Sunday, November 3, 2019

The road ahead in art

I have restricted interest in art. And that is pencils. And crayons. I am not into watercolours or oil.
If I follow Andrew Loomis books "Drawing Heads and Hands"(hardcopy that I possess) and "Fun with pencil"(digital copy) then my destination is reached.
There are many bad habits that I have. Not caring enough. Not experimenting enough. Reversing the bad habits is essential. It will take time.
Dear blog readers, have a nice day.

The road ahead in mathematics

First of all, I have got a paper in mathematics published. In the journal JETIR.
I also wish to grade my favourite mathematicians.
Niels Henrik Abel
Carl Gauss
Leonhard Euler
Colin Maclaurin
Srinivasa Ramanujan
Bernhard Riemann
Joseph Fourier
Among present Indian mathematicians I have admiration for Prof.Mahajan, TIFR. And Prof.CSSeshadri.
As I wrote earlier my lifetime aim is to understand the theory of complex functions, j invariant and Eisenstein series and elliptic functions.
I will need 1 year to read initial chapters of the book "Theory of Complex Functions". Then it is likely to be easy. And another year to complete the book.
That's all. All the best wishes dear readers.



Tuesday, October 1, 2019

My interests chart

Above is the chart of my interests and my grading of individual points of interests.
In drawing I want to improve caricatures and Manga. I am thinking of "Daily life", an Indian manga series.
In mathematics I want to learn Complex functions. And j series, Eisenstein series, Weirstrass, Reimann and Gauss.
In chess my visualisation has improved. Quite a bit since 3 months back. I have a tab chess app and I try  defeating it.
In music I want to just listen now. Mainly carnatic and pop.
Basically I need an excellent guru. In drawings. My interests in other three are less. And fading.

Tuesday, September 3, 2019

Mathematics to continue

I hurriedly wrote that my mathematical endeavors has ended.
No. It hasn't.
I shall continue to learn. I shall try and master "Theory of Complex Functions" by Reinhold Remmert.
Though the above is the book I shall be concentrating on; there are two more that I bought in Kindle that I shall be studying.  These are:-

I am not able to open the Kindle book Understanding Analysis by Stephen Abbot either in Kindle reader or in Kindle in Cloud. Possibly this can be opened in my Nexus tab. I have never opened this book. I shall do so in this weekend.
My focus is however "Theory of complex numbers", j invariant and Eisenstein series. And time target is lifetime.

Friday, August 30, 2019

Euler-Mascheroni constant, Gamma


I believe that I am getting the feel of Euler-Mascheroni constant. However my expressions are not strong.
This finishes my mathematical endeavours.


Tuesday, August 27, 2019

The sixth Rational Series expansion

I had made five Rational Series expansions. These were:-
1. n/(n+1) - (n-1)/n = 1/n = 1/(n+1)+1/(n+1)²+1/(n+1)³+1/(n+1)⁴+ . . . . . .
2. The sequence n/(n+1) - (n-2)/(n-1) and the connection this series had with triangle series. The growth of this series was like 1/(4 * triangle series term).
3. The numerator i.e (n - √(n+1)*√(n+1)) of the expression √n/√(n+1) -√(n+1)/√n was approximately 1/(2*n)
4. n²/(n+1)² - (n-1)²/n² is approximately 2/(n+1)²
5. n²/(n+1)² - (n-2)²/(n-1)² is approximately prime / (n*4)². This was the prime number generator and more than 30% of the results were prime.
Today, I made the sixth expression. And that is
6.  n/ (n+1) -  (n-2)/ (n-1) is approximately 1/n².
So six expressions have been made. It may be confusing for a normal reader of my blogs. But these may be important. I have called then # expressions.
I am able to better my rational series expressions to be more accurate. However Euler totient functions exists. Euler totient functions are better expressions than rational series expressions. I have no doubts about it.
More accurate rational expressions are:-
1.  The numerator i.e (n - √(n+1)*√(n+1)) of the expression √n/√(n+1) -√(n-1)/√n is more accurately 1/(2*n) + 1/(8*(n+1)³)
2. n²/(n+1)² - (n-1)²/n² is more accurately 2/(n+1)² + 1/(n+1)
3.  n/ (n+1) -  (n-2)/ (n-1) is more accurately 1/n² + 1/(2.n³).
This finishes my mathematical endeavors.

Saturday, August 24, 2019

My Zen in mathematics

I have got peace in mathematics.
Well mathematics is not similar to engineering and technology. In the sense that Euler did not copy Maclaurin to get the sine, cosine series in his e to the power (i theta). In engineering a gear box idea may be a patent. But in mathematics it is not. It is nature.
So rediscoveries were not affecting me. What was affecting me was the quality and quantity of my ideas. I used to think I am only 10% of the greats in mathematics.
But then yesterday a thought came that though my quality and quantity are less; the fact cannot be denied that my ideas came from a single stream of thought. The golden ratio.
This gave me my Zen. My peace.
Best wishes to my blog readers.