SNUx: Mathematical understanding of uncertainty offered by Seoul National University
- Public University
- Estd. 1946
SNUx: Mathematical understanding of uncertainty at SNU Overview
Duration | 12 weeks |
Total fee | ₹4,492 |
Mode of learning | Online |
Official Website | Go to Website  |
Course Level | UG Certificate |
SNUx: Mathematical understanding of uncertainty at SNU Highlights
- Earn a certificate from Seoul National University
- World-class institutions and universities
- Access to course materials
- Graded assignments and exams
SNUx: Mathematical understanding of uncertainty at SNU Course details
- For individuals who want to enhance their skills
- Basic probability theory including random variable, expectation, and variance
- Universal principles in probability theory such as law of large numbers, central limit theorem, and large deviation principles, and their applications
- Heavy-tailed phenomenon
- Theory random processes and applications to real world problem
- Theory of Markov chains and applications to simulation, randomization, and deep learning
- The first part of the series (three weeks) discusses the basics of probability theory such as the mathematical formulation of probability, random variables, expectation, and variance in a creative way as a means to quantify uncertainty
- The second part of the series (five weeks) introduces a few universal principles of probability theory. Standard theorems in probability theory such as the law of large numbers and the central limit theorems are introduced as fundamental examples of universal principles, and hence, are discussed from a unique perspective
- The third part of the series (four weeks) introduces the concept of Markov chain and then discusses various randomized algorithms as examples of Markov chains
SNUx: Mathematical understanding of uncertainty at SNU Curriculum
Lecture 1. Uncertainty: Control vs Exploit
A toy example
Control the uncertainty
Exploit the uncertainty
Lecture 2. Quantification of Uncertainty (1): Probability and Random Variables
Mathematical formulation of probability
Random variables
Independence
Lecture 3. Quantification of Uncertainty (2): Expectation and Variance
Expectation
Variance and standard deviation
Applications
Lecture 4. Universal Principle (1): Law of large numbers
Introduction to universality
Law of large numbers
Proof of law of large numbers
Applications
Lecture 5. Universal Principle (2): Central limit theorem
Central limit theorem
Applications to statistics
Lecture 6. Universal Principle (3): More on fluctuation
Heavy-tailed random variables
Large deviation principles
Lecture 7. Universal Principle (4): Random processes
Introduction to random processes
Simple random walk on a line
Applications to gambling
Lecture 8. Universal Principle (5): Universality of random processes
Universality in random walks
Galton-Watson tree
Lecture 9. How to use uncertainty? (1): Introduction to Markov Chains
Markov processes
Markov chains
Examples
Lecture 10. How to use uncertainty? (2): Universal principles of Markov chains
Stationary distribution
Universal principles for Markov chains
Lecture 11. How to use uncertainty? (3): MCMC and Cutoff phenomenon
Markov chain Monte Carlo (MCMC)
Markov chain mixing theory
Cutoff phenomenon
Lecture 12. How to use uncertainty? (4): Stochastic optimizations and deep learning
Gradient descent
Stochastic gradient descent
Mini-batch gradient descent
SNUx: Mathematical understanding of uncertainty at SNU Faculty details
SNUx: Mathematical understanding of uncertainty at SNU Entry Requirements
- Education: Graduate
- Not mentioned
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SNUx: Mathematical understanding of uncertainty at SNU Contact Information
1 Gwanak-ro, Gwanak-gu, Seoul, South Korea
Seoul ( Other - South Korea)
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