Daily Chaos

Mathematician's Apology

noreply@blogger.com (Sumant) — Thu, 12 Nov 2009 18:31:00 +0000

Hardy's Mathematician's apology figures among the must read for any Math major. The book was written when Hardy was over 60 and passed his prime. The book is a fast read and is divided into 29 sections . It begins with a lengthy forward by Snow detailing his accquaintance with Hardy and tidbits about the book. From the beginning Hardy is candid that it is his personal opinion and inspite of inputs from his reviewers remains firm in the stance he has chosen. Numerous books have been written since Hardy about what constitutes a beautiful mathematics. Hardy bites more than he can chew when he says applied mathematics is elementary and real mathematics is not. But then it was before the development of Nuclear bomb and advent of computer sciences. Hardy acknowledges that its not easy to keep defending his assertion he made in 1920s about real and applied mathematics.
He excoriates both Alfred Northwood and Hogben the other defenders of mathematics. He is especially critical of Hogben and I am sure most Mathematicians will readily identify with Hardy here.
It is hard to defend ones choice without defending oneself. Hardy comes out both proud and humble in this book. Its not a motivational book that would propel you into plunging heads down into mathematical water. He reminices about his collaboration with Littlewood and Ramanujam. His continued lamentation about getting old is unsettling when people like Avraham Trahtman continue to do ground breaking mathematics in their 60s. Hardy's disdain about expository mathematics appears sophomoric especially if you have read Paul Halmos "I want to be a Mathematician". Its one thing to come up with something and its other to make it accessible and provide insight into it. A great mathematical exposition kindles the interest of many otherwise many results gather dust.

Grading and other stuff

noreply@blogger.com (Sumant) — Thu, 29 Oct 2009 03:26:00 +0000

I am updating this from Morris Library. I came here to do some transaction. I am glad that today I was able to return the corrected midterms for my other two classes. I felt like I was procrastinating this for a while. I realize that I need to do more math for fun and learning and somehow I am getting caught up with things which aren't so important. So here I am at library I will check some journals before going home

One Minute

noreply@blogger.com (Sumant) — Thu, 22 Oct 2009 23:07:00 +0000

I read one minute manager few years back and yesterday before going to bed I pick that book again and I was pleasantly surprised that there were things in the book which I was using in my life while interacting with other people. One minute manager is one of the quickest read. The story has 3 main ideas
1. One minute goal
2. One minute praise
3. One minute reprimand
The idea behind one minute goal is to write your goal on a single sheet of paper. One minute praise is to catch people doing things right in the beginning and one minute reprimand comes later when people have been coached and have become independent and then they do mistake. When reprimanding such individuals one should be careful to point out their mistake and not making any judgement about the person and then letting the person know they can do it and leaving them on positive note.

Good Morning

noreply@blogger.com (Sumant) — Thu, 22 Oct 2009 15:14:00 +0000

Its 10:11 and I am in the JALC library updating this blog. I had a morning class today and surprisingly Mark was there to do the evaluation. I had a review sheet ready for the exam and then I covered the last topic. I have many good students and they are steadily improving. I am planing to give a speech today. It has to be informative and I still haven't decide what should be the exact topic. I considered talking about "Erdos" or talking about "How to solve it" or "Ramsey theory" or "Pigeon hole principle". Each of these are interesting topics and can elicit an aha response. Here is something I found that can be used as an online octave.

Calming

noreply@blogger.com (Sumant) — Thu, 22 Oct 2009 03:58:00 +0000

There is nothing more calming that working out few problems. I was looking at this problem that appeared in the recent Pi-Mu journal. Find the int(ln(1+x)/x,x,0,1). One easy way to solve this is using the series of ln(1+x)/x and then you end up with an alternating series which closely resembles bessel problem and then its easy to see that the even terms sum to bessel function. Check the solution here

Rambling Pascals' Wager

noreply@blogger.com (Sumant) — Tue, 20 Oct 2009 15:18:00 +0000

I love teaching and one of the reason is we all like to flaunt our opinions, however if you are careful you can see that there are many times you end up saying things which you have cursorily thought about and then your student comes up and say that it was a good idea and then you go back to see why was it so interesting. I remember mentioning Pascal in my class while introducing Pascal's triangle. A brief comment on his work on making a mechanical calculator. His contribution to math and religion. I even mentioned Pascal's wager and why it doesn't even amount to anything and then one of my student tells me that he did checked out Pascal's wager and found it fascinating. I read pascal's wager in Poulos book called irreligion and its one argument that many people would like to foist on you. They will tell you that how benevolent their god is and then how much he likes to punish people who won't believe in him. Now if you observe many of these people they don't really believe in what they say because their actions most of the time belie their belief and on one side when they say omnipotent god and on other side they have no compunction in fooling their on creator. Anyway I think I am digressing.
The pascal wager is "If god exists and you believe in god then you will go to heaven if god doesn't exist and you believe in god you have nothing to loose but if you don't believe in god and he exists then you are going to hell and you have everything to loose". I did a quick search on internet and ended up with this argument which has been my guiding philosophy when I made peace with the god.
"It is better to live your life as if there are no Gods, and try to make the world a better place for your being in it. If there is no God, you have lost nothing and will be remembered fondly by those you left behind. If there is a benevolent God, He will judge you on your merits and not just on whether or not you believed in Him."

Fractal solution, Plotting complex plane in Matlab

noreply@blogger.com (Sumant) — Tue, 13 Oct 2009 22:34:00 +0000

The following is a solution set for a function f(z) =z^4+8iz^2-25. The roots of the function are
2-i, -2+i, -1+2i and 1-2i
The color shows which values will converge to the solution in the complex place

The complete matlab program is as below

% Using Newton Basin method to plot in complex plane
% The complex function is z^4+8iz^2-25
% There are 4 roots 2-i, -2+i, -1+2i and 1-2i of the above function
% It shows how starting with different points root converge

tol =.01;
a=0;
b=2;
c=0;
d=2;
m=1000;
n=1000;
x=linspace(a,b,m); % Setting up the x axis Coordinate System a to b
y=linspace(c,d,n); % Setting up the y axis Coordinate System c to d
z1=2-i; % root 1
z2=-2+i; % root 2
z3=-1+2i; % root 3
z4=1-2i; % root 4
lmax=20;
r=ones(n,m); % Setting a n*m matrix to be all 1
for j=1:n
for k=1:m
z=x(k)+i*y(n-j+1); % Generating the complex number, Note n-j+1
if z == 0;
z = tol;
endif

for l = 1:lmax % Newton iteration
zz = (3*z^4+8*i*z^2+25)/(4*z^3+16*i*z); % Newton's Formula for Iteration
if abs(z-zz) < tol
if abs(z-z1) < tol
r(j,k) =1; %Red
elseif abs(z-z2) r(j,k) =55; %Pink
elseif abs(z-z3) r(j,k) =33; %Light Blue
elseif abs(z-z4) < tol
r(j,k) = 42; %Deep Blue
endif
break
else
z=zz;
endif

endfor
endfor
endfor

colormap('hsv')
image(r)
axis square
axis off

Happenings

noreply@blogger.com (Sumant) — Sun, 04 Oct 2009 22:28:00 +0000

I am posting this from Carbondale Library. I am just coming after attending the picnic for GLBT held at Church of Good Shepherd. It was great to see Hugh and Judy there and I think overall the picnic was great. They had plenty of food and I saw a lot of familiar faces in Carbondale. I also had time to do an hr long sitting with Jamie and Katherine today. We decided last week at Co-op to do it and everyone was glad we did it today. Yesterday I pretty much finished the Math book. Its more like a coffee table book with lots of interesting picture accompanying each article. It also had a butterfly curve. Which reads as exp(cos(x))-2*cos(4*x)+sin(x)^2/2. In the morning today I plotted the Newton Basin curve and that pic is awesome, I will be posting it here. The neat thing was it gave me an idea of how to plot complex numbers. The method is about finding which points converge and which won't converge to the roots of the polynomial with complex coefficients.

Toastmaster Judge

noreply@blogger.com (Sumant) — Tue, 29 Sep 2009 17:14:00 +0000

Last weekend was the first toastmaster meeting in our area. I served as a Judge for the tabletopics competition. The gist of the question was "If you could change one event in the history which event would you choose and why".

Math 62, Lacrisha and Andrea's Solution

noreply@blogger.com (Sumant) — Tue, 29 Sep 2009 16:46:00 +0000

This is a pic from two of my students who solved a problem in class. Look at the way they drew pictures which I think is pretty good. Math is fun and this reflects that.

Teaching and learning

noreply@blogger.com (Sumant) — Fri, 25 Sep 2009 02:53:00 +0000

I am updating this from Faner Lab. I came here after watching Terminator 4. The movie reeks of special effects and so it would be an enjoyable fair to most of the people. When I watch movies like that my mind usually start thinking about the people who made the sound and the effects and how they want to perceive those effects. Which makes the experience kind of a detached one and I think you just start to see the movie passively. That means your pulse rate don't go up and you don't curse the villain.

Today I also attended the Math club meeting at Bucky's dome. It was like a home coming visit. It was great to see Dr. Earnest, Dr. Hughes, Dr. McSorley, Dr. Fitzerald and Dr. Hundley. The weather was nice for a barbeque and there were vegetarian burgers too. It was good to see Rachel and Valerie who were doing the round around campus lake.

In the morning today I did the worksheet for my Math 52 class. Teaching 52 is different because here the students are learning really basic skill so I have to start with real basic examples and show them that they can do it. Its a different challenge. My 62 math class did very good on their 2nd test and some of the more taciturn students are beginning to open up. I am enjoying Math 113 because I am teaching logic and the class is becoming more synergistic.

Number Freak

noreply@blogger.com (Sumant) — Tue, 08 Sep 2009 19:39:00 +0000

I came across this book at the other day I was at Barne's and Noble and here are some quick notes.

Okra, Zuccini, Potato and Onion

noreply@blogger.com (Sumant) — Tue, 08 Sep 2009 19:35:00 +0000

This Friday I went out to winery at Walker's bluff with Georgian, Gillian and Katherine. Georgian gave me a motley of vegetables ranging from okra, pepper, zucchini and green beans. I cooked okra with potato and pepper and it tasted awesome. Here is the pic of that delicious cooked vegetables.

Gillian's Korean Meditation Chime

noreply@blogger.com (Sumant) — Tue, 08 Sep 2009 19:25:00 +0000

Review: Humble Pi: The role of mathematics

noreply@blogger.com (Sumant) — Sat, 29 Aug 2009 16:52:00 +0000

I really wanted to like this book but its pathetic. Its surprising that the author holds a Ph.D could subject himself to such ridicule and that gives us an ample reason why Mathematics need to be studied.
The author totally misses the point why Mathematics is important. You cannot appreciate if you cannot quantify things and math gives you an ability to quantify things. It gives you a handle to compare things and make sense of things based on your previous experiences. Smith hates math word problems and is not convinced that solving them has any real value and yet the problems he formulate in context of social science would need facility with word problems. Math is about beauty. Its about ability to make sense of things. Training in Math is much different than training in other subjects because instead of memorizing and getting accquainted with a bunch of facts Math challenges you to test your understanding. Math is the sole subject which makes you think and challenge your intution.
Smith makes a real asnine assumption that (since it was written in mid 1990s) that we Americans as a country are doing ok and since most of the people cannot solve the 350 pt problem it means Math knowledge is not required. Now I am reviewing this book in 2009 and so I definitely have solid evidence by my side that decades of neglecting math education has a dibilitating effect on the health of economy.

Teaching and learning

noreply@blogger.com (Sumant) — Mon, 24 Aug 2009 23:59:00 +0000

I am updating this one from the DuQuoin Center of John A Logan. Today I had a good day. I started my morning with the lecture at Carterville campus. I taught Math 113 there. Then I came to carbondale to attend Math 405 and Math 475 A, then Tim dropped me to DuQuoin center and I taught Math 62 here.

Jonathan Livingstone Seagull

noreply@blogger.com (Sumant) — Fri, 21 Aug 2009 21:23:00 +0000

There are not many books one need to read over and over again and then there are few books which one can read in few minutes and get centered. Jonathan Livingstone Seagull is one such book which I have read quite a number of times and today while waiting for Betsy to show up I read it again and I can say that I can see the peace percolating beneath the petina of everyday encounters.

Binary Magic Card

noreply@blogger.com (Sumant) — Fri, 21 Aug 2009 17:21:00 +0000

I think I first saw this in Ravi Vakil's book. Each card denotes a particular bit. So if there are 3 cards then we can have 8 different numbers. If there are 10 cards we can have all 1024 numbers. In this case we have chosen 5 cards thus all the days of the month are included. The trick works because binary representation of each number is unique. Look at example for number 13.

Mathematical A,B,C D

noreply@blogger.com (Sumant) — Fri, 21 Aug 2009 13:48:00 +0000

Like Edward Gorey. William Dunham has an alphabetical book.

Wow !!

noreply@blogger.com (Sumant) — Fri, 21 Aug 2009 13:27:00 +0000

There are moments in life when you sit back and wonder. I think mathematics and physics (well physics is just applied mathematics ;) ) is one subject which provides numerous such moments. I vividly recall my consternation when I was first taught that you cannot cool below absolute zero at 273.16 kelvin. That harmonic series is diverging and p series is converging. 2nd law of thermodynamics. There are different levels of infinity. Cantor's diagonal proof. Decimal expansions of Pi. Pi itself. Euler's constant e. Feeling after reading God Delusion. Conservation of energy that I couldn't make a self propelling vehicle by using two similar ends of magnets. The tea spoon mass of black hole could be so great that it could be higher than any known metal. Seeing Iron float on mercury. Bending of light through gravity. E = mc^2, Euler's formula. Making sense of complex number through matrices. That dipping your hand in liquid nitrogen will give you a cold burn so severe that your finger could splinter in to shards. Just trying to think about how big is infinity and how insignificant even our life is in the realm of our cosmos. That packing of elements in 9 dimension allows more room. Numerous mathematical puzzles.

Nietzche Quotes

noreply@blogger.com (Sumant) — Wed, 19 Aug 2009 22:55:00 +0000

Nietzche has lots of quotes some of them profound to many downright stupid and misogynist. The ones I like are

And those who were seen dancing were thought to be insane by those who could not hear the music.

Faith: not wanting to know what is true.

He who has a why to live can bear almost any how.

I cannot believe in a God who wants to be praised all the time.

Mystical explanations are thought to be deep; the truth is that they are not even shallow.

In case you are wondering where I got these quotes. Click here.

Graduation Pic

noreply@blogger.com (Sumant) — Tue, 18 Aug 2009 20:02:00 +0000

Ok, I have a Masters.

How much faith you have !

noreply@blogger.com (Sumant) — Sun, 16 Aug 2009 20:36:00 +0000

One thing I am trying to do is not to give advice to people however as you interact with more people its hard not to. The other day I wanted to strengthen some body's belief system by giving them advise on eternity. Now the argument I proposed is people shouldn't be overly concerned about how they are living this life. If they truly believe in the eternal life promise. Because lets say an eternal life is a trillion times the current life so if you are complaining then its akin to complain to somebody who gives you a trillion dollors minus 1$ and then that person is fretting over that single dollor instead of not seeing the value of the trillion dollors. That means if you are a true believer than this one life and its trivialities should be a minimal concern.

Du Quoin, Kinkaid

noreply@blogger.com (Sumant) — Sun, 16 Aug 2009 20:32:00 +0000

Yesterday I went to Marsha's house with Joelann, Tim and Jennifer. It was good to see Jay and few other people. We decided to do the next run at Du Quoin at the time of Du Quoin state fair. We are also doing the annual Kindkaid-pontoon boat thing next saturday. Which is a lot of fun.

Castle Waiting

noreply@blogger.com (Sumant) — Sun, 16 Aug 2009 20:29:00 +0000

Done reading with it, its a mixture of many themes from various novels an ok read.