# 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.

## 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
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
• 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

## 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)

## Control Theory

• PID Controller

## Optimization

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