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A Reference on Microsoft Word equation editor

FariD — Tue, 28 Jun 2022 22:52:29 +0430

The equation is a vital part of many technical manuscripts, including thesis and research papers. However, typing it in Microsoft Word is an arduous task. To cope with it, Microsoft Word introduced the LaTeX type equation editor feature which is termed "Math AutoCorrect" and is available since Microsoft Word 2007.

This article aims to elaborate on the most usages of the Microsoft Word equation editor.

A Reference on Microsoft Word equation editor

FariD — Tue, 28 Jun 2022 22:52:29 +0430

Enabling Math Autocorrect

In most versions of Microsoft Word, Math AutoCorrect is enabled by default. To ensure you can visit, File Menu → Options → Proofing → Autocorrect Options → Math AutoCorrect and ensure "Replace text as you type" is checked. These shortcuts work only inside the Equation Editor. However, to use it outside Equation Editor, “Use Math Autocorrect Rules outside of math regions“ should be checked.

Equation Editor Shortcut

The shortcut to get the equation editor is “Alt + =”, hold down the Alt key while pressing "=". Moreover, clicking on “Equations” under the “Insert” Tab will result in the same.

Space is an important part of the Math AutoCorrect shortcut. It invokes the conversion event which translates the typed equation into Mathematical Symbols/Operators. In this article, space is shown as for clarity.

Subscript & Superscript

The shortcut for subscript and superscript is _ and ^. Anything after _ or ^ will get converted into subscript or superscript respectively, after hitting space. To include space in subscript or superscript, group them in parenthesis or (). These grouping parentheses don’t appear after Math AutoCorrect. Grouping is also important as it distinguishes between a_i^2 and a_(i^2). To add pre-subscript or pre-superscript, use \zwsp along with _ and ^ sign.

A_circle		r^2
A_(big circle)		H^(2 square)
r^2_outer		r^2_(outer circle)
\zwsp_c		\zwsp^cR
\zwsp_c^dR		\zwsp_c^d_e^f

Greek letters

Greek letters have 24 alphabets. There are four distinct ways of typing the Greek alphabet in Microsoft Word. Of these, Math AutoCorrect method is the easiest to remember and the fastest of all four. This method of typing Greek letters is as easy as typing its spelling after \ (backslash). To get the lower case Greek Alphabet, type the name of Greek letter after \ in lower case, e.g. \alpha for \alpha, and for the upper use case type the name of Greek letter after \ in Title case, e.g. \Gamma for \Gamma.

Alpha	A	\Alpha	\alpha
Beta	B	\Beta	\beta
Gamma		\Gamma	\gamma
Delta		\Delta	\delta
Epsilon	E	\Epsilon	\epsilon
Zeta	Z	\Zeta	\zeta
Eta	H	\Eta	\eta
Theta		\Theta	\theta
Iota	I	\Iota	\iota
Kappa	K	\Kappa	\kappa
Lambda		\Lambda	\lambda
Mu	M	\Mu	\mu
Nu	N	\Nu	\nu
Xi		\Xi	\xi
Pi		\Pi	\pi
Rho	P	\Rho	\rho
Sigma		\Sigma	\sigma
Tau	T	\Tau	\tau
Upsilon		\Upsilon	\upsilon
Phi		\Phi	\phi
Chi	X	\Chi	\chi
Psi		\Psi	\psi
Omega		\Omega	\omega

Scientific and Mathematical Symbols

Equation editor shortcut for scientific and mathematical symbols like infinity, different arrows, operators (like partial, del, and nabla), conditional symbols, dot, cross, maps to, perpendicular, set symbols, for all, equivalent, congruent, angle, proportional, etc are given in the following table.

Infinity	∞	\infty	Hbar	ℏ	\hbar
Right Arrow	→	\rightarrow, ->	Left Arrow	←	\leftarrow
Up Arrow	↑	\uparrow	Down Arrow	↓	\downarrow
North-east Arrow	↗	\nearrow	North-west Arrow	↖	\nwarrow
South-east Arrow	↘	\searrow	South-west Arrow	↙	\swarrow
Left Right arrow	↔	\leftrightarrow	Up Down Arrow	↕	\updownarrow
Rightwards Double Arrow	⇒	\Rightarrow	Leftwards Double Arrow	⇐	\Leftarrow
Upwards Double Arrow	⇑	\Uparrow	Downwards Double Arrow	⇓	\Downarrow
Partial	∂	\partial	Nabla	∇	\nabla
Less Than Equal To	≤	\le	Greater Than Equal To	≥	\ge

Double Less Than	≪	\ll	Double Greater Than	≫	\gg
Times	𝑎 × 𝑏	a \times b	Tensor Product or O Times	𝑓(𝑡) ⊗ 𝑔(𝑡)	f(t)\otimes g(t)
Dot	𝑎 ⋅ 𝑏	a\cdot b	O Dot	𝑎 ⊙ 𝑏	a\odot b
O Plus	𝑥 ⊕ y	x\oplus y	O Minus	𝑥 ⊖ 𝑦	a\ominus y
Maps To	𝑎 ↦	a\mapsto b	Right Arrow with Hook	↪	\hookrightarrow
Dots	𝑎 … 𝑏	a\dots b	Center dots	𝑎 ⋯ 𝑏	a\cdots b
Perpendicular	𝑎 ⊥ 𝑏	a \bot b		𝑎 ⊤ 𝑏	a \top b
Intersection	𝐴⋂𝐵	A\bigcap B	Union	𝐴⋃𝐵	A \bigcup B
Big Square Cup	𝐴⨆𝐵	A\bigsqcup B	Big U with Plus	𝐴⨄𝐵	A \biguplus B
Star	𝑎 ⋆ 𝑏	a \star b	For All	∀	\forall

In	∈	\in	Exists	∃	\exists
Big Wedge	⋀	\bigwedge	Big Ve	⋁	\bigvee
Equiv	≡	\equiv	Congruent	≅	\cong
Not Equal To	≠	\ne	Approximately Equal	≈	\approx
Similar	∼	\sim	Similar To	≃	\simeq
Natural Joint of Bowtie	⋈	\bowtie	Box	□	\box
Subset	⊂	\subset	Empty Set	∅	\emptyset
Therefore	∴	\therefore	Because	∵	\because
Plus or minus	±	\pm or +-	Minus or plus	∓	\mp
Angle	∠	\angle	Proportional To	∝	\proto

Degree C

22 °C

22 \degc

Accent

The accent-like bars are used for various reasons, e.g. dot for denoting derivative. We can easily achieve these using the following word shortcuts.

Bar		x\bar
Double bar		x\Bar
Under bar		x\ubar
Double under bar		x\uBar
Acute		x\acute
Grave		x\grave
Vector		x\vec
Hat		x\hat
Left-right arrow		x\tvec
Left harpoon		x\lhvec
Right harpoon		x\rhvec
Dot		x\dot
Double dot		x\ddot
Triple dot		x\dddot
Four dot		x\ddddot
Breve		x\breve
Check		x\check
Tilde		x\tilde
Left arrow		x\lvec

Grouping and brackets

The equation editor causes brackets such as [], {}, and () to grow and fit the size of expression within them. However, the parenthesis used for grouping is not displayed in the final formatted expression. Albeit, the parenthesis which is required to be displayed, must be doubled. One for grouping which will vanish in the final formatted expression, and the other for display. Escape sequence (\ followed by the desired bracket is used to prevent the bracket from being reformatted.

	x/y	/ is used for fraction
	[x/y]	[] bracket automatically expands to adjust the fraction
	{x/y}
	(x/y)	Parentheses are displayed as they are not used for grouping
	a/(p+q)	Parentheses used for grouping (denominator here) are not displayed
	a/((p+q))	Parentheses used for grouping (denominator here) is not displayed
	[ a\atop b \close y
	\|(p\|q\|r)/(c+d)\|	Again parentheses used for grouping are not displayed
	\|a\|b\|x/(a+b)	Grouping parentheses not displayed
	\norm a \norm

Roots

Equation editor shortcut for square root, cube root and higher roots are \sqrt(), \cbrt() and \sqrt(n&x) respectively.

	\sqrt(x)
	\cbrt(x+1)
	\sqrt(n&x)

Matrices

The basic equation editor shortcut for creating an empty matrix of custom size is \matrix(@@&&&). Matrix size decided by number of @ (for rows) and & (for columns). The count of rows and columns is one less than the count of @ and & typed in the equation.

\matrix(@@&)
\pmatrix(@@&) or (\matrix(@@&)
\Vmatrix(@@&)
[\matrix(1&2&3@4&5&6@7&8&9)]
\pmatrix(1&2@3&4@5&6)

Piece wise function

There are two ways to insert a piece-wise function by using the Equation Editor shortcut. First one uses \cases() method while the second one uses \matrix(). In both cases, desired piecewise functions are entered inside the parenthesis.

Like the matrices, @ is used as a row separator. To get only the opening curly braces ‘{‘ which automatically extends the height of the piecewise function, use \close in place of closing ‘}’.

f(x) = {\cases(x,x>=0@-x,x<0)\close		@ is used as row separator and \close is required to ensure opening { expands vertically to cover all cases
f(x) = {\matrix(x & x>=0@-x & x<0)\close		Similar to above, & is used as column separator
f(x) = {\matrix(x & x>=0@-x & x<0)	Piecewise function without \close	Without \close, opening '{' doesn't expands

Integral, Sum and Product

Shortcuts for an integral sign, sum, and product signs are \int, \sum, and \prod. You can use _ and ^ for inserting text below and above signs, respectively.

\intf(x)dx
\int_x=0^1f(x)dx		_ for lower limit and ^ for upper limit
\iintf(x)dx		\iint for double integral
\iint\below(S)ds		use \below to put text below symbol
\iiint\above(V)dV		use \above to put text above symbol
\ointf(x)dx		\oint for cyclic integral, similarly use \oiint for cyclic double Sum, integral
\sum_(i=1)^nA_i		\sum_(i=1)^nA_i\sum for sum symbol and _ & ^ sign for getting text below and above sum. Parenthesis can be used for grouping text with spaces
\prod_(n=0)^Nx^n		Similar to sum.

A Reference on Microsoft Word equation editor

Tue, 28 Jun 2022 22:52:29 +0430

Enabling Math Autocorrect

Equation Editor Shortcut

The shortcut to get the equation editor is “Alt + =”, hold down the Alt key while pressing "=". Moreover, clicking on “Equations” under the “Insert” Tab will result in the same.

Subscript & Superscript

A_circle		r^2
A_(big circle)		H^(2 square)
r^2_outer		r^2_(outer circle)
\zwsp_c		\zwsp^cR
\zwsp_c^dR		\zwsp_c^d_e^f

Greek letters

Alpha	A	\Alpha	\alpha
Beta	B	\Beta	\beta
Gamma		\Gamma	\gamma
Delta		\Delta	\delta
Epsilon	E	\Epsilon	\epsilon
Zeta	Z	\Zeta	\zeta
Eta	H	\Eta	\eta
Theta		\Theta	\theta
Iota	I	\Iota	\iota
Kappa	K	\Kappa	\kappa
Lambda		\Lambda	\lambda
Mu	M	\Mu	\mu
Nu	N	\Nu	\nu
Xi		\Xi	\xi
Pi		\Pi	\pi
Rho	P	\Rho	\rho
Sigma		\Sigma	\sigma
Tau	T	\Tau	\tau
Upsilon		\Upsilon	\upsilon
Phi		\Phi	\phi
Chi	X	\Chi	\chi
Psi		\Psi	\psi
Omega		\Omega	\omega

Scientific and Mathematical Symbols

Infinity	∞	\infty	Hbar	ℏ	\hbar
Right Arrow	→	\rightarrow, ->	Left Arrow	←	\leftarrow
Up Arrow	↑	\uparrow	Down Arrow	↓	\downarrow
North-east Arrow	↗	\nearrow	North-west Arrow	↖	\nwarrow
South-east Arrow	↘	\searrow	South-west Arrow	↙	\swarrow
Left Right arrow	↔	\leftrightarrow	Up Down Arrow	↕	\updownarrow
Rightwards Double Arrow	⇒	\Rightarrow	Leftwards Double Arrow	⇐	\Leftarrow
Upwards Double Arrow	⇑	\Uparrow	Downwards Double Arrow	⇓	\Downarrow
Partial	∂	\partial	Nabla	∇	\nabla
Less Than Equal To	≤	\le	Greater Than Equal To	≥	\ge

Double Less Than	≪	\ll	Double Greater Than	≫	\gg
Times	𝑎 × 𝑏	a \times b	Tensor Product or O Times	𝑓(𝑡) ⊗ 𝑔(𝑡)	f(t)\otimes g(t)
Dot	𝑎 ⋅ 𝑏	a\cdot b	O Dot	𝑎 ⊙ 𝑏	a\odot b
O Plus	𝑥 ⊕ y	x\oplus y	O Minus	𝑥 ⊖ 𝑦	a\ominus y
Maps To	𝑎 ↦	a\mapsto b	Right Arrow with Hook	↪	\hookrightarrow
Dots	𝑎 … 𝑏	a\dots b	Center dots	𝑎 ⋯ 𝑏	a\cdots b
Perpendicular	𝑎 ⊥ 𝑏	a \bot b		𝑎 ⊤ 𝑏	a \top b
Intersection	𝐴⋂𝐵	A\bigcap B	Union	𝐴⋃𝐵	A \bigcup B
Big Square Cup	𝐴⨆𝐵	A\bigsqcup B	Big U with Plus	𝐴⨄𝐵	A \biguplus B
Star	𝑎 ⋆ 𝑏	a \star b	For All	∀	\forall

In	∈	\in	Exists	∃	\exists
Big Wedge	⋀	\bigwedge	Big Ve	⋁	\bigvee
Equiv	≡	\equiv	Congruent	≅	\cong
Not Equal To	≠	\ne	Approximately Equal	≈	\approx
Similar	∼	\sim	Similar To	≃	\simeq
Natural Joint of Bowtie	⋈	\bowtie	Box	□	\box
Subset	⊂	\subset	Empty Set	∅	\emptyset
Therefore	∴	\therefore	Because	∵	\because
Plus or minus	±	\pm or +-	Minus or plus	∓	\mp
Angle	∠	\angle	Proportional To	∝	\proto

Degree C

22 °C

22 \degc

Accent

The accent-like bars are used for various reasons, e.g. dot for denoting derivative. We can easily achieve these using the following word shortcuts.

Bar		x\bar
Double bar		x\Bar
Under bar		x\ubar
Double under bar		x\uBar
Acute		x\acute
Grave		x\grave
Vector		x\vec
Hat		x\hat
Left-right arrow		x\tvec
Left harpoon		x\lhvec
Right harpoon		x\rhvec
Dot		x\dot
Double dot		x\ddot
Triple dot		x\dddot
Four dot		x\ddddot
Breve		x\breve
Check		x\check
Tilde		x\tilde
Left arrow		x\lvec

Grouping and brackets

	x/y	/ is used for fraction
	[x/y]	[] bracket automatically expands to adjust the fraction
	{x/y}
	(x/y)	Parentheses are displayed as they are not used for grouping
	a/(p+q)	Parentheses used for grouping (denominator here) are not displayed
	a/((p+q))	Parentheses used for grouping (denominator here) is not displayed
	[ a\atop b \close y
	\|(p\|q\|r)/(c+d)\|	Again parentheses used for grouping are not displayed
	\|a\|b\|x/(a+b)	Grouping parentheses not displayed
	\norm a \norm

Roots

Equation editor shortcut for square root, cube root and higher roots are \sqrt(), \cbrt() and \sqrt(n&x) respectively.

	\sqrt(x)
	\cbrt(x+1)
	\sqrt(n&x)

Matrices

\matrix(@@&)
\pmatrix(@@&) or (\matrix(@@&)
\Vmatrix(@@&)
[\matrix(1&2&3@4&5&6@7&8&9)]
\pmatrix(1&2@3&4@5&6)

Piece wise function

Like the matrices, @ is used as a row separator. To get only the opening curly braces ‘{‘ which automatically extends the height of the piecewise function, use \close in place of closing ‘}’.

f(x) = {\cases(x,x>=0@-x,x<0)\close		@ is used as row separator and \close is required to ensure opening { expands vertically to cover all cases
f(x) = {\matrix(x & x>=0@-x & x<0)\close		Similar to above, & is used as column separator
f(x) = {\matrix(x & x>=0@-x & x<0)	Piecewise function without \close	Without \close, opening '{' doesn't expands

Integral, Sum and Product

Shortcuts for an integral sign, sum, and product signs are \int, \sum, and \prod. You can use _ and ^ for inserting text below and above signs, respectively.

\intf(x)dx
\int_x=0^1f(x)dx		_ for lower limit and ^ for upper limit
\iintf(x)dx		\iint for double integral
\iint\below(S)ds		use \below to put text below symbol
\iiint\above(V)dV		use \above to put text above symbol
\ointf(x)dx		\oint for cyclic integral, similarly use \oiint for cyclic double Sum, integral
\sum_(i=1)^nA_i		\sum_(i=1)^nA_i\sum for sum symbol and _ & ^ sign for getting text below and above sum. Parenthesis can be used for grouping text with spaces
\prod_(n=0)^Nx^n		Similar to sum.

LaTeX mathematic cheat sheet

FariD — Sun, 09 Jan 2022 15:55:28 +0330

A complete set of tables for writing in LaTeX which comprises:

Accents/diacritics
Standard functions
Modular arithmetic
Derivatives
Sets
Operators
Logic
Root
Relations
Geometric
Arrows
Special
Subscripts, superscripts, integrals
Fractions, matrices, multi lines
Parenthesizing big expressions, brackets, bars
Alphabets

LaTeX mathematic cheat sheet

FariD — Sun, 09 Jan 2022 15:55:28 +0330

Practically, LaTeX is the standard typesetting system for scientific writing. Most of the well-written equations that appeared in books and around the web are written using LaTeX.

Accents/diacritics

`\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}`
`\check{a} \bar{a} \ddot{a} \dot{a}`

Standard functions

`\sin a \cos b \tan c`
`\sec d \csc e \cot f`
`\arcsin h \arccos i \arctan j`
`\sinh k \cosh l \tanh m \coth n`
`\operatorname{sh}o\, \operatorname{ch}p\, \operatorname{th}q`
`\operatorname{arsinh}r\, \operatorname{arcosh}s\, \operatorname{artanh}t`
`\lim u \limsup v \liminf w \min x \max y`
`\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g`
`\deg h \gcd i \Pr j \det k \hom l \arg m \dim n`

Modular arithmetic

`s_k \equiv 0 \pmod{m}`
`a\, \bmod\, b`

Derivatives

\nabla\, \partial x\, dx\, \dot x\, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}, {\partial x_1\,\partial x_2}

Sets

`\forall \exists \empty \emptyset \varnothing`
`\in \ni \not\in \notin \not\ni \subset \subseteq \supset \supseteq`
`\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus`
`\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup`

Operators

`+ \oplus \bigoplus \pm \mp -`
`\times \otimes \bigotimes \cdot \circ \bullet \bigodot`
`\star */ \div \frac{1}{2}`

Logic

`\land (or \and) \wedge \bigwedge \bar{q} \to p`
`\lor \vee \bigvee \lnot \neg q \And`

Root

\sqrt{2} \sqrt[n]{x}

Relations

`\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}`
`< \le \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto`	\equiv \not \equiv \neq {\mbox{or}}\neq \propto \,">
`\lessapprox \lesssim \eqslantless \leqslant \leqq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox`

Geometric

\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ

Arrows

`\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow`
`\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow` `(or \impliedby) \Longrightarrow (or \implies) \Longleftrightarrow (or \iff)`
`\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow`
`\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons`
`\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow` `\rightarrowtail \looparrowright`
`\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow` `\leftarrowtail \looparrowleft`
`\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow`

Special

`\And \eth \S \P \% \dagger \ddagger \ldots \cdots \colon`
`\smile \frown \wr \triangleleft \triangleright \infty \bot \top`
`\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar`
`\ell \mho \Finv \Re \Im \wp \complement`
`\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp`

USubscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
Superscript	`a^2`
Subscript	`a_2`
Grouping	`a^{2+2}`
Grouping	`a_{i,j}`
Combining sub & super without and with horizontal separation	`x_2^3`
	`{x_2}^3`
Super super	`10^{10^{8}}`
Preceding and/or Additional sub & super	`_nP_k`
	`\sideset{_1^2}{_3^4}\prod_a^b`
	`{}_1^2\!\Omega_3^4`
Stacking	`\overset{\alpha}{\omega}`
	`\underset{\alpha}{\omega}`
	`\overset{\alpha}{\underset{\gamma}{\omega}}`
	`\stackrel{\alpha}{\omega}`
Derivatives	`x', y'', f', f''`
Derivatives	`x^\prime, y^{\prime\prime}`
Derivative dots	`\dot{x}, \ddot{x}`
Underlines, overlines, vectors	`\hat a\ \bar b\ \vec c`
	`\overrightarrow{a b}\ \overleftarrow{c d}\ \widehat{d e f}`
	`\overline{g h i}\ \underline{j k l}`
	`\not 1\ \cancel{123}`
Arrows	`A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C`
Overbraces	`\overbrace{ 1+2+\cdots+100 }^{\text{sum}\,=\,5050}`
Underbraces	`\underbrace{ a+b+\cdots+z }_{26\text{ terms}}`
Sum	`\sum_{k=1}^N k^2`
Sum (force `\textstyle`)	`\textstyle \sum_{k=1}^N k^2`
Product	`\prod_{i=1}^N x_i`
Product (force `\textstyle`)	`\textstyle \prod_{i=1}^N x_i`
Coproduct	`\coprod_{i=1}^N x_i`
Coproduct (force `\textstyle`)	`\textstyle \coprod_{i=1}^N x_i`
Limit	`\lim_{n \to \infty}x_n`
Limit (force `\textstyle`)	`\textstyle \lim_{n \to \infty}x_n`
Integral	`\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx`
Integral (alternate limits style)	`\int_{1}^{3}\frac{e^3/x}{x^2}\, dx`
Integral (force `\textstyle`)	`\textstyle \int\limits_{-N}^{N} e^x\, dx`
Integral (force `\textstyle`, alternate limits style)	`\textstyle \int_{-N}^{N} e^x\, dx`
Double integral	`\iint\limits_D \, dx\,dy`
Triple integral	`\iiint\limits_E \, dx\,dy\,dz`
Quadruple integral	`\iiiint\limits_F \, dx\,dy\,dz\,dt`
Line or path integral	`\int_C x^3\, dx + 4y^2\, dy`
Closed line or path integral	`\oint_C x^3\, dx + 4y^2\, dy`
Intersections	`\bigcap_1^n p`
Unions	`\bigcup_1^k p`

Fractions, matrices, multi-lines

Feature	Syntax	How it looks rendered
Fractions	`\frac{1}{2}=0.5`
Small ("text style") fractions	`\tfrac{1}{2} = 0.5`
Large ("display style") fractions	`\dfrac{k}{k-1} = 0.5`
Mixture of large and small fractions	`\dfrac{ \tfrac{1}{2}[1-(\tfrac{1}{2})^n] }{ 1-\tfrac{1}{2} } = s_n`
Continued fractions (note the difference in formatting)	\cfrac{2}{ c + \cfrac{2}{ d + \cfrac{1}{2} } } = a \qquad \dfrac{2}{ c + \dfrac{2}{ d + \dfrac{1}{2} } } = a
Binomial coefficients	`\binom{n}{k}`
Small ("text style") binomial coefficients	`\tbinom{n}{k}`
Large ("display style") binomial coefficients	`\dbinom{n}{k}`
Matrices	\begin{matrix} x & y \\ z & v \end{matrix}
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}
	\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)
Arrays	\begin{array}{\|c\|c\|\|c\|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0 \end{array}
Cases	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}
System of equations	\begin{cases} 3x + 5y + z &= 1 \\ 7x - 2y + 4z &= 2 \\ -6x + 3y + 2z &= 3 \end{cases}
Breaking up a long expression so it wraps when necessary	$f(x) = \sum_{n=0}^\infty a_n x^n$ $= a_0 + a_1x + a_2x^2 + \cdots$
Multiline equations	\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \end{align}
Multiline equations	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \end{alignat}
Multiline equations with alignment specified (left, center, right)	\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}
	\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}

Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Bad	`( \frac{1}{2} )`
Good	`\left ( \frac{1}{2} \right )`

You can use various delimiters with \left and \right:

Feature	Syntax	How it looks rendered
Parentheses	`\left ( \frac{a}{b} \right )`
Brackets	`\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack`
Braces (note the backslash before the braces in the code)	`\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace`
Angle brackets	`\left \langle \frac{a}{b} \right \rangle`
Bars and double bars (note: "bars" provide the absolute value function)	`\left \| \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \\|`
Floor and ceiling functions:	`\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil`
Slashes and backslashes	`\left / \frac{a}{b} \right \backslash`
Up, down and up-down arrows	`\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow`
Delimiters can be mixed, as long as `\left` and `\right` are both used	`\left [ 0,1 \right ) \left \langle \psi \right \|`
Use `\left.` or `\right.` if you don't want a delimiter to appear:	`\left . \frac{A}{B} \right \} \to X`
Size of the delimiters	`\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]`
	`\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle` `\Big\rangle \big\rangle`
	`\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg\\| \bigg\\| \Big\\| \big\\|`
	`\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil` `\bigg\rceil \Big\rceil \big\rceil`
	`\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow` `\bigg\Downarrow \Big\Downarrow \big\Downarrow`
	`\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots` `\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow`
	`\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash`

Alphabets

Greek alphabet
Boldface (greek)
`\Alpha \Beta \Gamma \Delta \Epsilon \Zeta`
`\Eta \Theta \Iota \Kappa \Lambda \Mu`
`\Nu \Xi \Omicron \Pi \Rho \Sigma \Tau`
`\Upsilon \Phi \Chi \Psi \Omega`
`\alpha \beta \gamma \delta \epsilon \zeta`
`\eta \theta \iota \kappa \lambda \mu`
`\nu \xi \omicron \pi \rho \sigma \tau`
`\upsilon \phi \chi \psi \omega`
`\varepsilon \digamma \vartheta \varkappa`
`\varpi \varrho \varsigma \varphi`
`\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}`
`\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda}` `\boldsymbol{\Mu}`
`\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma}` `\boldsymbol{\Tau}`
`\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}`
`\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon}` `\boldsymbol{\zeta}`
`\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda}` `\boldsymbol{\mu}`
`\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma}` `\boldsymbol{\tau}`
`\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}`
`\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}`
`\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}`

References:

Help:Displaying a formula in LaTeX - Meta (wikimedia.org)

LaTeX mathematic cheat sheet

Sun, 09 Jan 2022 15:55:28 +0330

Practically, LaTeX is the standard typesetting system for scientific writing. Most of the well-written equations that appeared in books and around the web are written using LaTeX.

Accents/diacritics

`\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}`
`\check{a} \bar{a} \ddot{a} \dot{a}`

Standard functions

`\sin a \cos b \tan c`
`\sec d \csc e \cot f`
`\arcsin h \arccos i \arctan j`
`\sinh k \cosh l \tanh m \coth n`
`\operatorname{sh}o\, \operatorname{ch}p\, \operatorname{th}q`
`\operatorname{arsinh}r\, \operatorname{arcosh}s\, \operatorname{artanh}t`
`\lim u \limsup v \liminf w \min x \max y`
`\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g`
`\deg h \gcd i \Pr j \det k \hom l \arg m \dim n`

Modular arithmetic

`s_k \equiv 0 \pmod{m}`
`a\, \bmod\, b`

Derivatives

\nabla\, \partial x\, dx\, \dot x\, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}, {\partial x_1\,\partial x_2}

Sets

`\forall \exists \empty \emptyset \varnothing`
`\in \ni \not\in \notin \not\ni \subset \subseteq \supset \supseteq`
`\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus`
`\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup`

Operators

`+ \oplus \bigoplus \pm \mp -`
`\times \otimes \bigotimes \cdot \circ \bullet \bigodot`
`\star */ \div \frac{1}{2}`

Logic

`\land (or \and) \wedge \bigwedge \bar{q} \to p`
`\lor \vee \bigvee \lnot \neg q \And`

Root

\sqrt{2} \sqrt[n]{x}

Relations

`\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}`
`< \le \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto`	\equiv \not \equiv \neq {\mbox{or}}\neq \propto \,">
`\lessapprox \lesssim \eqslantless \leqslant \leqq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox`

Geometric

\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ

Arrows

`\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow`
`\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow` `(or \impliedby) \Longrightarrow (or \implies) \Longleftrightarrow (or \iff)`
`\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow`
`\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons`
`\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow` `\rightarrowtail \looparrowright`
`\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow` `\leftarrowtail \looparrowleft`
`\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow`

Special

`\And \eth \S \P \% \dagger \ddagger \ldots \cdots \colon`
`\smile \frown \wr \triangleleft \triangleright \infty \bot \top`
`\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar`
`\ell \mho \Finv \Re \Im \wp \complement`
`\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp`

USubscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
Superscript	`a^2`
Subscript	`a_2`
Grouping	`a^{2+2}`
Grouping	`a_{i,j}`
Combining sub & super without and with horizontal separation	`x_2^3`
	`{x_2}^3`
Super super	`10^{10^{8}}`
Preceding and/or Additional sub & super	`_nP_k`
	`\sideset{_1^2}{_3^4}\prod_a^b`
	`{}_1^2\!\Omega_3^4`
Stacking	`\overset{\alpha}{\omega}`
	`\underset{\alpha}{\omega}`
	`\overset{\alpha}{\underset{\gamma}{\omega}}`
	`\stackrel{\alpha}{\omega}`
Derivatives	`x', y'', f', f''`
Derivatives	`x^\prime, y^{\prime\prime}`
Derivative dots	`\dot{x}, \ddot{x}`
Underlines, overlines, vectors	`\hat a\ \bar b\ \vec c`
	`\overrightarrow{a b}\ \overleftarrow{c d}\ \widehat{d e f}`
	`\overline{g h i}\ \underline{j k l}`
	`\not 1\ \cancel{123}`
Arrows	`A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C`
Overbraces	`\overbrace{ 1+2+\cdots+100 }^{\text{sum}\,=\,5050}`
Underbraces	`\underbrace{ a+b+\cdots+z }_{26\text{ terms}}`
Sum	`\sum_{k=1}^N k^2`
Sum (force `\textstyle`)	`\textstyle \sum_{k=1}^N k^2`
Product	`\prod_{i=1}^N x_i`
Product (force `\textstyle`)	`\textstyle \prod_{i=1}^N x_i`
Coproduct	`\coprod_{i=1}^N x_i`
Coproduct (force `\textstyle`)	`\textstyle \coprod_{i=1}^N x_i`
Limit	`\lim_{n \to \infty}x_n`
Limit (force `\textstyle`)	`\textstyle \lim_{n \to \infty}x_n`
Integral	`\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx`
Integral (alternate limits style)	`\int_{1}^{3}\frac{e^3/x}{x^2}\, dx`
Integral (force `\textstyle`)	`\textstyle \int\limits_{-N}^{N} e^x\, dx`
Integral (force `\textstyle`, alternate limits style)	`\textstyle \int_{-N}^{N} e^x\, dx`
Double integral	`\iint\limits_D \, dx\,dy`
Triple integral	`\iiint\limits_E \, dx\,dy\,dz`
Quadruple integral	`\iiiint\limits_F \, dx\,dy\,dz\,dt`
Line or path integral	`\int_C x^3\, dx + 4y^2\, dy`
Closed line or path integral	`\oint_C x^3\, dx + 4y^2\, dy`
Intersections	`\bigcap_1^n p`
Unions	`\bigcup_1^k p`

Fractions, matrices, multi-lines

Feature	Syntax	How it looks rendered
Fractions	`\frac{1}{2}=0.5`
Small ("text style") fractions	`\tfrac{1}{2} = 0.5`
Large ("display style") fractions	`\dfrac{k}{k-1} = 0.5`
Mixture of large and small fractions	`\dfrac{ \tfrac{1}{2}[1-(\tfrac{1}{2})^n] }{ 1-\tfrac{1}{2} } = s_n`
Continued fractions (note the difference in formatting)	\cfrac{2}{ c + \cfrac{2}{ d + \cfrac{1}{2} } } = a \qquad \dfrac{2}{ c + \dfrac{2}{ d + \dfrac{1}{2} } } = a
Binomial coefficients	`\binom{n}{k}`
Small ("text style") binomial coefficients	`\tbinom{n}{k}`
Large ("display style") binomial coefficients	`\dbinom{n}{k}`
Matrices	\begin{matrix} x & y \\ z & v \end{matrix}
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}
	\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)
Arrays	\begin{array}{\|c\|c\|\|c\|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0 \end{array}
Cases	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}
System of equations	\begin{cases} 3x + 5y + z &= 1 \\ 7x - 2y + 4z &= 2 \\ -6x + 3y + 2z &= 3 \end{cases}
Breaking up a long expression so it wraps when necessary	$f(x) = \sum_{n=0}^\infty a_n x^n$ $= a_0 + a_1x + a_2x^2 + \cdots$
Multiline equations	\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \end{align}
Multiline equations	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \end{alignat}
Multiline equations with alignment specified (left, center, right)	\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}
	\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}

Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Bad	`( \frac{1}{2} )`
Good	`\left ( \frac{1}{2} \right )`

You can use various delimiters with \left and \right:

Feature	Syntax	How it looks rendered
Parentheses	`\left ( \frac{a}{b} \right )`
Brackets	`\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack`
Braces (note the backslash before the braces in the code)	`\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace`
Angle brackets	`\left \langle \frac{a}{b} \right \rangle`
Bars and double bars (note: "bars" provide the absolute value function)	`\left \| \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \\|`
Floor and ceiling functions:	`\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil`
Slashes and backslashes	`\left / \frac{a}{b} \right \backslash`
Up, down and up-down arrows	`\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow`
Delimiters can be mixed, as long as `\left` and `\right` are both used	`\left [ 0,1 \right ) \left \langle \psi \right \|`
Use `\left.` or `\right.` if you don't want a delimiter to appear:	`\left . \frac{A}{B} \right \} \to X`
Size of the delimiters	`\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]`
	`\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle` `\Big\rangle \big\rangle`
	`\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg\\| \bigg\\| \Big\\| \big\\|`
	`\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil` `\bigg\rceil \Big\rceil \big\rceil`
	`\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow` `\bigg\Downarrow \Big\Downarrow \big\Downarrow`
	`\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots` `\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow`
	`\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash`

Alphabets

Greek alphabet
Boldface (greek)
`\Alpha \Beta \Gamma \Delta \Epsilon \Zeta`
`\Eta \Theta \Iota \Kappa \Lambda \Mu`
`\Nu \Xi \Omicron \Pi \Rho \Sigma \Tau`
`\Upsilon \Phi \Chi \Psi \Omega`
`\alpha \beta \gamma \delta \epsilon \zeta`
`\eta \theta \iota \kappa \lambda \mu`
`\nu \xi \omicron \pi \rho \sigma \tau`
`\upsilon \phi \chi \psi \omega`
`\varepsilon \digamma \vartheta \varkappa`
`\varpi \varrho \varsigma \varphi`
`\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}`
`\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda}` `\boldsymbol{\Mu}`
`\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma}` `\boldsymbol{\Tau}`
`\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}`
`\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon}` `\boldsymbol{\zeta}`
`\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda}` `\boldsymbol{\mu}`
`\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma}` `\boldsymbol{\tau}`
`\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}`
`\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}`
`\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}`

References:

Help:Displaying a formula in LaTeX - Meta (wikimedia.org)

TCL cheat sheet

FariD — Thu, 30 Sep 2021 12:40:38 +0330

The categories included in the TCL command list as a cheat sheet is presented below:

Mathematics Operands
Variable Operands
String Handlers
List Control
Array Handling
Dictionaries Manipulate
File Command
Procedures
Control Constructs
Input/Output

TCL cheat sheet

FariD — Thu, 30 Sep 2021 12:40:38 +0330

Mathematics Operands

Variable Operands

String Handlers

List Control

Array Handling

Dictionaries Manipulate

File Command

Procedures

TCL cheat sheet

Thu, 30 Sep 2021 12:40:38 +0330

Mathematics Operands

Variable Operands

String Handlers

List Control

Array Handling

Dictionaries Manipulate

File Command

Procedures

ML.NET: Credit Card Fraud Detection

FariD — Tue, 28 Sep 2021 09:04:52 +0330

As we know, ML.NET is an open-source and cross-platform (Windows, macOS, Linux) machine learning framework in which you can create custom ML models using C# or F# without having to leave the .NET ecosystem.
ML.NET lets reusing all the knowledge, skills, code, and libraries you already have as a .NET developer so that you can easily integrate machine learning into your web, mobile, desktop, games, and IoT apps.
Moreover, it has been designed as an extensible platform so that you can consume other popular ML frameworks (TensorFlow, ONNX, Infer.NET, and more) and have access to even more machine learning scenarios, like image classification, object detection, and more.
Finally, according to Microsoft's tests, it has high performance and accuracy.
Using a 9GB Amazon review data set, ML.NET trained a sentiment analysis model with 95% accuracy. Other popular machine learning frameworks failed to process the dataset due to memory errors. Training on 10% of the data set, to let all the frameworks complete training, ML.NET demonstrated the highest speed and accuracy.
I will discuss the fundamentals of ML.NET, explore some sample codes, and explain the basics of the Microsoft Machine-Learning framework with a sample code.

ML.NET: Credit Card Fraud Detection

FariD — Tue, 28 Sep 2021 09:04:52 +0330

The starting point for any ML.NET app is a class named MLContext. It begins by creating a new instance of MLContext class, and when you do so, you have the option to seed for a random number generator.
If you don't specify a seed, you'll get different results each time you train and score the model.

Loading a data set and creating a data pipeline

Preprocessing data in ML.NET is unique and different from other frameworks because it requires an explicit class of our data structure. To do so, we create a class called InputModel, and we will state all the columns of our data set.

For this article, we have used the Credit Card Fraud Detection data set from Kaggle. This data set contains 31 columns. The class of the transaction, either 0 or 1, the amount of the transaction, the time the transaction occurred, and 28 other columns.

Now that we have our data modeled, we need also to model what our output should look like; The below script can achieve this.

The next step should be loading downloaded .csv data; Having defined model input and datafile path, and other constructor options.

Afterward, we will define the data process configuration with pipeline data transformations.

Training and saving the Model

Next, setting the training algorithm and evaluating the quality of the Model.

Usage of the saved model and prediction of credit card fraud are included in program.cs on Github page.

ML.NET: Credit Card Fraud Detection

Tue, 28 Sep 2021 09:04:52 +0330

Loading a data set and creating a data pipeline

Now that we have our data modeled, we need also to model what our output should look like; The below script can achieve this.

The next step should be loading downloaded .csv data; Having defined model input and datafile path, and other constructor options.

Afterward, we will define the data process configuration with pipeline data transformations.

Training and saving the Model

Next, setting the training algorithm and evaluating the quality of the Model.

Usage of the saved model and prediction of credit card fraud are included in program.cs on Github page.

C# vs. Python: Choosing the Right Programming Language

FariD — Fri, 27 Aug 2021 19:59:12 +0430

C# and Python are one of the several popular programming languages because they are easy to learn, simple to use; moreover, they offer quality, performance, and fast development. Both C# and Python are object-oriented programming languages that aim to make them practical for real-world applications. However, some critical differences between them can help you decide which one is better for you to learn and use. This article discusses the differences between C# and Python by explaining when to use them and how they perform.

C# vs. Python: Choosing the Right Programming Language

FariD — Fri, 27 Aug 2021 19:59:12 +0430

Here are some key areas where we can see the differences between C# and Python:

Accessibility

One area where C# and Python differ is in their accessibility. Python was created as an open-source language, meaning the community is more extensive and available resources. C# recently became an open-source language, and the community might be slightly smaller. However, if you use C#, you may access Microsoft's formalized support system for a fee. Python, however, has no centralized support network. Its community of users can offer experience, troubleshooting, and general advice.

Speed

Python is dynamically typed, whereas C# is statically typed. That is, when you use a variable in Python, it generally doesn't matter what it is; the interpreter will declare them out at runtime. It could be a string, a float, or an integer; they will all print as what they are during runtime.

For C# all the types must be declared before runtime. If you misuse a float instead of a string, the compiler will complain. The variables must be the exact types to work. This means extra time ensuring that all of your types are in order which, in turn, means more time spent programming, but on the other side it allocates less resources to preform. Moreover, there are approaches that you can use to declare dynamic variables in C#.

Performance

When it comes to performance, there is a clear advantage of C# over Python. C# is a compiled language, and Python is an interpreted one. Python's speed depends heavily on its interpreter, with the main ones being CPython and PyPy. Regardless of which, the C# is much faster in most cases.

For some applications, it can be up to 44 times faster than Python. This is for several reasons—from Python's garbage collector to its dictionary lookups. It's also partly due to C# being a compiled language: it takes more work to write but runs more efficiently.

Tools

Both Python and C# have many different tools that you can use to make the development process more manageable. Microsoft offers several company-specific tools that are often free for individual users, while you can find many open-source tools for Python. It may take some time to learn all Microsoft's tools and plugins, though they can make the coding process faster once you understand them. Python's open-source tools could be easier to learn, but they may not be as comprehensive as the tools for C#.

Suitability

Choosing between C# and Python may depend on their respective relevance to your project. Some developers may use C# because of its object-oriented programming design and integration with the .NET framework. This can be helpful if you already understand Java, develop applications within Microsoft's platform, or need stable access to reliable support.

Because it's a high-level programming language, Python may be more suitable for projects with faster turnaround times. It has fewer language constructions and can be easier to learn with repeated use. As you increase your language knowledge, you can access a broader range of Python's valuable features.

Accuracy

C#'s development process includes a build and a compile step that can take additional time. The benefit is that the compiler can identify errors in syntax before they disrupt the system's functionality.

Python has limited ways to identify any syntax errors before they occur. While this can support an efficient development process, coding in Python may require the help of an experienced programmer who can ensure the accuracy, scalability, and comprehensiveness of the developer's work.

Reliability

C#'s infrastructure software can support more users with reduced server resources, and its performance may be slightly better than Python's. In Python, however, you can improve performance by implementing performance aids like compilers and syntax checkers.

Python's development process, including writing and code deployment, can be faster than C#. The language's high-performing nature, libraries of pre-written code, and clear syntax often allow for increased productivity.

Flexibility

Both C# and Python can offer flexibility for various projects. Python offers both high speed and performance and is easy to learn. It offers seamless cross-platform development, and its open-source libraries are comprehensive. For projects requiring Microsoft integration, guaranteed performance, or traditional syntax and libraries, C# may be more suitable. Both languages can be reliable choices depending on the needs and specifications of your project.

Readability

Python often delineates blocks of code with white space that can make it easier to read. In C#, developers delineate code blocks using braces and brackets, and the code can sometimes result in many lines of brackets. While still readable, some prefer the white space and simple structure of Python coding over the rows of brackets that sometimes occur in C#.

C# vs. Python: Choosing the Right Programming Language

Fri, 27 Aug 2021 19:59:12 +0430

Here are some key areas where we can see the differences between C# and Python:

Accessibility

Speed

Performance

Tools

Suitability

Accuracy

Reliability

Flexibility

Readability

Introduction to Machine Learning; Why should you use ML.NET

FariD — Mon, 16 Aug 2021 16:53:27 +0430

In this article, I will try to explain the basics and benefits of ML.NET. Firstly, the Types of Machine Learning have been discussed afterward the Architecture and High-Level Overview are considered, Finally the question "Why should we use ML.NET?" is answered.

Introduction to Machine Learning; Why should you use ML.NET

FariD — Mon, 16 Aug 2021 16:53:27 +0430

Types of Machine Learning

One of the most important concepts that we have brought up in the training or learning process. This is a necessary step for every machine learning algorithm during which the algorithm uses the data to learn how to solve the task at hand. In practice, we usually have some collected data based on which we need to create our predictions, or classification, or any other processing. This data is called a training set.

As we were able to see based on behavior during the training and the nature of the training set, we have a few types of learning:

Unsupervised learning – The training set contains only inputs. The network attempts to identify similar inputs and to put them into categories. This type of learning is biologically motivated but it is not suitable for all the problems.
Supervised learning – The training set contains inputs and desired outputs. This way the network can check its calculated output the same as the desired output and take appropriate actions based on that. In this article, we focus on this type of learning since it is used the most in the industry.
Reinforcement learning – The training set contains inputs, but the network is also provided with additional information during the training. What happens is that once the network calculates the output for one of the inputs, we provide information that indicates whether the result was right or wrong and possibly, the nature of the mistake that the network made. Sort of like the concept of reward and punishment for artificial neural networks. This concept is very interesting, but it is out of the scope of this book, so, in general, we will have only the first two types of training.

Architecture and High-Level Overview

Building an application with ML.NET consists of several steps:

Loading Data – Raw data must be loaded into memory and for this IDataView is used.
Creating a pipeline – The pipeline is composed of steps that either transform data or train a machine learning algorithm. ML.NET provides various transformational steps, like one-hot encoding and various machine learning algorithms.
Training a machine learning model – Once the pipeline is created, the training can be started. This is done using the Fit() method that is supported in all algorithms.
Evaluate – The model can be evaluated at any point and additional decisions can be made based on the evaluations.
Save – Once trained, the model is saved into a file. In general, the complete application should be built in a way that one microservice trains and evaluates the machine learning model, and the other microservice utilizes it.
Load – The machine learning model can be loaded and utilized for predictions.

Apart from the mentioned classes, there are several more components that we need to mention. The Estimator is the object we create during the creation of the pipeline. This model is not trained. The Transformer instance, on the other hand, is a trained model and it is also in charge of loading the model back into the memory.

Why should we use ML.NET?

In the end, let’s just see why should we consider ML.NET for our project. As it turned out ML.NET has really good performance. ML.NET trained a sentiment analysis model with 95% accuracy using a 9GB Amazon review data set. Other popular machine learning frameworks failed to process the dataset due to memory errors. Training on 10% of the data set, to let all the frameworks complete training, ML.NET demonstrated the highest speed and accuracy. The performance evaluation found similar results in other machine learning scenarios. Apart from that, ML.NET is easily extendable with different models from different technologies.

Extended with TensorFlow & more

ML.NET has been designed as an extensible platform so that you can consume other popular ML frameworks (TensorFlow, ONNX, Infer.NET, and more) and have access to even more machine learning scenarios, like image classification, object detection, and more.

Moreover, ML.NET is an open-source and cross-platform machine learning framework for .NET.

References:

Introduction to Machine Learning; Why should you use ML.NET

Mon, 16 Aug 2021 16:53:27 +0430

Types of Machine Learning

As we were able to see based on behavior during the training and the nature of the training set, we have a few types of learning:

Unsupervised learning – The training set contains only inputs. The network attempts to identify similar inputs and to put them into categories. This type of learning is biologically motivated but it is not suitable for all the problems.
Supervised learning – The training set contains inputs and desired outputs. This way the network can check its calculated output the same as the desired output and take appropriate actions based on that. In this article, we focus on this type of learning since it is used the most in the industry.
Reinforcement learning – The training set contains inputs, but the network is also provided with additional information during the training. What happens is that once the network calculates the output for one of the inputs, we provide information that indicates whether the result was right or wrong and possibly, the nature of the mistake that the network made. Sort of like the concept of reward and punishment for artificial neural networks. This concept is very interesting, but it is out of the scope of this book, so, in general, we will have only the first two types of training.

Architecture and High-Level Overview

Building an application with ML.NET consists of several steps:

Loading Data – Raw data must be loaded into memory and for this IDataView is used.
Creating a pipeline – The pipeline is composed of steps that either transform data or train a machine learning algorithm. ML.NET provides various transformational steps, like one-hot encoding and various machine learning algorithms.
Training a machine learning model – Once the pipeline is created, the training can be started. This is done using the Fit() method that is supported in all algorithms.
Evaluate – The model can be evaluated at any point and additional decisions can be made based on the evaluations.
Save – Once trained, the model is saved into a file. In general, the complete application should be built in a way that one microservice trains and evaluates the machine learning model, and the other microservice utilizes it.
Load – The machine learning model can be loaded and utilized for predictions.

Why should we use ML.NET?

Extended with TensorFlow & more

Moreover, ML.NET is an open-source and cross-platform machine learning framework for .NET.

References:

Subnet Mask and CIDR Subnet Table

FariD — Sun, 08 Aug 2021 01:23:24 +0430

Subnetting is the process of dividing one network into smaller networks. Collectively, the smaller networks are referred to as subnetworks (or subnets), and the singular subdivision is a subnetwork (more commonly referred to as a subnet). Every single computer that is connected to a subnet shares an identical portion of the IP address. This shared information is known as a routing prefix, and in IPV4 (Internet Protocol Version 4), the routing prefix is called a subnet mask. The subnet mask is a "quad-dotted decimal representation."

This IPv4 Subnet article can assist you in looking up how a network is broken up into subnets.

Subnet Mask and CIDR Subnet Table

FariD — Sun, 08 Aug 2021 01:23:24 +0430

Subnet Mask Definition

Every device has an IP address with two pieces: the client or host address (0) and the server or network address (1). IP addresses are either configured by a DHCP server or manually configured (static IP addresses). The subnet mask splits the IP address into the host and network addresses, thereby defining which part of the IP address belongs to the device and which part belongs to the network.

The device called a gateway or default gateway connects local devices to other networks. This means that when a local device wants to send information to a device at an IP address on another network, it first sends its packets to the gateway, which then forwards the data to its destination outside of the local network.

CIDR Subnet Table:

Subnet Mask	CIDR Prefix	Available client IP's
255.255.255.255	/32	1
255.255.255.254	/31	2
255.255.255.252	/30	4
255.255.255.248	/29	8
255.255.255.240	/28	16
255.255.255.224	/27	32
255.255.255.192	/26	64
255.255.255.128	/25	128
255.255.255.0	/24	256
255.255.254.0	/23	512
255.255.252.0	/22	1024
255.255.248.0	/21	2048
255.255.240.0	/20	4096
255.255.224.0	/19	8192
255.255.192.0	/18	16,384
255.255.128.0	/17	32,768
255.255.0.0	/16	65,536
255.254.0.0	/15	131,072
255.252.0.0	/14	262,144
255.248.0.0	/13	524,288
255.240.0.0	/12	1,048,576
255.224.0 0	/11	2,097,152
255.192.0.0	/10	4,194,304
255.128.0.0	/9	8,388,608
255.0.0.0	/8	16,777,216
254.0.0.0	/7	33,554,432
252.0.0.0	/6	67,108,864
248.0.0.0	/5	134,217,728
240.0.0.0	/4	268,435,456
224.0.0.0	/3	536,870,912
192.0.0.0	/2	1,073,741,824
128.0.0.0	/1	2,147,483,648
0.0.0.0	/0	4,294,967,296

Where do CIDR numbers come from?

The CIDR number comes from the number of ones in the subnet mask when converted to binary.

The typical subnet mask 255.255.255.0 is 11111111.11111111.11111111.00000000 in binary. This adds up to 24 ones, or /24 (pronounced ‘slash twenty-four’).

A subnet mask of 255.255.255.192 is 11111111.11111111.11111111.11000000 in binary or 26 ones, hence /26.

Class address ranges:

Class A = 1.0.0.0 to 126.0.0.0
Class B = 128.0.0.0 to 191.255.0.0
Class C = 192.0.1.0 to 223.255.255.0

Reserved address ranges for private (non-routed) use:

10.0.0.0 -> 10.255.255.255
172.16.0.0 -> 172.31.255.255
192.168.0.0 -> 192.168.255.255

Other reserved addresses:

127.0.0.0 is reserved for loopback and IPC on the localhost
224.0.0.0 -> 239.255.255.255 is reserved for multicast addresses

Note: The use of /31 networks is a particular case defined by RFC 3021 where the two IP addresses in the subnet are usable for point-to-point links to conserve IPv4 address space.

References:

Subnet Mask and CIDR Subnet Table

Sun, 08 Aug 2021 01:23:24 +0430

Subnet Mask Definition

CIDR Subnet Table:

Subnet Mask	CIDR Prefix	Available client IP's
255.255.255.255	/32	1
255.255.255.254	/31	2
255.255.255.252	/30	4
255.255.255.248	/29	8
255.255.255.240	/28	16
255.255.255.224	/27	32
255.255.255.192	/26	64
255.255.255.128	/25	128
255.255.255.0	/24	256
255.255.254.0	/23	512
255.255.252.0	/22	1024
255.255.248.0	/21	2048
255.255.240.0	/20	4096
255.255.224.0	/19	8192
255.255.192.0	/18	16,384
255.255.128.0	/17	32,768
255.255.0.0	/16	65,536
255.254.0.0	/15	131,072
255.252.0.0	/14	262,144
255.248.0.0	/13	524,288
255.240.0.0	/12	1,048,576
255.224.0 0	/11	2,097,152
255.192.0.0	/10	4,194,304
255.128.0.0	/9	8,388,608
255.0.0.0	/8	16,777,216
254.0.0.0	/7	33,554,432
252.0.0.0	/6	67,108,864
248.0.0.0	/5	134,217,728
240.0.0.0	/4	268,435,456
224.0.0.0	/3	536,870,912
192.0.0.0	/2	1,073,741,824
128.0.0.0	/1	2,147,483,648
0.0.0.0	/0	4,294,967,296

Where do CIDR numbers come from?

The CIDR number comes from the number of ones in the subnet mask when converted to binary.

The typical subnet mask 255.255.255.0 is 11111111.11111111.11111111.00000000 in binary. This adds up to 24 ones, or /24 (pronounced ‘slash twenty-four’).

A subnet mask of 255.255.255.192 is 11111111.11111111.11111111.11000000 in binary or 26 ones, hence /26.

Class address ranges:

Class A = 1.0.0.0 to 126.0.0.0
Class B = 128.0.0.0 to 191.255.0.0
Class C = 192.0.1.0 to 223.255.255.0

Reserved address ranges for private (non-routed) use:

10.0.0.0 -> 10.255.255.255
172.16.0.0 -> 172.31.255.255
192.168.0.0 -> 192.168.255.255

Other reserved addresses:

127.0.0.0 is reserved for loopback and IPC on the localhost
224.0.0.0 -> 239.255.255.255 is reserved for multicast addresses

Note: The use of /31 networks is a particular case defined by RFC 3021 where the two IP addresses in the subnet are usable for point-to-point links to conserve IPv4 address space.

References:

International Morse Codes and Arduino

FariD — Sat, 07 Aug 2021 23:48:43 +0430

This article shares mnemonics and a chart for the International Morse Codes plus an Arduino code to say .... . .-.. .-.. --- / .-- --- .-. .-.. -..

International Morse Codes and Arduino

FariD — Sat, 07 Aug 2021 23:48:43 +0430

Mnemonics for Morse Codes:

The source code for Arduino:

International Morse Codes and Arduino

Sat, 07 Aug 2021 23:48:43 +0430

Mnemonics for Morse Codes:

The source code for Arduino:

Two Youtube channels of mathematics

FariD — Sat, 07 Aug 2021 23:20:30 +0430

The below Youtube channels are highly recommended for bachelors since they will help to understand and visualize the semantics of math.

Dr. Trefor Bazett

Wild Egg Maths

Two Youtube channels of mathematics

FariD — Sat, 07 Aug 2021 23:20:30 +0430

The below Youtube channels are highly recommended for bachelors since they will help to understand and visualize the semantics of math.

Dr. Trefor Bazett

Wild Egg Maths

Two Youtube channels of mathematics

Sat, 07 Aug 2021 23:20:30 +0430

The below Youtube channels are highly recommended for bachelors since they will help to understand and visualize the semantics of math.

Dr. Trefor Bazett

Wild Egg Maths

Applied Numerical Analysis - F.Gerald O. Wheatley

FariD — Sat, 07 Aug 2021 21:17:27 +0430

This book is profoundly helpful in the case that you want to commence realizing how to apply mathematics in real-world problems; moreover, it is a general book since it only includes the algorithm pseudo-code.

By and large, this is old but gold, do not miss reading this book if you are passionate about mathematics and programming.

The list of contents and download links are available on the full article.

Applied Numerical Analysis - F.Gerald O. Wheatley

FariD — Sat, 07 Aug 2021 21:17:27 +0430

Applied Numerical Analysis - F.Gerald O. Wheatley

Sat, 07 Aug 2021 21:17:27 +0430