# Calculus Courses

On this page, you’ll find a flowchart describing the many possible pathways through Calculus at Colby, course descriptions for each of our first-year Calculus courses, and (for those who have already taken Calculus at Colby) a summary of how our courses were renumbered. If you are a new student seeking information on what Calculus course you should take and where to find the placement questionnaire, please visit this link.

As of Fall 2021, we are completely revitalizing our Calculus program, with the introduction of a brand-new Calculus I course for students who have taken Calculus before (MA 130). Here is a flowchart describing the birds-eye view of the possible pathways through Calculus. For more detailed information on placement, please visit this link.

**Course Descriptions**

*MA 119 & MA 120: *Designed for students who enter Colby with insufficient algebra and trigonometry background for Mathematics 125. It is expected that all students who complete Mathematics 119 will enroll in Mathematics 120 in the following January. The combination of 119 and 120 covers the same calculus material as Mathematics 125. Completion of 119 alone does not constitute completion of a College calculus course for any purpose; in particular, it does not qualify a student to take Mathematics 130 or 160 nor does it satisfy the quantitative reasoning requirement.

*MA 125 Single-Variable Calculus: *Calculus is the result of centuries of intellectual effort to understand and quantify change, such as the position of a moving object or the shape of a curve. Competent users of calculus understand its intellectual structure sufficiently to apply its ideas to a variety of intellectual pursuits. Topics include differential and integral calculus of one variable, including the calculus of exponential, logarithmic, and trigonometric functions. The course covers limits and continuity; differentiation and its applications, antiderivatives, the definite integral and its applications. This course is sufficient preparation for Mathematics 160.

*MA 130 Single-Variable Calculus Revisited: *Calculus studies rates of change and accumulation and is fundamental to quantitative work in the natural sciences, social sciences, and data science. This course assumes prior experience with calculus of a single variable and goes into more depth than Mathematics 125 but is less theoretical than Mathematics 135. Topics covered include limits, continuity, derivatives, and definite integrals of functions of one variable, including the major theorems governing their relationships and their applications. The emphasis is on developing conceptual understanding, rather than mere computation. A computer algebra system such as Sage, Mathematica, or MatLab is used.

*MA 135 Honors Calculus I: *The first in a two-course sequence that treats the material of Mathematics 125 and 160 with a focus on the intellectual structure behind the methods. Students will acquire a deep understanding of the theory and foundational facts of calculus, will be able to use the techniques in an intelligent manner, will understand and be able to explain the arguments that undergird those techniques, and will be able to construct original arguments of their own. Topics are presented as a deductive mathematical theory, with emphasis on concepts, theorems, and their proofs. May not be taken for credit if the student has earned credit for Mathematics 160. * *

*MA 160 Series and Multivariable Calculus: *A continuation of Mathematics 120, 125 or 130. Students will learn how to use infinite series, both to represent and to approximate functions, and will extend all of their skills from single-variable calculus to the multivariable setting. Topics: infinite series; vectors and analytic geometry in two and three dimensions; partial derivatives, differentials and the gradient; integration in two and three variables. * *

*MA 165 Honors Calculus II: *A continuation of Mathematics 135. Topics are essentially the same as for Mathematics 160, but they are presented as a deductive mathematical theory, with emphasis on concepts, theorems, and their proofs. Student who receive an A- or above will receive an exemption from taking Mathematics 274. May not be taken for credit if the student has earned credit for Mathematics 160. * *

All of our Calculus courses were revised and renumbered. If you are wondering how a Calculus course you’ve already taken at Colby compares to those on offer, here is a dictionary for translating:

- MA 101 & 102 became MA 119 & MA 120
- MA 121 became MA 125 (and was revised to better meet the backgrounds of students without prior calculus experience)
- MA 122 became MA 160
- MA 161 became MA 135
- MA 162 became MA 165