Introduction
Here I begin a new blog - actually my first blog - which I have named Nontrivial Exercises. Why this name?
I love math. I had the chance to study calculus in high school and enjoyed both the practical application to many complex problems and the satisfaction of the thorough and logical thought process that calculus afforded. I eventually chose to study math in college and earned a Bachelor of Science.
Many times in various collegiate math courses, we would engage ourselves in the oft-feared activities of proving theories, assertions, solutions. Proofs are, of course, one of the central concepts of higher math and are really nothing more than a logical sequence of assertions that you make with proper supporting evidence. Some proofs can become quite complex and tiring. Many require several sub-proofs of assertions made within the main proof.
At many junctures during these especially long and burdensome exercises, the professor, during his or her discourse on the proof at hand, would come to one of the sub-points within the larger proof that required more evidence. He or she would start down the list of evidence and points supporting the specific sub-point of the proof, and would come to a particular item that was patently obvious to someone with a PhD. in mathematics (it’s always "mathematics" if you have anything more than a Bachelor’s degree, never "math"). In an effort to complete the lecture in the allotted class time, the professor would judiciously decide that a particular obvious point required no further explanation in the class lecture and would declare that "it is a trivial exercise to prove that …". Sometimes we students would agree with this statement, many times we would not. Often it was a personal challenge for the eager among us to try to work it out on our own. I personally enjoyed this and at least attempted to figure out the problem on my own in most cases - with the exception being Abstract Algebra. Nevertheless, the true exposition of the "trivial exercise" could be had for the asking from the professor during office hours.
What these professors described as trivial, was to many of us actually quite significant. Further reflection and examination of the problem and eventual explanation led to our enhanced understanding of the specific issue and of the larger problem. Understanding and learning led to satisfaction and confidence.
I want this blog to be about examining the sometimes "trivial exercises" I have about me and working to think through them, interpret them, enjoy them, apply any new understanding to my life. This is not only or ever about the seemingly deep issues of life (life, death, taxes, good haircuts). It’s really about not glossing over or passing over experiences and things I learn and enjoy, but to really enjoy them, to really think about them, and to write about them here.
I would be honored for anyone to read along and add to the discussion.