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!

By the end of this semester you should:

- Be able to formulate a concise, precise mathematical arguments, including recognizing when it is complete or when further justification is needed
- Be able to read and communicate advanced technical concepts
- Be willing to approach a problem even if you do not know whether or not your approach will be successful. If it doesn't work out, try something else!
- Appreciate the necessity of rigorous mathematical arguments
- Continue in your development from being a consumer of mathematics to being a producer of mathematics

You should gain a deeper understanding of:

- Techniques for solving systems of linear equations
- The relationship between matrices and linear maps
- The definition of a vector space and a subspace
- Linear independence, spanning sets, and bases
- Eigenvectors and eigenvalues
- The dot product and orthogonality
- The singular value decomposition
- Applications of linear algebra, including to situations that are not clearly linear in nature

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.

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."

Your final grade will be determined by

Pre-Class Assignments | 10% |

Class Engagement/Participation | 10% |

Problem Sets | 25% |

Three Exams | 55% |

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.

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.

You will have a Problem Set due most Thursdays at 11:59 pm, submitted through Canvas. I firmly believe that one of the best ways to build your understanding of mathematics is to explore the ideas with other students. Therefore, you will work on the Problem Sets in groups of two, or possibly three, and each group will turn in a single set of solutions. I will randomly assign new groups for every problem set. Depending on the timing around exams and breaks, a few of the Problem Sets may be individual assignments instead. The Problem Sets will be graded by an upper division math student.

There are more details about the logistics and expectations for your write-ups on the Guidelines for Problem Sets page. Note that part of your individual grade on a problem set is based on whether or not you fill out the confidential Peer Evaluation(s) in Canvas.

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 Weekly Syllabus for dates of the exams.

First two exams will follow a similar format:

- There will be a brief in-class portion that emphasizes short computations and basic concepts.
- The majority of the exam will be takehome.

Third exam will be shorter and entirely takehome.

For all three exams, the takehome portions will be open-book, open-note assignments where you will have several days to work on them. 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:

- 25% of exam grade: Lower score of Exams 1 and 2
- 50% of exam grade: Higher score of Exam 1 and 2
- 25% of exam grade: Exam 3

For example, if your scores are 77 on Exam 1, 91 on Exam 2, and 87 on Exam 3, then your overall exam average will be 86.5.

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.

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.

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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.

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