Course Code MATH 647
Course Title Foundations of Calculus I
Online Offers
  • Fall 2021 (Instructor: Brian Forrest)
Course Location Online
Credit Weight 0.5
Course Description

This course will explore the foundations of differential calculus, the role of rigour in mathematics, and the use of sophisticated mathematical software. Topics include: A brief primer on logic and proof, axiom of choice and other ideas from set theory, convergence of sequences and the various forms of the completeness axiom for R, detailed study of limits, continuity and the Intermediate Value Theorem, fundamentals of differentiation and the importance of linear approximation, role of the Mean Value Theorem, the nature and existence of extrema, Taylor's Theorem and polynomial approximation, MAPLE as a tool for discovery.

Typical terms may not reflect online offerings.

Course Work and Exam Fall 2021 course outline (note 2)
Author(s) Brian Forrest
  • Corequisite: MATH 600, 692
System Requirements
  • A computer with Internet access is required for all online and multimodal courses. Please see the System Requirements.
Taught in English
Special Notes 1) This course is only open to students in the Master of Mathematics for Teachers program.
How to Register:
Waterloo Students
Enrol In, Drop, and Swap Classes Online
How to Register:
Non-Waterloo Students
How to Apply - Prospective Students
Fees Tuition Fees, Financial Aid, Scholarships, and Awards

  1. The Undergraduate Calendar and the Graduate Calendar are the official source for information about course details. Quest is the official source for Undergraduate and Graduate Schedule of Classes information. The offerings indicated on this site are unofficial and subject to change daily. The course instructor will provide the official course requirements and expectations at the start of term.
  2. If available, the example of a recent course outline is provided for general information only. It gives an overview of the course from a recent offering but it is not the course outline for the current offer and is subject to change. If you are currently taking this course, the official course outline that applies to this offer is in your online course.
  3. Library Requirements: Please see the online library access and Waterloo ID card information.
  4. For a list of any required textbooks and other materials to be purchased, go to the Waterloo BookStore.