Courses in the Calculus Sequence
The systematic study of mathematics begins with one of the following two alternative sequences:
Pre-Calculus (or Bulletin listing)
Calculus 1 (or Bulletin listing)
Calculus 2 (or Bulletin listing)
Calculus 3 (or Bulletin listing)
Calculus 4 (or Bulletin listing)
Accelerated Multivariable Calculus (or Bulletin listing)
or
Honors Math A and B (or Bulletin listing, Honors A and Bulletin listing, Honors B)
Honors Mathematics A-B is intended for students with a strong background in Calculus, a serious interest in mathematics, and a desire for a rigorous, theoretical approach. It is designed for students who are well-prepared and eager to engage with mathematics at a deep level. The course covers the material of linear algebra and multivariable calculus from a proof-based perspective, along with additional advanced topics chosen by the instructor. Honors Mathematics A-B provides an introduction to the Department’s upper-level undergraduate mathematics courses.
Calculus Placement, AP Credit, and Transfer of Credit
Placement in the Calculus Sequences
School of Engineering and Applied Science students should consult SEAS for Calculus placement information.
Columbia College and other non-SEAS students:
- For placement purposes, the Mathematics Department considers the following equivalent to Calculus 1 and 2 at Columbia:
- A score of 5 on the Calculus BC Advanced Placement.
- A score of 7 on the IB Mathematics: analysis and approaches HL exam (2021 or later) or a score of 7 on the IB HL Mathematics or Further Mathematics exams (2020 or earlier).
- A grade of A on the A-Level Further Mathematics examination in the U.K.
Students with any of these scores should begin with Calculus 3, Accelerated Multivariable Calculus, or Honors Math A. They do not need to take Calculus 1 or 2.
- For placement purposes, the Mathematics Department considers the following equivalent to Calculus 1 at Columbia:
- A score of 4 on the Calculus BC Advanced Placement exam.
- A score of 4 or 5 on the Calculus AB Advanced Placement exam.
- A score of 6 on the IB Mathematics: analysis and approaches HL exam (2021 or later) or a score of 6 on the IB HL Mathematics or Further Mathematics exams (2020 or earlier).
- A score of 6 or 7 on the IB Mathematics: applications and interpretation HL exam (2021 or later) or a score of 6 or 7 on the IB SL Mathematics exam (2020 or earlier). This does not include the IB “Mathematical Studies SL” exam.
- A grade of A on the A-Level Advanced Mathematics examination in the U.K.
- A grade of A in a full year of high school calculus.
Students with any of these scores may begin with Calculus 2 or Calculus 3. Note that Calculus 2 is not a prerequisite for Calculus 3. However, students who start with Calculus 3 may still need to take Calculus 2 if it is required for their program. In all cases, students MUST complete Calculus 2 before taking Calculus 4.
- All other students should start with Calculus 1 or Pre-Calculus.
- Prospective Economics majors should consult the Economics department Math Requirements page.
Credit for Advanced Placement and IB Exams
- Students with a score of 5 on the AP Calculus BC exam or 7 on the IB Mathematics: analysis and approaches HL exam may receive 6 points of AP credit upon completion of Calculus 3 or Accelerated Multivariable Calculus with a grade of C or higher. They will not receive AP credit if they take Calculus 1 or 2, or if they take no calculus at Columbia.
- Students with a score of 4 or 5 on the AP Calculus AB exam, a 4 on the AP Calculus BC exam, or a 6 on the IB Mathematics: analysis and approaches HL exam may receive 3 points of AP credit upon completion of either Calculus 2 or Calculus 3 with a grade of C or higher. They will not receive AP credit if they take Calculus 1, or if they take no calculus at Columbia.
Honors Mathematics A: Students with a strong interest in a proof-oriented, theoretical approach to mathematics, and who have a score of 5 on the AP Calculus BC exam or 7 on the IB Mathematics: analysis and approaches HL exam, may begin with Honors Mathematics A. This course is especially designed for prospective mathematics majors. Students who complete Honors Mathematics A with a grade of C or higher may receive 6 points of AP credit.
Transfer of Credit from Other Institutions
Students who wish to transfer credit for mathematics courses taken elsewhere should follow these guidelines:
- For Calculus courses and other MATH courses at the 2000 level or below, contact the Calculus Director.
- For MATH courses at the 3000 level or higher, contact the Director of Undergraduate Studies.
See the FAQ below for more information about transfer credit requirements and guidelines.
Contacts
For questions, please contact the relevant person below.
Director of Undergraduate Studies: Julien Dubedat
Calculus Director: George Dragomir
Course Textbook
Calculus I-IV and Accelerated Multivariable Calculus will be using
James Stewart, Calculus: Early Transcendentals, 9th edition.
WebAssign
WebAssign, an integrated online learning system linked with the course textbook, will be used in some Calculus I-III sections.
WebAssign is mandatory only for students enrolled in sections where it is specified (refer to your section’s syllabus). For all other sections, it remains optional but may serve as a helpful study resource. For details, visit the department’s WebAssign page.
Frequently Asked Questions
Placement and AP/IB Credit
Q: Is there a placement exam for Calculus?
A: No. The Mathematics Department does not offer a placement exam. Placement is determined by standardized exam scores (such as AP or IB) and high school coursework, as outlined on this page.
Q: If I place out of a Calculus course, do I automatically receive credit?
A: No. Placing out means you are not required to take the course for placement purposes, but it does not automatically grant academic credit. Credit is awarded primarily based on AP or IB scores. If you place out of a degree required Calculus course, you must take another course, typically a MATH course, to fulfill the missing credits. Consult your major department and advising dean for approval.
Q: My AP or IB scores place me into a certain Calculus course, but I’m unsure if it’s the right fit. What should I do?
A: Placement guidelines are based on extensive experience but are flexible. If you are uncertain, consult the Calculus Director. You may also choose to enroll in a lower-level course to strengthen your understanding.
Q: My AP or IB scores place me out of both Calculus I and II, and I took Multivariable Calculus at the college level during high school. Do I still need to take a course at Columbia to receive AP credit?
A: Yes. To receive AP credit, you must complete a 2000-level or higher MATH course at Columbia with a grade of C or higher. Courses taken during high school, even if college-level, do not count for Columbia credit.
Q: How does AP credit work?
A: AP credit is awarded only after you complete an appropriate Columbia Calculus course with a grade of C or higher. See the placement and credit section for full details.
Q: I completed a different secondary school program. Can I use my exam results for placement or credit?
A: In some cases, placement based on other national examinations may be possible. Contact the Calculus Director for evaluation. However, AP credit is awarded primarily based on AP and IB scores.
Transfer Credit
Q: What do I need to request transfer credit?
A: You must submit:
- Your intended major or program
- A full course syllabus (not just a catalog description), including topics covered, methods of instruction and assessment, and textbook details (with chapters covered)
- An unofficial transcript showing course completion and final grade.
Q: Is there a minimum grade required for transfer credit?
A: A passing grade is usually sufficient, but requirements may vary by department. Consult your major department and advising dean.
Q: Can I transfer an online course?
A: No, except for courses taken during the COVID-19 pandemic under special circumstances.
Q: Can I transfer credit for a college-level course I took while in high school?
A: No. College-level courses taken during high school do not earn Columbia credit. However, such coursework may inform placement decisions.
Q: Can I transfer credit for a course in Statistics, Computer Science, or Applied Physics?
A: No. The Mathematics Department evaluates transfer credit only for MATH courses it offers. Courses from other departments must be evaluated by the corresponding department, even if they include significant mathematical content.
Calculus Classes
Q: Can I switch between sections, levels, or sequences of Calculus?
A: During the Change of Program Period (first two weeks of the semester), you may switch freely between sections or sequences, subject to space availability. Afterward, until the Course Drop Deadline (around week 5), you may transfer into a lower-level course with approval from both the instructor and your advising dean.
Q: What calculator should I get for Calculus courses?
A: None. Calculators are not permitted during Calculus exams at Columbia, and you don’t really need one for coursework.
Q: Can I use my friend’s WebAssign account?
A: No. See the department’s WebAssign page for details regarding accessing WebAssign.
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