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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

contact


Peter Philip
LMU Munich
MR ID: 639375
Reference #
OMN:202109.111306

Attributes

Posted date
2021-09-13 23:17:32
Revised date
2023-03-05 10:53:49
Level
   Undergraduate
Notes type
   Standard Course Offering
Topic
   Introduction to Mathematics
      Introduction to Proofs
      Precalculus/Calculus
      Trigonometry
   Analysis
      Real Analysis
   Logic and Set Theory

Analysis I: Calculus of One Real Variable

1st part of 3-semester course on Calculus and Real Analysis: Starting with the basics of propositional calculus and set theory, we then introduce functions, relations, and proofs by induction. We study convergence of real and complex sequences and series, as well as continuity, differentiability, and Riemann integrability of functions of one real variable.
Appendix includes an introduction to axiomatic set theory and the axiom of choice as well as a construction of the real numbers.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v6 PDF (2.0M) 03/06/23