Open Math Notes

Resources and inspiration for math instruction and learning

Home Submit FAQ Contact My Notes

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


A carefully sequenced collection of problems for an inquiry-learning approach in a one-semester Introduction to Abstract Algebra Class. The topics developed include basic notions about groups and subgroups; cyclic groups; homomorphisms and isomorphisms; and cosets. The notes culminate with the concept of quotient groups and the first isomorphism theorem. The approach is fairly elementary. A student with just a little experience with sets, functions, and elementary proof writing will be able to make substantial independent progress through the notes, particularly with the support of peers or instructor in an inquiry-based learning environment.

Margaret L. Morrow
SUNY Plattsburgh

Feedback to the author(s)
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.

If checked, the author will not see your name or email address.
Limit 2000 characters; Plain text only
Optional; Limit 10M
Optional; Limit 10M