Modern Algebra
Group Theory, Ring Theory, Module Theory, Field Theory
Open Education Resources
I am interested about the development of open education resources (OERs)—free, online learning materials not restricted by copyright. OERs reduce financial barriers to learning [1] and have been proposed as an equity strategy for higher education [2].
Mathematics OERs
Note: all of the below are heavily under development, with tweaks and adjustments being made almost daily!
Graduate Algebra
Postmodern Algebra
Homological Algebra, Commutative Algebra, Local Cohomology
Other Graduate Courses
Note: these texts range from partially complete to almost entirely empty. Some are more akin to copied lecture notes than anything. We get there when we get there.
Analysis
The Real Numbers, Sequences and Series, Calculus of the Real Line, Metric Spaces
Topology
Topological Spaces, Invariants, Homotopy, Fundamental Groups, Homology
Discrete Mathematics
Combinations, Codes, and Graphs
Algebraic Geometry
Classical Affine Varieties, Projective Varieties, Blow-Ups, Schemes,
Undergraduate Level Courses
Foundations of Advanced Mathematics
Informal Logic, Proof Structures, Sets, Functions, Relations, Cardinality
Number Theory
Coming (not so) Soon
Linear Algebra
Coming (not so) Soon
Making Your Own OER
An increasing number of people have asked me how they might go about making an OER of their own. OERs usually use PreTeXt, and every link I provide below can be found through the PreTeXt site.
Beyond that, in terms of setting something up everything you need to know can be found here, and as it's written by the developers themselves, it will be more accurate than anything I could throw together.
However, the sheer volume can be a bit overwhelming at first.
Chapter 2 is a Getting Started Tutorial, though what I usually come back to for help is Section 5.2.
You'll need a GitHub account, Python, and a text editor, though the devs recommend Visual Studio Code, which I use as well.
All this is found in the Guide, but there are worse things than seeing the same information twice.
There is a very active PreTeXt support community that can be found here. The developers check in consistenty and have helped me several times with issues on my end, which was very kind of them.
References
[1] Mann, P. (2018). The impact of open educational resources on various student success metrics. The Idealis. Link
[2] Nipa, T. J., & Kermanshachi, S. (2020). Assessment of open educational resources (oer) developed in interactive learning environments. Education and Information Technologies, 25, 2521-2547. Link