Professional Course

Mathematical Understanding of Uncertainty

edX, Online
12 weeks
49 USD
Next course start
Inquire for more information See details
Virtual Classroom
12 weeks
49 USD
Next course start
Inquire for more information See details
Virtual Classroom
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Course description

Mathematical Understanding of Uncertainty

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. These universal principles are used to explain uncertainty in the real-world, and numerous interesting examples are introduced for illustration.

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. For example, riffle shuffle of playing cards, Markov chain Monte Carlo, and deep learning algorithms are discussed based on the modern theory of Markov chains.

The lecture series requires knowledge of calculus, but knowledge of higher mathematics and probability is not a pre-requisite.

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  • Virtual Classroom
  • Online
  • English

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Training content

  • Uncertainty: Control vs Exploit
  • Quantification of Uncertainty (1): Probability and Random Variables
  • Quantification of Uncertainty (2): Expectation and Variance
  • Universal Principle (1): Law of large numbers
  • Universal Principle (2): Central limit theorem
  • Universal Principle (3): More on fluctuation
  • Universal Principle (4): Random processes
  • Universal Principle (5): Universality of random processes
  • How to use uncertainty? (1): Introduction to Markov Chains
  • How to use uncertainty? (2): Universal principles of Markov chains
  • How to use uncertainty? (3): MCMC and Cutoff phenomenon
  • How to use uncertainty? (4): Stochastic optimizations and deep learning

Course delivery details

This course is offered through Seoul National University, a partner institute of EdX.

3-4 hours per week


  • Verified Track -$49
  • Audit Track - Free

Certification / Credits

What you'll learn

  • 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.

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