Open Math Notes

The goal of these notes is to help bridge the gap many students encounter between school and university, regarding the expectations about rigour and proofs. It covers basic logic and set theory, including aspects such as the Axiom of Choice. It also shows how the various systems of numbers can emerge out of set theory.

Amber Habib · Shiv Nadar University · Date posted: December 4, 2019

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The notes cover introduction to proofs, axioms of fields, complex numbers, some topology, and limits, continuity, derivatives, integrals, sequences and series. For teaching proof writing, many proofs contain in red color parts of proofs that should not be written down but should be thought. The non-constructive version of the notes have been used in Math 112 at Reed College for a 3-day a week schedule. The supplementary text is the constructive version for the 4-day a week schedule.

Irena Swanson · Reed College · Date posted: November 22, 2019 · Date revised: November 25, 2019

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An introduction to applications of model theory to valued fields including the results of Ax-Kochen and Ersov and the model theory of the field of p-adic numbers.

David Marker · University of Illinois at Chicago · Date posted: October 18, 2019

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Here is one of the best and the more recent books on Complex Dynamics in Higer Dimension. Here, we develop a calculus on positive closed currents of arbitrary bidegree on compact K{\"a}hler manifolds after
recalling a notion of super-potential associated to such currents by using deformations in the space of currents. We define in particular the intersection of such currents and the pull-back operator. We apply the theory of super-potentials to construct Green currents ...

Armand Azonnahin · Instituto de Matemática e Estatística da Universidade de São Paulo · Date posted: October 18, 2019

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These are the notes of a two-hour one-semester course on CAT(0) cube complexes which I taught in Muenster during winter term 2012/2013.

Topics covered are for example: Basic CAT(0) geometry, Gromov's link condition, half-space systems and Sageev's cubulation method, cubulating Coxeter groups and the Tits alternative.
Since most of the students neither had a strong background in metric geometry nor in group theory I tried to keep the material as elementary and selfcontained as possible.

Petra Schwer · Otto von Guericke University · Date posted: October 18, 2019 · Date revised: October 20, 2019

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