• User:MathKnight and he:משתמש:MathKnight and he:משתמש:MathKnight-at-TAU
• #Useful mathematics
• Help:formula

Gallery

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  Israel ישראל
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  Oxalis pes-caprae חמציצים
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  Anemone coronaria, Israel
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  IDF Caterpillar D9
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  IDF Caterpillar D9
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  Triceratops טריצרטופס
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  Tulip (Tulipa agenensis, צבעוני ההרים) in Israel
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  Rayonnant Gothic cathedral (Cologne cathedral)
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  Oxalis pes-caprae, Israel
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  Oxalis pes-caprae, Israel
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  Anemone coronaria, Israel
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  IDF D9 די-9 דובי
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  Saltwater Crocodile (Crocodylus prorsus)
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  Addax nasomaculatus
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  Plumeria rubra (פלומריה ריחנית)
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  Ara ararauna
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  IDF Caterpillar D9
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  Crocodylus niloticus (order Crocodilia)
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  Lightsaber - The coolest weapon ever
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  Oxalis pes-caprae
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  Nile Crocodile (Crocodylus niloticus)
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  Vibeke Stene - Gothic angel of music
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  Simone Simons - Gothic beauty
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  Coccinella septempunctata מושית השבע
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  Protaetia cuprea ignicollis נחושתית הקוצים
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  Shofar - Jewish ritual horn
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  Lane the Triceratops
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  Hatcher the Triceratops
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  Deinosuchus דיינוסוכוס
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  Epitonium scalare (Precious Wentletrap)
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  Lupinus pilosus
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  Gothic architecture
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  Oxalis pes-caprae, חמציץ נטוי, Israel
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  Cologne cathedral, Gothic style
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  Triceratops - skulls
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  Colorful Anemone coronaria in Dalia, Israel
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  Tower of London
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  Crocodylus porosus (Saltwater Crocodile, תנין הים)
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  Israeli beauty
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  Israeli Air Force F-16I Sufa
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  Merkava Mk 4M tank of the Israel Defense Forces
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  Apatosaurus (אפטוזאורוס)
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  Dinosaurs
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  Rayonnant Gothic Rose window (Notre-Dame de Paris)
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  Gothic architecture (Basilica of St Denis)
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  Coccinella septempunctata מושית השבע
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  Ara ararauna ארה כחולה-צהובה
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  Patagotitan פטגוטיטאן
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  Pavo cristatus (Peacock) טווס מצוי
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  Ulm Minster
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  Jerusalem, Walls and Tower of David, Israel
  מגדל דוד וחומות ירושלים, ירושלים, ישראל
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  Castel Nuovo, Naples, Italy
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  Clermont-Ferrand Cathedral, Rayonnant Gothic style
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  Coracias garrulus - כחל מצוי
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  Ulm Minster
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  YAMAM ימ"מ - Israel's Counter-Terrorism Unit
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  Flags of Israel in Jerusalem
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  IDF Caterpillar D9 (e)
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  Pavo cristatus
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  Bat (Chiroptera)
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  Tulips in Israel
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  IDF Caterpillar D9

Useful mathematics

• Classification Theory
  • Binary classifier
  • Sensitivity and Specificity
  • Receiver operating characteristic (ROC)
• Basic Probability and Statistics
  • Probability ${\displaystyle \left(\Omega ,{\mathcal {A)),\mathbb {P} \right)}$
  • Statistics
  • Expected value ${\displaystyle \mathbb {E} (X)=\sum _{i}x_{i}\cdot \mathbb {P} (X=x_{i})=\int x\,\mathrm {d} \mathbb {P} (X=x)=\int xf(x)\mathrm {d} x}$
  • Variance and Standard deviation ${\displaystyle \sigma ^{2}=\operatorname {Var} (X)=\operatorname {cov} (X,X)=\mathbb {E} {\big [}(X-\mathbb {E} [X])^{2}{\big ]}=\mathbb {E} [X^{2}]-(\mathbb {E} [X])^{2))$
  • Covariance ${\displaystyle \sigma _{X,Y}^{2}=\operatorname {cov} (X,Y)=\mathbb {E} {\big [}(X-\mathbb {E} [X])(Y-\mathbb {E} [Y]){\big ]}=\mathbb {E} [XY]-\mathbb {E} [X]\mathbb {E} [Y]}$
  • Covariance matrix ${\displaystyle \Sigma =\mathbb {E} \left[(\mathbf {X} -\mathbb {E} [\mathbf {X} ])(\mathbf {X} -\mathbb {E} [\mathbf {X} ])^{\rm {T))\right]}$, if ${\displaystyle \mathbf {X} =(X_{i})_{i=1}^{n))$ then ${\displaystyle \Sigma _{i,j}=\operatorname {cov} (X_{i},X_{j})}$
  • Conditional probability ${\displaystyle \mathbb {P} (A\mid B)={\frac {\mathbb {P} (A\cap B)}{\mathbb {P} (B)))}$
  • Bayes' theorem ${\displaystyle \mathbb {P} (A\mid B)={\frac {\mathbb {P} (B\mid A)\,\mathbb {P} (A)}{\mathbb {P} (B)))}$
  • Independence (probability theory) ${\displaystyle A\perp \!\!\!\perp B\iff \mathbb {P} (A\cap B)=\mathbb {P} (A)\mathbb {P} (B)\iff \mathbb {P} (A)=\mathbb {P} (A\mid B)\iff \mathbb {P} (B)=\mathbb {P} (B\mid A)}$
  • Conditional expectation
  • Normal distribution (Gaussian) ${\displaystyle X\sim {\mathcal {N))(\mu ,\sigma ^{2})}$ means ${\displaystyle \mathrm {d} \mathbb {P} (x)=f(x\mid \mu ,\sigma ^{2})={\frac {1}{\sqrt {2\pi \sigma ^{2))))e^{-{\frac {(x-\mu )^{2)){2\sigma ^{2))))={\frac {1}{\sqrt {2\pi \sigma ^{2))))\exp \left(-{\frac {(x-\mu )^{2)){2\sigma ^{2))}\right)}$
• Statistics
  • Statistics
  • Statistical hypothesis testing
  • p-value
  • Linear regression
  • Spearman's rank correlation coefficient
  • Likelihood function ${\displaystyle {\mathcal {L))(\theta \mid x)=p_{\theta }(x)=\mathbb {P} _{\theta }(X=x)}$
  • Maximum likelihood estimation (MLE) ${\displaystyle {\hat {\theta ))=\operatorname {arg\,\max } \((\mathcal {L))(\theta \mid x)\ \mid \ \theta \in \Theta \))$
• Signal Processing
  • Signal processing
  • Time series
  • Fourier analysis
  • Fourier transform and Laplace transform
  • Discrete-time Fourier transform (DTFT) ${\displaystyle X_{2\pi }(\omega )=\sum _{n=-\infty }^{\infty }x[n]\,e^{-i\omega n}\ \implies \ X_{1/T}(f)=X_{2\pi }(2\pi fT)\ {\stackrel {\mathrm {def} }{=))\sum _{n=-\infty }^{\infty }\underbrace {T\cdot x(nT)} _{x[n]}\ e^{-i2\pi fTn}\;{\stackrel {\mathrm {Poisson\;f.} }{=))\;\sum _{k=-\infty }^{\infty }X\left(f-k/T\right)}$
  • Convolution ${\displaystyle (f\ast g)(\tau )=\int _{-\infty }^{\infty }f(t)g(\tau -t)\mathrm {d} t=\int _{-\infty }^{\infty }f(\tau -t)g(t)\mathrm {d} t}$
  • Cross-correlation ${\displaystyle (f\star g)(\tau )=\int _{-\infty }^{\infty }f^{*}(t)g(t+\tau )\mathrm {d} t=\int _{-\infty }^{\infty }f(t-\tau )g(t)\mathrm {d} t}$
  • Auto-correlation
  • Autocovariance: for ${\displaystyle (X_{t})_{t\in \mathbb {N} ))$: ${\displaystyle C_{XX}(t,s)=\operatorname {cov} (X_{t},X_{s})=\mathbb {E} [X_{t}X_{s}]-\mathbb {E} [X_{t}]\mathbb {E} [X_{s}]}$
  • Low-pass filter
  • Recursive least squares filter (RLS)
  • Kalman filter (excellent introduction here)
  • Autoregressive–moving-average model (ARMA) = Autoregressive model (AR) and Moving-average model (MA)
  • Savitzky-Golay filter
  • Window function
• Differential equations
  • Partial differential equation (PDE)
  • Finite element method (FEM)
• Mathematical programming and Numerical analysis
  • Numerical analysis
  • MATLAB
  • Principal Components Analysis
  • Delaunay triangulation
  • COMSOL
  • Fast Fourier transform (FFT)
  • Gradient descent

Interesting Articles

• Israel
• Triceratops
• Nile Crocodile
• Saltwater Crocodile
• Deinosuchus
• IDF Caterpillar D9
• Israel Defense Forces
• Macrophage
• MATLAB

Useful Links

• Help:formula
• Gothic metal: List of gothic metal bands
• Triceratops
• Dinosaur size
• User:MathKnight/Sandbox

IDF Caterpillar D9 - דחפור די-9 בשירות צה"ל - User:MathKnight#IDF Caterpillar D9