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


This guide contains the essentials of the author's course in topology of undergraduates, mostly from the first two years of college. Much of it is suitable for high school students, especially those who are willing to think and experiment. Mainly the course concerns the topology of the real line. To reduce the use of arithmetic (and algebra) to a purely descriptive role, a concrete space is constructed in which points are maps from natural numbers to the natural numbers, i.e., sequences of positive integers. The lexicographic order is defined and the space of all such functions is given the order topology. All this is done slowly, introducing the student gradually to certain types of infinite processes.

F. Burton Jones
University of California at Riverside

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