# Foundations of Data Science II

## Module description

Continuing directly from Foundations of Data Science I, this module covers further fundamental aspects of data science and analytics. You will consolidate the knowledge acquired on FDS I and further develop your mathematical knowledge and skills, including basic elements of calculus, linear algebra, continuous probability theory and statistics.

We will show you how to use the popular and powerful language Python to solve computational tasks from these mathematical subjects, and acquaint you with popular Python libraries and packages for programming to solve problems arising from calculus, probability theory and statistics.

### Indicative syllabus

• Differentiation
• Indefinite and definite integration
• Solving systems of polynomial equations (e.g. Newton’s methods) and basic optimisation algorithm (e.g. gradient descent)
• Continuous probability (e.g. random variables, pdf, cdf, expectation, variance and correlation)
• Common distribution families (e.g. Poisson, normal distribution)
• Probabilistic inequalities and concentration (e.g. LNT, CLT)
• Statistical testing (e.g. hypothesis testing, chi-squared testing)
• Sampling and confidence intervals
• Eigenvalues and eigenvectors
• SVD decomposition
• Tools: Python

## Learning objectives

By the end of this module, you will have:

• knowledge of basic calculus, further linear algebra and matrix theory, continuous probability theory and statistics, and relevant Python libraries and packages
• satisfactory skills of programming in Python to solve computational tasks from calculus, linear algebra, continuous probability theory and statistics
• an understanding of the link between the basic knowledge acquired from the module and data science/analytics applications.