Way to Probabilist

Requirements: Analysis

B1-Under Probability

Basic concepts for chances. Offered Spring 2018.

Content: Formulation of random variables, Distribution functions, Conditional probability, Multivariate distributions, MGF, Central limit theorems.

B2-Under Stochastic Processes (General)

Real modeling evolving time. Theoretical, practical and computational! Offered Fall 2018.

Content: Markov chains, Poisson processes, Renewals, CTMC, BM.

B2-Random Walks and Diffusion Processes*

https://en.wikipedia.org/wiki/Random_walk

Partial sum of random variables/movements.

Keywords: Recurrence and transience, Asymptotic behavior.

B3-Random Structures*

Keywords: Probabilistic analysis of algorithms and stochastic optimizations, Random graphs and networks, Integrable probability (combinatorics).

B4-Intro 2 Math Statistical Physics*

The bridge between Probabilistic Math and the real world. In late 19th century, theoretical physicists use probability models to discuss the microscopic phenomena. Since then, probability goes to the direction different from statistics.

Keywords: Gibbs free energy, Ising models, Disordered systems, MCMC

B4-Measure and Probabilistic Models

Probability theory is based on measure theory since 1930's. Offered Fall 2020.

Indistinguishable is typical in physics.