No or Little Precalculus?  ~  No or Little Calculus?  ~  Have a Calculus background?

Multivariable Calculus & the 50-Series  ~  Can’t Decide?

After the 50-Series  ~  Have Transfer Credit?

The department does not offer a placement test; our courses are self-placed.  The information below constitutes general guidelines and recommendations.  Our courses sometimes have recommended prerequisites but these are purely as advice and are not enforced, so if you feel that your background is strong enough but you have not fulfilled recommended guidelines, you can still enroll in the course that you think is the best fit.

Calculus Background:

 ** Math 52 and 53 are independent of each other (but taken after Math 51).**

For those with little or no precalculus background, or wanting a refresher on those skills, the department has a precalculus resource portal.  See here for more information.

For those with little or no calculus background, the department offer two single-variable calculus sequences: Math 19-20-21 (the “20-series”) and Math 41-42 (the “40-series”).

• They are equivalent and cover the same material.
• The 20-series is a 3-quarter/one-year sequence.
• The 40-series is completed in two quarters.  (This series is recommended for future Engineering, Science, and Economics students.)
• Consider how comfortable you are with your high school algebra and geometry when deciding between Math 19 or 41.
• If you had some calculus in high school, but did not score at least 4 on the AB-level or at least 3 on the BC-level AP calculus exam, then we advise you to begin with Math 41.
• If you are comfortable with your calculus background and scored 4 on the AB-level or  3 on the BC-level AP calculus exam then we advise you to begin with Math 42, or Math 51 if you are confident with your calculus background.
• After completion of either Math 21 or Math 42, or if you scored 5 on the AB-level or either 4 or 5 on the BC-level AP calculus exam and remain comfortable with your knowledge of single-variable calculus, then you are prepared to take Math 51 (multivariable calculus and linear algebra).

Students who scored a 4 on the AP AB exam or a 3 on the BC exam: 
These scores earn you 5 units of credit (if transferred to the University and on your Stanford transcript) and place you out of Math 41.  You should begin with Math 42 in the Fall and Math 51 in the Winter.  If you are in this category and feel confident of your background in single-variable calculus, you may begin with Math 51.

Students who scored a 5 on the AP AB exam or a 4 or 5 on the BC exam:
These scores earn you 10 units of credit (if transferred to the University and on your Stanford transcript) and place you out of Math 41 and 42.  You should take Math 51-52-53, or the honors version, Math 51H-52H-53H during your freshman year.  

Courses Offered in Multivariable Mathematics (The 50s-Sequence)

Incoming freshmen with 10 units AP credit, this is the sequence for you!  For those of you who fit this category we strongly recommend taking Math 51-52-53 or the honors sequence, Math 51H-52H-53H, during your freshman year.

Math 51 (5 units) covers the basic geometry and algebra of vectors, matrices, linear transformations, and differential calculus of several variables.

Math 52 (5 units)  covers integral calculus of several variables, and in particular vector analysis. This uses the linear algebra learned in Math 51.

Math 53 (5 units)  integrates further topics in linear algebra with ordinary differential equations. These further topics include using eigenvalues and eigenvectors (from Math 51) to solve systems of differential equations.

For those with a very strong commitment to and interest in math, as well as a preference for a more conceptual and theoretical understanding of multivariable calculus and linear algebra, we recommend the  honors version of this sequence, Math 51H-52H-53H.  Placement into the honors sequence requires a 5 on the BC-level AP exam or permission of the instructor.

Math 51H-52H-53H (5 units each) Three-quarter sequence covers the material of 51, 52, 53, and additional advanced calculus and ordinary and partial differential equations. Unified treatment of multivariable calculus, linear algebra, and differential equations with a different order of topics and emphasis from standard courses. Students should know one-variable calculus very well and have an interest in a theoretical approach to the subject.

Either of these sequences will supply you with the necessary mathematical background for most majors in science and engineering.

Still can’t decide?

Look over each syllabus for the courses you’re choosing between.  You can also sit in on both classes and decide within the first couple weeks of the quarter.  Feel free to email one of the instructors, too, for input.  If you still have questions, please contact our Director of Undergraduate Studies.

After the 50-series

After completing the basic background in multivariable calculus, linear algebra, and differential equations, there is a wide variety of 100-level courses you may take. Which courses to take and the order in which to take them depends on your major and your general mathematical interests.  

• The courses which introduce writing proofs are Math 113, Math 120, and Math 171.

If you need assistantce, consult ExploreCourses, your academic advisor, or our Director of Undergraduate Studies.

Transfer Credit for Math Courses

Any questions concerning the applicability of transfer courses towards that major or prerequisites for another department’s courses must be resolved within the other major or department.  If you are a Math major and want to use transfer credit towards your major requirements, please see our Transfer Credit Process page.