Mathematics

Topics Analytic Functions & Cauchy-Riemann Equations Contour Integration & Residue Theorem Laurent Series & Singularities Conformal Mapping Important Theorems Cauchy’s Integral Theorem Cauchy’s Integral Formula Residue Theorem Rouché’s Theorem Maximum Modulus Principle

All of the site favicons that I use have been generated by contour plots of the complex logarithm and complex exponential functions.

Experiments

HSV | Viridis | Cividis | Inferno | Jet | Magma | Plasma | Rainbow | Turbo

Real

Imaginary

Absolute

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1. Linear Algebra

Topics Vector Spaces & Linear Independence Matrix Operations & Determinants Eigenvalues & Eigenvectors Linear Transformations Orthogonality & Inner Products Singular Value Decomposition (SVD) Important Theorems Rank-Nullity Theorem Invertible Matrix Theorem Spectral Theorem (Diagonalization of Symmetric Matrices) Cayley-Hamilton Theorem Gram-Schmidt Process Perron-Frobenius Theorem (Positive Matrices)

Topics Convexity & Optimization Techniques Gradient Descent & Newton’s Method Lagrangian & Duality Theory Integer & Combinatorial Optimization Linear Programming & Simplex Method Important Theorems KKT Conditions (Karush-Kuhn-Tucker) Lagrange Multipliers Strong & Weak Duality (Linear Programming) Farkas' Lemma Von Neumann’s Minimax Theorem

Topics Axioms of Probability (Kolmogorov) Random Variables & Distributions Expectation & Variance Bayesian Probability Stochastic Processes & Markov Chains Important Theorems Kolmogorov’s Axioms Law of Large Numbers (Weak & Strong) Central Limit Theorem (CLT) Bayes’ Theorem Markov & Chebyshev Inequalities Borel-Cantelli Lemma Martingale Convergence Theorem

Topics Metric Spaces & Topology Sequences & Series of Functions Continuity & Differentiability Measure Theory & Lebesgue Integration Important Theorems Bolzano-Weierstrass Theorem Heine-Borel Theorem Monotone Convergence Theorem (MCT) Fatou’s Lemma & Dominated Convergence Theorem (DCT) Arzelà–Ascoli Theorem

Topics Descriptive Statistics (Mean, Median, Variance) Inferential Statistics (Hypothesis Testing, Confidence Intervals) Regression & Estimation Maximum Likelihood Estimation (MLE) Bayesian Statistics & Inference Important Theorems Gauss-Markov Theorem (Best Linear Unbiased Estimator) Likelihood Ratio Test Theorem Cramér-Rao Bound (MLE) Fisher’s Theorem (Sufficiency) Chi-Square & t-Distributions Neyman-Pearson Lemma