Course Information

Welcome to MATH 416: Abstract Linear Algebra! Linear algebra is an essential component of modern mathematics, physics, and computer science. This course will provide a rigorous treatment of the subject, focusing on the structure and beauty of vector spaces, linear maps, eigenvectors, and much more. In addition to being elegant and powerful, the course content will also provide ample opportunity for us to understand what mathematics is, what mathematicians do, and how they actually do it! Our official syllabus can be downloaded here; however, I've included some of the most important points below for easy reference.

• Instructor: Jacob Beckey
• Grader: Hyun Tark
• Meeting times: Mon, Wed, Fri — 1:00–1:50 PM, 136 Davenport Hall
• Office Hours: Mon, Wed 2–3 PM, Room TBD (or by appointment)

Contact & Communication

• Instructor's email: jbeckey@illinois.edu
• My office: 72 Computing Applications Building (hopefully changing to Harker Hall soon!)
• Grader's email: htark2@illinois.edu

Please reach out if you have questions about course content, assignments, or logistics.

Schedule & Grading

Grading Breakdown

My goal in this course is to help you deeply learn linear algebra while also developing your ability to think abstractly, write cogent proofs, and work collaboratively. Education research has made clear that active engagement increases student learning outcomes and, even more importantly, mathematics is a fundamentally social endeavor. As such, class participation is a significant part of your grade. This grade will be determined based on participation, not correctness, of in-class clicker questions and pre-lecture quizzes. To accomodate unforeseen circumstances, I will drop the lowest two homework grades, the lowest midterm grade, and 5 participation items. With those caveats, your grade will be calculated based on the following breakdown.

• Participation: 20%
• Homework: 30%
• Midterm Exams: 30%
• Final Exam: 20%

Important Dates

• Midterm Exam 1: Friday, September 26
• Midterm Exam 2: Friday, October 24
• Midterm Exam 3: Wednesday, November 19
• Final Exam: Wednesday, December 17 (7-10pm, location TBD)

Course Materials

Required Materials

• Textbook: Axler, Linear Algebra Done Right
• Technology: iClicker app (see student instructions here)

Suggested Resources

• Book: Vector: A Surprising Story of Space, Time, and Mathematical Transformation by Robyn Arianhod
• Video series: Essence of Linear Algebra by Grant Sanderson (3Blue1Brown on YouTube)

Weekly Outline