Mathematics 330 Homepage

Spring 2025 University of Nevada Reno

330 LINEAR ALGEBRA I (3+0) 3 credits

Vector analysis continued; abstract vector spaces; bases, inner products; projections; orthogonal complements, least squares; linear maps, structure theorems; elementary spectral theory; applications. Corequisite(s): MATH 283 R.

Instructor  Course Section                     Time
------------------------------------------------------------------------
Eric Olson  Math 330-1001 Linear Algebra       10:00-10:50AM MWF PE104

Course Information

Instructor:: Eric Olson
email:: Please contact me through WebCampus
Office:: MWF 11:00-11:50am in DMSC 238 and through Zoom by appointment
Homepage:: http://fractal.math.unr.edu/~ejolson/330/
Required Texts:: Linear Algebra and Its Applications, n-th Edition by David C. Lay.; https://www.pearson.com/mylab (class registration code)
Other resources:: MIT Open Courseware, Gilbert Strang, Spring 2010.; 18-06-linear-algebra-spring-2010; Introduction to Applied Linear Algebra, Boyd and Vandenberghe.; http://vmls-book.stanford.edu/

Student Learning Outcomes

Upon completion of this course, students will be able to

Solve linear systems using Gaussian elimination.
Minimize least squares by Gram-Schmidt orthogonalization.
Find LU, QR and UΣV^T matrix factorizations.

Lecture Notes

Announcements

[28-Feb-2025] Exam 1 Review

The first in-class exam will be February 28 and cover up to and including Section 2.5. Here is a sample exam to help you review for the exam.

Sample for Exam 1

[22-Jan-2025] Welcome Spring 2025

My lecture notes should complement the notes you take in class. I'd recommend comparing the notes you take with the ones I post after class along with the relevant sections from the text. Then use these three sources of information to create a final version of your notes. In my experience reviewing the lecture in this way is important.

There will be online exercises available from the Pearson MyLab webpage. In addition to the exercises and written homework, there will be two exams and a final exam. In person attendance is mandatory for all exams and the final.

Grading

     Exam 1                    75 points
     Exam 2                    75 points
     MyLab Math Online         50 points
     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.

Quiz and Exam Schedule

There will be two exams each one covers material from the start of the course up to the time the exam is given. The final exam will be cumulative and test everything learned the entire semester. Details and a study guide will be provided prior to each exam. In person attendance is mandatory for all exams and the final.

Jan 22 -- Section 1.1 Systems of Linear Equations
Jan 24 -- Section 1.2 Row Reduction and Echelon Forms

Jan 27 -- Section 1.4 The Matrix Equations Ax=b
Jan 29 -- Section 1.5 Solution Sets of Linear Systems
Jan 31 -- Section 1.5 Solution Sets of Linear Systems (continued)

Feb 03 -- Section 1.7 Linear Independence
Feb 05 -- Section 1.8 Introduction to Linear Transforms
Feb 07 -- Section 1.9 The Matrix of a Linear Transformation

Feb 10 -- Section 2.1 Matrix Operations
Feb 12 -- Section 2.2 The Inverse of a Matrix
Feb 14 -- Section 2.3 Characterizations of Invertible Matrices

Feb 17 ***President's Day***
Feb 19 -- Section 2.4 Partitioned Matrices
Feb 21 -- Section 2.5 Matrix Factorizations

Feb 24 -- Section 2.8 Subspaces of Rⁿ
Feb 26 -- Section 2.9 Dimension and Rank
Feb 28 -- Exam 1

Mar 03 -- Section 3.1 Introduction to Determinants
Mar 05 -- Section 3.2 Properties of Determinants
Mar 07 -- Section 3.3 Cramer's Rule, Volume and Linear
          Transformations

Mar 10 -- Section 3.3 Cramer's Rule, Volume and Linear 
          Transformations (continued)
Mar 12 -- Section 4.1 Vector Spaces and Subspaces
Mar 14 -- Section 4.2 Null Spaces, Column Spaces, Row Spaces
          and Linear Transformations

Mar 17 -- Section 4.3 Linearly Independent Sets; Bases
          
Mar 19 -- Section 4.5 The Dimension of a Subspace
Mar 21 -- Section 4.6 Change of Basis

Mar 24 ***Spring Break***
Mar 26 ***Spring Break***
Mar 28 ***Spring Break***

Mar 31 -- Section 5.1 Eigenvalues and Eigenvectors
Apr 02 -- Section 5.2 The Characteristic Equations
Apr 04 -- Section 5.3 Diagonalization

Apr 07 -- Section 5.4 Eigenvectors and Linear Transformations
Apr 09 -- Section 5.5 Complex Eigenvalues
Apr 11 -- Exam 2

Apr 14 -- Section 6.1 Inner Product, Length and Orthogonality
Apr 16 -- Section 6.2 Orthogonal Sets
Apr 18 -- Section 6.2 Orthogonal Sets (continued)

Apr 21 -- Section 6.3 Orthogonal Projections
Apr 23 -- Section 6.4 The Gram-Schmidt Process
Apr 25 -- Section 6.5 Least Squares Problems

Apr 28 -- Section 7.1 Diagonalization of Symmetric Matrices
Apr 30 -- Section 7.4 The Singular Value Decomposition
May 02 -- Section 7.4 The Singular Value Decomposition (continued)

May 05 -- Review and Catch Up
May 07 ***Prep Day***

May 09 ***Final Exam at 10:15am***

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. I am available to meet in my office or through Zoom.

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.

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.

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, 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.

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 Friday, May 9, 2025 from 10:15am-12:15pm in PE104.

Last Updated: Wed Feb 19 09:09:06 AM PST 2025