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