Welcome to the course webpage for the Summer 2022 (Second Session) manifestation of MATH 117: Advanced Linear Algebra at the University of California, Santa Cruz.

The official syllabus for the course is located here. Feel free to download it. For your convenience, most of the information can also be found on this page and throughout the site.

Basic Course Information

• Prerequisites: MATH 21 or AMS 10 and either MATH 100 or CMPS 101. Prerequisites waived for non- UCSC students.
• Credits/Workload: This is a five-week course worth 5 credits towards your degree. According to UCSC, an ordinary ten-week course has a workload of approximately 3 hours per credit. Since this is a compressed version of a ten-week course, you should expect a workload of (at most) 30 hours per week, including time spent in lectures. I highly recommend that you spend at least 20 hours per week on this course.
• Textbook: The lectures will not follow any particular textbook. Therefore, there is no required textbook for the course. Some optional textbooks can be found on Canvas.
• Zoom Meetings: We will have synchronous Zoom meetings every Monday, Wednesday, & Friday from 1:00PM - 3:30PM. The Zoom room information will be posted on Canvas. The first meeting is on July 25th, 2022 and the last meeting is on August 26th, 2022. Lectures will not be recorded. Detailed handwritten lecture notes from each meeting will be posted promptly on the course webpage.
• Course Webpage: You're on it! Assignments will typically be posted here. If there are any notes from our meetings, they will be posted here as well.
• Teaching Assistant: Our TA is Brandon Owens. You can contact him via Zulip or via email. Brandon will hold weekly office hours and discussion sections. You are highly encouraged to attend these!
  • TA Email:
  • TA Office Hours: Tues 10:00AM (via Zoom)
  • Discussion Sections: Tu/Th 11:00AM (via Zoom)
  During sections, Brandon will discuss the most recent Daily Assignment. Sections and office hours begin the first week of class.
• Canvas: The Canvas webpage will be used for hosting grades, Zoom links, and administering the exams.
• Zulip: We will be using Zulip as a discussion forum for the course. Our forum is located here: https://math117.zulipchat.com/. You will receive an invitation to join via your .edu email. Zulip is similar to Discord, except it has far better $\LaTeX$ integration. The purpose of the forum is to facilitate class discussion.
• Accessibility: I am strongly committed to making my course as accessible as possible. If you encounter materials that are not accessible to you, or experience a barrier to your participation, please bring this to my attention and I will gladly work with you to ensure accessibility. I am also happy to honor any accommodations letters from the Disability Resource Center (DRC) that you would like to confidentially bring to my attention.
• Course Content: This is a proof-based course in advanced linear algebra. Our ambitious goal is to cover the following topics:
  1. Vector spaces: groups; fields; vector spaces; subspaces, linear combinations; linear independence, bases, dimension; coordinates; axiom of choice, existence of bases; free vector spaces.
  2. Linear Maps: linear maps; image and kernel; isomorphisms; behavior of linear maps on bases; spaces of linear maps, algebras of linear operators; matrix representations of linear maps, change of basis, similarity; direct sums; quotients; first isomorphism theorem, rank-nullity theorem; systems of linear equations.
  3. Duality and multilinear algebra: linear functionals, dual space, dual bases, naturality of the double dual, dual transformation; multilinear forms, tensor products; alternating multilinear forms, determinants.
  4. Canonical forms: eigenvalues and eigenvectors; the characteristic polynomial; the minimal polynomial; diagonalizable operators; invariant subspaces; the Jordan canonical form.
  5. Orthogonality: inner product spaces; orthogonality; linear functionals on inner product spaces; the adjoint; self-adjoint operators; unitary and orthogonal operators; projections; the spectral theorem for self-adjoint operators.
• Learning Outcomes: Upon successful completion of the course, students will be able to do the following within the topic of linear algebra:
  1. Recall the basic definitions, theorems, and techniques.
  2. Distinguish truth from falsehood and create examples and counterexamples.
  3. Competently and confidently solve a variety of problems that require techniques from linear algebra.
  4. Communicate mathematical ideas and arguments in clear, convincing, and concise language..
  5. Construct concise and correct proofs.

Assessments

• Assessment Distribution: Your score is a nonnegative real number calculated as the weighted average of the following assessments. Click the links to learn more.
  • Daily Assignments (10%)*
  • Weekly Assignments (50%)
  • Midterm Exam (20%)*
  • Final Exam (20%)*
  * Assignment weights were updated 7/24/22. See syllabus for details.
• Submitting Assignments: All reading assignments and weekly assignments must be submitted via gradescope.
  
  • All daily and weekly assignments must be submitted via gradescope. When you submit your files, you will be prompted to select, for each specified problem or activity, the pages on which the associated work/solution are located. You are required to accurately identify the pages associated to each problem. If you fail to do so, you may receive a “No Pass” (if it is a daily assignment) or you may lose credit for each problem for which the pages are not correctly identified (if it is a weekly assignment).
  • Weekly assignments must be written using $\LaTeX$. All other assignments can be handwritten. It is your responsibility to make sure your handwritten submission is legible and easy to read. If you submit work that is difficult or impossible to read, you will not receive credit for it, and you will not be allowed to resubmit. There are numerous free smart phone apps that allow you scan your work and save it as a .pdf.
    
• Late Work Policy: I will not, under any circumstance, accept late submissions for daily assignments. Late submissions of weekly assignments and exams are only accepted, at my sole discretion, in extreme circumstances, such as in the case of a medical emergency. Extreme circumstances must be brought to my attention as soon as possible and must be adequately documented.
• Letter Grades: Your final letter grade depends on your score. Final letter grades are assigned according to the following score ranges:
  

  A+	96-100		B+	86-89		C+	76-79		D+	66-69		F	0-59
  A	93-95		B	83-85		C	73-75		D	63-65
  A-	90-92		B-	80-82		C-	70-72		D-	60-62

  
  Score ranges may be adjusted (to your advantage) according to class performance. Scores falling in be- tween two ranges will be rounded up. For example, according to the ranges above a final score of 75.1 will earn the letter grade C+ (rounded up), whereas a final score of 74.9 will earn the letter grade C (no rounding).
• P/NP Grading: A passing grade (P) will be awarded if your score would earn a letter grade of C or higher. Otherwise, you will not receive a passing grade (NP). Warning: a score earning the letter grade of C- is NOT passing, contrary to popular belief.