### 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)

or

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:

- with a score of 5 on the Calculus BC Advanced Placement (AP) exam must begin with Calculus 3 (or Honors Math A).
- with a score of 4 on the Calculus BC Advanced Placement exam, or a score of 4 or 5 on the Calculus AB Advanced Placement exam must begin with Calculus 2.
- with a score of 6 or 7 on the IB HL Calculus exam, or a grade of A or B on the A-Level GCE Further Maths exams must begin with Calculus 2.
- with an A grade in a full-year high school calculus course must begin with Calculus 2.
- with other AP scores, below an A in a full year high school calculus course, or less than a full year of calculus in high school must begin with Calculus 1.

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 HL Mathematics or Further Mathematics exams.
- An A on the A-Level Further Mathematics exam in the U.K.

Students with any of these scores should begin with Calculus 3, 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 HL Mathematics or Further Mathematics exams.
- A score of 6 or 7 on the IB SL Mathematics exam. (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 AB exam, a 4 on the AP BC exam, or a 6 on the IB 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 BC exam or 7 on the IB HL exam may receive 6 points of AP credit upon completion of Calculus 3 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 BC AP 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*: Professor Chiu-Chu Liu

*Calculus Director*: Professor Michael Thaddeus

*Undergraduate Administrative Assistant*: Crispina Pincus

### WebAssign

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

### Course Textbook

Calculus I-IV will be using the 8th edition of the textbook:

James Stewart, *Calculus: Early Transcendentals*, 8th Edition

This is available as a package consisting of a loose-leaf book and access to WebAssign from the publisher for $170.95, with ISBN number 978-1-305-71030-6. The same package is available at the bookstore, with ISBN number 978-1-305-61669-1. If you already have a copy of the book, or only want an electronic version, you can get this together with WebAssign from the publisher for $125, with ISBN number 978-1-285-85825-8.

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.

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 $94 for one semester, $125 for multiple terms (usable if you take more than one semester of Calculus). 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.