Books

These are the online books I'm working on, which cover the main topics of machine learning, computer science, signal processing, algorithms and mathematics. The books are far from complete, I constantly work on them but decided to publish them in part to get early feedback and to ship the content today and not tomorrow.

Analysis

• Sets
• Mappings
• Natural numbers and Induction
• Integers
• Rational numbers
• Real numbers
• Complex numbers
• Quaternions
• Intervals
• Limits
• Sequences
• Series
  • Konvergenz
  • Power Series
  • Exponentialreihe
  • Taylor Series
  • Fourier series
• Real Functions
  • Continuity of functions
  • Trigonemetric functions
  • Exponential function
  • Lambert W Function
  • Logarithmen
• Differential calculus
  • Local extrema
  • Mean value theorem
  • Convecity
• Integral calculus
  • Riemann integral
  • Improper integral
• Integration and Differentiation

Stochastics

• Probability Theory
  1. Random Variable
  2. Expected Value
  3. Conditional Probability
  4. Density / Mass
  5. Independence
  6. Convergence
  7. Simulation
• Statistics
• Monte Carlo integration

Stochastic Processes

1. Posson-Point-Process
2. Gaussian Process
3. Markov Chains

Linear Algebra

• System of linear equatnions
• Vectors
  1. Addition, scalar multiplication
  2. Hyperplanes
• Vector spaces
• Linear Transformations
  1. Basis & Dimensions
• Matrix
  1. Linear Transformations
  2. Block Matrix
  3. Square Matrix
  4. Inverse
  5. Gauss-Jordan Elimination
• Trace & Determinants
  1. Definition
  2. Existence
  3. Determinant & Volume
• Norms
  1. P-Norms
  2. Condition number
  3. Spectral Radius
  4. Series and sequence of linear operators
  5. Convergence
• Eigenvalues
  1. Definition
  2. Characteristic polynomial
  3. Diagonalizable matrix
  4. Trigonalization
  5. Powers of endomorphism
  6. Jordan normal form
• Factorization
  1. Cholesky / LU
  2. LDU / LDPU
  3. PLU
  4. QR
• Simplex Method
  1. Pablos Problem
• Eucleadian Vector spaces
  1. Dot-Product
  2. Bilinear form
  3. Orthogonality
  4. 2D Perp Operator
  5. 2D Perp-Product
  6. 3D Cross-Product
  7. Self adjugate
• Tensor Products & Duality
  1. Dual Spaces
  2. Duality and scalar products
  3. Tensor products
  4. Multilinear Algebra
• Applications
  1. Markov
  2. Pagerank / SVD
  3. Bisector of two vectors

Number Theory

• Diffie Hellman Key Exchange

Algorithms

• Minimum spanning tree
• Second smallest element in array

Machine Learning

• Linear Regression
• Logistic Regression
• Linear Discriminant Analysis
• Classification and Regression Trees (CART)
• Boosting and AdaBoost
• Random Forest
• Naive Bayes
• k-Nearest Neighbor (kNN)
• Support Vector Machines (SVM)
• Gaussian Process Regression (GPR)

Signal Processing

• Average Filter

Information Theory

Control Theory

• PID Controller

Game Theory

Music Theory

Logics

Localization

Robotics

Optimization

• Linear Programming
• Gradient Descent
• Newton Method
• BFGS
• Line Search
• Simulated Annealing
• Bayesian Optimization

Computer Graphics

• Line-Segment Intersection
• Line-Segment Ellipse Intersection
• Line-Segment Bezier-Curve Intersection
• Mathematics of 2D Hit-testing
• GLSL Functions

Kinematics

• Ackerman Steering
• Wheel Loader Steering

Linux

MySQL

Algebra

• Solving Quadratic Equations

Cheat Sheets

• Git

Proofs

• Vector Rotation using Quaternions
• Construction of a quaternion using two vectors
• N^th derivative of sine and co-sine
• Rounded Corners on Path Segment