Open Math Notes

Resources and inspiration for math instruction and learning

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


Scott F. Beaver
Western Oregon University
Reference #


Posted date
2020-11-20 09:46:13
Revised date
2020-11-20 09:47:11
Notes type
   Standard Course Offering
   Inquiry-Based Learning (IBL)
      Real Analysis

Advanced Calculus I and II

Provides an Inquiry-Based Learning approach to the theoretical underpinnings of differential and integral calculus, in the setting of two 10-week terms. The course proceeds as students use definitions, axioms and previous theorems to prove new theorems. A variety of examples are provided to help augment students' concept images. Sequences and series of both real numbers and of real-valued functions are treated rigorously, generating a sufficient prerequisite knowledge base from which to prove the basic foundations of calculus.

This title previously published Journal of Inquiry-Based Learning in Mathematics, Issue No. 9 (Oct. 2008). Here is the url:

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Instructor notes v1 PDF (156K)