let no-one ignorant of geometry enter here
Mathematics
This page pairs well with Probability.
Statistical Inference
Definition
(Random Sample & Model)
Let \(X=(X_1,\ldots,X_n)\) be i.i.d. from a parametric family \(\{F_\theta:\theta\in\Theta\subset\mathbb{R}^p\}\).
The parameter \(\theta\) is unknown; inference uses the randomness of \(X\) to learn about \(\theta\).
This page pairs well with Statistics.
Elements of Probability Theory
Definition
(Random Experiment, Sample Space, Events)
A random experiment has uncertain outcomes.
The sample space $S$ is the set of all possible outcomes.
An event $E$ is a subset of $S$. The certain event is $S$; the impossible event is $\varnothing$.
You should see gathered listings from this directory below:
Topics Set Theory & Boolean Algebra Logic & Proof Techniques Combinatorics & Counting Graph Theory Number Theory (Divisibility, Modular Arithmetic) Recurrence Relations Finite Automata & Formal Languages Discrete Probability
Important Theorems De Morgan’s Laws (Logic & Boolean Algebra) Pigeonhole Principle (Combinatorics) Inclusion-Exclusion Principle (Counting) Euler’s Formula for Graphs ( Handshaking Lemma ( Chinese Remainder Theorem (Number Theory) Fermat’s Little Theorem ( RSA Cryptosystem & Modular Inverses Master Theorem (Recurrence Relations)
I am finding Real Analysis to be more difficult than any other mathematics that I have studied before. I can seem to verify the truth of statements because they seem right; but I am having a difficult time producing rigorous and correct proofs.
It seems that High-School children (on the internet) are able to self-study Fomin with success. Bitterly, we remind ourselves:
"Comparison is the thief of Joy"—Theodore Roosevelt (probably)
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
HSV | Viridis | Cividis | Inferno | Jet | Magma | Plasma | Rainbow | Turbo
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
- 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