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centerthe Cartesian product of the direct product of
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right Set Theory
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3 bgcolor=#d0f0d0 align=center<div style="font-size:200%"></div>
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"http://wwwinformationdelightinfo/information/entry/coproduct" class="copylinks">Coproduct
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3
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3
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centercoproduct over … from … to … of
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right Category Theory
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3 bgcolor=#d0f0d0 align=center<div style="font-size:200%">′ <br/><br/><sup>•</sup></div>
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"http://wwwinformationdelightinfo/information/entry/derivative" class="copylinks">Derivative
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3''f'' ′(''x'') is the derivative of the function ''f'' at the point ''x'', ie, the Slope of the Tangent to ''f'' at ''x'' <br/>
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3If ''f''(''x'') := ''x''<sup>2</sup>, then ''f'' ′(''x'') = 2''x''
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center… prime<br><br> derivative of
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right Calculus
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6 bgcolor=#d0f0d0 align=center<div style="font-size:200%">∫</div>
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"http://wwwinformationdelightinfo/information/entry/indefinite_integral" class="copylinks">Indefinite Integral or Antiderivative
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3∫ ''f''(''x'') d''x'' means a function whose derivative is ''f''
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3 ∫''x''<sup>2</sup> d''x'' = ''x''<sup>3</sup>/3 + C
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centerindefinite integral of<br><br> the antiderivative of
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right Calculus
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"http://wwwinformationdelightinfo/information/entry/definite_integral" class="copylinks">Definite Integral
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3∫<sub>''a''</sub><sup>''b''</sup> ''f''(''x'') d''x'' means the signed Area between the ''x''-axis and the Graph of the Function ''f'' between ''x'' = ''a'' and ''x'' = ''b''
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3∫<sub>0</sub><sup>''b''</sup> x<sup>2 </sup> d''x'' = ''b''<sup>3</sup>/3
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centerintegral from … to … of … with respect to
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right Calculus
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3 bgcolor=#d0f0d0 align=center<div style="font-size:200%">∮</div>
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"http://wwwinformationdelightinfo/information/entry/contour_integral" class="copylinks">Contour Integral or closed Line Integral
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3Similar to the integral, but used to denote a single integration over a closed curve or loop It is sometimes used in physics texts involving equations regarding Gauss's Law , and while these formulas involve a closed Surface Integral , the representations describe only the first integration of the volume over the enclosing surface Instances where the latter requires simultaneous double integration, the symbol would be more appropriate A third related symbol is the closed Volume Integral , denoted by the symbol
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3
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centercontour integral of
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right Calculus
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9 bgcolor=#d0f0d0 align=center<div style="font-size:200%">∇</div>
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"http://wwwinformationdelightinfo/information/entry/gradient" class="copylinks">Gradient
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3∇''f'' (x<sub>1</sub>, …, x<sub>''n''</sub>) is the vector of partial derivatives (''∂f'' / ''∂x''<sub>1</sub>, …, ''∂f'' / ''∂x''<sub>''n''</sub>)
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3If ''f'' (''x'',''y'',''z'') := 3''xy'' + ''z''&2, then ∇''f'' = (3''y'', 3''x'', 2''z'')
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center Del , Nabla , Gradient of
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right Vector Calculus
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"http://wwwinformationdelightinfo/information/entry/divergence" class="copylinks">Divergence
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3<math>
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3If <math> ec v := 3xy\mathbf{i}+y^2 z\mathbf{j}+5\mathbf{k} </math>, then <math>
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centerdel dot, divergence of
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rightvector calculus
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"http://wwwinformationdelightinfo/information/entry/curl" class="copylinks">Curl
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3<math>
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3If <math> ec v := 3xy\mathbf{i}+y^2 z\mathbf{j}+5\mathbf{k} </math>, then <math>
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centercurl of
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rightvector calculus
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6 bgcolor=#d0f0d0 align=center<div style="font-size:200%">∂</div>
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"http://wwwinformationdelightinfo/information/entry/partial_differential" class="copylinks">Partial Differential
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3 With ''f'' (x<sub>1</sub>, …, x<sub>''n''</sub>), ∂f/∂x<sub>i</sub> is the derivative of ''f'' with respect to x<sub>i</sub>, with all other variables kept constant
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3 If ''f''(x,y) := x<sup>2</sup>y, then ∂''f''/∂x = 2xy
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centerpartial, d
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right Calculus
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"http://wwwinformationdelightinfo/information/entry/Boundary_(topology)" class="copylinks">Boundary
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3 ∂''M'' means the boundary of ''M''
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3 ∂{x : <nowiki></nowiki>x<nowiki></nowiki> ≤ 2} = {x : <nowiki></nowiki>x<nowiki></nowiki> = 2}
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centerboundary of
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right Topology
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6 bgcolor=#d0f0d0 align=center<div style="font-size:200%">&perp</div>
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"http://wwwinformationdelightinfo/information/entry/perpendicular" class="copylinks">Perpendicular
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3''x'' &perp ''y'' means ''x'' is perpendicular to ''y'' or more generally ''x'' is orthogonal to ''y''
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3If ''l'' &perp ''m'' and ''m'' &perp ''n'' then ''l'' <nowiki></nowiki> ''n''
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centeris perpendicular to
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right Geometry
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| |
"http://wwwinformationdelightinfo/information/entry/bottom_element" class="copylinks">Bottom Element
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3''x'' = &perp means ''x'' is the smallest element
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3&forall''x'' : ''x'' ∧ &perp = &perp
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centerthe bottom element
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right Lattice Theory
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3 bgcolor=#d0f0d0 align=center<div style="font-size:200%"><nowiki></nowiki></div>
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"http://wwwinformationdelightinfo/information/entry/parallel_(geometry)" class="copylinks">Parallel
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3''x'' <nowiki></nowiki> ''y'' means ''x'' is parallel to ''y''
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3If ''l'' <nowiki></nowiki> ''m'' and ''m'' &perp ''n'' then ''l'' &perp ''n''
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centeris parallel to
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right Geometry
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| |
3 bgcolor=#d0f0d0 align=center <div style="font-size:200%"></div>
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"http://wwwinformationdelightinfo/information/entry/entailment" class="copylinks">Entailment
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3 ''A''  ''B'' means the sentence ''A'' entails the sentence ''B'', that is in every model in which ''A'' is true, ''B'' is also true
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3 ''A''  ''A'' ∨ ¬''A''
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centerentails
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right Model Theory
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3 bgcolor=#d0f0d0 align=center <div style="font-size:200%"></div>
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"http://wwwinformationdelightinfo/information/entry/inference" class="copylinks">Inference
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3''x''  ''y'' means ''y'' is derived from ''x''
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3 ''A'' → ''B''  ¬''B'' → ¬''A''
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centerinfers or is derived from
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right Propositional Logic , Predicate Logic
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| |
3 bgcolor=#d0f0d0 align=center <div style="font-size:200%"></div>
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"http://wwwinformationdelightinfo/information/entry/normal_subgroup" class="copylinks">Normal Subgroup
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3 ''N''  ''G'' means that ''N'' is a normal subgroup of group ''G''
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3 ''Z''(''G'')  ''G''
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centeris a normal subgroup of
|
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right Group Theory
|
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6 bgcolor=#d0f0d0 align=center<div style="font-size:200%">/</div>
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"http://wwwinformationdelightinfo/information/entry/quotient_group" class="copylinks">Quotient Group
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3 ''G'' / ''H'' means the quotient of group ''G'' Modulo its subgroup ''H''
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3 {0, ''a'', 2''a'', ''b'', ''b''+''a'', ''b''+2''a''} / {0, ''b''} =
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center mod
|
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right Group Theory
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| |
3 ''A''/~ means the set of all ~ Equivalence Class es in ''A''
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| |
3 If we define ~ by x ~ y ⇔ x &minus y ∈ , then <br/>/~ = } : x ∈ (0,1]}
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center mod
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| |
right Set Theory
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| |
6 bgcolor=#d0f0d0 align=center<div style="font-size:200%">≈</div>
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3''x'' ≈ ''y'' means ''x'' is approximately equal to ''y''
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3π ≈ 314159
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centeris approximately equal to
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| |
righteverywhere
|
| |
"http://wwwinformationdelightinfo/information/entry/isomorphism" class="copylinks">Isomorphism
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| |
3 ''G'' ≈ ''H'' means that group ''G'' is isomorphic to group ''H''
|
| |
3 ''Q'' / {1, &minus1} ≈ ''V'', <br />where ''Q'' is the Quaternion Group and ''V'' is the Klein Four-group
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center is isomorphic to
|
| |
right Group Theory
|
| |
3 bgcolor=#d0f0d0 align=center<div style="font-size:200%">~</div>
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"http://wwwinformationdelightinfo/information/entry/order_of_magnitude" class="copylinks">Order Of Magnitude
|
| |
3 ''m'' ~ ''n'' means the quantities ''m'' and ''n'' have the same Order Of Magnitude , or general size <br><br>(''Note that'' ~ ''is used for an approximation that is poor, otherwise use '' ≈ )
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| |
32 ~ 5<br><br> 8 × 9 ~ 100<br><br> but π<sup>2</sup> ≈ 10
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rightroughly similar<br><br> Poorly Approximates
|
| |
right Approximation Theory
|
| |
3 bgcolor=#d0f0d0 align=center<div style="font-size:200%">〈,〉<br/><br/>( )<br/><br/>< , ><br/><br/>·<br/><br/>:</div>
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"http://wwwinformationdelightinfo/information/entry/Inner_product_space" class="copylinks">Inner Product
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| |
3〈''x'',''y''〉 means the inner product of ''x'' and ''y'' as defined in an Inner Product Space <br/>
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| |
3The Standard Inner Product between two vectors ''x'' = (2, 3) and ''y'' = (−1, 5) is:<br/>〈x, y〉 = 2 × −1 + 3 × 5 = 13<br/><br/>
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| |
centerinner product of
|
| |
right Linear Algebra
|
| |
3 bgcolor=#d0f0d0 align=center<div style="font-size:200%"></div>
|
| |
"http://wwwinformationdelightinfo/information/entry/tensor_product" class="copylinks">Tensor Product
|
| |
3 ''V''  ''U'' means the tensor product of ''V'' and ''U''
|
| |
3 {1, 2, 3, 4}  {1, 1, 2} = <br/>
|
| |
center tensor product of
|
| |
right Linear Algebra
|
| |
3 bgcolor=#d0f0d0 align=center<div style="font-size:200%"></div>
|
| |
"http://wwwinformationdelightinfo/information/entry/convolution" class="copylinks">Convolution
|
| |
3 ''f''  ''g'' means the convolution of ''f'' and ''g''
|
| |
3 <math>(f g )(t) = \int f( au) g(t - au)\, d au</math>
|
| |
center convolution, convoluted with
|
| |
right Functional Analysis
|
| |
3 bgcolor=#d0f0d0 align=center<div style="font-size:200%"><math>\bar{x}</math><br/></div>
|
| |
"http://wwwinformationdelightinfo/information/entry/mean" class="copylinks">Mean
|
| |
3<math>\bar{x}</math> (often read as "x bar") is the Mean (average value of <math>x_i</math>)
|
| |
3<math>x = \{1,2,3,4,5\} \bar{x} = 3</math>
|
| |
centeroverbar, … bar
|
| |
right Statistics
|
| |
3 bgcolor=#d0f0d0 align=center<div style="font-size:200%"><math> \overline{z} </math>
|
| |
"http://wwwinformationdelightinfo/information/entry/complex_conjugate" class="copylinks">Complex Conjugate
|
| |
3<math> \overline{z} </math> is the complex conjugate of ''z''
|
| |
3<math> \overline{3+4i} = 3-4i </math>
|
| |
centerconjugate
|
| |
right Complex Numbers
|
| |
3 bgcolor=#d0f0d0 align=center<div style="font-size:200%"><math> riangleq</math></div>
|
| |
3<math> riangleq</math> means equal by definition When <math> riangleq</math> is used, equality is not true generally, but rather equality is true under certain assumptions that are taken in context Some writers prefer ≡
|
| |
3<math>p(x_1,x_2,,x_n) riangleq \prod_{i=1}^n p(x_i x_{\pi_i})</math>
|
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centerequal by definition
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righteverywhere
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