Math 54 Spring 2021

One-on-one meetings: There are a limited number of appointments on bcourses. Sign up for a 30 minute slot to ask questions about the course or review specific concepts.

Review session: Thursday 2-4 pm PDT.

Questions and Feedback

Do you have a question you want me to address in the next discussion section? Or do you have any feedback about my teaching? Let me know by writing it in the box below.

Worksheets

• Discussion 1: Systems of linear equations. Solutions.
• Discussion 2: Row reduction. Worksheet. Solutions.
• Discussion 3: Vector arithmetic and span. Worksheet. Solutions.
• Discussion 4: Matrices and linear independence. Worksheet. Solutions.
• Discussion 5: Geometry of solution sets. Worksheet. Solutions.
• Discussion 6: Linear transformations. Worksheet. Solutions.
• Discussion 7: One-to-one and onto functions, composition of functions. Worksheet. Solutions.
• Note: for more practice with basic properties of functions and other mathematical terminology, see the notes and homework assignment I made when I taught this class in Summer 2017.
• Discussion 8: Composition and inverses of functions and matrices. Worksheet. Partial solutions.
• Discussion 9: Matrix algebra. Worksheet. Solutions.
• The midterm is coming up soon. See the “Links” section below for useful resources, including archives of old exams. Also, try looking at Nikhil’s websites from previous semesters when he taught this course (which include practice exams): Fall 2016, Fall 2018, Spring 2020. If you want even more review, try looking at my website from when I taught this course in Summer 2017.
• Midterm 1 review. Worksheet. Solutions. Notes from first review session and notes from second review session.
• Discussion 10: Bases and linear transformations. Notes.
• Discussion 11: Abstract vector spaces. Worksheet. Partial Solutions.
• Discussion 12: Coordinates. Worksheet. Solutions.
• Discussion 13: The matrix of a linear transformation. Worksheet. Solutions.
• Discussion 14: Change of coordinates. Worksheet. Solutions.
• Discussion 15: Eigenvectors. Worksheet. Solutions.
• Discussion 16: Diagonalization. Worksheet. Solutions.
• Discussion 17: Complex Eigenvalues. Worksheet. Solutions.
• Discussion 18: Dot Product. Worksheet. Solutions.
• Discussion 19: Orthogonal Bases and Projections. Worksheet. Solutions.
• Discussion 20: Gram-Schmidt and Least Squares. Worksheet. Partial Solutions.
• Midterm 2 review. Worksheet. Notes from review session (including solutions to some of the worksheet problems) and notes from discussion on Monday.
• Discussion 21: Spectral theorem. Notes 1 and notes 2.
• Discussion 22: SVD. Worksheet and partial solutions.
• Discussion 23: Intro to ODEs. Worksheet, solutions, part 1 and solutions, part 2.
• Discussion 24: Complex roots and initial value problems. Worksheet and partial solutions.
• Discussion 25: Systems of linear ODEs. Worksheet, solutions, part 1 and solutions, part 2.
• Discussion 26: Inner product spaces. Notes.
• Discussion 27: Fourier series. Notes.
• Final exam review. Worksheet and notes from the review session.

Quizzes and Homework

Quizzes are released on gradescope every Wednesday and you will 24 hours to complete them. Scored quizzes and official solutions will be provided within one week.

Homework will be posted on the course website after each lecture and will be due the following week on Tuesday on gradescope. Solutions will be posted the next day on bcourses and scores will be available within one week.

See the official course website for more details.

A Comment on Learning Mathematics

It is natural when learning about a new topic in mathematics to be confused or to think you understand something when you actually don’t. However, it can often feel embarrassing to admit to being confused or to answer a question if your answer may be wrong. It is very useful to learn to overcome this feeling of embarrassment and to speak up even when you are not sure you are correct. For this reason, I will try my best to encourage everyone to ask questions and to answer them without judgement.

Links

Logistics

• Course website. The most official source of all information about this class.
• Piazza. Ask and answer questions related to this class. Also contains a list of times and zoom links for all GSI discussion sections and office hours.
• Gradescope. The place to submit all homework, quizzes and exams.
• Bcourses. Contains all worksheets, quiz solutions and lecture notes.

Resources for learning linear algebra

• Student Learning Center. The SLC organizes an adjunct class, study groups, drop-in tutoring and exam reviews for math 54.
• 3Blue1Brown linear algebra videos. A nice series of videos explaining the foundations of linear algebra in an intuitive way.
• David Nadler’s Math 54 page. The lecture notes may be helpful (you’ll need to scroll pretty far down the page to see them).

Old worksheets and old exams

• Math 54 worksheets. The math department’s archive of worksheets containing many practice problems.
• Archive of past exams. The math department’s archive of old math 54 exams.
• Even more past exams. TBP’s archive of old math 54 exams. Not officially endorsed by the math department, so caveat lector.

Other useful stuff

• Tool (made by Kyle Miller) for visualizing linear transformations
• The Matrix Cookbook. A useful collection of facts and algorithms in linear algebra. It mostly focuses on things that are not covered in math 54, but it is a good resource to be aware of if you encounter linear algebra in the future.