# Calculus Theory

## Related Courses at Universities

Many universities offer an theoretical calculus sequence (often called
"honors calculus") which uses either Spivak or a similar text such as Apostol.
Here are a few examples.

## What Next?

Calculus Theory is a rigorous treatment of single-variable calculus.
The obvious next step is to continue with a similar rigorous treatment of
multivariable calculus. In fact some universities, notably Harvard and
Stanford, do not even bother to offer their own version of our course, figuring
their incoming students have already taken Calculus AB or BC in high school.
Their honors sequences start out with theoretical multivariable calculus.
This is typically very hard for students even with a strong BC course who have
never had experience with proofs before, and now must learn them in a very
complicated setting. After our course you will be extremely well prepared
for an honors-level multivariable calculus course. If you are going to a
school whose honors calculus sequence starts with single-variable, you should
explain your background and determine whether you should wait until the
multi-variable part begins (sometimes it is only offered in the Spring semester)
or whether it is better to start from the beginning even though you will be
relearning material already covered in this course.

### Harvard

There are two Harvard courses that naturally follow this course, Math 23 and
Math 25. Math 25 is considered to be the harder of the two. There is
an even harder course, Math 55, which is quite famous, but it is intended for
truly exceptional students who have already studied a great deal of college
mathematics (and maybe some grad school level math) in high school.

### Stanford

The single honors sequence at Stanford starts with Math 51H, and is
apparently comparable to Harvard's Math 25.