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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

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Algebraic Fredholm Theory

These notes develop, for vector spaces over arbitrary fields, the purely algebraic parts of basic Fredholm theory, emphasizing, (without any mention of topology or continuity) how the Fredholm index describes invertibility and spectra for Fredholm operators. The exposition culminates in a Fredholm-inspired analysis of the spectra of multiplication operators on spaces of holomorphic functions.

Joel Shapiro
Portland State University

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