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.