Math 21
Autumn 2026
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Course Description and Prerequisites

Math 21 is a 4 credit course in introductory calculus, the last one 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. Topics covered include improper integrals, sequences, infinite series, power series, Taylor series, and Applications.

If you have not previously taken a calculus course at Stanford, you must have taken the math placement diagnostic exam to register for this course.

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. Here is a Precalculus Refresher.

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.

Learning Goals

  • Understand the meaning of an improper integral and be able to interpret convergence/divergence of these objects.
  • Learn the meaning of convergence and divergence for infinite sequences and series, and apply convergence tests for infinite series.
  • Apply knowledge of infinite series to power series. Use power series to analyze various transcendental functions.

Instructor

  • Prof. Jared Duker Lichtman
    Office: 380-382Q2
    Email: jdl18(at)stanford(dot)edu
    Lectures: MWF 12:30-1:20 in 370-370

  • Prof. Weite Pi
    Office: 380-382C
    Email: wpi(at)stanford(dot)edu
    Lectures: MWF 1:30-2:20 in 370-370

  • Dr. Christine Taylor
    Office: 380-381J
    Email: taylor13(at)stanford(dot)edu
    Lectures: MWF 10:30-11:20 in 370-370

  • Dr. Wojciech Wieczorek Office: 380-381E
    Email: wojciech(at)stanford(dot)edu
    Lectures: MWF 9:30-10:20 and 11:30-12:20 both in 370-370

Teaching Assistants

  • Selim Amar
    Office: 380-380G
    Email: selama(at)stanford(dot)edu
    Sections: T 9:30-10:20 and 10:30-11:20 in Thornton 110

  • Naseebullah Andar
    Office: SLTC104
    Email: andar(at)stanford(dot)edu
    Sections: T 1:30-2:20 in Thornton 110 and 2:30-3:20 in 380-380Y

  • Hikari Iwasaki
    Office: 380-380L
    Email: iwasakih(at)stanford(dot)edu
    Sections: T 12:30-1:20 in 380-380Y and 1:30-2:20 in 380-380F

  • Matthew Kendall
    Office: 380-381F
    Email: mkend(at)stanford(dot)edu
    Sections: T 9:30-10:20 in Hewlett 102 and 12:30-1:20 in Thornton 110

  • Alex Lopez
    Office: 380-381N
    Email: alexanderlopez(at)stanford(dot)edu
    Sections: T 11:30-12:20 in Thornton 110 and 2:30-3:20 in 380-380F

  • Yingzi Yang
    Office: 380-380L
    Email: yyingzi(at)stanford(dot)edu
    Sections: T 9:30-10:20 and 10:30-11:20 in ANKO 109

  • Zhuo Zhang
    Office: 380-381L
    Email: zhuozh(at)stanford(dot)edu
    Sections: T 11:30-12:20 and 12:30-1:20 in ANKO 108

Office Hours and Tutoring

You are encouraged to attend the office hours provided by any of the teaching staff. 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.

The Stanford University Mathematics Organization (SUMO) works with the Stanford Math department to provide free drop-in tutoring services for Math 21. The tutors are Stanford undergraduates available to answer any questions you have about the material and homework in Math 21. Just show up and the tutors will help you out. Starting the second week of each quarter, SUMO tutoring for Math 21 is on Sunday, Monday, and Tuesday evenings. Tutoring continues through Dead Week but excludes university holidays.

The Center for Teaching and Learning offers free drop-in and individual appointment tutoring. To schedule an individual appointment, visit studentlearning.stanford.edu/tutoring. To view our drop-in schedule and to view information about tutoring for other courses, visit tutoring.stanford.edu.

Textbook

The textbook for this course is OpenStax Calculus Volume 2 freely available online. (OpenStax is the text for Math 19 and Math 20 as well.) This course mainly focuses on topics from section 3.7 and chapters 5 and 6.

In-Person Policies

Students should attend the in-person lecture and discussion section to which they are officially assigned. This ensures that classrooms do not exceed official room capacity, and supports prompt notification should a specific section need to move online at short notice. Course messages are sent out via Canvas, please ensure that your Canvas notifications are on so that you receive any announcements promptly.

As standard practice, lectures and discussion sections in Mathematics courses are taught in-person. As such, Zoom links will not be provided. Additionally, in-person lectures and discussion sections will not be recorded. The use of personal recording devices (including taking photos) is prohibited without prior permission from the instructor.

Students who miss class due to illness (including COVID-19) should make arrangements to obtain lecture notes from other students in the class. As standard practice, there are no make-up exams or remote exams. If you will miss an exam due to illness, please reach out to your instructor for more information.

Grades

Your grade will be based on the following components:

  • Homework: 10% (total points earned divided by 90% of total possible points, not to exceed 100%)
  • Midterm Exam 1: 25%
  • Midterm Exam 2: 25%
  • Final Exam: 40%
  • Post-Lecture Review Problems on Canvas (Optional/Bonus): 2%

There are no predetermined numerical cutoffs for letter grades.

Homework

There will be weekly homework posted on the homework page.

Your solutions to the assigned homework will be graded and returned to you.

Homework will be due every week on Wednesday at 9am, starting on September 30. For details about handing in your homework, see the homework page.

Late homework will be not be accepted under any circumstances; however, your total homework score will be multiplied by 10/9 (not to exceed 100%) at the end of the quarter; please do not rely on this scaling factor early in the term.

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 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.

Exams

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 and discussion section, but there will always be some harder problems. The material covered by each exam is given by the suggested reading and homework.

All exams for Math 21 this quarter are proctored, closed-book, closed-notes, with no calculators or other electronic aids (phones, calculators, smart watch, smart glasses etc.) permitted. Individual exams will be neither curved nor scaled.

A reference sheet with helpful material will be provided for each exam. The sheet will also be released in advance so you have time to see what is included on it. Exams will not require the use of calculators. Students will be required to temporarily surrender electronic devices (phones, smart watch, smart glasses) while taking the exam (a clock will be provided in the exam room).

The evening midterm dates are given below; it is your responsibility to verify right now that you can attend these exams. Please fill out the ACCOMMODATIONS & FLEXIBILITY FORM as soon as possible if you have a permissible schedule conflict (e.g., course or competition) with a midterm. In any case, if you need to reschedule the exam to an alternate sitting (which by department policy must be slightly earlier on the same day), you must do so no later than two weeks before the exam. The date and time of the final exam are set by the University and cannot be changed.

There will be a mandatory seating chart for exams, which will be posted/distributed in the exam classroom. Please arrive early for the exam so that you can find your assigned seat. Failure to sit in your assigned seat will be considered a breach of the Stanford Honor Code and be handled accordingly.

  • Midterm 1: Thursday, October 15, 5:30pm-7pm
  • Midterm 2: Thursday, November 5, 5:30pm-7pm
  • Final exam: Tuesday, December 8, 12:15pm-3:15pm

You are required to take the exams at the scheduled date and time. Exact room assignments will be announced when they are available. Check for exam conflicts right away and contact us: Except in case of emergency, you must inform us of exam conflicts at least two weeks prior to the exam, together with a valid reason for the conflict. The allowable reasons are course-related or NCAA sanctioned competition-related schedule. The final exam cannot be rescheduled. Please also note the university policy that it is your responsibility to make sure that you will be available at the announced final exam time and that you do not have two exams at the same time. Stanford's policy declares that you accept the final exam schedule when you continue in the classes past the Final Study List deadline, i.e. Friday October 9 5pm. If two exams conflict, you must not register for both classes.

For more information, see the Exams page. See also the exam-studying advice in Tips for a Successful Calculus Course.

Academic Integrity

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. You are fully responsible for adhering to the requirements of the Honor Code. In particular, it is forbidden to
  • Collaborating with another student or any other person on an exam.
  • Copying from another's homework or exam, or allowing another student to copy your work.
  • Communicating with a person other than the teaching staff via email, text messaging, Google, any form of social media, messenger, chat rooms, message boards, etc., about anything related to the exam.
  • Plagiarism of material that you did not create, such as copying parts of posted solutions or text wholesale from anywhere, including the internet. The work that you submit must be your own. This also includes representing another's work as your own.
  • Sharing the exam questions or anything in your solutions with any other person for any reason. The restrictions on sharing exam content applies until 11:59PM on the exam date.
The university is well-aware of "academic educational sites", such as Chegg, Slader, CourseHero, etc. Their use in connection with a course assignment or exam is an Honor Code violation that is taken very seriously at Stanford.

It is forbidden to share a copy of your written work from the current or a prior quarter with another student, or to make it available (say on a shared server, public or private) in such a way that it could be reasonably expected to be obtained by another student; it is additionally forbidden to copy the work of another or otherwise submit the work of another as your own. For the purposes of this course and general University policy, "the work of another" includes the output of AI chatbots as well as that of online "study" repositories or so-called "tutoring" sites.

More information about the Stanford Honor Code can be found here.

Exam Proctoring

All exams in this course will be proctored. Please see Math Exam Instructions here.

Access and Accommodations

If you experience disability, please register with the Office of Accessible Education (OAE). Professional staff will evaluate your needs, support appropriate and reasonable accommodations, and prepare an Academic Accommodation Letter for faculty. To get started, or to re-initiate services, please visit oae.stanford.edu. The "OAE" is located at 563 Salvatierra Walk (phone: 1-650-723-1066).

To receive academic accommodations in this course, you must provide an accommodation letter from the OAE, dated in the current quarter, by filling out the ACCOMMODATIONS & FLEXIBILITY FORM to detail the specific accommodations you will need in this course. Letters are preferred by the end of week 2, and at least two weeks in advance of any exam for us to have adequate time to arrange the accommodations.

New accommodation letters, or revised letters, can be submitted throughout the quarter; please note that there may be constraints in fulfilling last-minute requests. Alerting the course staff of Math 21 is not equivalent to filling out the ACCOMMODATIONS & FLEXIBILITY FORM and may not result in your receiving timely accommodations.

ACE Program

ACE (Additional Calculus for Engineers) is a program run by the School of Engineering for all students (not just prospective engineering majors). More info on ACE is available here, including a link to the application due Friday of Week 1 at 5pm). Only students who have applied and been accepted should attend these sessions.

Other Important Policies

  • Please see important math course policies on exam conflicts, academic accommodations, AI guidance, and taking exams. It is your responsibility to thoroughly read this information.
  • 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 contact 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.

Autumn 2026 -- Department of Mathematics, Stanford University