Syllabus Math 253: Linear Algebra

Required Text: Contemporary Linear Algebra, Anton & Busby

“It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.” - E. Artin

Course Objectives & Student Learning Outcomes

The structures and theorems of linear algebra are among the most commonly applied concepts in modern mathematics. They appear in abstract algebra, functional analysis, analytic geometry, graph theory, game theory, physics, engineering, computer science, chemistry, economics, and host of other fields.

Through this course you will come to understand the ways in which systems of linear equations, matrices, and linear transformations are all shadows cast by the same central object. You will continue your progress towards increased abstraction - generalizing your geometric intuition to higher dimensions and more abstract spaces; mastering matrix operations; and strengthening your proof-writing and logical reasoning skills. Your grade will be based on your level of achievement in each of the following student learning outcomes:

• Your content knowledge (including your geometric and algebraic reasoning skills)

• Your ability to independently research and apply the tools of linear algebra

• Your technical writing and speaking ability

Topics Covered

include, but are not limited to:

• Linear Independence and Dependence

• Systems of Linear Equations

• Matrices and Matrix Algebra

• Linear Transformations

• Eigenvalues and Eigenvectors

• Vector spaces, Bases, Dimension, and the Four Fundamental Subspaces of a Matrix

Class Engagement: Students are expected to attend 2 of the math colloquium talks given throughout the semester. A schedule of talks can be found on the Math Department website, and linked to from the course WISE site. The goal of this attendance requirement is to introduce you to the diversity and vitality of current mathematics research, and to include you in the Math Department community. In addition, there will be in-class investigations, and out of class Perusall readings (including texts, podcasts, and videos) assigned to supplement class discussions. Your grade for this component of the course will be based on how meaningfully you engage in these activities and discussions, as based on your attendance and the quality of your in-class and Perusall contributions. Perusall assesses how integral your contributions are to the conversation – hence engaging with the Perusall readings early and often will increase your score.

Individual Exams: There will be one midterm and one cumulative final exam (celebrations? denouements? an assessment by any other name is just as exciting). More details about the structure of these exams will be given in class.

Group Exams: There will be two group exams. These exams are done in groups of two or three, with each group member having a unique problem to work on. Group members proof-read each other’s work and offer suggestions. Of the 50 points possible for each group exam, 40 will be based on your work and 10 will be based on your proof-reading of team member’s exams. Each team member is allowed one page, one-sided, of notes. For more information, see the handout on Group Exams https://sites.google.com/willamette.edu/groupexaminformationpage/home

Homework: Throughout the semester I will assign homework sets that reinforce class concepts and provide the opportunity to apply the theorems and techniques discussed in class. Homework will come in three flavors: computational WeBWorK assignments, theoretical problem sets, and applied python programming assignments. I encourage you to do these homework sets collaboratively, but make sure the work you turn in is completely your own. If you decide to collaborate on theoretical or applied problem sets, make sure everyone listed as an author contributes to the assignment, and understands all the elements of the solution. Copying files of others without attributing them, providing your files to be copied, or putting your name on work you do not understand and did not contribute sufficiently to is a violation of the honor code.

Solutions to the theoretical problem sets should be LaTeXed and turned in during class. A list of useful LaTeX resources is available here: https://willamette.edu/~emcnicho/courses/LaTeX.html.

Applied python programming assignments should be completed using CoLab and turned in by sharing your CoLab file with me.

WeBWorK is an online homework distribution and grading system. The best feature of WeBWorK is that when you enter an answer to a homework problem, the system immediately tells you whether the answer is correct. You can try a problem as many times as you like. Once you get the answer right, that fact is immediately recorded (provided it is before the due date), and any wrong answers are not counted in your grade. Here are some tips for using WeBWorK: https://sites.google.com/willamette.edu/webwork/home.

Student Responsibility

I will do everything in my power to help you learn, but it is up to you to make the most of this experience by coming to class prepared and ready to engage in discussion. The following actions are all critical for your success in this class. If there are barriers to you doing any of the following, please let me know.

ASK QUESTIONS & THINK CRITICALLY. Throughout the course you should be asking yourself “Why are we doing this? Why does this method work? How is this related to other topics I’ve learned?” Ask questions in class, after class, during office hours, whenever! If you are confused or having problems with a certain section of the material talk to me about it. It is best to clear up confusions right away, and if you have a question, almost certainly other members of class do to. Be the brave one and speak up! The whole class will benefit from your questions.

DO THE ASSIGNMENTS. As you know, mathematics is not a spectator sport. At the same time, it can be a frustrating endeavor to engage in alone. Think of it as a team sport! I strongly encourage, and may even require, you to work with your fellow students on homework assignments.

SPEND TIME STUDYING. Willamette’s Credit Hour Policy holds that for every hour of class time there is an expectation of 3 hours of work outside of class. You should anticipate spending approximately 9 hours outside of class engaged in course-related activities. To master the content of this course you will need to invest time and effort. Set aside time for both homework and studying. A good approach would be to spend approximately 1-2 hours on reading the sections and making study notes, 3-6 hours doing the assigned problems, and 1-3 hours studying for tests each week. This course is completely manageable, and you can do well in it as long as you engage from the beginning.

How to Get Unstuck

Linear Algebra is a course rich in content that can only be understood by approaching it from multiple perspectives. It is natural to feel a little lost or confused at times. What should you do? Discuss! Ask questions! You can start conversations on the course Discord channel, bring questions up in class, email me, go to the department tutoring, arrange to meet with me, arrange to meet with other students, attend office hours, etc. We now have the capability to meet in person or virtually, so there are even more ways to talk things through with me or your classmates.

Asking Questions in Class

Sometimes it's hard to know what exactly to ask, so here are some some ideas if you need inspiration:

• I'm a little confused on that last point, could you go over that again?

• How does this tie-into the overarching subject of this chapter?

• How did you know to take that step? I don't think I would have known to do that.

• Can we quickly review the definition of <insert word here>? I've forgotten what that means.

• Is it possible to quickly review why <thing 1> implies <thing 2>? It's not obvious to me.

• How would I recognize what kind of <proof technique, calculation approach, etc.> to use here? Are there particular clues to look out for?

Course Policies

Inclusivity Statement: Willamette University values diversity and inclusion; we are committed to a climate of mutual respect and full participation. My goal is to create a learning environment that is effective, equitable, inclusive, and welcoming. If there are aspects of the instruction or design of this course that result in barriers to your inclusion, assessment of your work, or your achievement, please notify me as soon as possible. I will gladly honor your request to address you by your affirmed name or gender pronoun. Please advise me of this at any point in the semester so that I may make appropriate changes to my records. If I accidentally use an incorrect gender pronoun or mispronounce your name when addressing you, please let me know, in whatever manner makes you comfortable, so that I can make every effort to correct that error.

Students with disabilities are encouraged to contact the Accessible Education Services office in Smullin 155 at 503-370-6737 or Accessible-info@willamette.edu to discuss a range of options to removing barriers, including accommodations.

Missed Classes: Please make every effort to attend all classes and be an active participant in class activities and discussions. Much of your learning and understanding of new mathematical ideas will come from thinking and talking about them in class. If for some reason you are unable to attend class or turn in an assignment, please let me know as soon as possible, preferably before the missed class or assignment. I know how important athletic commitments, personal events, and religious traditions can be, and will do my best to accommodate your personal needs.

Cell Phone/Screen Policy: Unless specifically stated for class use, no phones, laptops, iPads, or other devices which take your eyes off your fellow classmates and the class discussion are allowed. Electronic devices must be turned off or silenced during class meetings. If your phone goes off, or it is clear that you are using one of these devices during class, you will be responsible for bringing treats for the entire class at the next class meeting.

Health: As a student, you may experience a range of challenges that can interfere with learning, such as strained relationships, increased anxiety, substance use, feeling down, difficulty concentrating and/or lack of motivation. These mental health concerns or stressful events may diminish your academic performance and reduce your ability to participate in daily activities. Willamette services are available and treatment does work. If you think you need help, please contact Bishop Health as soon as possible at http://willamette.edu/offices/counseling/. Crisis counseling is available 24/7 at WUTalk: 503-375-5353 and Campus Safety is available at 503-370-6911. Emergency resources are also available from the Psychiatric Crisis Center at 503-585-4949 and the National Suicide Prevention Lifeline at 1-800-273-8255.

Willamette is a community committed to fostering safe, productive learning environments, and we value ethical sexual behaviors and standards. Title IX and our school policy prohibit discrimination on the basis of sex, which regards sexual misconduct including discrimination, harassment, domestic and dating violence, sexual assault, and stalking. We understand that sexual violence can undermine students academic success, and we encourage affected students to talk to someone about their experiences and get the support they need. Please be aware that as a mandatory reporter I am required to report any instances you disclose to Willamette’s Title IX Coordinator. If you would rather share information with a confidential employee who does not have this responsibility, please contact our confidential advocate at confidential-advocate@willamette.edu. Confidential support also can 4 be found with SARAs and at the GRAC (503-851-4245); and at WUTalk - a 24-hour telephone crisis counseling support line (503-375-5353). If you are in immediate danger, please call campus safety at 503-370-6911.

Academic Integrity: Students of Willamette University are members of a community that values excellence and integrity in every aspect of life. As such, we expect all community members to live up to the highest standards of personal, ethical, and moral conduct. Students are expected not to engage in any type of academic or intellectually dishonest practice and encouraged to display honesty, trust, fairness, respect, and responsibility in all they do. Plagiarism and cheating are especially offensive to the integrity of courses in which they occur and against the College community as a whole. These acts involve intellectual dishonesty, deception, and fraud, which inhibit the honest exchange of ideas. Ignorance of what constitutes plagiarism shall not be considered a valid defense. Plagiarism and cheating may be grounds for failure in the course and/or dismissal from the College. For more information, see http://willamette.edu/cla/catalog/policies/plagiarism-cheating.php. If you are unsure of what constitutes cheating, please ask me. These are the practices I expect you to follow in each of the components of the course:

on collaboration: You may, and are encouraged to discuss things with fellow students, and get help from your professor, textbook, notes, or calculator. However, your submitted written work should be your own or a collaboration with your assignment group. Copy/pasting sections of another's assignment or code, reading and paraphrasing another source, or providing your assignment to be copied by others, are violations of university policy. When working on a group assignment, all members of the group should contribute to producing all components of the finished product. Writing your name on work you did not contribute to in a substantive manner is a violation of university policy.

on individual tests: Throughout the course there will be individual tests and/or quizzes. Your work on these assessments should be your own, and you may not receive help from any source other than your professor (unless directed otherwise).

Intellectual Property & Privacy: Class materials and discussions including recorded lectures are for the sole purpose of educating the students enrolled in the course. The release of such information (including but not limited to directly sharing, screen capturing, or recording content) is strictly prohibited, unless the instructor states otherwise. Doing so without the permission of the instructor will be considered an Honor Code violation and may also be a violation of other state and federal laws, such as the Copyright Act. 5

DACA/Undocumented Student Advocate: Willamette is committed to supporting our DACA/Undocumented students in a variety of ways. This year, Olivia Muñoz is the contact person for all DACA/undocumented students can provide those students with a number of external and internal resources that are available. Her contact information is email:omunoz@willamette.edu, Office: 3rd Floor UC, Phone: 503-370-6447.

SOAR Center Offerings (Food, Clothing, and School Materials): The Students Organizing for Access to Resources (SOAR) Center strives to create equitable access to food, professional clothing, commencement regalia, and scholarly resources for WU and Willamette Academy students. The SOAR Center is located in the Putnam University Center’s third floor, across from the Harrison Conference Room. The space houses the Bearcat Pantry, Clothing Share, and First-Generation Book Drive and is maintained by committed students and advisers. Please check www.willamette.edu/go/soar for current hours of operation and email soar-center@willamette.edu for any questions or concerns.

Important Dates

Week 1: 1/17 (Tue) First day of classes

Week 3: 1/30 (M) A/D Deadline

Week 4: 2/6 (M) C/NC Deadline

Week 6: 2/20-21 (M-Tue) Mid-semester break - No Classes

Week 10: 3/22 (W) Withdraw Deadline

Week 11: 3/27-31 (M-F) Spring Break - No Classes

Week 13: 4/11-14 Registration for Fall

Week 14: 4/19 (W) SSRD - No Classes

Week 16: 5/3 (W) Last Day of Classes

Week 17: 5/9 (Tue) Final Exam 8-11am