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Course Policies Math 221 Linear ALgebra, Fall 2024

Overview

At the very basic level, Linear Algebra is concerned with solving systems of linear equations like \begin{eqnarray*} 2x + 3y + 2z & = & 10 \\ x - 6y + 2z & = & 2 \end{eqnarray*} The beauty of Linear Algebra is that these seemingly mundane algebraic questions have very deep geometric interpretations. We will be able to play off the algebraic and geometric viewpoints against each other to gain insights and build intuition about both. Fundamental to developing this intuition is an understanding of the relationship between matrices and linear transformations, which are special types of maps from n-dimensional space to m-dimensional space.

The interconnections among systems of linear equations, matrices, and linear transformations provide a framework for applications in many different areas, from computer science, to statistics, to machine learning. Some of the specific uses of Linear Algebra that we will look at this semester include applications to computer graphics, finding the least-squares regression line for a set of data, and reducing the resolution of an image using the singular value decomposition.

The course will stretch you to think in new ways, but it will be really rewarding. Plus, the mathematics is beautiful.

This is going to be a really fun semester!

Goals for a 200-level Mathematics Course

By the end of this semester you should:

Goals Specific to Linear Algebra

You should gain a deeper understanding of:

Expectations

Mathematics is a very active discipline that is best learned by doing rather than by observing. One of the features that makes your Wheaton education so special is that we have time in small classes to explore material together. The class meetings are not intended to be a complete encapsulation of the course material, but instead will focus on the major concepts from the Pre-Class Assignments and clarifying the more subtle ideas in the course. It is important that you are present and engaged during the class meetings, but a significant part of your learning will occur outside of class during office hours or when working on problem sets.

You should expect to put in approximately 3 hours outside of class for each scheduled hour of class. In other words, expect to spend a roughly 9 hours per week on Linear Algebra outside of the scheduled class meetings. There will be some weeks where you spend more time, and there may be some weeks where you spend slightly less.

The Honor Code

We operate under the Wheaton Honor Code for all of your academic work at Wheaton. This carries certain freedoms and responsibilities for both you as a student and me as a professor. I take this quite seriously.

Most likely, no Honor Code issues will arise this semester. If you are uncertain about whether a particular situation falls under the Honor Code, then please consult with me. However, if an Honor Code issue does come up, I will assume that you are prepared for the full consequences. Remember that you should write out, and sign, the following statement on all course work:

"I have abided by the Wheaton College Honor Code in this work."

Evaluation

Your final grade will be determined by

Pre-Class Assignments 5%
Class Engagement/Participation 15%
Problem Sets and Final Assignment 30%
Two Exams 50%

Pre-Class Assignments

The purpose of reading the text before class is that if you are familiar with the basic concepts and definitions, then the class meetings can be devoted to the major ideas and subtleties of the material. Mathematical understanding is built in stages, and you will absorb the material more quickly if the class meetings are your second exposure to the fundamental ideas.

The Pre-Class Assignments are posted on the course webpage and include three or so questions that you should be able to answer after you have completed the reading. You will submit your responses through Canvas.

I will grade the Pre-Class Assignments using a binary scale: If you make a serious attempt, you will get full credit, whether or not your answers are completely correct. The purpose of these questions is to encourage you to engage with the material before class. If you've read the text but don't understand how to answer a question, it is perfectly fine to say "I did the prep work but don't see how to approach this question." You'll definitely understand by the end of the end of the week!

Notice that the Pre-Class Assignments are due at 11:59 pm on Monday! This will give me enough time to review your responses before our class on Tuesday morning. You will be allowed to drop one Pre-Class assignment at the end of the semester.

Class Engagement/Participation

A significant part of the class meetings will be devoted to working in small groups on problems that delve more deeply into the content introduced in the Pre-Class Assignments and discussed at the beginning of class. A substantial amount of your learning will happen during these collaborative sessions by bouncing ideas off of other students and seeing how other groups approach the problems. Each group will upload the work they've completed by the end of class to Canvas so that everyone can see how others have thought about the problems.

I will also determine your Engagement/Participation grade for each class meeting using a binary scale: You were present and engaged with your peers or you weren't. However, I also know that there may be times when you have a valid reason for missing class. I'll be really flexible, so if you need to miss class, please let me know. Let's just keep the lines of communication open.

Problem Sets

You will have a Problem Set due most Fridays at 12:30 pm, submitted through Canvas. The Problem Sets will be graded by an upper division math student. You will be allowed to drop one Problem Set assignment at the end of the semester.

I firmly believe that one of the best ways to build your understanding of mathematics is to explore the ideas with other students. Therefore, I strongly encourage you to discuss the Problem Sets with other students outside of class. However, the answers that you give should represent your own thinking about solutions, and you must each write up your own solutions independently.

Under no circumstances can you look at another student's write-up or share your write-up with another student! If you do work with other students, you must cite them on your on a Problem Set solutions. If you fail to do this, I will view it as a violation of the Honor Code.

There are more details about my expectations for your write-ups on the Guidelines for Problem Sets page.

There will be a Final Assignment due during Finals Week that will consist of a few problems based on content not covered on the exams as well as a cumulative component. This assignment will count for the equivalent of three Problem Sets. You cannot drop this assignment.

Exams

The purpose of the exams is for you to demonstrate your understanding of the course material and, just as importantly, to give you feedback on where your understanding is strong and where you may need more work. See the Tentative Daily Syllabus for dates of the exams.

The exams will follow a similar format:

I will provide more details about the structure of the exams as the time gets closer.

I know that exams can be stressful, especially with the other academic, extracurricular, and family commitments that you may have. To try to reduce some of this stress concerning your grade, I will weight your exam scores by differing amounts: The lower of your exam scores will count for 1/3 of your exam grade, and the higher score will count for 2/3 of your exam grade.

Getting Help with Linear Algebra

Please come see me during my drop-in office hours! No appointment necessary! If you have a conflict and cannot make my office hours, please email me and we can set up an appointment for another time.

Remember that the goal of the course is to help you learn Linear Algebra and develop your mathematical thinking! If there's any point where you feel that the structure of the class isn't working for you, please come by and we can figure out some possible strategies.

Accessibility Services

Wheaton College is committed to providing equitable access and supportive services for all students to fully access and thrive in the academic, residential and social aspects of student life at Wheaton College. Affirmatively, Wheaton provides appropriate accommodations for eligible students with documented disabilities to afford equal access to educational programs and services. Individuals with disabilities and other access concerns requiring accommodations or information on accessibility should reach out to Accessibility Services at the Filene Center, either via email at accessibility@wheatoncollege.edu or via phone at (508) 286-3794.

Wheaton Student Support & Wellness Resources

The Counseling Center is the confidential and FREE mental health resource on campus for all students. To learn about services, check out the website, or give the office a call at 508-286-3905. Additionally, the Mental Health Support Line is available anytime the CC is not, by calling the front desk 508-286-3905 and following voicemail prompts to be connected to a clinician (24/7, available in languages other than English, and accessible from anywhere you are in the world).

The Filene Center strives to support your learning pathway by fostering successful academic, career, and personal development. The academic advising staff will work collaboratively with you, faculty and campus resources to ensure that you have the access and guidance to become a confident and reflective learner at Wheaton and beyond. Contact us at advising@wheatoncollege.edu.

Many other offices on campus can also help support the holistic wellness of students. For students who identify as low-income, first-gen, LGBTQ+, or have a faith or spiritual practice they adhere to, the Center for Social Justice and Community Impact and Center for Religious and Spiritual Life (the Base) are good places for support and engagement. The Marshall Center for Intercultural Learning supports BIPOC students and those working towards breaking down barriers across differences, and the Center for Global Education supports international students, and students seeking educational opportunities abroad. The Title IX Office supports students through sexual and gender based misconduct, and the Bias Incident Response Team supports individuals through a wide variety of bias events. We encourage you to reach out to any and all of these offices for support.

Health Services through Norton Medical Center is available to support students with a variety of physical health needs including specialty support for GYN and STI care. Contact the office at 508-285-9500 to make an appointment for care. There is no copay for visits and most services are free, with select procedures and labs billed to insurance.


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