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 in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use 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
  • Mary Pugh | University of Toronto
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University


The notes cover introduction to proofs, axioms of fields, complex numbers, some topology, and limits, continuity, derivatives, integrals, sequences and series. For teaching proof writing, many proofs contain in red color parts of proofs that should not be written down but should be thought. The non-constructive version of the notes have been used in Math 112 at Reed College for a 3-day a week schedule. The supplementary text is the constructive version for the 4-day a week schedule.

Irena Swanson
Reed College

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Open Math Notes authors welcome substantive, useful feedback that helps them develop and improve their notes. Comments submitted through this site may be posted on the Open Math Notes web pages next to the appropriate Note.

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