### Courses in the Calculus Sequence

The systematic study of mathematics begins with one of the following two alternative sequences:

Pre-Calculus

Calculus 1 (or at the registrar)

Calculus 2 (or at the registrar)

Calculus 3 (or at the registrar)

Calculus 4 (or at the registrar)

Accelerated Multivariable Calculus (or at the registrar)

or

Honors Math A and B (or at the registrar)

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 (from 2021) 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 (from 2021) 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 (from 2021) 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. *

Starting Fall 2021, the **9th edition** of the textbook will gradually replace the 8th edition used in the past years. That is, the 9th edition will be used for Calculus I starting Fall 2021, for Calculus II and III starting Spring 2022, and for Calculus IV and Accelerated Multivariable Calculus starting Summer 2022.

### WebAssign

Some sections of all Calculus classes will be using WebAssign, an on-line system integrated with the course textbook.

This is available as a package consisting of the loose-leaf version of the textbook and multi-term access to WebAssign from the publisher for $145.95, with ISBN number 9780357537299. The same package is available at the bookstore and from other sellers, possibly with a lower price. If you already have a copy of the book, or only want an electronic version, you can get this together with Cengage Unlimited from the publisher for $119.99. Note that this price includes access to all textbooks and learning platforms in the Cengage library, some of which may be used in other Columbia courses. If WebAssign will not be used in your section, and you don’t want to purchase access, it is possibly to rent the hardcopy textbook (for $99.49) or purchase access to the ebook (for which the price ranges from $38.99 to $61.49 depending on the duration of access).

Access to WebAssign is only required for students in those sections of Calculus that will be using it to assign homework problems. In other cases it is optional, but students may find it a useful study tool. See our WebAssign page for a list of which sections require WebAssign.

Note that used versions of the textbook will not come with WebAssign access.

Access to WebAssign and the eBook version of the textbook for one semester can be purchased directly from WebAssign after enrolling in the appropriate class there. The price is $100 for one semester, $125 for multiple terms (usable if you take more than one semester of Calculus). Cengage Unlimited includes access to WebAssign. It is no longer possible to purchase just access to WebAssign, it is sold together with the eBook.

### 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.