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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


Peter Philip
LMU Munich
MR ID: 639375
Reference #


Posted date
2021-10-20 11:27:15
Revised date
2023-03-05 11:01:10
Notes type
   Standard Course Offering
   Introduction to Mathematics
      Introduction to Proofs
      Linear Algebra
      Commutative Algebra
      Group Theory
   Logic and Set Theory

Linear Algebra I

First part of two-semester course on Linear Algebra: Starting with the basics of propositional calculus and set theory, we then introduce functions, relations, and proofs by induction. After proving necessary facts regarding groups, rings, and fields, we study Linear Algebra's core subjects, i.e. vector spaces, linear maps, matrices, and linear systems. Appendix includes an introduction to axiomatic set theory and the axiom of choice.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v4 PDF (1.6M) 03/06/23