Math/CS 466/666

Fall 2026 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/466-26/

Course Textbook:
A.C. Faul, A Concise Introduction to Numerical Analysis, CRC Press, 2016.

Abhinav Jha, Numerical Methods, Lecture Notes, IIT Gandhinagar, 2026

Supplemental References:
Driscoll and R.J. Braun, Fundamentals of Numerical Computation, Julia Edition.

Hosking, Joe, Joyce and Turner, First Steps in Numerical Analysis, 2nd Edition, Arnold, 1996.

Germund Dahlquist and Ake Bjorck, Numerical Methods, Dover, 2003.

Other Books:
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.

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

Student Learning Outcomes

Upon completion of this course, students will be able to

In-Class Computer Labs

Homework

Homework 1: Due Friday Sep 11
pdf
Homework 2:
under construction
Homework 3:
under construction
Homework 4:
under construction
Homework 5:
under construction
Homework 6:
under construction

Projects

Project 1:
under construction

Lecture Notes

Announcements

[11-Sep-2026] Julia Code

I have translated the Matlab code appearing on page 30 in the text into Julia as myLU.jl.

[09-Sep-2026] Julia Code

I have translated the Matlab code appearing on page 25 in the text into Julia as forward.jl.

[24-Aug-2026] Welcome Fall 2026

I am looking forward to seeing you August 24 starting the first week of class.

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

Grading

     Midterm                   50 points
     10 Computing Labs         10 points each
     Project                   20 points
     6 Homeworks                5 points each
     Final                    100 points
    ------------------------------------------
                              300 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 24 -- 1.1 Floating Piont Arithmetic
       \\ 1.2 Overflow and Underflow
        \ 1.3 Absolute, Relative Error, Machine Epsilon
Aug 26 -- 1.4 Forward and Backard Error Analysis
        \ 1.5 Loss of Significance
Aug 28 -- Lab 1 Quadratic Equations

Aug 31 -- 1.6 Robustness
        \ 1.7 Error Testing and Order of Convergence
Sep 02 -- 1.8 Computational Complexity
        \ 1.9 Condition
Sep 04 -- Lab 2 Scientific Visualization

Sep 07 ***Labor Day***
Sep 09 -- 2.1 Simultaneous Linear Equations
        \ 2.2 Gaussian Elimination and Pivoting
Sep 11 -- 2.3 LU Factorization
        \ 2.4 Cholesky Factorization

Sep 14 -- 2.5 QR Factorization
        \ 2.6 The Gram-Schmidt Algorithm
Sep 16 -- 2.7 Givens Rotations
        \ 2.8 Householder Reflections
Sep 18 -- Lab 3 Solving Linear Systems

Sep 21 -- 2.9 Linear Least Squares
        \ 2.10 Singular Value Decomposition
Sep 23 -- 2.11 Iterative Schemes and Splitting
        \ 2.12 Jacobi and Gauss--Seidel Iterations
Sep 25 -- 2.13 Relaxation
        \ 2.14 Steepest Descent Method

Sep 28 -- 2.15 Conjugate Gradients
        \ 2.16 Krylov Subspaces and Pre-Conditioning
Sep 30 -- 2.17 Eigenvalues and Eigenvectors
        \ 2.18 The Power Method
Oct 02 -- Lab 4 The Spectral Norm

Oct 05 -- 2.19 Inverse Iteration
          2.20 Deflation
Oct 07 -- 3.1 Lagrange Form of Polynomial Interpolation
Oct 09 -- Lab 5 Polynomial Interpolation

Oct 12 -- 3.2 Newton Form of Best Approximations
          3.3 Polynomial Best Approximations
Oct 14 -- 3.4 Orthogonal Polynomials
          3.5 Least-Squares Polynomial Fitting
Oct 16 -- Lab 6 Polynomial Fitting

Oct 19 -- Review
Oct 21 -- Midterm
Oct 23 -- 3.6 The Peano Kernel Theorem
        \ 3.7 Splines

Oct 26 -- 4.1 Bisection, Regula Falsi and Secant Method
        \ 4.2 Newton's Method
Oct 28 -- 4.3 Broyden's Method
        \ 4.4 Householder Methods
Oct 30 ***Nevada Day***

Nov 02 -- 4.5 Mueller's Method
        \ 4.6 Inverse Quadratic Interpolation
Nov 04 -- 4.7 Fixed Point Iteration Theory
        \ 4.8 Mixed Methods
Nov 06 -- Lab 7 Newton's Method

Nov 09 -- 5.1 Mid-Point and Trapezium Rule
        \ 5.2 The Peano kernel Theorem
Nov 11 -- 5.3 Simpson's Rule
        \ 5.4 Newton--Cotes Rules
Nov 13 -- Lab 8 Polynomials and Eigenvalues

Nov 16 -- 5.5 Gaussian Quadrature
        \ 5.6 Composite Rules
Nov 18 -- 5.7 Multi-Dimensional Integration
        \ 5.8 Monte Carlo Methods
Nov 20 -- Lab 9 Gaussian Quadrature

Nov 23 -- 6.1 One-Step Methods
        \ 6.2 Multistep methods, Order and Cnosistency
Nov 25 -- 6.3 Order Conditions
        \ 6.4 Stiffness and A-Stability
Nov 27 ***Family Day***

Nov 30 -- 6.6 Backward Differentiation Formulae
          6.7 The Milne and Zadunaisky Device
Dec 02 -- 6.8 Rational methods
          6.9 Runge--Kuta Methods
Dec 04 -- Lab 10 Numerical Integration

Dec 07 -- Review
Dec 10 ***Prep Day***

Dec 16 ***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 or Grok. Using these tools aligns with the course learning outcomes/student goals for an in-depth understanding of numerical methods. Note that answers obtained from any source should be verified and fully understood for homework to have a positive learning outcome.

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 note that some of these large language models can 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, personal communications as well as generative AI. Adding the text "please include all relevant citations with your output" to the prompt can help avoid missing citations.

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.

Diversity

This course is designed to comply with the UNR Core Objective 10 requirement on diversity and equity. More information about the core curriculum may be found in the UNR Catalog.

Statement on Academic Success Services

Your student fees cover usage of the University Math Center, (775) 784-4433; University Tutoring Center, (775) 784-6801; and University Writing & Speaking Center, (775) 784-6030. 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.

Statement of Disability Services

Any student with a disability needing academic adjustments or accommodations is requested to speak with me or the Disability Resource Center (Pennington Achievement Center Suite 230) as soon as possible to arrange for appropriate accommodations. This course may leverage 3rd party web/multimedia content, if you experience any issues accessing this content, please notify your instructor

Mental Health Support Statement

There are times when you may experience difficulties in life, and you may benefit from seeking help. Mental health services are available to you as a student at no additional cost through Counseling Services at the Pennington Student Achievement Center. This includes same-day in-person and tele mental health initial consultations, brief individual counseling, and group counseling sessions. Limited same-day appointments can be scheduled online via Counseling Services or by calling 775-784-4648. Additional brief drop-in "Let's Talk" student consultations are also available in the Counseling Services Annex located at the southwest corner of Great Basin Hall.

Veteran Statement

Veterans, Reservists, National Guard and military connected family members may wish to check the office of Veteran Services for benefits and support. Besides processing VA educational benefits, the department offers a variety of programs year-round to support student academic and personal success while transitioning to higher education and throughout your educational experience. They welcome inquiries regarding VA benefits and assist in navigating resources, the campus, and in the Reno community.

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 16, 2026 from 12:45-2:45pm in DMS106.
Last Updated: Mon Aug 18 10:26:44 AM PDT 2026