Basic Linear Algebra Theories
Basic Operations of Vectors
View Points on Matrix Multiplication
Meaning of Row Vector and Inner Product
Matrix as Linear Transformation
Geometric Meaning of Determinant
Eigenvalue and Eigenvector
Relationship of Four Fundamental Subspaces
Change of Basis
Elementary Square Matrices
LU Decomposition
Gauss/Gauss-Jordan Elimination
Applications of Linear Algebra
Principal Component Analysis(PCA)
EigenValue Decomposition(EVD)
Meaning of Complex Eigenvalue and Eigenvector
Linear Regression
Geometric Meaning of Pseudo Inverse
QR Decomposition
Singular Value Decomposition(SVD)
NMF(Non-negative Matrix Factorization)
Correlation and Inner Product
Geometric Meaning of Jacobian Matrix
Geometric Meaning of Hessian Matrix
Linear Algebra and Fourier Transform
Circulant Matrix and Convolution
Eigenvector of Circulant Matrix and Fourier Matrix
Geometric Meaning of Gauss-Jordan Elimination
Why does Wronskian work?
Independent Component Analysis(ICA)
Geometric Meaning of Cramer's Rule
Cholesky Decomposition
Positive Definite Matrix
Mahalanobis Distance
Basic Calculus
Derivation of Taylor Series and Its Meaning
Geometric Meaning of L'Hopital's Rule
$\int x^{dx}-1=$?
Multivariate Calculus
Gradient of Scalar Field
Divergence of Vector Field
Curl of Vector Field
Laplacian of Scalar Field
Meaning of Multiple Integral
Line Integral on Vector Field
Vector Field and Path Independence
Green's Theorem
Flux of Vector Field(2D)
Divergence Theorem(2D)
Normal Vector of Infinitesimal Curved Surface
Surface Integral of Vector Field(3D)
Stokes' Theorem
Divergence Theorem(3D)
Ordinary Differential Equation
Modeling with Differential Equations
Direction Fields and Euler's Method
Euler's Number e and Homogeneous Differential Equation
Separable Differential Equations
Solution to 1st Order Linear Differential Equations
Bernoulli Equation
Modeling with System of Differential Equations
Phase Plane
Trace-Determinant plane
Solving Second-Order Linear Differential Equations (1)
Solving Second-Order Linear Differential Equations (2)
Reduction of Order
Meaning of Non-Homogeneous Differential Equation
Method of Undetermined Coefficients
Method of Variation of Parameters
Euler-Cauchy Differential Equation
Boundary Value Problem (BVP)
Linear Operators and Function Space
Eigenfunction Expansion
Sturm Liouville Theory
Solution with Green's Funcion
Partial Differential Equation
Meaning of Heat/Wave Equation
Meaning of Laplace Equation
Machine Learning
Gradient Descent
Optimization Method with Momentum - ADAM
Linear Regression
Logistic Regression
Support Vector Machine(SVM)
Naive Bayes Classifier
ROC curve
Restricted Boltzmann Machine
AutoEncoder
Variational AutoEncoder
Layer-wise Relevance Propagation
k-means algorithm
GMM & EM Algorithm
Probability & Statistics Basics
Binomial Distribution
Geometric Distribution
Poisson Distribution
Exponential Distribution
Gaussian Integral
Derivation of Normal Distribution
Meaning of Central Limit Theorem
Proof of Central Limit Theorem
Chi-Square Distribution and Test
Markov Inequality and CHebyshev Inequality
Chernoff Bound
Statistical Inference
Statistical Inference - Big Picture
Meaning of Sampling and Standard Error
Sample variance is divided by n-1 instead of n
Meaning of t-value and Student's t-test
Meaning of F-value and Analysis of Variance
The Theory of Praying for Failure - Null Hypothesis and Alternative Hypothesis.
Meaning of p-value
Meaning of Confidence Interval
Type-1 and Type-2 error
Paired Sample t-test
Repeated Measures ANOVA (RM ANOVA)
Chi-Square Distribution and Test
Nonparametric Statistics
Wilcoxon Rank Sum Test
Wilcoxon Signed Sum Test
Jackknife & Bootstrap
Permutation Test)
Bayesian Statistics
Meaning of Bayes' Theorem
Maximum Likelihood Estimation(MLE)
GMM & EM Algorithm
Naive Bayes Classifier
Kalman Filter
Rejection Sampling
Markov Chain Monte Carlo
Information Theory
Information Entropy
KL divergence
Complex number and Euler's formula
Meaning of Imaginary Numbers
Location of Imaginary Roots
Meaning of Degrees and Radians
Meaning of Natural Number e
Deriving Euler's Formula with Differential Equation
Geometric Meaning of Euler's Formula
Exponential Functions with Negative Bases
Phasor
Signal Processing
Introduction to Signals and Systems
Basics of Sinusoids
Basics of Complex Number
Phasor
Linear Time Invariant(LTI) System
Discrete Convolution and Impulse Response
Sampling Continuous Signal to Discrete Signal
Continuous Time Convolution
Signal Space
Continuous Time Fourier Series
Continuous Time Fourier Transform
Discrete Time Fourier Series
Discrete Time Fourier Transform
Fourier Transform and Phase
Shannon's Sampling Theorem
Frequency Sampling and DFT
Frequency Resolution
Laplace Transform
Z-Transform
Laplace Transform and Z-Transform
Negative Frequency
Time-Frequency Uncertainty
Savitzky-Golay Filter
Butterworth Filter
Chebyshev Filter
Frequency Transformation
Hilbert Transform
Wiener Kinchin Theorem
Wold's Theorem

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Feb 11, 2020

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