Introduction to Data Science

COURSE OBJECTIVE
For the data to tell a story, data scientists need to make use of statistics. Probability theory provides a foundation and the necessary language for statistics. The knowledge of concepts of probability theory can be used as a backbone of many important concepts in data science. This is why an introduction to data science should essentially contain elements of probability theory. This course is an elementary introduction to probability theory for data scientists. The aim is to gain understanding of the theoretical knowledge with an emphasis on the mathematical foundation of modeling and gain experience with applications of this theory.

By the end of this course, participants will:
(1) have detailed knowledge of mathematics of probability theory;
(2) become familiar with the concepts like axioms of probability, random variables, limit theorems;
(3) understand the bridge between probability theory and practice; (
4) demonstrate a thorough knowledge of the core areas of probability theory and data science.

COURSE CONTENT
This course covers the topics of introductory and elementary probability theory for data scientists and it promises a comprehensive understanding of theoretical and practical applications of probability theory by bridging the theory and practice.

In particular upon a brief discussion of combinatorial analysis, the students will be introduced to axioms of probability and the concepts of conditional probability and independence. Then, the concept of random variables including will be discussed. This part will mainly cover discrete and continuous random variables and jointly distributed random variables. Next, the concept of expectation in probability theory will be discussed. This part will include expectations of sums of random variables, moments, moments generating functions. Finally, students will be briefly introduced to limit theorems such as central limit theorems and laws of large numbers.

TEACHING METHODS
Lectures and tutorials

TYPE OF ASSESSMENT
Intermediate exam – Individual assessment
Final exam – Individual assessment
Individual assignments - Individual assessment

RECOMMENDED BACKGROUND KNOWLEDGE
Knowledge of statistical methods and Python is highly recommended