Monday No. 1092

This morning, 8 am, Mathematical Logic.  2 hours of frantic recitation of definitions and conventions to get everyone on the same page.  Not too bad considering; I followed almost everything, and the potential for interest still remains.  I'll definitely stick with it to see at least what next week is like.  A gem from Prof. Szabo: "Truth is sometimes a hopeless task."

Conjecture and Proof went well, going over our first problem set, and a few various topics in vector spaces.  Finally came Classical Algebra, the three-week course which sounded promising.  Emphasis on "sounded."  The prof is a retired St. Olaf guy who comes in to run a January term in number theory for St. Olaf kids and then sticks around to teach three weeks of classical algebra.  We reviewed topics from session 1 in both sessions 2 and 3, in fairly minute detail each time.  He seems to rejoice in doing long polynomial expansions on the board and concluding that they must equal to 1... or negative 1... oh no, wait, that's negative 1 so that must be negative 1 to the third power, which is negative 1... so yes, equal to one.  Or at least that's what we spend a quarter of our lecture time doing.  We also covered the proofs of the principle of mathematical induction (which he claimed most of us probably saw in grade school??) and the division algorithm in exquisite detail.  Which of course required a five-minute presentation of the well-ordering principle as background knowledge, complete with hemming and hawing about how to pose the definition:  to treat bounded above and bounded below as separate cases which imply maximal and minimal values, respectively, or to simply say "bounded" and be done with it, or, wait!, perhaps just bounded below and leave the bounded above case to symmetry.  Thankfully he spared us the proof.  This seems to be a total dud of a class, which is unfortunate given that the material is, indeed, "classic."  Fortunately, we only meet three more times.