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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.
- Dr. Gene Kim
- Joey Zou (admin TA)
- Calista Bernard
- Haoya Li
- Zhiqi Li
- Dat Nguyen
Dat's Jamboard link
- Kevin Yang (ACE)
- Zhengqing Zhou
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.
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).
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
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
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.
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.
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: http://oae.stanford.edu).
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.
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
- 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.