Math/CS 466/666

Fall 2025 University of Nevada Reno

Math 466/666 NUMERICAL METHODS I (3+0) 3 credits

Numerical solution of linear systems, including linear programming; iterative solutions of non-linear equations; computation of eigenvalues and eigenvectors, matrix diagonalization. Prerequisite(s): MATH 330.

Instructor  Course Section                     Time              Room
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Eric Olson  Math 466/666 Numerical Methods I   MWF noon-12:50pm  DMSC106

Course Information

Instructor:: Eric Olson
email:: Please contact me through WebCampus
Office:: MWF 1:00-1:50pm in DMS 238 and through Zoom by appointment
Homepage:: http://fractal.math.unr.edu/~ejolson/466/
Course Textbook:: T.A. Driscoll and R.J. Braun, Fundamentals of Numerical Computation, Julia Edition, SIAM, 2022.; Online web version Julia edition of the textbook.; Unified Julia, MATLAB and Python edition of the textbook.
Supplemental References:: Hosking, Joe, Joyce and Turner, First Steps in Numerical Analysis, 2nd Edition, Arnold, 1996.; Germund Dahlquist and Ake Bjorck, Numerical Methods, Dover, 2003.; Clemens Heitzinger, Algorithms with JULIA, Springer, 2022.
Other Books:: Lloyd Trefethen, Numerical Linear Algebra, Siam 1997.; Justin Solomon, Numerical Algorithms: Methods for Computer Vision, Machine Learning and Graphics, CRC Press, 2015.; Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, Second Edition, Dover, 1978.; Richard Hamming, Numerical Methods for Scientists and Engineers, Second Edition, Dover, 1986.; Endre Suli, David F. Mayers, An Introduction to Numerical Analysis, 1st Edition, Cambridge University Press, 2003.; Jeffery Leader, Numerical Analysis and Scientific Computation, Pearson, 2004.

Class Handouts

Course materials specific for this section of Math 466 are available by clicking on this link. Details for how to access these files may be found on our course page in WebCampus.

Information about Software

The Julia 1.10 Language, official documentation and software download.
Support Materials in Julia, Python and Matlab for the Textbook.
Thomas Breloff, Plots--Powerful Convenience for Visualization in Julia.

Student Learning Outcomes

Upon completion of this course, students will be able to

The effects of rouding error in numerical computation.
Newton's method, interpolation and numerical Linear Algebra.
Practical use of the computer to solve numerical problems.

In-Class Computer Labs

LAB1 due Sep 12

Homework

Exercise 1.1.1(a,b,c), 1.1.3(a,b)
Exercise 1.2.1, 1.2.2, 1.2.3, 1.2.4
Exercise 1.3.3

Lecture Notes

Lecture 1: Floating Point
Lecture 2: Double Precision
Lecture 3: Arithmetic
Lecture 4: Conditioning
Lecture 5: Vandermonde Matrix
Lecture 6: Matrix Operations
Lecture 7: Outer Products
Lab 1: Quadratic Equations
Lecture 8: LU Factorization (mylu.jl)
Lecture 9: Asymptotic Efficiency

Announcements

[10-Sep-2025] Student Discount

The student discount code for the textbook is available but password protected here. Since this discount is available only to enrolled students, the username and password needed for access are given in WebCampus. I will also explain how to obtain the discount code in class.

[03-Sep-2025] Student Discount

I have requested a 20 percent student discount for the printed version of our textbook. Please wait until I hear from the publisher. I am expecting to receive a code that you can use when ordering.

[23-Aug-2025] Setting up Julia

We will be using the Julia edition of Fundamentals of Numerical Computation by Driscoll and Braun. I will set up all necessary software including the Julia programming language and support files for the text in the computing lab reserved for the course. Since the software is free and open source you may wish to set it up at home or on a laptop computer. Instructions how to set up your computing environment are here.

Note that the textbook in available online in a Julia only version as well as a combined Julia, Matlab and Python version. I will focus on Julia in the course. If you are an expert with Matlab or Python you may choose to use those instead; however, I will be unable to provide as much help with those languages.

[25-Aug-2025] Welcome Fall 2025

I am looking forward to seeing you August 25 starting the first week of class.

There will be a number of in-class computing labs and quizzes, a theoretical exam, a practical exam and a final exam. In person attendance is mandatory for all computing labs, quizzes, exams and the final.

Grading

     Theoretical Midterm       50 points
     Practical exam            50 points
     5 Computing Labs          10 points each
     Final                    100 points
    ------------------------------------------
                              250 points total

Exams and quizzes will be interpreted according to the following grading scale:

    Grade        Minimum Percentage
      A                 90 %
      B                 80 %
      C                 70 %
      D                 60 %

The instructor reserves the right to give plus or minus grades and higher grades than shown on the scale if it is believed they are warranted.

Calendar

Aug 25 -- Chapter 1.1: Floating-Point Numbers
Aug 27 -- Chapter 1.2: Problems and Conditioning
Aug 29 -- Chapter 1.3: Algorithms

Sep 01 ***Labor Day***
Sep 03 -- Chapter 1.4: Stability
Sep 05 -- Chapter 2.1: Polynomial Interpolation

Sep 08 -- Chapter 2.2: Computing with Matrices
Sep 10 -- Chapter 2.3: Linear Systems
Sep 12 -- Computing Lab 1

Sep 15 -- Chapter 2.4: LU factorization
Sep 17 -- Chapter 2.5: Efficiency of Matrix Computations
Sep 19 -- Chapter 2.6: Row Pivoting

Sep 22 -- Chapter 2.7: Vector and Matrix Norms
Sep 24 -- Chapter 2.8: Conditioning of Linear Systems
Sep 26 -- Computing Lab 2

Sep 29 -- Chapter 2.9: Exploiting Matrix Structure
Oct 01 -- Chapter 3.1: Fitting Functions to Data
Oct 03 -- Chapter 3.2: The Normal Equations

Oct 06 -- Chapter 3.3: The QR Factorization
Oct 08 -- Chapter 3.4: Computing QR Factorizations (optional)
Oct 10 -- Computing Lab 3

Oct 13 -- Chapter 4.1: The Rootfinding Problem
Oct 15 -- Chapter 4.2: Fixed-point Iteration
Oct 17 -- Chapter 4.3: Newton's Method

Oct 20 -- Chapter 4.4: Interpolation-based Methods
Oct 22 -- Chapter 4.5: Newton for Nonlinear Systems
Oct 24 -- Chapter 4.6: Quasi-Newton Methods

Oct 27 -- Chapter 4.7: Nonlinear Least Squares (optional)
Oct 29 -- Theoretical Midterm
Oct 31 ***Nevada Day***

Nov 03 -- Chapter 5.1: The Interpolation Problem
Nov 05 -- Chapter 5.2: Piecewise Linear Interpolation
Nov 07 -- Computing Lab 4

Nov 10 -- Chapter 5.4: Finite Differences
Nov 12 -- Chapter 5.5: Convergence of Finite Differences
Nov 14 -- Chapter 5.6: Numerical Integration

Nov 17 -- Chapter 6.1: Basics of Initial-Value Problems
Nov 19 -- Chapter 6.2: Euler's Method
Nov 21 -- Computing Lab 5

Nov 24 -- Chapter 6.3: IVP Systems
Nov 26 -- Chapter 6.4: Runge-Kutta Methods
Nov 28 ***Family Day***

Dec 01 -- Chapter 6.5: Adaptive Runge-Kutta
Dec 03 -- Chapter 6.6: Multistep Methods
Dec 05 -- Practical Exam

Dec 08 -- Chapter 6.7: Implementation of Multistep Methods
Dec 10 ***Prep Day***

Dec 17 ***Final Exam at 12:45-2:45pm***

Course Policies

Communications Policy

Lectures and classroom activities will held in person. If you wish to set up an appointment for office hours please send me a message through WebCampus.

Late Policy

Students must have an approved university excuse to be eligible for a make-up exam. If you know that you will miss a scheduled exam please let me know as soon as possible.

AI Policy

In this course you are welcome to use generative artificial intelligence/large language model tools (such as ChatGPT, Claude, Gemini, Grok, Perplexity, etc.). Using these tools aligns with the course learning outcomes/student goals for an in-depth understanding of calculus.

Please be aware that many AI companies collect and store personal information. Please do not enter your confidential information as part of a prompt.

Also, please note that some of these large language models may make up or hallucinate information. These tools may reflect misconceptions and biases of specific data. Students are responsible for checking facts, finding reliable sources for, and making a critical examination of any work that is submitted.

Plagiarism

Students are encouraged to work in groups and consult resources outside of the required textbook when doing the homework for this class. Please cite any sources you used to complete your work including Wikipedia, other books, online discussion groups, generative AI such as ChatGPT as well as personal communications. Note that answers obtained from any source should be verified and fully understood for homework to have a positive learning outcome. In all cases your sources need to be cited.

Exams and quizzes, unless otherwise noted, will be closed book, closed notes and must reflect your own independent work.

Academic Conduct

Bring your student identification to all exams. Work independently on all exams and quizzes. Behaviors inappropriate to test taking may disturb other students and will be considered cheating. Don't send electronic messages, talk or pass notes with other students during a quiz or exam. Homework may be discussed freely. When taking a quiz or exam don't read notes or books unless explicitly permitted. Sanctions for violations are specified in the University Academic Standards Policy.

If you are unclear as to what constitutes cheating, please consult with me.

Statement on Academic Success Services

Your student fees cover usage of the University Math Center, University Tutoring Center, and University Writing and Speaking Center. These centers support your classroom learning; it is your responsibility to take advantage of their services. Keep in mind that seeking help outside of class is the sign of a responsible and successful student.

Equal Opportunity Statement

The University of Nevada Department of Mathematics and Statistics is committed to equal opportunity in education for all students, including those with documented physical disabilities or documented learning disabilities. University policy states that it is the responsibility of students with documented disabilities to speak with the Disability Resource Center during the first week of each semester to discuss appropriate accommodations to ensure equity in grading, classroom experiences and outside assignments. For assistance with accessibility, or to report an issue, please use the Accessibility Help Form. The form is set up to automatically route your request to the appropriate office that can best assist you.

Diversity

This course is designed to comply with UNR Core Objective 10. More information about the core curriculum may be found in the UNR Catalog here.

Statement on Audio and Video Recording

Surreptitious or covert video-taping of class or unauthorized audio recording of class is prohibited by law and by Board of Regents policy. This class may be videotaped or audio recorded only with the written permission of the instructor. In order to accommodate students with disabilities, some students may be given permission to record class lectures and discussions. Therefore, students should understand that their comments during class may be recorded.

Final Exam

The final exams will be held in person at the time listed in the standard schedule of final exams for this section. Namely, the final exam is Wednesday, December 17, 2025 from 12:45-2:45pm in DMS106.

Last Updated: Mon Aug 18 10:26:44 AM PDT 2025