Bayes' Theorem: Updating Probability with "New Evidence", the Core of AI and Statistics
Categories
162 pages
Mathematics
Diverse Proofs of the Pythagorean Theorem: From Geometry and Algebra to Einstein
Euler's Polyhedron Formula: The Magic of Topology Shown by V - E + F = 2
The Möbius Strip and Klein Bottle: A Fascinating World of Surfaces with No 'Inside' or 'Outside'
Fermat's Little Theorem: The Nature of Primes and the Foundation of Modern Cryptography (RSA)
Fundamental Theorem of Algebra: Proof That an n-th Degree Equation Always Has n Complex Roots
Groups, Rings, and Fields: An Introduction to Modern Algebra Abstracting 'Structure' Itself
Pell's Equation: The Charm of Diophantine Equations with Infinite Solutions and Continued Fractions
The Euclidean Algorithm: Fast GCD Calculation and Humanity's Oldest Algorithm from Antiquity
Cayley-Hamilton Theorem: The Wondrous Property of a Matrix Satisfying Its Own Characteristic Equation
Diagonalization and Jordan Normal Form: The Ultimate Classification Method for Expressing Complex Matrices Simply
Geometric Meaning of the Determinant: More Than Just a Formula, It's the 'Volume Scale Factor' and 'Orientation Reversal'
Method of Least Squares: Finding the 'Best Fit Line' for Scattered Data using Linear Algebra
Singular Value Decomposition (SVD): Decomposing Any Matrix into Rotations and Scaling for Data Compression and AI
Eigenvalues and Eigenvectors: Special Vectors That Don't Change Direction Under Matrix Transformations and Their Applications
Gram-Schmidt Process: An Algorithm to Realign Distorted Basis Vectors into Neat, Mutually Orthogonal Vectors
Laplace Transform: The Technique of Transforming Difficult Differential Equations into Algebraic Equations
Residue Theorem: Brilliantly Solving Complex Real Integrals Using 'Singularities' in the Complex Plane
The Gamma Function: Euler's Masterpiece Extending the Factorial to Continuous Reals and Complex Numbers
Cauchy's Integral Theorem: The Beautiful Foundation of Complex Analysis Where Integrals Vanish
