor R,$P=(\frac{E}{R+r})^{2}\times R$
This expression can be rewritten as follows ,
$P= E^{2}\times (\sqrt{R} +\frac{r}{\sqrt{R}})^{-2}$
Now carefully see the part containing R and r, for the power P to be maximum this part should be minimum. We know that if the product of two variables is constant then their sum would be minimum if the variables are equal (another form of saying AM-GM inequality). Here the product of $\sqrt{R}$ and $\frac{r}{\sqrt{R}}$ is a constant , so the sum would be minimum if
$\sqrt{R}=\frac{r}{\sqrt{R}}$
i.e, $R=r$

Isn’t this elegant? Its almost like a three line solution. I don’t understand why people want to use calculus for this problem. One can also use their knowledge of quadratic equations to solve this question. It doesn’t matter how much subject you learned but how perfectly you learnt it.

What I want to tell finally is that Calculus is intended for the analysis of complex functions in some particular situations where the you can’t use basic theorems anymore to analyze its behavior. And no high school students are required to deal with such functions. So its better not to use it unnecessarily without any purpose, otherwise if you use it will just make things tedious and complex.

P.S. Thanks to my friend for her valuable suggestions and corrections in the draft I have written.

# My Unorganised Life

December 16 2011 12:58PM

Long time  I haven’t posted anything. My first semester ended a nearly a week back. It’s mini-disaster in my IISc academic life. It’s okay, one semester is not the entire life, world is not going to end here. I learned few basic concepts in topology. Well coming to the point, Yesterday I somehow ran into a Manga coloring contest page in a Naruto fans website. I saw a link to deviant-art saying “Basic Manga Coloring Tutorial”. I got excited and practiced it. This was the result of it.

August 8 2011 6:10PM

After a long time I wanted to write something here, Here it goes. One week has passed by in IISc. The courses are just picking up their pace. Math Prof is teaching in an excellent way in which I think Solomon sir used to teach. I can find some similarities in MPS Sir and Dipitiman Sen (Phy Prof). Anyway  I am liked this place teachers and classes. I think the work load will increase in future so I have to be careful in future (as well as now). Forgot to mention there are few guys who are asking some ridiculous questions that is irritating me a bit.   Well I am happy that I am learning Algorithm and Program Design (that to by working on a Linux system). I have found some guys to hang out with so I am kind of not alone in this place. I think that’s all for now.

July 14 2011 11:35PM

Today I am feeling very good. It’s because of several reasons I’ll mention some here. Today I have spent two hours with Ranjith in the morning. He is kind of totally infatuated by exploring Mathematics. I could see a lot of joy in face and an interest to explore the subject. I could hardly see  any of my classmates like that these days. Today my heart-felt very light due to a friend of mine. Thanks a lot to her. I am not doing any work I have to get a bit serious from tomorrow. 15 more days to go for IISc.

July 12 2011 9:45PM

It has been 4 days since I came home but I have the feeling of as if I came just now I don’t why. This visit to my home I am talking with my mom frequently than before I mean at least I am replying her very frequently. I was playing jokes, satire with her which I rarely used to do in past. I think Bangalore played me some sort of magic on me (may be).  I am already excited about College’s First day desperately  waiting for it. I am studying literally nothing I am just reading novels What the hell am I doing ?

July 5 2011 2:41PM

I spent a few days in the last with Suryateja , he gave me feel that a mathematician can only express who is in search of a true understanding in the subject as I feel. Anyway as my math interest is revived I am getting back on track with math I think so. My summer project is coming to end this Thursday.  I’ll continue my reading in home if possible.  Yesterday night I wrote my Project Report using MikTeX. Almost finished a few minor changes are left here and there.

June 28 2011 8.35PM

Last night I spent time with Chanchal which happened accidentally. He told me the research culture in IISc. As usual some things are totally rocked my mind in the negative sense but it is not expected from an institute like IISc as from the public view. Today I had a pleasant day. I attended a seminar on Representation of linear groups over local rings by Pooja Singla from Ben-Gurion University. The talk seemed to be energetic for me but I could barely understand anything in the whole lecture. I have solved my C programs which were pending in the afternoon. It couldn’t start my calculus reading due to last night incident I hope at least I can start it today.

June 27 2011 9.37PM

Today I did clean up for all the garbage around the system and put back most of the equipments to their respective places. I am satisfied and feeling with work I have done today but I couldn’t do much programming today. I have a few unsolved problems of C, so I’ll try to solve them at night.  I want to read the some calculus for the past few days  but I am delaying it, I have to give it a start today. That’s all for now.

June 25 2011 9.51PM

Today also nothing interesting was done in the lab. I continued my C++ learning in afternoon and evening for some time.  I did some experiments with coding and they were successful. Now I’ll resume back to my learning process.

June 25 2011 5.36AM

My energy levels are on its last leg because of this night out programming. I think I’ll leave now and I hope today afternoon some interesting work will be done.

June 25 2011 5.06AM

I researched the past hour on Google Reader, Buzz, and Blogger. I sort of understood basic idea but it is still vague to me.  I started following some people whom I know. I have to wait and see how my perceptions are going to change. I want to point out one more thing yesterday the whole day I spent with Suryateja G, he totally amazed me with his way of looking at the problems. His arguments about uniqueness in problem I posed was wonderful. I think I still have got some energy to do some more programming so I’ll continue with that.

June 25 2011 2.29AM

I am presently reading a book called C++ without Fear -Brian Overland. Nearly reached 10% of it. I learned to write a few programs giving input, getting output. Basically the most fundamental programs.

June 25 2011 12.59AM

In the middle of night I am trying to learn C++ in my department lab of IISc, Bangalore. Well I am pretty much not doing that I am facebooking a lot. I dont know how this night is going to end up.