Section menuClose menu Columbia College


Master Syllabus

Print this Syllabus « Return to Previous Page

Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 380
Course Title: Advanced Calculus I
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

Rigorous development of some central ideas in analysis including limits, continuity and differentiability. Prerequisite: Grade of C or higher in MATH 222 or MATH 235 and C or higher in MATH 225.

Prerequisite(s) / Corequisite(s):

Grade of C or higher in MATH 222 or MATH 235 and C or higher in MATH 225.

Course Rotation for Day Program:

Offered odd Fall.

Text(s): Most current editions of the following:

Introduction to Real Analysis
By Bartle, Robert and Donald Sherbert (John Wiley and Sons, Inc.)
Course Learning Outcomes
  1. Prove results about the topology of the real line and make connections between the topology and limits of sequences. 
  2. Prove results related to continuous function, such as the Intermediate Value Theorem, and determine if functions are continuous or uniformly continuous. 
  3. Prove results related to differentiable functions, such as the Mean Value Theorem, and determine if functions are differentiable. 
  4. Compute limits of sequences, limits of functions, and derivatives of functions using the appropriate definition or theorem. 
Major Topics/Skills to be Covered:
  • Topology of the real numbers
  • Limits of sequences
  • Limits of functions
  • Continuity and the intermediate value theorem
  • Differentiability and the mean value theorem
Culminating Experience Statement:

Material from this course may be tested on the Major Field Test (MFT) administered during the Culminating Experience course for the degree. 
During this course the ETS Proficiency Profile may be administered.  This 40-minute standardized test measures learning in general education courses.  The results of the tests are used by faculty to improve the general education curriculum at the College.


Recommended maximum class size for this course: 20

Library Resources:

Online databases are available at You may access them from off-campus using your CougarTrack login and password when prompted.

Prepared by: Suzanne Tourville Date: September 28, 2015
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course learning outcomes and cover the subjects listed in the Major Topics/Skills to be Covered section. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

Office of Academic Affairs