Computational Methods for Simulation and Machine Learning

Department: 
MATH
Course Number: 
4740
Hours - Lecture: 
3
Hours - Total Credit: 
3
Typical Scheduling: 
Every Fall

This course introduces students to the essential methods and tools important for Mathematics and Computing. It provides a comprehensive introduction to numerical methods fundamental in modeling, simulation and machine learning. This course will help students to establish an understanding of algorithmic approaches to tackle real-life problems involving matrix computations, optimization, and differential equations.  

MATH 4740 is cross-listed with CX 4740. 

Prerequisites: 

Multivariable Calculus (MATH 2550, 2551, or 2561) and MATH 3406

Course Text: 

The course is based on lecture notes that are collected from different books or research papers. Here are some references: 

 

  • Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong, Cambridge University Press, 2020. 

  • Pattern Recognition and Machine Learning, Chris Bishop, Springer.  

  • Mathematics Aspects of Deep Learning, edited by Philip Grohs and Gitta Kutyniok, Cambridge University Press, 2023.  

Topic Outline: 

Week 

Topic 

1 

Introduction to numerical methods for simulation and machine learning and error analysis 

2 

Topics in numerical linear algebra: QR factorization and least squares 

3-4 

Topics in numerical linear algebra: conditioning and stability 

5-6 

Systems of equations 

7-8 

Iterative methods 

9 

Interpolation and Polynomial Approximation 

10 

Introduction to optimization  

11-12 

First and second order methods for unconstrained optimization 

13 

Convergence analysis in optimization  

14 

Stochastic methods in optimization 

15 

Computational methods for simulation and machine learning