Calculus Courses, Placement, and Transfer Credit
This page explains the Mathematics Department’s calculus sequence, placement guidelines, AP and IB credit, transfer-credit procedures, and readiness resources.
Incoming students should begin with the Calculus Placement section below.
Quick Links
- Courses in the Calculus Sequence
- Calculus Placement
- AP and IB Credit
- Transfer Credit
- Calculus Readiness Resources
- Textbook and WebAssign
- 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 |
|---|---|---|
| College Algebra and Analytic Geometry | MATH UN1003 | Bulletin listing |
| 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
School of Engineering and Applied Science students:
Please consult SEAS for calculus placement information.
Barnard students:
Please contact the Barnard Mathematics Department for calculus placement and credit transfer.
The placement guidelines below apply to Columbia College 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 Mathematics: Analysis and Approaches HL exam, 2021 or later.
- A score of 7 on the IB HL Mathematics or Further Mathematics exam, 2020 or earlier.
- A grade of A on the A-Level Further Mathematics examination in the United Kingdom.
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 Mathematics: Analysis and Approaches HL exam, 2021 or later.
- A score of 6 on the IB HL Mathematics or Further Mathematics exam, 2020 or earlier.
- A score of 6 or 7 on the IB Mathematics: Applications and Interpretation HL exam, 2021 or later.
- 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 United Kingdom.
- A grade of A in a full year of high school calculus.
Students with one of these scores 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 and IB Examinations
Placement and academic credit are not the same.
An exam score may allow you to begin in a higher-level calculus course, but credit is awarded only after you complete the required Columbia course.
| Exam Result | Possible Credit | Columbia Course Requirement |
|---|---|---|
| AP Calculus BC score of 5, or IB Mathematics: Analysis and Approaches HL score of 7 | 6 points | Complete Calculus III or Accelerated Multivariable Calculus with a grade of C or higher. |
| AP Calculus AB score of 4 or 5, AP Calculus BC score of 4, or IB Mathematics: Analysis and Approaches HL score of 6 | 3 points | Complete Calculus II or Calculus III with a grade of C or higher. |
- Students eligible for 6 points do not receive AP 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 AP 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 AP credit.
Transfer of Credit from Other Institutions
Students requesting transfer credit for mathematics courses taken elsewhere should contact the appropriate department representative.
| Course Level | Contact |
|---|---|
| Calculus courses and other MATH courses at the 2000 level or below | Calculus Director: George Dragomir |
| MATH courses at the 3000 level or above | Director of Undergraduate Studies: Julien Dubedat |
A transfer-credit request should include:
- your intended major or academic program;
- a complete course syllabus, not only a catalog description, including topics covered, methods of instruction and assessment, textbook information, and chapters covered;
- an unofficial transcript showing course completion and the final grade.
See the Transfer Credit FAQ below for additional requirements and restrictions.
Calculus Readiness Resources
The department offers free resources to help students review prerequisite material and make an informed placement decision.
Precalculus Bootcamp for Calculus I Readiness
The Precalculus Bootcamp is designed for students preparing for Calculus I. It focuses on the algebra, equations and inequalities, functions and graphs, exponentials and logarithms, and trigonometry that Calculus I assumes.
| Review Notes | Explanations, worked examples, formulas, exercises, and reminders about important precalculus techniques. |
|---|---|
| Worksheets | Six focused worksheets covering algebra, rational expressions and radicals, exponents and logarithms, functions, exponential and logarithmic functions, and trigonometry. |
| In-Person Help | Drop-in help rooms during the shopping period, with TAs assigned to specific worksheets and topics. |
The Precalculus Bootcamp is not a substitute for a full precalculus course.
If many of the topics feel unfamiliar, a full precalculus course may be better preparation before Calculus I.
Bootcamp materials, schedules, and registration information are available on the Precalculus Bootcamp CourseWorks page.
Free WebAssign Bootcamp
The department also offers a free online WebAssign Bootcamp with self-paced review for students preparing for:
- the Precalculus Bootcamp
- Calculus I
- Calculus II
- Calculus III.
Access dates, class keys, enrollment instructions, and additional WebAssign information are available on the department’s WebAssign 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.
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 AP or IB scores and completion of the 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 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. Enrollment details are available on the department’s WebAssign page. Students who remain uncertain may contact the Calculus Director.
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 AP credit?
Yes. To receive AP 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 AP and IB Credit 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. Contact the Calculus Director for an evaluation. However, academic credit is awarded primarily according to Columbia’s AP and IB credit policies.
Transfer Credit
What do I need to submit with a transfer-credit request?
Your request must include:
- your intended major or academic program;
- a full course syllabus, not only a catalog description, including topics, teaching format, assessment methods, textbook information, and chapters covered;
- an unofficial transcript showing course completion and the final grade.
Is there a minimum grade required for transfer credit?
A passing grade is usually sufficient, but requirements may vary by department. Consult your major department and advising dean.
Can I transfer an online course?
No, except for courses taken during the COVID-19 pandemic under special circumstances.
Can I transfer a college-level course taken while I was in high school?
No. College-level courses taken during high school do not earn Columbia credit. Such coursework may, however, be considered when determining placement.
Can the Mathematics Department award transfer credit for Statistics, Computer Science, Engineering, or Applied Physics courses?
No. The Mathematics Department evaluates transfer credit only for MATH courses that it offers. Courses offered by other departments must be evaluated by the corresponding department, even if they contain substantial mathematical material.
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. The bootcamp includes review notes, focused worksheets, and in-person help sessions.
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 WebAssign page for current access information.
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