### 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 Math A-B is aimed at students with a strong interest in and aptitude for Mathematics who also have a strong Calculus background from high school. This is a course for the best prepared and most able mathematics students. It covers the material of multivariable calculus and linear algebra from a thoroughly mathematical point of view as well as other topics chosen by the instructor. This course serves as an introduction to the upper level undergraduate mathematics courses offered by the Department.

### 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).
- An A on the A-Level Further Mathematics exam 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. - An A on the A-Level Mathematics exam or a B in A-Level Further Mathematics exam 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 either Calculus 2 or Calculus 3. Note that such students who decide to start with Calculus 3 may still need to take Calculus 2 since it is a requirement or prerequisite for other courses. In particular, they MUST take Calculus 2 before going on to Calculus 4.

- All other students should start with Calculus 1.
- Prospective Economics majors should consult the Economics department Math Requirements page.

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.

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.

*Honors mathematics A:* Students who want a proof-oriented theoretical sequence and have a score of 5 on the AP Calculus BC exam may begin with Honors Mathematics A, which is especially designed for mathematics majors. Upon completion of this course with a grade of C or higher, they may receive 6 points of AP credit.

### Contacts

For questions either contact your instructor or the relevant person below.

*Director of Undergraduate Studies*: Mu-Tao Wang

*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 utilized in most sections of all Calculus I-III classes.

Access to WebAssign is mandatory only for students enrolled in sections of Calculus where it is specified. In other instances, it remains optional, yet students might find it a beneficial study tool.

For sections where WebAssign is not required, you have the option to use the class key columbia 1789 6401. This key provides access to a dedicated course featuring all available problems for Calculus I, II, III, and IV. Refer to our WebAssign page for a list of sections requiring WebAssign.

It’s important to note that used versions of the textbook do not include WebAssign access.

For maximum value, we recommend purchasing **Cengage Unlimited**, encompassing multi-term WebAssign usage and granting access to all texts from the publisher (some of which may be used in other Columbia courses). Priced at $129, this is a *one-time purchase covering* *all your calculus courses at Columbia*.

Please remember to purchase your access code after signing in for one of the WebAssign classes offered at Columbia, using the class key for sections that do not use WebAssign.

#### Free Calculus Bootcamp

Columbia and Barnard students can use the class key columbia 2136 3739 to access a Calculus Bootcamp class on WebAssign, which is specifically designed to prepare students for Calculus I, II, or III. It serves as a valuable resource, aiding in the review of essential concepts within these calculus courses. Access to the WebAssign Calculus Bootcamp is *free throughout the month of January*. To register, use the provided class key and choose “Temporary Access” during the registration process.

### Frequently Asked Questions

**Q: ***Is it possible to switch between sections, levels and sequences of calculus?
*

**A**: Students can always go to the first few lectures of one Calculus class and then, if it seems appropriate, switch to another level or a different sequence. Such transfers require the approval of the instructors and, after the drop/add date, the class dean.

**Q: ***I am not sure that, following department guidelines, the scores on my AP exam place me in the appropriate section. What should I do?
*

**A:**These are guidelines only, but they are based on years of experience.

**Q: ***How does Advanced Placement credit work?
*

**A:**See the discussion under placement.

**Q: ***What pocket calculator should I get?
*

**A:**Calculators are not allowed in Calculus exams. You do not need a calculator.

**Q: ***Can I use my friend’s WebAssign account?
*

**A**: No.