Gaurish Korpal

Gaurish Korpal

Posts by Tags

Edwin Hewitt

Erdos

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

algorithm

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

amd

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

analysis

android

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

arithmetic

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

asus

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

bertrand's postulate

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

bicylinder

c

calculus II

chebyshev

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

chromebook

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

coloring

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

combinatorics

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

computations

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

computer science

conjecture

conway

counting

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

crostini

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

dnf

doodling

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

engineering

fedora

figures

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

geogebra

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

geometry

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

graph theory

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

graphs

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

grid

hp mini

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

hyperreal

inkscape

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

intel

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

knuth

latex

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

lenovo

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

linux

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

linux mint

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

logic

magma

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

manas ranjan sahoo

Space filling curve

4 minute read

Published:

In this post I would like to share my old writeup about there existence of a continuous surjective map from $\mathbb{R}$ to $\mathbb{R}^2$. In other words, we will prove that that Hilbert’s Curve is a continuous surjective map. The proof presented here was explained by Dr. Manas Ranjan Sahoo, 3 years ago on 15th April 2016.

matplotlib

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

matthew scroggs

metric spaces

Space filling curve

4 minute read

Published:

In this post I would like to share my old writeup about there existence of a continuous surjective map from $\mathbb{R}$ to $\mathbb{R}^2$. In other words, we will prove that that Hilbert’s Curve is a continuous surjective map. The proof presented here was explained by Dr. Manas Ranjan Sahoo, 3 years ago on 15th April 2016.

mir

mpmath

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

my research

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

non-standard analysis

number theory

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

numix

numpy

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

online

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

open-source

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

openSUSE

papers

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

pc

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

pdf

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

pentium

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

pfgplots

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

philosophy

piskunov

plots

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

prime numbers

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

problem solving

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

Spot The Flaw

less than 1 minute read

Published:

Many of you must have seen numerous examples of such situations where we get an absurd result and have to spot flaw in proof.

problem-solving

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

Hello World

less than 1 minute read

Published:

Here is my first post.

programming

proof

python

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

racket

rclone

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

reading

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

red hat

richert

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

ryzen

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

sagemath

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

script

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

security

sierpinski

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

solution

sum of primes

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

surface area

sympy

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

tablet

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

terminal-emulator

thinkpad

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

tikz

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

tikzcd

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

topology

Space filling curve

4 minute read

Published:

In this post I would like to share my old writeup about there existence of a continuous surjective map from $\mathbb{R}$ to $\mathbb{R}^2$. In other words, we will prove that that Hilbert’s Curve is a continuous surjective map. The proof presented here was explained by Dr. Manas Ranjan Sahoo, 3 years ago on 15th April 2016.

turner

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

ubuntu

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

vector graphics

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

vim

vim plug

vimrc

vimtex

wacom

writing

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

xfce

xfce4-terminal