Retired UCI math professor Steven Roman has just started making a series of Group Theory lectures on YouTube.
Retired UCI math professor Steven Roman has just started making a series of Group Theory lectures on YouTube. No prior experience in group theory is necessary. He’s the author of the recent Fundamentals of Group Theory: An Advanced Approach. [1]
He hopes to eventually also offer lectures on ring theory, fields, vector spaces, and module theory in the near future.
Fundamentals of Group Theory by Steven Roman
References
[1]
S. Roman, Fundamentals of Group Theory: An Advanced Approach, 2012th ed. Birkhäuser, 2011.
Peter Woit has just made the final draft (dated 10/25/16) of his new textbook Quantum Theory, Groups and Representations: An Introduction freely available for download from his website. It covers quantum theory with a heavy emphasis on groups and representation theory and “contains significant amounts of material not well-explained elsewhere.” He expects to finish up the diagrams and publish it next year some time, potentially through Springer.
I finally have finished a draft version of the book that I’ve been working on for the past four years or so. This version will remain freely available on my website here. The plan is to get professional illustrations done and have the book published by Springer, presumably appearing in print sometime next year. By now it’s too late for any significant changes, but comments, especially corrections and typos, are welcome.
At this point I’m very happy with how the book has turned out, since I think it provides a valuable point of view on the relation between quantum mechanics and mathematics, and contains significant amounts of material not well-explained elsewhere.
Download a pre-publication version of the book which will be published by Cambridge University Press.
The book arises from notes of courses taught at the second year graduate level at the University of Minnesota and is suitable to accompany study at that level.
“Why should we want to know about representations over rings that are not fields of characteristic zero? It is because they arise in many parts of mathematics. Group representations appear any time we have a group of symmetries where there is some linear structure present, over some commutative ring. That ring need not be a field of characteristic zero.
Here are some examples.
[…]
In the theory of error-correcting codes many important codes have a non-trivial symmetry group and are vector spaces over a finite field, thereby providing a representation of the group over that field.”
Peter Webb (math.umn.edu)