Math 21
Spring 2019

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Course Description and Prerequisites

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
    Office: 380-381C
    Email: skimport(at)stanford(dot)edu
    Lectures: MWF 9:30-10:20, 10:30-11:20 (both in 380-380Y)

  • Dr. Christine Taylor
    Office: 380-381J
    Email: taylor13(at)stanford(dot)edu
    Lectures: MWF 11:30-12:20 (in 380-380C), 1:30-2:20 (380-380W)

Teaching Assistants

  • Ipsita Datta
    Office: 380-381A
    Email: ipsi(at)stanford(dot)edu
    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
    Office: 380-380N
    Email: zizzo(at)stanford(dot)edu
    Sections: Tu 10:30-11:20, 11:30-12:20 (both in School of Education 313)

  • Bogdan Zavyalov
    Office: 380-381N
    Email: bogdzav(at)stanford(dot)edu
    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)
    Office: 380-381L
    Email: advaw(at)stanford(dot)edu
    Section: Tu 1:30 - 3:20 (only available to members of the ACE program)

Office Hours

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.

Additional drop-in 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 classes.

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 difficulties.

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 holidays.


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: or by contacting Joseph Brown, the Associate Director of the Diversity and First-Gen Office (; Old Union Room 207). Dr. Brown is available to connect you with resources and support while ensuring your privacy.

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).

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.

Attending Section

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 learning.

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.

You MUST 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 circumstances.

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 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.


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.

All 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 accordingly.

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.

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 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.

Student Athletes

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.

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 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 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 2019 -- Department of Mathematics, Stanford University
Problems with this page? Contact Dr. Kimport so we can fix the problem.