Open Math Notes

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use 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 Science of Proof: Mathematical Reasoning and Its Limitations

This is a book on mathematical logic with an approach through systematic proof. It begins with natural deduction, a formalization of usual mathematical proof. It introduces templates that always produce a proof, if a proof exists. A more systematic account of proof leads to the completeness theorem and the compactness theorem. The compactness theorem is related to non-standard models; the book concludes with examples of how this works.

William FARIS · University of Arizona · Date posted: July 25, 2020

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A course on the Weil conjectures

Notes by Davide Lombardo from a 2019 course by Tamás Szamuely devoted to Deligne's proof of the Riemann Hypothesis for smooth projective varieties over finite fields. Katz's recent proof of the hypersurface case and Esnault's spectacular application of the integrality theorem are also discussed. The course concludes with a brief survey of the main results of 'Weil II'.

Tamás Szamuely · University of Pisa · Davide Lombardo · University of Pisa · Date posted: July 7, 2020

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An Introduction to Groups and Rings

A first course in abstract algebra based on lecture notes for a course in the University of Glasgow

Andrew Baker · University of Glasgow · Date posted: July 7, 2020 · Date revised: August 4, 2020

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A survey of classical and modern geometries: Version 1.5

A textbook in geometry from the perspective of an algebraist. Originally published in 2000, currently out of print and under revision.

Arthur Baragar · University of Nevada, Las Vegas · Date posted: June 26, 2020 · Date revised: July 11, 2020

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Weil cohomology in practice

A survey of the Weil conjectures, their applications, and the approaches them via etale and p-adic cohomologies.

Kiran Kedlaya · University of California, San Diego · Date posted: June 22, 2020 · Date revised: June 23, 2020

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Showing 1 - 5 of 110 result(s)