Some perspective for students on these times and how to reflect about life in the classroom

Sometimes when we think about teaching, we imagine this very serious professor on a podium or a blackboard dictating a very technical lesson. The professor is the only one speaking. If this is a math professor, he or she will only talk about math. Now in this era of multiple distrations and instant gratification, we need to go the extra mile and make students reflect about where are they going in life and if their habits are helping towards achieving their dreams. I mentioned to them that I read books in the subwway or the bus and do some grading or prepare the lesson of the day. The I asked them if they could count how many people in the wagon are looking at their cellphone: texting, playing a game, looking at some social media platform (the picture of someone eating pasta), etc. They smiled at me because they knew this is common. I did not want to sound like a broken record or that mom who is giving unsolicited advise. However, I suggested for them to take advantage of those moments of solitude to read a book, journal or reflect about an idea. We do not need to be making videos to gain approval from other people. Do it if you like but be careful with what is motivation behind it. I remembered sending and assignement where they had to take a picture of a proof of a proposition in the subway or other place outside campus or a classroom...a place where it is not common to see people writing proofs. I got pictures of people working on stairways in the city, a laundroamat, at the subway station while waiting for a train, the beach and during a subway ride. I hope this connected them with their own thoughts. At least they did not look at their cellphone screen for a few minutes :) We need independent thinkers, not that person who is competing in social media to post better pictures or catchy phrases than his/her friends. Dare to be different, it does not matter how you look, what is your financial situation, your life circumstances. Many things in life are ephemeral but your essence as a human being and as an intellectual is unique and can persist through time.

Algorithms, big-O and number theory

It has been a while since last time I published in this blog. Today I posted final grades and started to reflect about what we learn during the semester. We talked about big-O. We did an example where we found that a fucntion was O(x^2) by finding an upper bound for the orginal function when c is greater of equal for some real number k. We showed some plots to illistrate this point. We then moved to talked about module m atithmetic, reminders, Euclidean algoritm, etc. I was surpised to see that students really liked this part of the course. I wish I would have spent more time on it. We gave simple examples of how to ecrypt messages. Also, we showed propositions related to the greated common divisor between two numbers and how to find it using the Euclidean algorithm. Perhaps students will never forget about this french mathematician, Bezout (I'll add the tilda later.) With Bezout's identity, they can find the Bezout's coefficients of them is the inverse of one of the numbers involved in the greatest common divisor. Finding the inverse help us solve equations involvinf arithmetic module m. So every time we needed to find an inverse modul m, I would ask: "Do you remember the french name we need?" It makes me so happy to say "Bezout, Bezout!!!" at loud.