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


Margaret L. Morrow
SUNY Plattsburgh
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)
      Group Theory

Introduction to Abstract Algebra

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.

This title previously published Journal of Inquiry-Based Learning in Mathematics, Issue No. 26 (May 2012). Here is the url:

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Instructor notes v1 PDF (160K)
Student notes v1 PDF (124K)