Open Math Notes

A self-contained introduction to the theory of Commutative Algebra, at
a level that is accessible to students or researchers who have already
completed a standard two-semester Introduction to Abstract Algebra
course. Topics include fundamentals of rings and modules, an
introduction to Homological Algebra, integral extensions, primary
decomposition theorems, Krull dimension, derivations, differentials,
normal rings, regular rings, divisor class groups and classical ideal
theory.

Timothy Ford · Florida Atlantic University · Date posted: October 3, 2024

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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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