Working with OpenMP

Here I will discuss the OpenMP and its usage in high performance computing using different languages.

Here are some links to learn and apply OpenMP.

OpenMP on Ubuntu (from medium.com)

OpenMP is the language or API that is used to communicate with different processors (or cores) in the same node (note that a node is a collection of number of processors). Any high performance computing use OpenMP because to use more than a processor for a single job, you need to use OpenMP.

Save this program in a file helloSerial.c and run.


{example program with serial running which include the time taken to complete}


Now, check this program helloParellel.c

{simple parellel program which include the time take to complete}

The parallel program is faster. Why?


Some frequently asked questions.

What is a processor?
What is a node?
What is a thread?
What is a core?
What is dual core in laptops?

Python blogs follow

https://scientific-python-101.readthedocs.io/numpy/math.html

How to remove a coloumn from multiple coloumn in Linux

I have a list of coordinates (x,y,z). In addition to that, there are additional columns which are necessary.  How to remove this?

AWK can be used in a simple manner.

USE:

awk '{print $2, $3, $4}' inFile.txt > coordinates.xyz

This will create the file coordinates.xyz with the necessary coordinates.

White background in Jmol, Iqmol and Avogadro

For publication, you may need white background structures. Here is how you can do it.

Jmol

Right click on the screen
Select Color
Select Background
Select the color (white)
Now you will get the white background

How to read all the questions and answers without registering (without username and password)

When you search for a question in google, you come up with a first link from Quora. You click it and you read the answer. Suddenly, you find another question from quora (on the side bar) and you want to read it too. But, the problem is that the site would ask you to register to read more.

To avoid registration, you can do following.

1. Search in normal mode
2. Open the first link normally
3. Now, if you want to read more of the Quora questions, right-click on the link and open in incognito mode. In this way, you can read all the questions.

It won't work if you do everything in incognito-mode.

How to highlight the novelty of your research in a research paper to publish in a journal?

In any peer-reviewed journal, the first question asked would be "What is the novelty of your work". It is important to ask this question to yourself and answer in your research introduction.

A quote from an answer given by Baba in Quora: "Virtually 99.999+% of the research work is incremental. The new elements they bring is either in the method, connecting the dots in a new way that was not previously thought of before, or observation of an effect that was not seen before. This does not dilute the achievement of the authors of the work. However, taking already existing building blocks and making a new figurine out of the said blocks can be argued that in itself is not novel. It is a highly skilled art form, and not easy."

Here are the ways to find out the novelty of your work and also some tips to improve your paper writing process.

1. Do a through literature survey and find out what are the key differences between your work and and research already done.
2. Systematically analyze the already published papers, reference books, patents, conference papers, etc and find out what should be done.
3. Establish that the results you got has never reported before or the method you have used is new in case what your work is improving a methodology.
4. Write the paper when you start the work. Use the writing process as a tool to generate ideas and discover ideas and fuel to your thought process.
5. Use tools like Mendeley or any other paid to write the paper for reference management.
6. Use LaTeX to format your paper. In mathematics, if you submit paper written using word processors, it may be considered unprofessional. I remember some incident related to this and I will write about this later (probably this is related to solving a famous mathematical problem). When the number of equations, figures, references get more and more, you would end up with difficulty if you use word processors. So, you need LaTex.
7. In the results and discussion, discuss the results obtained by other authors and discuss how your result is new or adds more to the field. You also generate new insights based your results and already reported results.
8. In the conclusion highlight the results obtained and insights advances in your field or study.

Notes on LaTeX symbols and usage.

Symbols I use the most

Text modification

Some of the frequently used symbols:

superscript - \textsuperscript{th}


subscript    - \textsubscript{s}



infinity       - \infty


dash            - the latex command is "---"

How to type single bond, double bond and triple bonds in LaTeX (for chemists)?

I found following is useful for Chemists.

https://www.overleaf.com/learn/latex/Chemistry_formulae

How to add multi-line comments in LaTeX?.

\iffalse
Comment text that you don't want to appear in paper.
\fi

Next question will appear here. 

next
anserComment 
will appear here.

See this page on Wikipedia 

Letters

${\displaystyle \alpha }$ \alpha ${\displaystyle \beta }$ \beta ${\displaystyle \gamma }$ \gamma ${\displaystyle \delta }$ \delta ${\displaystyle \epsilon }$ \epsilon ${\displaystyle \zeta }$ \zeta

${\displaystyle \eta }$ \eta ${\displaystyle \theta }$ \theta ${\displaystyle \iota }$ \iota ${\displaystyle \kappa }$ \kappa ${\displaystyle \lambda }$ \lambda ${\displaystyle \mu }$ \mu

${\displaystyle \nu }$ \nu ${\displaystyle \xi }$ \xi ${\displaystyle \mathrm {o} }$ \omicron ${\displaystyle \pi }$ \pi ${\displaystyle \rho }$ \rho ${\displaystyle \sigma }$ \sigma

${\displaystyle \tau }$ \tau ${\displaystyle \upsilon }$ \upsilon ${\displaystyle \phi }$ \phi ${\displaystyle \chi }$ \chi ${\displaystyle \psi }$ \psi ${\displaystyle \omega }$ \omega

${\displaystyle \varepsilon }$ \varepsilon ${\displaystyle \vartheta }$ \vartheta ${\displaystyle \varkappa }$ \varkappa ${\displaystyle \varpi }$ \varpi ${\displaystyle \varrho }$ \varrho ${\displaystyle \varphi }$ \varphi ${\displaystyle \varsigma }$ \varsigma

${\displaystyle \Gamma }$ \Gamma ${\displaystyle \Delta }$ \Delta ${\displaystyle \Theta }$ \Theta ${\displaystyle \Lambda }$ \Lambda ${\displaystyle \Upsilon }$ \Upsilon ${\displaystyle \Xi }$ \Xi ${\displaystyle \Phi }$ \Phi

${\displaystyle \Pi }$ \Pi ${\displaystyle \Psi }$ \Psi ${\displaystyle \Sigma }$ \Sigma ${\displaystyle \Omega }$ \Omega ${\displaystyle \ }$ ${\displaystyle \digamma }$ \digamma ${\displaystyle \ }$

${\displaystyle \aleph }$ \aleph ${\displaystyle \beth }$ \beth ${\displaystyle \gimel }$ \gimel ${\displaystyle \daleth }$ \daleth ${\displaystyle \ }$ ${\displaystyle \ }$ ${\displaystyle \ }$

${\displaystyle \forall }$ \forall ${\displaystyle \exists }$ \exists ${\displaystyle \nexists }$ \nexists ${\displaystyle \Finv }$ \Finv ${\displaystyle \Game }$ \Game ${\displaystyle \backepsilon }$ \backepsilon

${\displaystyle \imath }$ \imath ${\displaystyle \jmath }$ \jmath ${\displaystyle \ell }$ \ell ${\displaystyle \Bbbk }$ \Bbbk ${\displaystyle \amalg }$ \amalg ${\displaystyle \nabla }$ \nabla ${\displaystyle \mho }$ \mho

${\displaystyle \partial }$ \partial ${\displaystyle \eth }$ \eth ${\displaystyle \hbar }$ \hbar ${\displaystyle \hslash }$ \hslash ${\displaystyle \Im }$ \Im ${\displaystyle \Re }$ \Re

${\displaystyle \wp }$ \wp ${\displaystyle \emptyset }$ \O ${\displaystyle \emptyset }$ \emptyset ${\displaystyle \varnothing }$ \varnothing ${\displaystyle \complement }$ \complement ${\displaystyle \circledS }$ \circledS

${\displaystyle {\acute {a}}}$ \acute{a} ${\displaystyle {\hat {a}}}$ \hat{a} ${\displaystyle {\ddot {a}}}$ \ddot{a} ${\displaystyle {\bar {a}}}$ \bar{a} ${\displaystyle {\tilde {a}}}$ \tilde{a}

${\displaystyle {\grave {a}}}$ \grave{a} ${\displaystyle {\check {a}}}$ \check{a} ${\displaystyle {\dot {a}}}$ \dot{a} ${\displaystyle {\breve {a}}}$ \breve{a} ${\displaystyle {\vec {a}}}$ \vec{a}

${\displaystyle \prime }$ \prime ${\displaystyle \backprime }$ \backprime ${\displaystyle \P }$ \P ${\displaystyle \S }$ \S ${\displaystyle \mathrm {\AA} }$ \AA

${\displaystyle {\frac {abc}{def}}}$ \frac{abc}{def} ${\displaystyle {\sqrt {abc}}}$ \sqrt{abc} ${\displaystyle {\sqrt[{n}]{abc}}}$ \sqrt[n]{abc}

${\displaystyle {\overline {abc}}}$ \overline{abc} ${\displaystyle {\underline {abc}}}$ \underline{abc} ${\displaystyle {\overrightarrow {abc}}}$ \overrightarrow{abc} ${\displaystyle {\overleftarrow {abc}}}$ \overleftarrow{abc}

${\displaystyle \overbrace {abc} }$ \overbrace{abc} ${\displaystyle \underbrace {abc} }$ \underbrace{abc} ${\displaystyle {\widehat {abc}}}$ \widehat{abc} ${\displaystyle \ }$

Fonts

${\displaystyle {\mathcal {A}}}$ \mathcal{A}	${\displaystyle {\mathcal {ABCDEFGHIJKLMNOPQRSTUVWXYZ}}}$
${\displaystyle \mathbb {A} }$ \mathbb{A}	${\displaystyle \mathbb {ABCDEFGHIJKLMNOPQRSTUVWXYZ} }$
${\displaystyle {\mathfrak {A}}}$ \mathfrak{A}	${\displaystyle {\mathfrak {ABCDEFGHIJKLMNOPQRSTUVWXYZ}}}$ ${\displaystyle {\mathfrak {abcdefghijklmnopqrstuvwxyz}}}$ ${\displaystyle {\mathfrak {0123456789}}}$
${\displaystyle {\mathsf {A}}}$ \mathsf{A}	${\displaystyle {\mathsf {ABCDEFGHIJKLMNOPQRSTUVWXYZ}}}$ ${\displaystyle {\mathsf {abcdefghijklmnopqrstuvwxyz}}}$ ${\displaystyle {\mathsf {0123456789}}}$
${\displaystyle \mathbf {A} }$ \mathbf{A}	${\displaystyle \mathbf {ABCDEFGHIJKLMNOPQRSTUVWXYZ} }$ ${\displaystyle \mathbf {abcdefghijklmnopqrstuvwxyz} }$ ${\displaystyle \mathbf {0123456789} }$
${\displaystyle {\textbf {A}}}$ \textbf{A}	${\displaystyle {\textbf {ABCDEFGHIJKLMNOPQRSTUVWXYZ}}}$ ${\displaystyle {\textbf {abcdefghijklmnopqrstuvwxyz}}}$ ${\displaystyle {\textbf {0123456789}}}$

Common functions

${\displaystyle \sin }$ \sin ${\displaystyle \arcsin }$ \arcsin ${\displaystyle \sinh }$ \sinh ${\displaystyle \ }$

${\displaystyle \cos }$ \cos ${\displaystyle \arccos }$ \arccos ${\displaystyle \cosh }$ \cosh ${\displaystyle \ }$

${\displaystyle \tan }$ \tan ${\displaystyle \arctan }$ \arctan ${\displaystyle \tanh }$ \tanh ${\displaystyle \ }$

${\displaystyle \cot }$ \cot ${\displaystyle \coth }$ \coth ${\displaystyle \sec }$ \sec ${\displaystyle \csc }$ \csc

${\displaystyle \exp }$ \exp ${\displaystyle \log }$ \log ${\displaystyle \ln }$ \ln ${\displaystyle \lg }$ \lg

${\displaystyle \min }$ \min ${\displaystyle \max }$ \max ${\displaystyle \inf }$ \inf ${\displaystyle \sup }$ \sup

${\displaystyle \lim }$ \lim ${\displaystyle \liminf }$ \liminf ${\displaystyle \limsup }$ \limsup ${\displaystyle \ }$

${\displaystyle \arg }$ \arg ${\displaystyle \deg }$ \deg ${\displaystyle \det }$ \det ${\displaystyle \dim }$ \dim

${\displaystyle \gcd }$ \gcd ${\displaystyle \hom }$ \hom ${\displaystyle \ker }$ \ker ${\displaystyle \Pr }$ \Pr

Big symbols

${\displaystyle \prod }$ \prod ${\displaystyle \bigcap }$ \bigcap ${\displaystyle \bigwedge }$ \bigwedge

${\displaystyle \coprod }$ \coprod ${\displaystyle \bigcup }$ \bigcup ${\displaystyle \bigvee }$ \bigvee ${\displaystyle \bigsqcup }$ \bigsqcup

${\displaystyle \sum }$ \sum ${\displaystyle \biguplus }$ \biguplus ${\displaystyle \bigoplus }$ \bigoplus ${\displaystyle \bigotimes }$ \bigotimes ${\displaystyle \bigodot }$ \bigodot

${\displaystyle \int }$ \int ${\displaystyle \oint }$ \oint ${\displaystyle \iint }$ \iint ${\displaystyle \iiint }$ \iiint ${\displaystyle \iiiint }$ \iiiint

Arrows

${\displaystyle \leftarrow }$ \leftarrow ${\displaystyle \Leftarrow }$ \Leftarrow ${\displaystyle \leftharpoonup }$ \leftharpoonup ${\displaystyle \leftharpoondown }$ \leftharpoondown ${\displaystyle \leftleftarrows }$ \leftleftarrows

${\displaystyle \rightarrow }$ \rightarrow ${\displaystyle \Rightarrow }$ \Rightarrow ${\displaystyle \rightharpoonup }$ \rightharpoonup ${\displaystyle \rightharpoondown }$ \rightharpoondown ${\displaystyle \rightrightarrows }$ \rightrightarrows

${\displaystyle \uparrow }$ \uparrow ${\displaystyle \Uparrow }$ \Uparrow ${\displaystyle \upharpoonleft }$ \upharpoonleft ${\displaystyle \upharpoonright }$ \upharpoonright ${\displaystyle \upuparrows }$ \upuparrows

${\displaystyle \downarrow }$ \downarrow ${\displaystyle \Downarrow }$ \Downarrow ${\displaystyle \downharpoonleft }$ \downharpoonleft ${\displaystyle \downharpoonright }$ \downharpoonright ${\displaystyle \downdownarrows }$ \downdownarrows

${\displaystyle \longleftarrow }$ \longleftarrow ${\displaystyle \Longleftarrow }$ \Longleftarrow ${\displaystyle \hookleftarrow }$ \hookleftarrow ${\displaystyle \leftrightharpoons }$ \leftrightharpoons ${\displaystyle \leftrightarrows }$ \leftrightarrows ${\displaystyle \Lleftarrow }$ \Lleftarrow ${\displaystyle \Lsh }$ \Lsh ${\displaystyle \leftarrowtail }$ \leftarrowtail ${\displaystyle \twoheadleftarrow }$ \twoheadleftarrow ${\displaystyle \curvearrowleft }$ \curvearrowleft ${\displaystyle \circlearrowleft }$ \circlearrowleft ${\displaystyle \looparrowleft }$ \looparrowleft

${\displaystyle \longrightarrow }$ \longrightarrow ${\displaystyle \Longrightarrow }$ \Longrightarrow ${\displaystyle \hookrightarrow }$ \hookrightarrow ${\displaystyle \rightleftharpoons }$ \rightleftharpoons ${\displaystyle \rightleftarrows }$ \rightleftarrows ${\displaystyle \Rrightarrow }$ \Rrightarrow ${\displaystyle \Rsh }$ \Rsh ${\displaystyle \rightarrowtail }$ \rightarrowtail ${\displaystyle \twoheadrightarrow }$ \twoheadrightarrow ${\displaystyle \curvearrowright }$ \curvearrowright ${\displaystyle \circlearrowright }$ \circlearrowright ${\displaystyle \looparrowright }$ \looparrowright

${\displaystyle \leftrightarrow }$ \leftrightarrow ${\displaystyle \longleftrightarrow }$ \longleftrightarrow ${\displaystyle \updownarrow }$ \updownarrow ${\displaystyle \nleftarrow }$ \nleftarrow ${\displaystyle \nrightarrow }$ \nrightarrow ${\displaystyle \nleftrightarrow }$ \nleftrightarrow

${\displaystyle \Leftrightarrow }$ \Leftrightarrow ${\displaystyle \Longleftrightarrow }$ \Longleftrightarrow ${\displaystyle \Updownarrow }$ \Updownarrow ${\displaystyle \nLeftarrow }$ \nLeftarrow ${\displaystyle \nRightarrow }$ \nRightarrow ${\displaystyle \nLeftrightarrow }$ \nLeftrightarrow

${\displaystyle \mapsto }$ \mapsto ${\displaystyle \longmapsto }$ \longmapsto ${\displaystyle \multimap }$ \multimap ${\displaystyle \ }$ ${\displaystyle \rightsquigarrow }$ \rightsquigarrow ${\displaystyle \leftrightsquigarrow }$ \leftrightsquigarrow

${\displaystyle \swarrow }$ \swarrow

${\displaystyle \searrow }$ \searrow

${\displaystyle \nwarrow }$ \nwarrow

${\displaystyle \nearrow }$ \nearrow

Order symbols

Some of the following symbols require \usepackage{amssymb} in the preamble

${\displaystyle <}$ < ${\displaystyle \leq }$ \leq ${\displaystyle \ }$ ${\displaystyle \leqq }$ \leqq ${\displaystyle \ }$ ${\displaystyle \ }$ ${\displaystyle \leqslant }$ \leqslant

${\displaystyle >}$ > ${\displaystyle \geq }$ \geq ${\displaystyle \ }$ ${\displaystyle \geqq }$ \geqq ${\displaystyle \ }$ ${\displaystyle \ }$ ${\displaystyle \geqslant }$ \geqslant

${\displaystyle \nless }$ \nless ${\displaystyle \nleq }$ \nleq ${\displaystyle \lneq }$ \lneq ${\displaystyle \nleqq }$ \nleqq ${\displaystyle \lneqq }$ \lneqq ${\displaystyle \lvertneqq }$ \lvertneqq ${\displaystyle \nleqslant }$ \nleqslant

${\displaystyle \ngtr }$ \ngtr ${\displaystyle \ngeq }$ \ngeq ${\displaystyle \gneq }$ \gneq ${\displaystyle \ngeqq }$ \ngeqq ${\displaystyle \gneqq }$ \gneqq ${\displaystyle \gvertneqq }$ \gvertneqq ${\displaystyle \ngeqslant }$ \ngeqslant

${\displaystyle \vartriangleleft }$ \vartriangleleft ${\displaystyle \trianglelefteq }$ \trianglelefteq ${\displaystyle \lesssim }$ \lesssim ${\displaystyle \lessapprox }$ \lessapprox ${\displaystyle \prec }$ \prec ${\displaystyle \preceq }$ \preceq ${\displaystyle \precsim }$ \precsim ${\displaystyle \precapprox }$ \precapprox

${\displaystyle \vartriangleright }$ \vartriangleright ${\displaystyle \trianglerighteq }$ \trianglerighteq ${\displaystyle \gtrsim }$ \gtrsim ${\displaystyle \gtrapprox }$ \gtrapprox ${\displaystyle \succ }$ \succ ${\displaystyle \succeq }$ \succeq ${\displaystyle \succsim }$ \succsim ${\displaystyle \succapprox }$ \succapprox

${\displaystyle \ntriangleleft }$ \ntriangleleft ${\displaystyle \ntrianglelefteq }$ \ntrianglelefteq ${\displaystyle \lnsim }$ \lnsim ${\displaystyle \lnapprox }$ \lnapprox ${\displaystyle \nprec }$ \nprec ${\displaystyle \npreceq }$ \npreceq ${\displaystyle \precnsim }$ \precnsim ${\displaystyle \precnapprox }$ \precnapprox

${\displaystyle \ntriangleright }$ \ntriangleright ${\displaystyle \ntrianglerighteq }$ \ntrianglerighteq ${\displaystyle \gnsim }$ \gnsim ${\displaystyle \gnapprox }$ \gnapprox ${\displaystyle \nsucc }$ \nsucc ${\displaystyle \nsucceq }$ \nsucceq ${\displaystyle \succnsim }$ \succnsim ${\displaystyle \succnapprox }$ \succnapprox

${\displaystyle \eqslantless }$ \eqslantless ${\displaystyle \lessgtr }$ \lessgtr ${\displaystyle \lesseqgtr }$ \lesseqgtr ${\displaystyle \lesseqqgtr }$ \lesseqqgtr

${\displaystyle \eqslantgtr }$ \eqslantgtr ${\displaystyle \gtrless }$ \gtrless ${\displaystyle \gtreqless }$ \gtreqless ${\displaystyle \gtreqqless }$ \gtreqqless

${\displaystyle \ll }$ \ll ${\displaystyle \lll }$ \lll ${\displaystyle \lessdot }$ \lessdot ${\displaystyle \preccurlyeq }$ \preccurlyeq ${\displaystyle \curlyeqprec }$ \curlyeqprec

${\displaystyle \gg }$ \gg ${\displaystyle \ggg }$ \ggg ${\displaystyle \gtrdot }$ \gtrdot ${\displaystyle \succcurlyeq }$ \succcurlyeq ${\displaystyle \curlyeqsucc }$ \curlyeqsucc

Set symbols

${\displaystyle \subset }$ \subset ${\displaystyle \Subset }$ \Subset ${\displaystyle \sqsubset }$ \sqsubset ${\displaystyle \triangleleft }$ \triangleleft ${\displaystyle \blacktriangleleft }$ \blacktriangleleft

${\displaystyle \supset }$ \supset ${\displaystyle \Supset }$ \Supset ${\displaystyle \sqsupset }$ \sqsupset ${\displaystyle \triangleright }$ \triangleright ${\displaystyle \blacktriangleright }$ \blacktriangleright

${\displaystyle \cap }$ \cap ${\displaystyle \Cap }$ \Cap ${\displaystyle \sqcap }$ \sqcap ${\displaystyle \vartriangle }$ \vartriangle ${\displaystyle \blacktriangle }$ \blacktriangle

${\displaystyle \cup }$ \cup ${\displaystyle \Cup }$ \Cup ${\displaystyle \sqcup }$ \sqcup ${\displaystyle \triangledown }$ \triangledown ${\displaystyle \blacktriangledown }$ \blacktriangledown

${\displaystyle \in }$ \in ${\displaystyle \subseteq }$ \subseteq ${\displaystyle \ }$ ${\displaystyle \ }$ ${\displaystyle \subseteqq }$ \subseteqq ${\displaystyle \ }$ ${\displaystyle \ }$ ${\displaystyle \sqsubseteq }$ \sqsubseteq

${\displaystyle \ni }$ \ni ${\displaystyle \supseteq }$ \supseteq ${\displaystyle \ }$ ${\displaystyle \ }$ ${\displaystyle \supseteqq }$ \supseteqq ${\displaystyle \ }$ ${\displaystyle \ }$ ${\displaystyle \sqsupseteq }$ \sqsupseteq

${\displaystyle \notin }$ \notin ${\displaystyle \nsubseteq }$ \nsubseteq ${\displaystyle \subsetneq }$ \subsetneq ${\displaystyle \varsubsetneq }$ \varsubsetneq ${\displaystyle \nsubseteqq }$ \nsubseteqq ${\displaystyle \subsetneqq }$ \subsetneqq ${\displaystyle \varsubsetneqq }$ \varsubsetneqq ${\displaystyle \ }$

${\displaystyle \uplus }$ \uplus ${\displaystyle \nsupseteq }$ \nsupseteq ${\displaystyle \supsetneq }$ \supsetneq ${\displaystyle \varsupsetneq }$ \varsupsetneq ${\displaystyle \nsupseteqq }$ \nsupseteqq ${\displaystyle \supsetneqq }$ \supsetneqq ${\displaystyle \varsupsetneqq }$ \varsupsetneqq ${\displaystyle \ }$

Equality and inference

${\displaystyle =}$ = ${\displaystyle \neq }$ \neq ${\displaystyle \equiv }$ \equiv ${\displaystyle \thickapprox }$ \thickapprox ${\displaystyle \approx }$ \approx ${\displaystyle \approxeq }$ \approxeq ${\displaystyle \cong }$ \cong ${\displaystyle \ncong }$ \ncong

${\displaystyle \sim }$ \sim ${\displaystyle \thicksim }$ \thicksim ${\displaystyle \nsim }$ \nsim ${\displaystyle \simeq }$ \simeq ${\displaystyle \backsim }$ \backsim ${\displaystyle \backsimeq }$ \backsimeq ${\displaystyle \eqsim }$ \eqsim

${\displaystyle \doteq }$ \doteq ${\displaystyle \div }$ \div ${\displaystyle \doteqdot }$ \doteqdot ${\displaystyle \fallingdotseq }$ \fallingdotseq ${\displaystyle \risingdotseq }$ \risingdotseq

${\displaystyle \triangleq }$ \triangleq ${\displaystyle \circeq }$ \circeq ${\displaystyle \eqcirc }$ \eqcirc ${\displaystyle \bumpeq }$ \bumpeq ${\displaystyle \Bumpeq }$ \Bumpeq ${\displaystyle \asymp }$ \asymp

${\displaystyle \mid }$ \mid ${\displaystyle \shortmid }$ \shortmid ${\displaystyle \vdash }$ \vdash ${\displaystyle \dashv }$ \dashv ${\displaystyle \Vdash }$ \Vdash ${\displaystyle \ }$

${\displaystyle \parallel }$ \parallel ${\displaystyle \shortparallel }$ \shortparallel ${\displaystyle \vDash }$ \vDash ${\displaystyle \ }$ ${\displaystyle \Vvdash }$ \Vvdash ${\displaystyle \models }$ \models

${\displaystyle \nmid }$ \nmid ${\displaystyle \nshortmid }$ \nshortmid ${\displaystyle \nvdash }$ \nvdash ${\displaystyle \ }$ ${\displaystyle \nVdash }$ \nVdash ${\displaystyle \ }$

${\displaystyle \nparallel }$ \nparallel ${\displaystyle \nshortparallel }$ \nshortparallel ${\displaystyle \nvDash }$ \nvDash ${\displaystyle \ }$ ${\displaystyle \nVDash }$ \nVDash ${\displaystyle \ }$

Brackets

${\displaystyle \lfloor }$ \lfloor ${\displaystyle \llcorner }$ \llcorner

${\displaystyle \rfloor }$ \rfloor ${\displaystyle \lrcorner }$ \lrcorner

${\displaystyle \lceil }$ \lceil ${\displaystyle \ulcorner }$ \ulcorner

${\displaystyle \rceil }$ \rceil ${\displaystyle \urcorner }$ \urcorner

${\displaystyle |}$ | ${\displaystyle \vert }$ \vert

${\displaystyle \|}$ \| ${\displaystyle \Vert }$ \Vert

${\displaystyle \{}$ \{ ${\displaystyle \}}$ \}

${\displaystyle \langle }$ \langle ${\displaystyle \rangle }$ \rangle

${\displaystyle /}$ / ${\displaystyle \backslash }$ \backslash

${\displaystyle [}$ [ ${\displaystyle ]}$ ]

${\displaystyle (}$ ( ${\displaystyle )}$ )

Other symbols

${\displaystyle \infty }$ \infty ${\displaystyle \propto }$ \propto ${\displaystyle \varpropto }$ \varpropto ${\displaystyle \bowtie }$ \bowtie ${\displaystyle \ltimes }$ \ltimes ${\displaystyle \rtimes }$ \rtimes

${\displaystyle \intercal }$ \intercal ${\displaystyle \dotplus }$ \dotplus ${\displaystyle \times }$ \times ${\displaystyle \wr }$ \wr ${\displaystyle \pitchfork }$ \pitchfork

${\displaystyle \surd }$ \surd ${\displaystyle \setminus }$ \setminus ${\displaystyle \diagdown }$ \diagdown ${\displaystyle \diagup }$ \diagup ${\displaystyle \leftthreetimes }$ \leftthreetimes ${\displaystyle \rightthreetimes }$ \rightthreetimes

${\displaystyle \perp }$ \perp ${\displaystyle \between }$ \between ${\displaystyle \asymp }$ \asymp ${\displaystyle \angle }$ \angle ${\displaystyle \measuredangle }$ \measuredangle ${\displaystyle \sphericalangle }$ \sphericalangle

${\displaystyle \bot }$ \bot ${\displaystyle \wedge }$ \wedge ${\displaystyle \barwedge }$ \barwedge ${\displaystyle \doublebarwedge }$ \doublebarwedge ${\displaystyle \therefore }$ \therefore ${\displaystyle \ }$

${\displaystyle \top }$ \top ${\displaystyle \vee }$ \vee ${\displaystyle \veebar }$ \veebar ${\displaystyle \ }$ ${\displaystyle \because }$ \because ${\displaystyle \ }$

${\displaystyle \pm }$ \pm ${\displaystyle \curlywedge }$ \curlywedge ${\displaystyle \smallfrown }$ \smallfrown ${\displaystyle \frown }$ \frown ${\displaystyle \bigtriangleup }$ \bigtriangleup ${\displaystyle \triangle }$ \triangle

${\displaystyle \mp }$ \mp ${\displaystyle \curlyvee }$ \curlyvee ${\displaystyle \smallsmile }$ \smallsmile ${\displaystyle \smile }$ \smile ${\displaystyle \bigtriangledown }$ \bigtriangledown ${\displaystyle \ }$

${\displaystyle \cdot }$ \cdot ${\displaystyle \circ }$ \circ ${\displaystyle \bullet }$ \bullet ${\displaystyle \centerdot }$ \centerdot

${\displaystyle \cdots }$ \cdots ${\displaystyle \vdots }$ \vdots ${\displaystyle \ldots }$ \ldots ${\displaystyle \ddots }$ \ddots

${\displaystyle \circledcirc }$ \circledcirc ${\displaystyle \circleddash }$ \circleddash ${\displaystyle \circledast }$ \circledast ${\displaystyle \bigcirc }$ \bigcirc ${\displaystyle \divideontimes }$ \divideontimes ${\displaystyle \ }$

${\displaystyle \odot }$ \odot ${\displaystyle \oplus }$ \oplus ${\displaystyle \ominus }$ \ominus ${\displaystyle \otimes }$ \otimes ${\displaystyle \oslash }$ \oslash ${\displaystyle \ }$

${\displaystyle \boxdot }$ \boxdot ${\displaystyle \boxplus }$ \boxplus ${\displaystyle \boxminus }$ \boxminus ${\displaystyle \boxtimes }$ \boxtimes ${\displaystyle \Box }$ \Box ${\displaystyle \ }$

${\displaystyle \diamondsuit }$ \diamondsuit ${\displaystyle \clubsuit }$ \clubsuit ${\displaystyle \heartsuit }$ \heartsuit ${\displaystyle \spadesuit }$ \spadesuit ${\displaystyle \ }$

${\displaystyle \lozenge }$ \lozenge ${\displaystyle \blacklozenge }$ \blacklozenge ${\displaystyle \square }$ \square ${\displaystyle \blacksquare }$ \blacksquare ${\displaystyle \ }$

${\displaystyle \diamond }$ \diamond ${\displaystyle \Diamond }$ \Diamond ${\displaystyle \ast }$ \ast ${\displaystyle \star }$ \star ${\displaystyle \bigstar }$ \bigstar

${\displaystyle \sharp }$ \sharp ${\displaystyle \flat }$ \flat ${\displaystyle \natural }$ \natural ${\displaystyle \dagger }$ \dagger ${\displaystyle \ddagger }$ \ddagger

Alphabets with special characters on it.

LaTeX command	Sample	Description
\`{o}	ò	grave accent
\'{o}	ó	acute accent
\^{o}	ô	circumflex
\"{o}	ö	umlaut, trema or dieresis
\H{o}	ő	long Hungarian umlaut (double acute)
\~{o}	õ	tilde
\c{c}	ç	cedilla
\k{a}	ą	ogonek
\l{}	ł	barred l (l with stroke)
\={o}	ō	macron accent (a bar over the letter)
\b{o}	o	bar under the letter
\.{o}	ȯ	dot over the letter
\d{u}	ụ	dot under the letter
\r{a}	å	ring over the letter (for å there is also the special command \aa)
\u{o}	ŏ	breve over the letter
\v{s}	š	caron/háček ("v") over the letter
\t{oo}	o͡o	"tie" (inverted u) over the two letters
\o	ø	slashed o (o with stroke)