Open Math Notes

These notes
arise from teaching courses in geometry for more than 40 years. These were mainly classes for future secondary mathematics teachers. In speaking with educators about the class, I decided that these students should
see an axiomatic development of geometry. Instead of the formal development of Euclidean
geometry, the development of a geometry that was different from this
usual geometry might better serve them as understanding how an axiomatic mathematics system was developed.

David Royster · University of Kentucky · Date posted: August 10, 2024

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This can be used for an intro to proofs course, or a reference in a proof-based course Designing any guide or text on mathematical proof leads to a discussion of sets first or propositions first. We introduce a little of each first, and then constantly bring the discussion back to categorizing what each kind of thing is, with emphasis on mathematical language.

Edward Kim · University of Wisconsin-La Crosse · Date posted: July 11, 2024

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Lecture notes from a Part III course at the University of Cambridge, UK

Oleg Pikhurko · University of Warwick · Date posted: July 10, 2024

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This book covers an advanced or honors undergraduate course in complex variables and, at the same time, an introductory graduate course in complex functions. It is aimed at a wide population of students with diverse backgrounds, welcoming also those who had no previous exposure to complex numbers. The book is a tool to prepare all of them, in a guided manner suitable for active self-study. It is based on the author's lecture notes for his classes at the University of Texas at Dallas.

Vladimir Dragovic · The University of Texas at Dallas · Date posted: May 21, 2024 · Date revised: May 24, 2024

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These are the lecture notes used for topics courses on symplectic geometry and topology; the only prerequisites are familiarity with smooth manifolds and differential forms. Introductory material includes the geometry of Hamiltonian flows, symplectic linear algebra, almost complex and related geometric structures, and the Moser technique and its applications. Additional topics include Weinstein surgery, Lefschetz fibrations, and generating functions.

Michael Usher · University of Georgia · Date posted: May 15, 2024

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