Abstract Nonsense

Crushing one theorem at a time

The Deal VII

So, here’s what’s coming up in the next trimester of my schooling. The math courses I’m taking are

  1. Analysis II.  This covers basic multidimensional analysis as is covered in the second part of Rudin and some measure theory as in the beginning portions of Royden. I hope to write occasional posts on this.
  2. The continuation of this Finite Dimensional Vector Space independent study. I hope to continue doing what I’m doing with that.A course on
  3. The Representation Theory of Finite and Compact groups using Barry Simon’s book by the same name. I hope to post as frequently about this as I do with Halmos. That said, Barry Simon’s book (while being superb in all other aspects!) doesn’t have any problems. Thus, I will have to find problems out of other books (I will post which books, sections, etc. they are from). If anyone has any suggestions of problems from other books please let me know!  There will be an interesting dichotomy because of this book. Namely, although this book is rudimentary (compared to most rep. theory books) it assumes a fair bit of knowledge of linear algebra. So, there is a chance that one will assume facts not covered yet in my side-along discussions of Halmos. I will begin this with a review of basic group theory. Go through some basic ideas so we (mostly I) can get warmed up and, on the off-chance that there is someone who has never done group theory can at least have a reference; also it will help sync up the notation I use and the notation used by any reader. I will cover (not necessarily in this order or in this post format)
  • The basic definitions of group and subgroup and some of the necessary or convenient theorems
  • Homomorphisms
  • Cosets and Normal Groups including the three Isomorphism Theorems
  • Cyclic Groups
  • Permutation Groups
  • Finite Abelian Groups (The Structure Theorem)
  • Group Actions
  • Sylow Theorems
  • Semi-direct Products

December 23, 2010 - Posted by | Uncategorized

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