MAT 331 Learning Material

Our Github page:

https://github.com/letaoZ/MAT331

The whole course will be divided into two parts

1) IID random variables-- TWO Theorems and many models

2)Markov Chains-- compare results given by Theorems and computers

Sequentially, our schedules:

• Sample quiz: here, solution

• Week 1 : ALL

• Homework -- written, lab, lab_solution

• Lecture 01: 01/23 Introduction and Basic Probability review -- Chapter 1.2 & 4.1 of Grinstead

• Slides

  • Lab 01: 01/25 basic python

  • Slides , Code

• Week 2 : ALL

• Homework -- written, lab, lab_solution

• Lecture 02: 01/30 Continuous random variables, E(X), Var(X) review-- Chapter 2.2, 5 & 6 of Grinstead

• Slides

  • Lab 02: 02/01 basic python, numpy

  • Slides, Code

• Week 3: ALL

• Homework: No homework, due to quiz next week

• Lecture 03: 02/06 Law of Large Numbers-- Chapter 8.1 of Grinstead

• Slides

• Lab 03: 02/08 Numpy, plot

• Code

• Week 4: ALL

• Homework: written, lab, lab_solution

• Lecture 04: 02/13 Quiz, Central Limit v.s. Law of Large Numbers 9.2 Grinstead;

• what is sampling? -- building a sampler from a uniform distribution -and Inverse_transform_method

• Slides

• Lab 04: 02/15 rand, plot, and sampling

• Inverse Sampling Code, Lab Code, Inverse Sampling Notes

• Week 5: ALL

• Homework: Practice_midterm, Lab,lab_solution

• Lecture 05: 02/20 Central Limit 9.1 of Grinstead

• Application of Central Limit-- Hypothesis Testing. Use of Z table

• slides

• Lab 05: 02/22 Law of Large Number VS Central Limit

• Code

• Week 6: ALL

• Homework: Practice_midterm

• Lecture 06: 02/27 Normal distribution (show up everywhere), Hypothesis Testing, Maximal Likelihood Estimation

• slides

• Lab 06: All you need to know about "Linear Regression"

• Code

• Week 7: ALL

• no Homework

• Lecture 07: 03/06 midterm

• Lab 07: 03/08 arange vs linspace, plotting tricks, and revisit past labs

• Code

• Week 8: Spring Break -- No Homework

• Week 9: ALL

• Homework: written, Lab, Lab_solution

• Lecture 09: Maximal Likelihood Estimation (here)

• slides

• Lab 09: Monte Carlo Estimation

• Code

• Week 10: ALL

• Homework: written, Lab, Lab_solution

• Lecture 10: Finished MLE and linear regression (here), Start learning Markov Chain (chapter 11 of Grinstead)

• slides

• Lab 10: Monte Carlo Estimation and other numerical methods

• Code

• Week 11: ALL

• Homework: written

• Lecture 11: More Markov Chain (chapter 11 of Grinstead) -- power of matrices

• slides

• Lab 11: Timing on different machines, read file in Python, and basic linear algebra

• Code, Download the data files on the bottom of this webpage or go here

• Week 12: ALL

• Homework: written, lab, lab_solution

• Lecture 12: Quiz and More Markov Chain (chapter 11 of Grinstead) -- power of matrices

• slides

• Lab 12: Linear Algebra in Python, Absorbing Markov Chain simulation

• Code

• Week 13: ALL

• Homework: written, lab, lab_solution

• Lecture 13: Stationary matrix, time to absorption, absorption probability

• slides

• Lab 13: Linear Algebra in Python, Absorbing Markov Chain simulation

• Code

• Week 14: ALL

• Homework: Practice Final

• Lecture 14: Quiz and More Markov Chain (chapter 11 of Grinstead) -- power of matrices

• slides

• Week 15: ALL

• Homework: Practice Final, Practice Final Answer Key

• Lecture 15: More applied examples of Markov Chains

• slides