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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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William FARIS
University of Arizona
MR ID: 199164
Reference #
OMN:202007.110832

Attributes

Posted date
2020-07-25 14:07:37
Revised date
2020-07-25 14:07:37
Level
   Undergraduate
   Graduate
Notes type
   Standard Course Offering
Topic
   Logic and Set Theory

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.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v1 PDF (624K) 07/25/20