Applied Probability and Uncertainty Analysis
Learn how probability theory helps understand, control, and utilize real-world uncertainty in modern applications.
Learn how probability theory helps understand, control, and utilize real-world uncertainty in modern applications.
This comprehensive course offers a unique perspective on probability theory and its applications in handling real-world uncertainty. Starting with fundamental concepts, the course progresses through universal principles to advanced applications in modern algorithms. Students learn how probability theory can be practically applied to understand and exploit uncertainty, with special focus on Markov chains, Monte Carlo methods, and deep learning applications. The course combines theoretical foundations with practical examples, making complex concepts accessible while maintaining mathematical rigor.
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What you'll learn
Master fundamental probability concepts including random variables and expectation
Understand universal principles like the law of large numbers and central limit theorem
Analyze random processes and their real-world applications
Apply Markov chain theory to practical problems
Implement modern randomized algorithms using probability concepts
Skills you'll gain
This course includes:
PreRecorded video
Graded assignments, exams
Access on Mobile, Tablet, Desktop
Limited Access access
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There are 12 modules in this course
This course provides a comprehensive exploration of probability theory and uncertainty analysis, structured in three main parts. The first section covers fundamental probability concepts including random variables, expectation, and variance. The second part examines universal principles such as the law of large numbers and central limit theorems. The final section focuses on Markov chains and their applications in modern algorithms, including Monte Carlo methods and deep learning. Throughout the course, theoretical concepts are illustrated with practical examples and real-world applications.
Uncertainty: Control vs Exploit
Module 1 · 1 Weeks to complete
Quantification of Uncertainty (1)
Module 2 · 1 Weeks to complete
Quantification of Uncertainty (2)
Module 3 · 1 Weeks to complete
Universal Principle (1): Law of Large Numbers
Module 4 · 1 Weeks to complete
Universal Principle (2): Central Limit Theorem
Module 5 · 1 Weeks to complete
Universal Principle (3): More on Fluctuation
Module 6 · 1 Weeks to complete
Universal Principle (4): Random Processes
Module 7 · 1 Weeks to complete
Universal Principle (5): Universality of Random Processes
Module 8 · 1 Weeks to complete
How to Use Uncertainty? (1)
Module 9 · 1 Weeks to complete
How to Use Uncertainty? (2)
Module 10 · 1 Weeks to complete
How to Use Uncertainty? (3)
Module 11 · 1 Weeks to complete
How to Use Uncertainty? (4)
Module 12 · 1 Weeks to complete
Fee Structure
Instructors
1 Course
Mathematics Expert Advances Probability Theory Education at SNU
Dr. Insuk Seo serves as an Associate Professor in the Department of Mathematical Sciences at Seoul National University, where she specializes in probability theory and stochastic processes. Through her course "Mathematical understanding of uncertainty," she helps students grasp complex concepts in probability theory and its applications. As a faculty member at one of Korea's premier mathematics departments, she contributes to advancing mathematical education and research in uncertainty quantification and stochastic analysis. Her teaching focuses on making advanced mathematical concepts accessible while maintaining rigorous academic standards that SNU is known for.
1 Course
Teaching Assistant Supports Advanced Mathematics Education at SNU
Jeeho Ryu serves as a Teaching Assistant in the Department of Mathematical Sciences at Seoul National University, where he supports instruction in the course "Mathematical understanding of uncertainty." Working alongside Professor Insuk Seo, he helps students grasp fundamental concepts in probability theory, stochastic processes, and mathematical analysis of uncertainty. His role contributes to maintaining SNU's high standards in mathematics education while helping students develop strong theoretical foundations in probability and statistics
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