We will follow a draft of a Linear Algebra book that I am writing: Current version.
For an excellent overview of the core ideas of Linear Algebra (with high-quality visualizations), I strongly recommend the video series Essence of Linear Algebra by 3Blue1Brown.
In addition, I encourage you to consult other books and online resources to help learn the material, as these sources provide different perspectives on the subject. For linear algebra books, I recommend the following:
- Linear Algebra by Jim Hefferon. Available online.
- A Course in Linear Algebra by David B. Damiano and John B. Little.
We will also spend a significant portion of time learning how to write mathematical proofs. For additional references on mathematical writing and notation, I recommend the following:
- Book of Proof by Richard Hammack. Available online.
- Mathematical Reasoning: Writing and Proof by Ted Sundstrom. Available online.
- How to Prove It by Daniel Velleman.
For general advice on making the transition from a computational perspective of mathematics to a more conceptual understanding (including how to think logically and how to write mathematics), consider reading the following:
- How to Think Like a Mathematician by Kevin Houston.
- How to Study as a Mathematics Major by Lara Alcock.
There will be two different types of homework assignments:
- Problem Sets will be due at 4:00pm on most Mondays and Fridays. Your solutions should be uploaded to Gradescope. These assignments contain a mixture of computational exercises, explanations, and short proofs. Your lowest two Problem Set scores will be dropped.
- Writing Assignments will be due at the beginning of class on most Wednesdays. You should turn in a paper version of your solutions in class. The problems on these assignments are more conceptual or theoretical, and will require significant explanation. Your solutions should consist of careful arguments written in complete sentences (augmented by mathematical symbolism where appropriate). A major goal of these problems is to teach the fundamentals of mathematical language and mathematical inferences, along with proper use of terminology and notation. As a result, they will be graded at a high standard involving much more than getting the "correct answer". Take the time to write and revise these as you would in a paper in other courses. Your lowest Writing Assignment score will be dropped.
Throughout the semester, there will be a few additional assignments that ask you to reflect on how you are approaching the material in this class. They are designed to help you figure out what works for you, what does not work for you, and how to adjust your learning practices as a result. These assignments will only be graded on the basis of completion and thoughtfulness.
There will be three in-class exams and a scheduled three-hour final exam.
In-class exams dates: February 19, April 3, and April 29.
Final exam date: Thursday, May 16 at 2:00.
If you want to learn how to present your work professionally, as well as keep digital records, I recommend learning how to typeset your solutions. LaTeX is a wonderful free typesetting system which produces high-quality documents at the cost of only a small amount of additional effort (beyond the nontrivial start-up cost of learning the fundamentals). If you plan to do any kind of mathematical or scientific writing in the future, you will likely use LaTeX, so it is worth your time to familiarize yourself with it. Feel free to ask me questions about how to use LaTeX, and/or to send you the LaTeX file for homework assignments.
Consult the general Grinnell College policy on Academic Honesty and the associated booklet for general information.
Homework: If you enjoy working in groups, I strongly encourage you to work with others in the class to solve the homework problems. If you do collaborative work or receive help form somebody in the course, you must acknowledge this on the corresponding problem(s). Writing "I worked with Sam on this problem" or "Mary helped me with this problem" suffices. You may ask students outside the course for help, but you need to make sure they understand the academic honesty policies for the course and you need to cite their assistance as well. Failure to acknowledge such collaboration or assistance is a violation of academic honesty.
If you work with others, your homework must be written up independently in your own words. You cannot write a communal solution and all copy it down. You cannot read a solution (from another person, a website, etc.) and alter it slightly in notation/exposition. Discussing ideas and/or writing parts of computations together on whiteboards or scratch paper is perfectly fine, but you need to take those ideas and write the problem up on your own. Under no circumstances should you look at another student's completed written work.
I encourage you to look at other books or online sources for additional help in understanding concepts and ideas, but you must cite other books or online sources if they provide you with an idea that helps you solve a problem. However, you may not do any of the following:
- Specifically search or look for solutions to homework problems in books or online sources.
- Solicit help for homework problems from online forums.
- Prompt an LLM (or other AI-assisted tool) or computer algebra system (such as Mathematica) to help you with the computation or proof for a specific assigned problem.
Exams and Final: You may neither give nor receive help. Books, written notes, computers, phones, and calculators are not permitted at any time during a testing period.
I encourage students with documented disabilities to discuss reasonable accommodations with me so that they can fully participate in the course. Students will also need to have a conversation with, and provide documentation of your disability to, the Coordinator for Disability Resources, Jae Baldree, located on the first floor of Steiner Hall (x3089).
I encourage students who plan to observe holy days that coincide with class meetings or assignment due dates to consult with me as soon as possible so that we may reach a mutual understanding of how you can meet the terms of your religious observance and also the requirements for this course.