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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

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The Skewes Number

Subject: the Skewes number \Xi, the least integer for which \pi(x), the number of primes up to x, exceeds li(x), the logarithmic integral of x. Theme: the explicit formula of Riemann. This is the thread which runs through the course. Novel aspects: Can you hear the Riemann Hypothesis? This is a unique self-contained text which contains the theory of the Skewes number, and also includes the numerical realm. Mostly undergraduate level, partly graduate level. Many exercises included.

Roger Plymen
Manchester University, UK

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