Skip to 0 minutes and 4 seconds There is a hidden language that governs chance, uncertainty and predictions. It’s a language of probability.
Skip to 0 minutes and 11 seconds Understanding this language is more crucial today than ever: it’s at the heart of the scientific discoveries, financial strategies and technological innovations defining our era. This course will guide you on a structured journey into the heart of probability theory.
Skip to 0 minutes and 31 seconds This course explores the theory of probability starting with its foundational principles: you will learn essential definitions theorems and methods along with some practical applications. The course introduces fundamental ideas and concepts necessary to understand more complex topics. For example we will explore the idea of a probability space, the concept of random variables and notable examples, the computations of probabilities and expectations. From there we move on to more advanced results from the theory. These include
Skip to 1 minute and 6 seconds two important limit theorems: the weak law of large numbers and the central limit theorem. Probability theory is ever more relevant in today’s world, for example in science
Skip to 1 minute and 17 seconds and engineering: here it is used for modeling uncertainty in physical systems it is applied in signal processing and control theory especially when dealing with noise and certain data.
Skip to 1 minute and 30 seconds Economics and finance: here it’s essential in risk assessment and pricing of financial derivatives; it helps in forecasting and decision making under uncertainty, for example in stock market predictions and insurance modeling.
Skip to 1 minute and 42 seconds It is important in data science and computing: here it provides the foundation for machine learning algorithms, such as bias in inference and mark of chains. It is applied in data analysis to handle uncertainty missing data and randomness in large data sets. It is also used for optimization problems, such as finding the best solution under uncertainty or using Monte Carlo simulations. This course provides a structured approach to understanding key principles of the theory. By the end of the course you will have developed a solid grasp of the subject, and you’ll have the fundamental tools to be able to understand its relevance in different context. Enjoy the course!
