In working with graphs so far we've been able to lean on our visual system to literally see if a graph is connected, or to help us spy out the minimal spanning tree or shortest route. But it's no help when graphs get moderately large or complex. Which brings us to matrix multiplication. Multiplying matrices unlocks a rich set of interpretations of system graphs. This week it will enable us to tell if a graph is connected and which nodes are reachable from which others. Next week we will use it to trace the dynamic evolution of systems using Markov models.
Matrix multiplication is a fussy procedure, but it is mechanical, and you might as well start muttering the key incantation to yourself now "the column above times the row to the left".
And three tidbits ðŠð°ðĐ
It's a shame that it's just as the course ends that we finally have the tools to consider some of the most interesting questions.
The travelling salesman problem. The salesman's seemingly simple question has us bump up against one of the boundaries of mathematics.
The Rule of 72. What do you do when there isn't an efficient, exact mathematical solution? Use a rule of thumb or heuristic.
Game trees. How do computers keep beating people at games? They build game trees to look into the future and see how it will play out.
The end is in sight! ðĪŠ (Even the emails are getting shorter)
The last day of classes is next Tuesday, just one week from today. The last assignment is posted. And this week and next are short weeks. Don't lose your grip now!
Office Hours
I'll be in my
Zoom
"office" again this week on Monday, Wednesday and Friday
from
10:30 am to 11:30 am. Come on by if you have questions.
That's all for now!
Hang in there, you're almost done,
Tim
"All things are difficult before they are easy" ~ Chinese proverb
