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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


Theodore Shifrin
University of Georgia (emeritus)
Reference #


Posted date
2018-01-17 17:12:25
Revised date
2023-12-09 14:30:32
Notes type
   Standard Course Offering
      Differential Geometry

Differential Geometry

A First Course in Curves and Surfaces

A rigorous course (below the level of doCarmo's undergraduate text) in curves and surfaces with a prerequisite of linear algebra and multivariable calculus. (Note: This text has been used by dozens of instructors around the world, as well as by plenty of individual students who've come across it.)

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v3 PDF (1.9M) 12/11/23