Math 51
Spring 2021

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Course Description and Prerequisites

Linear Algebra and Multivariable Calculus are two of the most widely used mathematical tools in quantitative work across all fields of study. This course develops conceptual understanding and problem-solving skills in both, highlighting how multivariable calculus is most naturally understood in terms of linear algebra, and addresses a variety of real-world applications.

Our focus is on teaching you skills that underlie a wide array of applications and preparing you for all courses involving advanced quantitative work (across all sciences, engineering, economics, computer science, statistics, and so on).

  • relate the algebra of systems of linear equations to the geometry of vectors, acquiring the ability to "see" in dimensions far beyond 3 (thinking is seeing!);
  • analyze the behavior of multivariable functions via partial derivatives, and combine that information with tools of linear algebra (such as matrices and eigenvalues) to solve optimization problems;
  • apply your newly acquired visual skills in high dimensions to gain insight into a variety of real-world applications across data science, natural sciences, and economics.
  • Instructor

    • Dr. Gene Kim
      Office: Zoom
      Email: genebkim(at)stanford(dot)edu

    Teaching Assistants

    • Joey Zou (admin TA)
      Office: Zoom
      Email: zou91(at)stanford(dot)edu

    • Calista Bernard
      Office: Zoom
      Email: calista(at)stanford(dot)edu
    • Haoya Li
      Office: Zoom
      Email: lihaoya(at)stanford(dot)edu
    • Zhiqi Li
      Office: Zoom
    • Dat Nguyen
      Office: Zoom
      Email: dpnguyen(at)stanford(dot)edu
      Dat's Jamboard link
    • Kevin Yang (ACE)
      Office: Zoom
      Email: kyang95(at)stanford(dot)edu
    • Zhengqing Zhou
      Office: Zoom
      Email: zqzhou(at)stanford(dot)edu

    Office Hours

    You are encouraged to attend the office hours provided by any of the instructors or teaching assistants, regardless of which lecture you are enrolled in. No appointment is necessary, just drop in at the scheduled office hours with your questions!

    The scheduled office hours for any given week can be found on the Office Hours page. Note that they might change slightly from week to week so it's always a good idea to check both the time and location before walking all the way across campus hopping on Zoom.


    The textbook for Math 51 is available for free to Stanford students! This is the third year that we are using a textbook specifically written for this course by the Stanford Math department in consultation with colleagues in many other departments. The book is free and available in electronic version only. The textbook can be downloaded via this link.

    The book contains much more than is covered in the course. It also includes many fully worked examples, helpful for studying (akin to "odd-numbered exercises with solutions in the back"). We hope it will be a useful resource for topics that you may encounter in later coursework. On the second page of the introduction, you will find the e-mail address for reporting any corrections, typos, etc. The authors of the text are very eager to hear from you.

    Attending Lecture

    Attendance is not required at lecture, yet regular attendance is important to your success in this class. A student who misses class is responsible for finding out what was discussed and learning the material that was covered on that day. The teaching team is not responsible for re-teaching material missed by a student who did not attend class regardless of the reason for the absence, though we are willing to address any points of confusion in office hours (whether you were in class or not).

    Attending Section

    Discussion sessions are a great additional resource we have in Math 51. Held at various times on Tuesdays and Thursdays this term, they will provide opportunities to see more guided examples and try your hand at exercises with a member of the teaching team present. More exposure to and practice with the material will greatly add to your learning.


    Your grade will be based on the following components:

    • Homework: 30%
    • Questionnaires: 6%
    • Quizzes: 64%


    There will be weekly homework posted on the homework page.

    Homework will be due every week on Wednesday at 10:00 a.m. Stanford time. For details about handing in your homework, see the homework page.

    Absolutely no late homework will be accepted. This is due to the fact that homework solutions will be posted immediately after the deadline.

    Out of nine total homework assignments, the lowest score will be dropped in final course average calculations.

    Homework and the Honor Code

    You are bound by the Stanford Honor Code for all work submitted for Math 51, including the homework assignments. For homework, we encourage you to use your book and all your notes, come to office hours, talk with any tutor(s) you have, and collaborate with your peers. We believe that thinking about math and conversing about math is an important part of the learning process.

    However, we expect that the work you submit is work you have written yourself and reflects your understanding of the problem and how to solve it. If you work on a problem with someone else, DO NOT copy their solution and instead, write it up on your own.

    Finding a solution off of the internet, copying it without thought onto your homework, and then submitting it for credit is a violation of the Stanford Honor Code and will be addressed as such.

    Pre-Class Reading Questionnaires (PCRQ)

    A pre-class reading questionnaire (PCRQ) will be released 24 hours before every lecture. Each PCRQ will have a few questions about the targeted reading (mentioned in the weekly announcements); these will be graded on effort. There will also be a check-in question, based on the previous chapter, which will be graded on accuracy. For each week, the top two scores among the PCRQs for that week will count towards final average calculations. Note that Weeks 1 and 9 will have two PCRQs, and Weeks 2 - 8 will have three.


    There will be an 1-hour quiz on Fridays of Weeks 2 through 10. The material for the quiz will be based on the homework due on Wednesday of that week (material covered the week before). For more information, see the Quizzes page.

    Out of nine total quizzes, your quiz average for final grade calculations will be done as follows. Consider the following two calculations:

  • (4/6)*(four highest scores out of Quizzes 1 - 7) + (1/6)*(Quiz 8 score) + (1/6)*(Quiz 9 score)
  • Provided that your Quiz 9 score is greater than or equal to 50%, (3/4)*(six highest scores out of Quizzes 1 - 7) + (1/4)*(higher score out of Quizzes 8 and 9)

  • If your Quiz 9 score is greater than or equal to 50%, the higher of the two options will be used in your final course average calculations, and if your Quiz 9 score is below 50%, the first option will be used in your final course average calculations.

    In particular, you can skip 3 of the first 7 quizzes if you plan to get graded under the first option. Bear in mind that mathematics beyond the high school level is a cumulative subject, so if you skip a quiz, then the skills it involves can be very relevant in later quizzes too. The reason for quizzes 8 and 9 being treated differently is beacuse the material near the end of the course is not only a synthesis of much that has come before, but it is also of tremendous utility throughout many other fields and so is particularly important; so we aim to provide motivation to keep learning the material throughout the term.

    Office of Accessible Education accommodations

    Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066, URL:

    Once you have done so, please let your instructor know as soon as possible so that proper accommodations can be made. For accommodations on quizzes, your instructor must have your letter from OAE no later than one week prior to the exam. Otherwise, we may not have sufficient time to make the accommodations.

    Other important policies

    • Extra credit assignments: Occasionally students ask for extra credit in order to improve their grade. While we can recommend additional practice problems, we cannot offer them for credit as it would be unfair to the entire class if only a small number of students were allowed a chance to improve their grade. If you become worried about your understanding and grade in the course, please see your instructor as soon as possible for advice.
    • Calculator policy: Calculators are not used in a systematic way in Math 51. Calculators will not be needed on any of the quizzes. Occasionally, homework problems may call for the use of a scientific or graphing calculator, and it is fine to use them for this purpose.
    • Honor code policy: By Math Department policy, any student found to be in violation of the Honor Code on any assignment or exam in this course will receive a final course letter grade of NP.
    Spring 2021 -- Department of Mathematics, Stanford University
    Problems with this page? Contact Dr. Kim so we can fix the problem.