5EZCO - Mathematics 3: Probability theory

Mathematics 3 is a core course for the Bachelor program Electrical Engineering.

Mathematics is the foundation upon which engineering sciences are built and is at the core of disciplines that drive technological developments and innovations in the digital age. This course introduces students to the mathematics of probability and statistics, indispensable in the fields of communication, signal processing, control, quantum science, and machine learning, among others.

Course structure

The course is structured into 5 chapters, each taught over 1-2 weeks:

• Ch.1: Introduction, axioms and models (1 week/2 lectures)
• Ch.2: Discrete random variables (1.5 weeks/3 lectures)
• Ch.3: Continuous random variables (1.5 weeks/3 lectures)
• Ch.4: Multiple (i.e. two) random variables (1-1.5 week/2-3 lectures)
• Ch.5: Applications (1.5-2 weeks/3-4 lectures)

Learning goals

This course will introduce student to probability theory and statistics, and develop the students’ ability to construct and analyse probabilistic models in a way that combines mathematical rigour and intuitive understanding. The ultimate objective is to enable students to use the theory to model, analyse and solve engineering systems and problems. After completing the course, the student should be able to:

• Explain basic concepts and techniques of probability and random variables.
• Derive and compute various properties of discrete and continuous random variables.
• Explain concepts and definitions related to stochastic processes.
• Derive basic estimators and understand their performances.
• Formulate how the above concepts and techniques are applied to technical engineering problems.

Lecturers