Suggestions for a learning roadmap for universal algebra?
I think a useful combination of resources for universal algebra would ideally, when taken together:
- Provide ample motivation behind the various developments in the field.
- Either provide powerful intuitions, or avoid them altogether, in an effort to not cripple the learner's imagination.
- Provide a clear formal development (or, minimizes the number of "rabbits pulled out of a hat").
- Be self-contained.
- Be well written.
I look forward to your suggestions, and thank you sincerely in advance!
This is a good question, and Eran gives a good answer. Here is another collection of resources (which I just created in response to this question):
https://github.com/UniversalAlgebra/UAResources
Although there are many pages scattered around the interweb that collect valuable resources in universal algebra and lattice theory, it seems to me that none of them (except possibly http://universalalgebra.org) encourage contributions from all members of the math community. Consequently, we don't have one authoritative, central repository that people could point to when answering questions like this one.
The UAResources repository is just a quick first pass, but maybe it will grow with community support. One thing in particular that UAResources currently lacks is a "road map" that would directly answer to the OP's question.
Perhaps someone is willing to fill in the "Road Map" section of the README.md page at https://github.com/UniversalAlgebra/UAResources#road-map
I must admit that I am still in the process of learning universal algebra, so my answer may not be as good as that of a researcher in the field, for example.
My recommendation is for Clifford Bergman's Universal Algebra. It is very clearly written and organized. The book has a large bibliography and gives good introductions to many of the current research areas.
Other good resources are the book by Burris and Sankappanavar and the book by McKenzie, McNulty, and Taylor. Burris and Sanka's book is available for free online and Mckenzie is one of the premier researchers in universal algebra.
Once you have learned enough of the basics you could probably begin reading one of the following:
Hobby and McKenzie's book on tame congruence theory
McKenzie and Freese's book on commutator theory
Clark and Davey's book on duality theory