MATH 341: Linear Algebra and Matrix Theory

Course Unique Number: 55065

General Information

Instructor: David Clark (clark@math.utexas.edu)

Lectures: Monday, Wednesday, Friday, 1:00pm-1:50pm. Hosted on Zoom: https://utexas.zoom.us/j/92926320829. Notes will be provided after each lecture. Recordings of the lectures will be available on Zoom.

Office hours: Tuesday 11am-noon, Thursday 2pm-3pm, Sunday 3pm-4pm, or by appointment. Hosted on Zoom, https://utexas.zoom.us/j/5689856057.

TA Office hours:Qianyu Hao (qhao@utexas.edu). Monday and Wednesday, 9am-10am. Hosted on Zoom: https://utexas.zoom.us/j/97776289198.

Text: Elementary Linear Algebra, 5th ed., by Andrilli and Hecker, ISBN 978-0-12-800853-9, published by Academic Press.

Piazza: There will be a discussion board monitored by the instructor and teaching assistant. This will be the best location to ask questions about the course.

Course webpage: http://www.ma.utexas.edu/users/clark/Courses/2021/Spring/341/.

Course Description

The emphasis in this course is on understanding the concepts and learning to use the tools of linear algebra and matrices. Some time will be devoted to learning to do proofs. The fundamental concepts and tools of the subject covered are:

• Matrices: matrix operations, the rules of matrix algebra, invertible matrices.
• Linear equations: row operations and row equivalence, elementary matrices, solving systems of linear equations by Gaussian elimination, inverting a matrix with the aid of row operations.
• Vector spaces: vector spaces and subspaces, linear independence and span of a set of vectors, basis and dimension, the standard bases for common vector spaces.
• Inner product spaces: Cauchy-Schwarz inequality, orthonormal bases, the Gramm-Schmidt procedure, orthogonal complement of a subspace, orthogonal projection.
• Determinants: the definition and basic properties of determinants. Cramers rule.
• Eigenvalues: eigenvalues and eigenvectors, diagonalizability of a real symmetric matrix, canonical forms.

Prerequisites

The prerequisite is a grade of at least C- in Mathematics 408D, 408L, or 408S.

Grading for this Course

Homework: There will be homework assigned after each lecture. The homework must be submitted online using Gradescope by the date posted, typically about four days after it becomes available.

Exams: There will be three midterm exams, two held during the usual class period, and the third during the scheduled final exam time. The first two midterms are tentatively scheduled for February 24 and April 14. The third midterm exam is scheduled for Thursday, May 13, 9:00am-10:15pm. Please mark on your calendars now the time and date of the exams. Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams. Access to the exams will be provided through Gradescope. Completed exams will be uploaded to Gradescope. Any student with difficulties uploading the exam should email the exam to the instructor. Any student, who is unable to take an exam at the scheduled time, should contact the insturctor to make alternative arrangements.

Grading Scheme: The final grade will be determined by the grading scheme:

Activity	Percentage
Homework	40%
Midterm Exams	60%

Letter Grades

The grading convention, 90.00-100% A, 86.67-90.00% A-, 83.33-86.67% B+, 80-83.33% B, 76.67%-80.00% B-, 73.33-76.67% C+, 70.00-73.33% C, 66.67%-70.00% C-, 63.33-66.67% D+, 60.00-63.33% D,56.67%-60.00% D-, less than 56.67% F, will be followed. If for some reason there is a deviation from this scale it will be applied uniformly to the whole class. Changes to the scale will only make the scale more generous.

University Policies

University Code of Conduct: The core values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the university is expected to uphold these values through integrity, honesty, trust, fairness, and respect toward peers and community.

Student Honor Code: "As a student of The University of Texas at Austin, I shall abide by the core values of the University and uphold academic integrity."

Academic Integrity: A fundamental principle for any educational institution, academic integrity is highly valued and seriously regarded at The University of Texas at Austin. More specifically, you and other students are expected to maintain absolute integrity and a high standard of individual honor in scholastic work undertaken at the University. This is a very basic expectation that is further reinforced by the University's Honor Code. At a minimum, you should complete any assignments, exams, and other scholastic endeavors with the utmost honesty which requires you to:

• acknowledge the contributions of other sources to your scholastic efforts;
• complete your assignments independently unless expressly authorized to seek or obtain assistance in preparing them;
• follow instructions for assignments and exams, and observe the standards of your academic discipline; and
• avoid engaging in any form of academic dishonesty on behalf of yourself or another student.

Sharing of Course Materials is Prohibited: No materials used in this class, including, but not limited to, lecture hand-outs, videos, assessments (quizzes, exams, papers, projects, homework assignments), in-class materials, review sheets, and additional problem sets, may be shared online or with anyone outside of the class unless you have my explicit, written permission. Unauthorized sharing of materials promotes cheating. It is a violation of the University’s Student Honor Code and an act of academic dishonesty. I am well aware of the sites used for sharing materials, and any materials found online that are associated with you, or any suspected unauthorized sharing of materials, will be reported to Student Conduct and Academic Integrity in the Office of the Dean of Students. These reports can result in sanctions, including failure in the course.

Class Recordings: Class recordings are reserved only for students in this class for educational purposes and are protected under FERPA. The recordings should not be shared outside the class in any form. Violation of this restriction by a student could lead to Student Misconduct proceedings.

Excused Absences: For an absence to be excused you must provide legitimate documentation prior to or no later than one week after your absence. Excused absences include:

1. Illness (must have a signed note from your physician on their letterhead; generic “no excuse” form letters from University Health Services will not be accepted)
2. Critical family events (e.g., weddings or funerals)
3. Official UT events (e.g., games if you’re an athlete, concerts if you’re a band member)
4. Religious Holy Days

Drop dates: January 22 is the last day to drop without approval of the department chair; February 3 is the last day to drop the course for a possible refund; April 5 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class, referred to as Q drop, except for urgent and substantiated, nonacademic reasons. Under Texas law, you are only allowed six Q drops while you are in college at any public Texas institution. For more information, see: http://www.utexas.edu/ugs/csacc/academic/adddrop/qdrop. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page, http://registrar.utexas.edu/calendars/20-21/.

University Resources for Students

Your success in the class is important to me. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

Personal or Family Emergencies: If you you experience a personal or family emergency (death in the family, protracted sickness, serious mental health issues) you should contact Student Emergency Services in the Office of the Dean of Students. Student Emergency Services supports students by providing the most comprehensive outreach, assistance, intervention, and referrals. They will also work with you to communicate with me and your other professors and let them know of your situation. http://deanofstudents.utexas.edu/emergency/index.php

BeVocal:BeVocal is a university-wide initiative to promote the idea that individual Longhorns have the power to prevent high-risk behavior and harm. At UT Austin all Longhorns have the power to intervene and reduce harm. To learn more about BeVocal and how you can help to build a culture of care on campus, go to http://wellnessnetwork.utexas.edu/BeVocal

Title IX Reporting Title IX is a federal law that protects against sex and gender-based discrimination, sexual harassment, sexual assault, sexual misconduct, dating/domestic violence and stalking at federally funded educational institutions. UT Austin is committed to fostering a learning and working environment free from discrimination in all its forms. When sexual misconduct occurs in our community, the university can:

1. Intervene to prevent harmful behavior from continuing or escalating.
2. Provide support and remedies to students and employees who have experienced harm or have become involved in a Title IX investigation.
3. Investigate and discipline violations of the university’s relevant policies(https://titleix.utexas.edu/relevant-policies).

Services for Students with Disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Division of Diversity and Community Engagement, Services for Students with Disabilities at 471-6259 (voice) or 232-2937 (video phone) or http://ddce.utexas.edu/disability/

Behavior Concerns Advice Line (BCAL): If you are worried about someone who is acting differently, you may use the Behavior Concerns Advice Line to discuss by phone your concerns about another individual’s behavior. This service is provided through a partnership among the Office of the Dean of Students, the Counseling and Mental Health Center (CMHC), the Employee Assistance Program (EAP), and The University of Texas Police Department (UTPD). Call 512-232-5050 or visit http://www.utexas.edu/safety/bcal

Campus Safety and Security: In case of an emergency evacuation, please be aware of the following recommendations the Office of Campus Safety and Security has outlined to keep you and others safe. Additional information may be available at 512-471-5767 or http://www.utexas.edu/safety/.

• Occupants of buildings on The University of Texas at Austin campus are required to evacuate buildings when a fire alarm is activated. Alarm activation or announcement requires exiting and assembling outside.
• Familiarize yourself with all exit doors of each classroom and building you may occupy. Remember that the nearest exit door may not be the one you used when entering the building.
• Students requiring assistance in evacuation shall inform their instructor in writing during the first week of class.
• In the event of an evacuation, follow the instruction of faculty or class instructors.
• Do not re-enter a building unless given instructions by the following: Austin Fire Department, The University of Texas at Austin Police Department, or Fire Prevention Services office.
• Information regarding emergency evacuation routes and emergency procedures can be found at: http://www.utexas.edu/emergency

Counseling and Mental Health Center: Students often encounter non-academic difficulties during the semester, including stresses from family, health issues, and lifestyle choices. The Counseling and Mental Health Center (CMHC) provides counseling, psychiatric consultation, and prevention services that facilitate students' academic and life goals and enhance their personal growth and well-being. Counseling and Mental Health Center, Student Services Bldg (SSB), 5th Floor, open M-F 8am-5pm. Tel. 512-471-3515 (appointments), 512-471-CALL (crisis line), or www.cmhc.utexas.edu

Student Rights and Responsibilities

• You have a right to a learning environment that supports mental and physical wellness.
• You have a right to respect.
• You have a right to be assessed and graded fairly.
• You have a right to freedom of opinion and expression.
• You have a right to privacy and confidentiality.
• You have a right to meaningful and equal participation.
• You have a right to learn in an environment that is welcoming to all people.

With these rights come responsibilities:

• You are responsible for taking care of yourself, managing your time, and communicating with the teaching team and with others if things start to feel out of control or overwhelming.
• You are responsible for acting in a way that is worthy of respect and always respectful of others.
• Your experience with this course is directly related to the quality of the energy that you bring to it, and your energy shapes the quality of your peers' experiences.
• You are responsible for creating an inclusive environment and for speaking up when someone is excluded.
• You are responsible for holding yourself accountable to these standards, holding each other to these standards, and holding the teaching team accountable as well.

Personal Names and Pronouns: Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, culture, religion, politics, sexual orientation, gender, gender variance, and nationalities. Class rosters are provided to the instructor with the student's legal name, unless they have added a "preferred name" with the Gender and Sexuality Center. I will gladly honor your request to address you by a name that is different from what appears on the official roster and by the gender pronoun you use. Please advise me of this early in the semester so that I may make appropriate changes to my records.

Schedule