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Math 21 is a 4 credit course in introductory
calculus, third in the Math 19-20-21 sequence. The class provides
an introduction to the idea of infinite accumulation, first in the
form of improper integral and then for series. Course policies
(including grading and exams) can be found on this page. For a
week-by-week breakdown of the material, see the Course Schedule page.
Students are expected to have a strong foundation in precalculus, such
as comfort with the concept of functions, equations of lines, trig
and inverse trig, ability to manipulate algebraic expressions,
factoring polynomials, etc. Further, students are expected to be familiar with the material of
Math 19 and Math 20. In particular, students should be comfortable with the
idea of a limit, the idea of the derivative and the integral, and taking
derivatives/integrals of a wide range of functions. Students
should know (and know when to apply) the product rule, chain
rule, substitution, and integration by parts. Students who are unsure of their
background should see their instructor as early as
possible. Students who want to brush up on their precalculus
skills can find more resources on this page.
- Dr. Sam Kimport
Lectures: MWF 9:30-10:20, 10:30-11:20 (both in 380-380Y)
- Dr. Christine Taylor
Lectures: MWF 11:30-12:20 (in 380-380C), 1:30-2:20 (380-380W)
- Ipsita Datta
Sections: Tu 9:30-10:20 (in 200-219), 10:30-11:20 (in
200-202), 12:30-1:20 (in 200-013)
- Zach Izzo
Sections: Tu 10:30-11:20, 11:30-12:20 (both in School of
- Bogdan Zavyalov
Sections: Tu 9:30-10:20 (in 380-380F), 11:30-12:20
(in 90-92Q), 12:30-1:20 (in 380-381U)
- Adva Wolf (ACE)
Section: Tu 1:30 - 3:20 (only available to members of
the ACE program)
You are encouraged to attend the office hours
provided by any of the instructors or course 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.
Free VPTL Tutoring:
Want to meet with an experienced peer to discuss course
concepts, think through a problem set, or prepare for an
upcoming exam? VPTL offers free drop-in and appointment
tutoring for MATH 19, in addition to tutoring for a number
of other courses. For more information and to schedule an
appointment, visit our tutoring
appointments and drop-in schedule page.
tutoring: SUMO works with the Stanford Math
Department to provide peer tutoring services for a number
of introductory math classes, including MATH 19, 20,
21. The peer tutors are available to answer any questions
you have about the material and homework in these
Peer tutoring hours are drop-in; just show up and our
tutors will help you out. Feel free to come and work on
your homework even if you don't have any specific
questions. Many students work on their homework during
tutoring, asking questions if they encounter
Starting the second week of each quarter, tutoring for
Math 19, 20, and 21 will occur Tuesday and Thursday from
6:00 PM to 10:00 PM in room 380-381T. Tutoring will
continue through Dead Week but exclude university
The textbook for this course is Calculus: Single
Variable, 7th edition,
by Hughes-Hallett, Gleason, McCallum, et al. (This was
the textbook for Math 19 and Math 20.) This course mainly focus on topics
from Sections 7.6 and 7.7, as well as Chapters 9 and 10.
All practice problems and suggested reading are
taken from the book, so you should have a copy. It is a
valuable additional resource for learning the course
material besides lecture.
For your convenience the textbook is
available for purchase at the Stanford bookstore. However, this is a
pretty standard textbook and you might be able to buy it elsewhere new
or used for a lower price.
Affordability of Course Materials
Stanford University and its instructors are committed
to ensuring that all courses are financially accessible to
all students. If you are an undergraduate who needs
assistance with the cost of course textbooks, supplies,
materials and/or fees, you are welcome to approach your instructor
directly. If would prefer not to approach them directly,
please note that you can ask the Diversity & First-Gen
Office for assistance by completing their questionnaire on
course textbooks & supplies: http://tinyurl.com/jpqbarn
or by contacting Joseph Brown, the Associate Director of
the Diversity and First-Gen Office (firstname.lastname@example.org;
Old Union Room 207). Dr. Brown is available to connect you
with resources and support while ensuring your privacy.
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).
Students are strongly encouraged to attend the
lecture they are registered for. We recognize
that schedules can vary week-to-week, so you are invited
to attend whichever lecture works subject to available seating! HOWEVER: we strongly
recommend that you stick with a single instructor when
possible. The instructors are following the same
syllabus and weekly schedule but pacing can be different.
Therefore, switching between instructors may result in
missing topics or examples.
Discussion sessions are a great additional resource
we have in Math 21. Held at various times on Tuesdays
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
You are required
to attend discussion session with a TA at least
5 weeks of the term, though we strongly encourage you to
have it in your schedule every week. Failure to do so
will impact your grade.
enroll in a discussion section via Axess. If you
only enrolled in a lecture and not a section, you will
need to drop your lecture and then re-enroll, being sure to
select a discussion section.
Your grade will be based on the following components:
- Homework: 10%
- Attendance of TA sections: 5%
- Midterm Exam 1: 25%
- Midterm Exam 2: 25%
- Final Exam: 35%
Grades will be assigned using the "standard curve"
(94-100: A, 90-94: A-, 87-90: B+, 84-87: B, 80-84: B-,
etc.) as a lower bound but beyond that, do not have
predetermined cutoffs. This means that if your numerical
weighted average is an 85, your course grade will be a B
or higher. The exact cureve is based on the averages on
all exams and not computed until the final has been graded.
The "A+" grade is extremely rare and is only given at
the instructors' discretion to students who do
expectionally well in the course.
There will be weekly homework posted on the homework page.
Homework will be due every week on
Wednesday at 9am. For details about handing in your
homework, see the homework page.
Upon enrollment in the course, all subsequent homework
assignments will count towards your homework grade. If you enroll
by April 10, you are elligible to have your lowest
homework score dropped from your total score at the end of
the quarter. To qualify for this, you must complete the
assignment at this
link by April 10.
Late homework will be accepted only under very exceptional
Homework and the Honor Code
You are bound by the Stanford Honor Code for all
work submitted for Math 21, 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.
There will be two EVENING midterm exams and a university scheduled
final exam. Most of the problems on the exams will be similar to the
problems in the weekly homework, but there will always be some
harder problems. The material covered by each exam is given by the
suggested reading and homework, including the practice problems.
exams for Math 21 this quarter are closed-book, closed-notes, with no
calculators or other electronic aids permitted . Individual exams will
be neither curved nor scaled -- we use your raw score in all grade computations.
The evening midterm dates are given below; it is your responsibility to verify right now
that you can attend these exams. Please contact your instructor
as soon as possible if you will not be able to attend one of the
midterms. In any case, if you need to reschedule the exam you must do
so no later than two weeks before the exam. The final exam cannot be
rescheduled, per department policy.
You will have assigned seating for exams. The seating
chart will be posted in the exam classroom on the day of the exam; you
are responsible for arriving a few minutes early to find your seat
before the exam starts. Failure to sit in your assigned seat will be
considered a breach of the Stanford Honor Code and be handled
If an emergency occurs and you need to miss an exam, contact your instructor as soon as possible.
- Midterm 1: Wednesday, April 24, 7:00pm - 8:30pm
- Midterm 2: Wednesday, May 15, 7:00pm - 8:30pm
- Final exam: Friday, June 7, 7:00pm - 10:00pm
For more information, see the Exams page.
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 exams, 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.
If you are involved in a sport which may require you
to travel this quarter, and especially if you will miss
either of the midterms, please let the instructor know as
soon as possible so that appropriate accommodations can be
made. If you do not let the instructor know at least a
week in advance of a missed exam, you may be denied the
opportunity to take it at an alternate time or on the road. You are also
responsible for homework while traveling. See the homework page for information
about turning in homework.
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 the
Math 19-20-21 sequence. Calculators are not allowed or needed on any of
the exams. 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.