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
- Random Variable
- Expected Value
- Conditional Probability
- Density / Mass
- Independence
- Convergence
- Simulation
- Statistics
- Monte Carlo integration
Stochastic Processes
- Posson-Point-Process
- Gaussian Process
- Markov Chains
Linear Algebra
- System of linear equatnions
- Vectors
- Addition, scalar multiplication
- Hyperplanes
- Vector spaces
- Linear Transformations
- Basis & Dimensions
- Matrix
- Linear Transformations
- Block Matrix
- Square Matrix
- Inverse
- Gauss-Jordan Elimination
- Trace & Determinants
- Definition
- Existence
- Determinant & Volume
- Norms
- P-Norms
- Condition number
- Spectral Radius
- Series and sequence of linear operators
- Convergence
- Eigenvalues
- Definition
- Characteristic polynomial
- Diagonalizable matrix
- Trigonalization
- Powers of endomorphism
- Jordan normal form
- Factorization
- Cholesky / LU
- LDU / LDPU
- PLU
- QR
- Simplex Method
- Pablos Problem
- Eucleadian Vector spaces
- Dot-Product
- Bilinear form
- Orthogonality
- 2D Perp Operator
- 2D Perp-Product
- 3D Cross-Product
- Self adjugate
- Tensor Products & Duality
- Dual Spaces
- Duality and scalar products
- Tensor products
- Multilinear Algebra
- Applications
- Markov
- Pagerank / SVD
- Bisector of two vectors
Number Theory
Algorithms
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
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