Course Syllabus

MATH 91 Linear Algebra (Fall 2022)

• Enrollment issues or other questions about math courses? Please contact the registrar or the Math Department Undergraduate Advising Team.
• Question that might be useful for other students to hear? Please ask on Ed discussion! (Ed discussion is linked in course navigation on the left.)

Course Description

This will be a first course in linear algebra, with an emphasis on topics most useful to students in Data Science and Statistics. Core material will include algebra and geometry of vectors and matrices; systems of linear equations; eigenvalues and eigenvectors; Gram-Schmidt and least squares; symmetric matrices and quadratic forms; singular value decomposition and other factorizations. Possible applications may include Markov chains and Perron-Frobenius, dimensionality reduction, and linear programming. Most material will be developed over the real numbers with their Euclidean geometry, with complex numbers and their Hermitian geometry introduced and utilized where helpful. The course will include lectures and discussion sections, weekly homework and quizzes, a midterm and a final exam. 

Class number

32192

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Text

We will be using notes in development for this course:

Gupta, Nadler & Paulin, Linear Algebra (version: December 9, 2022)

We will have a category on the Ed forum for helpful feedback: typos, suggestions, confusions, and contributions. Additionally, we will be thrilled to include useful material such as examples, pictures, exercises, etc provided by students.  

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Exams, Quizzes, and Homework

Exams

Midterm: during Thursday 9/29 lecture; to cover all material in Chapters 1-4.

Final Exam: Exam group 14, Thursday 12/15, 11:30am-2:30pm; to cover all course material.

Quizzes

There will be quizzes each week. They will be modeled on the sample quizzes contained in the modules.

Homework

Each week contains homework. You are encouraged to discuss ideas with other students. However, you must write and submit your solutions independently.

Gradescope

Gradescope will be used for submission of the homework. For instructions on how to scan and upload on Gradescope, see this video on submitting PDF homework and this handout with recommended scanning apps.

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Grading

Grading policy: Based on homework (10%), quizzes (30%), midterm (20%) and the final exam (40%).

We will drop your three lowest quiz scores and your three lowest homework scores.

Participation: We will not require attendance, but active participation in support of other students (for example, in asking and answering questions on the Ed discussion) will be used to raise your grade as possible.

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Course Policies

Academic honesty: You are expected to rely on your own knowledge and ability, and not use unauthorized materials or represent the work of others as your own. Protect your integrity and follow the honor code: "As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others."

There will be no make-up exams or quizzes. No late homework will be accepted.

Grades of Incomplete will be granted only for dire medical or personal emergencies that cause you to miss the final, and only if your work up to that point has been satisfactory.

Students with Disabilities

If you require course accommodations due to a physical, emotional, or learning disability, contact UC Berkeley’s Disabled Students' Program (DSP). Notify the instructors and GSI through course email of the accommodations you would like to use.

UC Berkeley is committed to providing robust educational experiences for all learners. With this goal in mind, we have activated the ALLY tool for this course. You will now be able to download content in a format that best fits your learning preference. PDF, HTML, EPUB, and MP3 are now available for most content items. For more information visit the alternative formats link or watch the video entitled, "Ally in bCourses."

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Useful Resources

Academic Resources

Some previous Math 54 course web pages:

• David Nadler's Fall 2017 Math 54.
• Nikhil Srivastava's Fall 2016 Math 54.
• David Nadler's Fall 2015 Math 54.
• David Nadler's Fall 2014 Math 54.
• Katrin Wehrheim's's Fall 2014 Math 54.
• Alberto Grunbaum's Fall 2013 Math 54.
• Alberto Grunbaum's Fall 2012 Math 54.
• Maciej Zworski's Spring 2012 Math 54.
• Olga Holtz's Fall 2010 Math 54.
• Peyam Tabrizian's Math 54 web page.
• George Melvin's Math 54 webpage.

Study help and tutoring:

• Study groups, reviews, and drop-in tutoring at the Student Learning Center.
• Math department list of tutors.

Some previous Math 54 exams:

• Math department archive
• Tau Beta Pi archive

Math 54 Worksheets.

Some online linear algebra:

• J. Strom, K. Astrom, and T. Akenine-Moller, Immersive Linear Algebra, "The world's first linear algebra book with fully interactive figures." (Thanks to Alven Wang for the link.)
• 3Blue1Brown, Essence of Linear Algebra, youtube videos. (Thanks to Carly de Frondeville for the link.)

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