Probability and Statistics for Computing and Machine Learning

Department: 
MATH
Course Number: 
3740
Hours - Lecture: 
3
Hours - Total Credit: 
3
Typical Scheduling: 
Every Spring

This 3-credit hour course introduces essential concepts in probability and statistics for students in the Mathematics and Computing undergraduate major.The course focuses on and works toward concepts in probability and statistics that are important for problems in computing and machine learning, such as statistical inference, in particular parameter estimation, and sampling/simulation methods such as Monte Carlo methods.  This is in contrast to topics in hypothesis testing and confidence intervals that may be more important to students in the natural sciences.  

The course will be required for all students in the Mathematics and Computing major, whatever their chosen concentration.  It is designed to use computing to explore probability and statistical concepts and integrates mathematical and computational thinking in teaching the topics of the course.

 

MATH 3740 is crosslisted with CX 3740.   

Prerequisites: 

Multivariable Calculus: MATH 2550, 2551, or 2561. 

Course Text: 

  • Modern Introduction to Probability and Statistics: Understanding Why and How, Dekking et al., Springer 

  • Probability and Statistical Inference, Hogg, Tanis, and Zimmerman, 9th edition, Pearson 

Topic Outline: 

Week 

Topic 

1 

Introduction to probability 

2 

Random variables, expectation and variance 

3-4 

Discrete and continuous probability distributions, probability density and mass functions 

5-6 

Joint random variables, independence, conditional probability, covariance 

7-8 

Concentration inequalities and central limit theorems 

9-10 

Maximum likelihood estimation 

11 

Bayesian estimation  

12 

Statistical models of linear regression and classification 

13 

goodness-of-fit tests  

14 

Bayesian simulation 

15 

Markov chain Monte Carlo