Probability and Statistics: To p or not to p

Course Description

Embark on an exciting journey into the world of probability and uncertainty with this comprehensive course offered by SNUx. "Probability and Statistics: To p or not to p" is an introductory-level course designed to provide students with a deep understanding of probability theory, its universal principles, and real-world applications. This 12-week course is divided into three parts, each focusing on essential aspects of probability and its practical use in various fields.

What Students Will Learn

Students will gain a solid foundation in probability theory, including:

• Basic concepts such as random variables, expectation, and variance
• Universal principles like the law of large numbers and central limit theorem
• Heavy-tailed phenomena and large deviation principles
• Theory of random processes and their real-world applications
• Markov chains and their use in simulation, randomization, and deep learning

Pre-requisites

The course requires knowledge of calculus. However, prior knowledge of higher mathematics and probability is not necessary.

Course Content

• Basics of probability theory
• Mathematical formulation of probability
• Random variables, expectation, and variance
• Universal principles in probability theory
• Law of large numbers and central limit theorem
• Heavy-tailed phenomena
• Random processes and their applications
• Markov chains and their universal principles
• Markov chain Monte Carlo (MCMC)
• Stochastic optimization and deep learning algorithms

Who This Course Is For

This course is ideal for:

• Students interested in mathematics, statistics, or data science
• Professionals looking to enhance their understanding of probability and its applications
• Anyone curious about the role of uncertainty in various fields and how it can be quantified and exploited

Real-World Applications

The skills acquired in this course have numerous real-world applications, including:

• Data analysis and interpretation in various industries
• Financial modeling and risk assessment
• Machine learning and artificial intelligence
• Scientific research and experimentation
• Decision-making under uncertainty in business and policy-making
• Optimization of processes in engineering and manufacturing
• Simulation and modeling in fields such as physics, biology, and social sciences

Syllabus