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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Showing 1 - 5 of 191 result(s)

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.

Peter Philip · LMU Munich · Date posted: September 13, 2021 · Date revised: September 17, 2021

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Analysis II: Topology and Differential Calculus of Several Variables

2nd part of 3-semester course on Calculus and Real Analysis:
Convergence and function continuity are studied in normed
and metric spaces as well as in abstract topological spaces
(where net convergence is used). Topological notions of interest
include separation, compactness, and connectedness.
The part on advanced differential calculus includes the
chain rule, Taylor's theorem, necessary and sufficient
conditions for extrema, as well as constrained optimization.

Peter Philip · LMU Munich · Date posted: September 13, 2021 · Date revised: September 17, 2021

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Analysis III: Measure and Integration Theory of Several Variables

3rd part of 3-semester course on Calculus and Real Analysis:
A detailed introduction to abstract measure theory is followed
by the study of abstract integration of real- and complex-valued measurable maps.
Noteworthy theorems include dominated convergence,
Fubini, and change of variables. L^p spaces are studied,
including an introduction to convolution and Fourier transform.
An introductory section on the integration over submanifolds of R^n
culminates in the Gauss-Green Theorem.

Peter Philip · LMU Munich · Date posted: September 13, 2021 · Date revised: September 17, 2021

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Gaussian Elimination and LU Decomposition

There is more to Gaussian Elimination than meets the eye.This note reviews
Gaussian elimination in various forms from both a computer programming and numerical analysis viewpoint.

gary knott · Civilized Software Inc. · Date posted: July 27, 2021

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Fourier Transforms

The four main types of Fourier transforms are defined and some of their properties and interrelationships are derived. The four types of Fourier transforms are: those defined on periodic functiions defined on R, discrete periodic functions, rapidly-diminishing functions, and linear functionals on rapidly-diminishing functions.,

gary knott · Civilized Software Inc. · Date posted: July 10, 2021

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Showing 1 - 5 of 191 result(s)