Primer 1: Mathematics
The Mathematics Primer covers the foundations which underpin the data science and quantitative finance courses.
In particular, the Mathematics Primer covers the following topics:- Linear algebra: vector spaces, linear operators, geometry, matrix decomposition, matrix operations
- Calculus: differentiation, Taylor expansion, integration, monotone and convex functions
- Optimization: smooth programming, convex programming, quadratic regularization, selection problems
- Statistics: representations of distributions, conditioning, normal, lognormal, binary mixture distributions
Syllabus
The course covers in depth the Mathematics topics in the Lab.Linear algebra - fundamentals
• Key notation tenets
• Vector spaces
• Linear transformations
• Inner product spaces
• Metric and normed spaces
Linear algebra - advanced
• Spectral decomposition
• Matrix transpose-square-root
• Matrix operations
Calculus
• Differentiation
• Discrete derivatives
• Taylor expansion
• Integration
• Monotone functions
• Convexity
Optimization
• Fundamental concepts
• Smooth programming
• Convex programming
• Quadratic regularization
• Selection problems
Statistics
• Representations of a distribution
• Conditioning
• Normal distribution
• Lognormal distribution
• Quadratic normal distributions
• Exponential family distributions
• Scenario-probability distributions
• Binary mixtures