Skip to main content

Style

I often tell people that I love math, but math is big and I don't love all of it, certainly not in the same way.

This past calendar year I taught two very different introductory courses in Abstract Algebra and Analysis. Both are foundational---they were categories on my oral comprehensive exams in graduate school---but as different as night and day in terms of the style in which the topics act. The first one focused on articulating structures that would be useful in different contexts; the latter identifying what the notion of closeness means in different contexts.

Many topics in math have very different styles. I've taught a special topics course twice on Combinatorics which has such a very different way of approaching problems (articulate collections relevant to the context and count the size of the collections in different ways).  Multivariable Calculus for all of its techniques have some basic principles (run a curve through it, use the Chain Rule) that makes it easy to keep in my head as a teacher.

For the past couple of months I have been struggling with rereading yet again about tensors in the context of General Relativity. The basic concepts are appealing but the notation for expressing them is in my humble opinion God-awful, as in leading me to pray to my deity for swift release.  

Comments

Post a Comment

Popular posts from this blog

Betrayal

I caught a student cheating on a final exam this morning. I had a line of sight on them and watched for ten minutes as they took their cellphone out of their pocket, kept it below their table, typed into it, read it, put it away, then wrote on the exam, repeating this cycle over and over again.  I was a bit surprised as the exam was open notes but this student had not attended many of our classes, just stopping by for exams, and I conjecture that they had no notes to open. I confronted the student who admitted that they had done wrong in an inarticulate non-confessional way. By the afternoon they had signed off on the honor code violation report to avoid further investigation and possible sanctions beyond failing the exam.  Is anger the right emotion to feel now? I had a working relationship with the student, although they had not contributed much to it. They had deceived me in order to gain unwarranted advantage over their peers in the class and that is not right. I don't wan...
1 comment
Read more

Accountability

Mathematics as a discipline teaches accountability. Every claim, whether it be a computation result or a statement (theorem) about how things work is accountable. We teach this accountability developmentally, with lower expectations at the beginning, and sometimes folk who study mathematics casually don't understand this. In my multivariable calculus classes, which I teach most frequently, I usually phrase my expectations as "give me a reason to believe your answer", citing my time working at an investment bank where my recommendations had financial repercussions and my supervisor never took my word for anything. In higher-level mathematics classes such as Abstract Algebra or Analysis I can be more explicit: these are the things we all agree to assume, these are the proof techniques which we understand; can you make an argument that convinces the community who have accepted those axioms and rules of inference that what you claim is true? We work hard to remove the ego fro...
Post a Comment
Read more

Holiday Break

I have been teaching for 37 years now, and I go through many of the same things at the end of the Fall semester each year. There is relief at the completion of a significant task (teaching each of my classes) but there is a good deal of physical and mental weariness and aches. I could sleep for several days straight if not for my sleep disorder. By and large my mind is not very sharp and as an introvert I try to be pleasant with loved ones but am not outgoing at all. With age the feeling of being drained deepens in more and more ways. Of course this is when we have, almost every year, taken a road trip to visit birth families in the Northeast, a full day of driving each way, often involving winter weather far worse than what we are accustomed to in NC. I love my birth family members as well but as with my created family I am weary and not very outgoing. The conversation is rarely about me and my day-to-day life but rather about younger family members and family friends that I do not kn...
Post a Comment
Read more