Modern techniques to analyze data and derive predictions for future events are deeply rooted in mathematical techniques.

The course builds a solid base to understand the concepts behind advanced algorithms used to process, analyze, and predict data and observations and enables students to follow future research, especially in the fields of data-intensive sciences.

The course reviews differentiation and integration and then discusses partial differentiation, differentiation, vector algebra and vector calculus. Matrix calculation and vector spaces are fundamental to many modern data processing algorithms and are discussed in detail. Calculations based on Tensors are introduced.

Common metrics are discussed from an informational, theoretical point of view.

1. Calculus
   1. Differentiation & Integration
   2. Partial Differentiation & Integration
   3. Vector Analysis
   4. Calculus of Variations
2. Integral Transformations
   1. Convolution
   2. Fourier Transformation
3. Vector Algebra
   1. Scalars and Vectors
   2. Addition, Subtraction of Vectors
   3. Multiplication of Vectors, Vector Product, Scalar Product
4. Vector Calculus
   1. Integration of Vectors
   2. Differentiation of Vectors
   3. Scalar and Vector Fields
   4. Vector Operators
5. Matrices and Vector Spaces
   1. Basic Matrix Algebra
   2. Determinant, Trace, Transpose, Complex, and Hermitian Conjugates
   3. Eigenvectors and Eigenvalues
   4. Diagonalization
   5. Tensors
6. Information Theory
   1. MSE
   2. Gini Index
   3. Entropy, Shannon Entropy, Kulback Leibler Distance
   4. Cross Entropy