Calculus Courses and Placement
This page explains the Mathematics Department’s calculus sequence, placement guidelines, and credit for AP, IB, and other examinations.
Students requesting placement based on prior calculus coursework or evaluation of coursework taken at another institution should review the department’s Placement and Transfer Credit page.
Incoming students should begin with the Calculus Placement section below.
Quick Links
- Courses in the Calculus Sequence
- Calculus Placement
- Credit for AP, IB, and Other Examinations
- Placement and Transfer Credit Requests
- Textbook and WebAssign
- Calculus Readiness Resources
- Frequently Asked Questions
Courses in the Calculus Sequence
Students beginning the systematic study of mathematics usually follow one of two paths: the standard calculus sequence or the Honors Mathematics sequence.
Standard Calculus Sequence
| Course Name | Course Code | Bulletin |
|---|---|---|
| Calculus I | MATH UN1101 | Bulletin listing |
| Calculus II | MATH UN1102 | Bulletin listing |
| Calculus III | MATH UN1201 | Bulletin listing |
| Calculus IV | MATH UN1202 | Bulletin listing |
| Accelerated Multivariable Calculus | MATH UN1205 | Bulletin listing |
Honors Mathematics Sequence
Students with a strong calculus background and a serious interest in mathematics may instead consider Honors Mathematics A and B.
Honors Mathematics A–B is intended for students who are well prepared, interested in a rigorous and theoretical approach, and eager to engage with mathematics at a deeper level. The sequence covers linear algebra and multivariable calculus from a proof-based perspective, together with additional topics selected by the instructor. It also provides an introduction to the department’s upper-level undergraduate courses.
Calculus Placement
Columbia College and General Studies students:
- To request calculus placement, examination credit, or evaluation of prior calculus coursework for possible transfer credit, complete the Calculus Placement and Credit Evaluation Form. Questions may be directed to the Calculus Director, George Dragomir.
School of Engineering and Applied Science students:
- Please consult SEAS for calculus placement information and review the First-Year/Sophomore Technical Requirements page.
Barnard students:
- Please contact the Barnard Mathematics Department for calculus placement and transfer credit. Questions may be directed to Lindsay Piechnik.
The placement guidelines below apply to Columbia College and General Studies students and other non-SEAS and non-Barnard students.
Placement equivalent to Calculus I and II
For placement purposes, the Mathematics Department considers any of the following equivalent to Calculus I and Calculus II at Columbia:
- A score of 5 on the AP Calculus BC exam.
- A score of 7 on the IB Diploma Mathematics: Analysis and Approaches (AA) HL exam.
- A grade of A* on the GCE A-Level Mathematics examination in the UK.
- A grade of A or A* on the GCE A-Level Further Mathematics examination in the UK.
Students with one of these scores should begin with Calculus III, Accelerated Multivariable Calculus, or Honors Mathematics A. They do not need to take Calculus I or Calculus II.
Placement equivalent to Calculus I
For placement purposes, the Mathematics Department considers any of the following equivalent to Calculus I at Columbia:
- A score of 4 on the AP Calculus BC exam.
- A score of 4 or 5 on the AP Calculus AB exam.
- A score of 6 on the IB Diploma Mathematics: Analysis and Approaches (AA) HL exam.
- A score of 6 or 7 on the IB Diploma Mathematics: Applications and Interpretation (AI) HL exam.
- A grade of A on the standard A-Level Mathematics examination in the UK.
- A grade of A in a full year of high school calculus, with no external examination taken.
Students with one of these scores or grades may begin with Calculus II or Calculus III.
Calculus II is not a prerequisite for Calculus III. However, students who begin with Calculus III may still need Calculus II if it is required by their major or program. All students must complete Calculus II before taking Calculus IV.
All other students
Students who do not meet one of the placement criteria above should begin with Calculus I or Precalculus.
Prospective Economics majors should also consult the Economics Department’s Math Requirements page.
Credit for AP, IB, and Other Examinations
Placement and academic credit are not the same.
An examination score may allow you to begin in a higher-level calculus course, but examination credit is awarded only after you complete an additional MATH course at Columbia.
| Eligible Examination Result | Possible Credit | Columbia Course Requirement |
|---|---|---|
|
6 points | Complete Calculus III or Accelerated Multivariable Calculus with a grade of C or higher. |
|
3 points | Complete Calculus II or Calculus III with a grade of C or higher. |
- Students eligible for 6 points do not receive examination credit if they take Calculus I or Calculus II, or if they take no calculus at Columbia.
- Students eligible for 3 points do not receive examination credit if they take Calculus I, or if they take no calculus at Columbia.
Honors Mathematics A
Students with a strong interest in proof-oriented mathematics and 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. The course is especially appropriate for prospective mathematics majors. Students who complete Honors Mathematics A with a grade of C or higher may receive 6 points of examination credit.
Prior Calculus Coursework and Transfer Credit
Students seeking calculus placement based on prior coursework, or evaluation of calculus coursework taken at another college or university for possible transfer credit, should review the department’s Placement and Transfer Credit page.
Columbia College and General Studies students:
- Complete the Calculus Placement and Credit Evaluation Form.
- Questions may be directed to the Calculus Director, George Dragomir.
SEAS and Barnard students:
- Do not use this form. Follow the instructions for your school on the Placement and Transfer Credit page.
Course Textbook and WebAssign
Textbook
Calculus I–IV and Accelerated Multivariable Calculus use:
James Stewart, Calculus: Early Transcendentals, 9th edition.
WebAssign
WebAssign is an online learning system connected to the course textbook. It is used in some Calculus I–III sections.
- WebAssign is required only in sections where the syllabus states that it is required.
- In other sections, WebAssign is optional but may still be useful for additional practice.
- Students in a section requiring WebAssign must use the class key provided by their instructor.
For access information, free bootcamp enrollment, and purchasing guidance, visit the department’s WebAssign page.
Calculus Readiness Resources
The department offers free resources to help students review prerequisite material and make an informed placement decision. Details about the Precalculus Bootcamp, worksheets, in-person help, and the free online WebAssign Bootcamp are available on the department’s Calculus Readiness page.
Frequently Asked Questions
Placement and AP/IB Credit
Is there a placement exam for Calculus?
No. The Mathematics Department does not offer a calculus placement exam. Placement is determined by standardized examination scores, such as AP or IB scores, and high-school coursework, according to the guidelines on this page.
If I place out of a calculus course, do I automatically receive academic credit?
No. Placement and academic credit are separate. Placing out means that you are not required to take the course for placement purposes. It does not automatically grant Columbia credit. Credit is awarded primarily on the basis of eligible examination scores and completion of the additional required Columbia course. If you place out of a calculus course required by your degree program, you may need to take another course, typically a MATH course, to replace the missing credits. Consult your major department and advising dean.
My AP or IB scores place me into a certain calculus course, but I am not sure it is the right fit. What should I do?
The placement guidelines are based on extensive experience, but students may choose a lower-level course if they would benefit from additional review. Students considering Calculus I may use the department’s Precalculus Bootcamp to review the expected background and identify areas that need more practice. Students preparing for Calculus I, II, or III may also use the free online WebAssign Bootcamp. See the Calculus Readiness page and the department’s WebAssign page.
My scores place me out of Calculus I and II, and I took multivariable calculus during high school. Do I still need a Columbia course to receive examination credit?
Yes. To receive examination credit, you must complete an appropriate 2000-level or higher MATH course at Columbia with a grade of C or higher. Courses taken during high school, even when taught at the college level, do not receive Columbia transfer credit.
How does AP credit work?
AP credit is awarded only after you complete the appropriate Columbia mathematics course with a grade of C or higher. See the Credit for AP, IB, and Other Examinations section above for full details.
I completed a different secondary-school program. Can I use my examination results for placement or credit?
In some cases, placement based on other national examinations may be possible. Submit the examination through the Calculus Placement and Credit Evaluation Form. Academic credit is awarded according to Columbia’s applicable examination-credit policies.
Prior Calculus Coursework and Transfer Credit
How do I request calculus placement or transfer-credit evaluation based on prior coursework?
Columbia College and General Studies students should complete the Calculus Placement and Credit Evaluation Form.
Before submitting the form, review the requirements and restrictions on the department’s Placement and Transfer Credit page.
Can college-level calculus taken during high school be considered?
College-level coursework completed before high-school graduation generally does not earn Columbia transfer credit. It may, however, be considered for calculus placement. Report the coursework through the Calculus Placement and Credit Evaluation Form and indicate that it was completed while you were in high school.
Does placement approval mean that I will receive transfer credit?
No. Placement and transfer credit are separate determinations. Prior coursework may allow you to begin with a higher-level calculus course without receiving academic credit.
If a course you place out of is required for your major or program, you may need to complete an additional course to replace the missing credits. Consult your academic adviser or the Director of Undergraduate Studies in your major or program.
Calculus Classes
Can I switch between sections, course levels, or calculus sequences?
During the Change of Program Period, normally the first two weeks of the semester, students may switch between sections or sequences, subject to space availability. After that period and before the Course Drop Deadline, usually around the fifth week, students may transfer into a lower-level course with approval from both the instructor and the advising dean.
What calculator should I buy for calculus?
None. Calculators are not permitted on Columbia calculus examinations and are not necessary for the course.
Can I use another student’s WebAssign account?
No. WebAssign accounts are individual. See the department’s WebAssign page for access and enrollment information.
I am not sure whether I am ready for Calculus I. What should I do?
Begin by reviewing the prerequisite topics and trying the worksheets in the Precalculus Bootcamp. It is designed to help you identify whether your algebra, functions, exponential and logarithmic skills, and trigonometry are sufficiently familiar for Calculus I. The free WebAssign Bootcamp also provides self-paced readiness review for Calculus I, II, and III. See the Calculus Readiness page for details.
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