Math/CS 466/666
466/666 NUMERICAL METHODS I (3+0) 3 credits
Instructor Course Section Time Room
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Eric Olson Math 466/666 Numerical Methods I TR 3:00-4:15pm DMS106
Course Information
- Instructor:
- Eric Olson
- email:
- ejolson at unr dot edu (better to contact me through
WebCampus).
- Office:
- DMS 238 and through Zoom by appointment.
- Homepage:
- https://fractal.math.unr.edu/~ejolson/466-21/
- Assistant:
- Jordan Blocher
- Live Stream:
- If you can't come to class due to sickness, quarantine or other
reasons, please join via the Zoom link in
WebCampus.
- Required Texts:
- Justin Solomon,
Numerical Algorithms: Methods for Computer
Vision, Machine Learning and Graphics, CRC Press, 2015.
- Supplemental Texts on Numerical Methods:
- 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.
Information about Software
Lecture Notes
Student Learning Outcomes
Upon completion of this course
- Students will be able to implement a numerical method to solve a
nonlinear equation using the bisection method and Newton's method.
- Students will be able to solve linear systems using direct and
iterative methods.
- Students will be able to construct interpolating functions.
Announcements
[13-Dec-2021] Exam 1 Solutions
I have posted my solutions of Exam 1 for your
convenience. Please look at my solutions to see if there are
any improvements you can make to yours or I can make to mine.
[11-Dec-2021] Homework 2 Solutions
I have posted my solutions of Homework 2 for your
convenience. Please look at my solutions to see if there are
any improvements you can make to yours or I can make to mine.
[15-Dec-2021] Final Exam
The final exam will be held in person on Wednesday, December 15
from 2:30 to 4:30pm at DMS 106. Given the excellent results on
the computing exam last week, the final will consist of only a
written exam and no computing component. Please prepare and know
the topics listed on review for the in-class midterm that was
given October 26 along with the following additional topics:
- State the power method for finding the eigenvector corresponding
to the (unique) eigenvalue of largest magnitude for a matrix A
(Oct 7 and 19)
- Given the eigenvalues of B=ATA be able to compute the
matrix 2 norm of A (Nov 9)
- Be able to find an interpolating polynomial through given
points (xi,yi) using the Lagrange basis functions
(Nov 18)
- Proof of the polynomial interpolation theorem (Nov 16 and 18)
- Relationship between the QR and Cholesky factorization (Homework 2)
- Analysis of the matrix A=uvT where uTv=1 (Homework 2)
Note this is a closed-book, closed-notes, no computers and calculators exam.
Attendance is mandatory to take the test unless you have made arrangements
with the DRC or have other special considerations.
Please bring your student identification to the final.
[02-Dec-2021] Computing Exam
The in-class computing exam will be Thursday December 2. This will
be an open book, open notes, open web browser and web search exam.
Do not use any email, post questions to forums or use any other
type of electronic messaging service during the exam.
In preparation please know how to perform the following:
- Given a matrix A find the Hausholder reflector H so
the first column of HA is a vector of the form ce1,
that is, the first column has been reduced to a non-zero
element below which are all zeros.
- Perform n iterations of Newtons method for a specified
function f starting from a specified initial condition x0.
- Given a matrix A and a starting vector X0 perform
n iterations of the power method to approximate the eigenvector whose
eigenvalue is largest in magnitude. Use the Rayleigh quotient (least
squares) to approximate the eigenvalue.
- Given a specified sequence an use the Kahan summation
formula to accurately find the sum for n=1,2,...,N of the terms an.
That is, compute Σn=1N an using
Kahan summation.
- Find the interpolating polynomial through specified points
(xk,yk) for k=1,2,...,n and evaluate that
polynomial at the point x=α.
You will be asked to complete two of four problems based on the
above material to receive full credit. For Math 666 or extra
credit please complete a third problem. Note this exam is meant
to test that you can use the computer for practical computation.
It is fine to bring your own notebook computer to use during the
exam but please make sure you have sufficient power and that the
software is properly installed.
[15-Dec-2021] Final Exam
The final exam will be held on Wednesday,
December 15 from 2:30 to 4:30pm at DMS 106.
[15-Dec-2021] Project 2
This project explores the
polar decomposition of an invertible matrix.
Please form your own teams on
WebCampus consisting of 3 to 4 students and
welcome any student who wishes
to join your group so no people are left out.
If you prefer to work independently that is also fine.
Each team should present their work in the form of a typed
report using clear and properly punctuated English.
Pencil and paper calculations may be typed or hand written.
Where appropriate include full program listings and output.
Every team member should participate in the work and
be prepared to independently answer questions concerning
the material.
One report per team
must be submitted through WebCampus as a single pdf file
to complete this project.
[27-Oct-2021] Homework 2
Please work the following problems from our text:
- Problems 5.7, 5.8, 5.12
- Problems 6.3, 6.6, 6.11
These problems will be due on Nov 30, 2021.
[10-Nov-2021] Project 1 Solutions
I have posted my solutions of Project 1 for your
convenience. Please look at my solutions to see if there are
any improvements you can make to yours or I can make to mine.
[26-Oct-2021] In Class Written Exam
There will be a written exam in class on Tuesday October 26
covering the following topics from the lecture and homework:
- Statement of Newton's method (Aug 26)
- Proof and interpretation of quadraditic convergence (Aug 26)
- Example of loss of precision (Sep 7)
- Backwards error analysis and condition number (Sep 7 and Sec 23)
- Compute matrix 1 and ∞ norms (Sep 21)
- Prove Hausholder reflector is an othogonal matrix (Sep 30)
- Eigenvectors of distinct eigenvalues are independent (Oct 14)
- Eigenvalues of a Hermitian matrix are real (Oct 14)
- Factor a matrix A into LU by hand (Homework 1)
- Operations for interval arithmetic (Homework 1)
No computers or calculators will be allowed.
Attendance is mandatory to take the test unless you have made
arrangements with the DRC or have other special considerations.
Please bring your student identification to the exam.
[17-Oct-2021] Homework 1 Solutions
I have posted my solutions of Homework 1 for your
convenience. Please look at my solutions to see if there are
any improvements you can make to yours or I can make to mine.
[01-Oct-2021] Homework 1 Due
Please turn in your homework as a scanned pdf file to WebCampus
by midnight on Friday October 1.
[24-Sep-2021] Project 1
This project explores the Cholesky factorization of a
symmetric positive definite matrix.
For this project the class has not been randomly grouped
into teams. Instead, please form your own teams on
WebCampus consisting
of 3 to 4 students.
Please welcome any student who wishes
to join your group so no people are left out.
If you prefer to work independently that is also fine.
Each team should present their work in the form of a typed
report using clear and properly punctuated English.
Pencil and paper calculations may be typed or hand written.
Where appropriate include full program listings and output.
Every team member should participate in the work and
be prepared to independently answer questions concerning
the material.
One report per team
must be submitted through WebCampus as a single pdf file
to complete this project.
[09-Sep-2021] Homework 1
Please work the following problems from our text:
- Problems 2.4, 2.5, 2.9, 2.11
- Problems 3.1, 3.3, 3.11, 3.12
These problems will be due on Oct 1, 2021.
[23-Aug-2021] Welcome to Fall 2021
I am looking forward to seeing you Tuesday. As you may know, the campus
currently has mandatory mask rules in place. To avoid people getting sick
while attending class not only is it import to follow these and related
guidelines, but to understand the spirit in which these rules were made.
Please employ your best judgment to prevent the spread of the epidemic
and its contagious variants.
Do not come to class if you are sick--even if it's something other than
COVID-19. If you are subject to quarantine because of exposure to the
disease, please stay home. If you are already sick or in quarantine and
can't come on the first day of class, check the
WebCampus page for this
course later today for the Zoom link and other information.
While this section of Math 466/666 is not high-flex, in anticipation of
increased absences due to the epidemic I will live-stream our class
meetings each day at a link available in WebCampus and maintain an
online archive of course materials including lecture notes, assignments
and other announcements. Unless there is a change in policy, in-person
attendance will be required for all exams and the final.
Last year I discovered that Zoom worked well for office hours as it
provided greater flexibility to meet with students: Our meeting times
can be arranged around individual schedules and there is no need to go
to campus just to ask a question. Please send me a message on WebCampus
to schedule all office hours.
As in previous semesters, students should avoid congregating around
instructional space entrances before or after class sessions and exit
the instructional space immediately after the end of instruction to
help ensure social distancing and allow for the persons attending the
next scheduled class session to enter. Note that students who cannot
wear a face covering due to a medical condition or disability, or who
are unable to remove a mask without assistance may seek accommodation
through the Disability Resource Center.
[22-Aug-2017] Textbook Announced
The primary textbook we will be using for the course
is Numerical Algorithms: Methods for Computer Vision, Machine Learning
and Graphics by Justin Solomon.
A free pdf version
of this book is available from Justin's website at CSAIL MIT.
This is a standard numerical methods text covering the standard
topics that includes a few remarks about computer vision and machine learning.
Hardbound versions may be obtained from
Amazon and other online booksellers
Grading
1 Exam on Theory 50 points
1 Exam on Computing 50 points
1 Final Exam 100 points
2 Homework Assignments 20 points each
2 Programming Projects 30 points each
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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 he believes they are warranted.
Final Exam
The final exam will be held in person on Wednesday, December 15
from 2:30 to 4:30pm at DMS 106.
Course Policies
Communications Policy
Lectures and classroom activities will held in person and live streamed
through through Zoom at the scheduled meeting time listed in MyNevada
for this course. Please check
the canvas page for the Meeting ID and Join URL under the Zoom tab
if you are unable to make it to class.
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. Homework may be turned in late--with a
possible deduction of points depending on the circumstances--as long as
I have not already graded the assignment.
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 as well as personal communications. Exams
and quizzes, unless otherwise noted, will be closed book, closed notes
and must reflect your own independent work. Please consult the section
on academic conduct below for additional information.
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
here.
COVID-19 Policies
Statement on COVID-19 Training Policies
Students must complete and follow all guidelines as stated in the Student
COVID-19 Training modules, or any other trainings or directives provided
by the University.
Statement on COVID-19 Face Coverings
In response to COVID-19, and in alignment with State of Nevada Governor
Executive Orders, Roadmap to Recovery for Nevada plans, Nevada System
of Higher Education directives, the University of Nevada President
directives, and local, state, and national health official guidelines
face coverings are required at all times while on campus, except when
alone in a private office. This includes the classroom, laboratory,
studio, creative space, or any type of in-person instructional activity,
and public spaces.
A "face covering" is defined as a covering that fully covers a person's
nose and mouth, including without limitation, cloth face mask, surgical
mask, towels, scarves, and bandanas (State of Nevada Emergency Directive 024).
Students that cannot wear a face covering due to a medical condition or
disability, or who are unable to remove a mask without assistance may seek
an accommodation through the Disability Resource Center.
Statement on COVID-19 Social Distancing
Face coverings are not a substitute for social distancing. Students shall
observe current social distancing guidelines where possible in accordance
with the Phase we are in while in the classroom, laboratory, studio,
creative space (hereafter referred to as instructional space) setting and
in public spaces. Students should avoid congregating around instructional
space entrances before or after class sessions. If the instructional
space has designated entrance and exit doors students are required to
use them. Students should exit the instructional space immediately after
the end of instruction to help ensure social distancing and allow for
the persons attending the next scheduled class session to enter.
Statement on COVID-19 Disinfecting Your Learning Space
Disinfecting supplies are provided for you to disinfect your learning
space. You may also use your own disinfecting supplies.
Contact with Someone Testing Positive for COVID-19
Students must conduct daily health checks in accordance with CDC
guidelines. Students testing positive for COVID-19, exhibiting
COVID-19 symptoms or who have been in direct contact with someone
testing positive for COVID-19 will not be allowed to attend in-person
instructional activities and must leave the venue immediately. Students
should contact the Student Health Center or their health care provider to
receive care and who can provide the latest direction on quarantine and
self-isolation. Contact your instructor immediately to make instructional
and learning arrangements.
Local, State and Federal COVID-19 Information
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.
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.
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 over Zoom or in the classroom
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.
Final Exam
The final exam will be held in person on Wednesday, December 15
from 2:30 to 4:30pm at DMS 106.
Last Updated:
Tue Nov 23 08:39:53 AM UTC 2021