Nets, Puzzles, and Postmen: An Exploration of Mathematical Connections

Technically, I abandoned this book, but I’m still counting it as read because I learned a lot from it.

What I learned is that network theory is actually a thing. It’s a branch of mathematics. And, weirdly, a lot of the seemingly unsolvable story problems you read as a kid are actually network theory problems. In fact, a shocking number of practical, everyday problems in business and science are actually applications of network theory.

There’s a huge vocabulary involving network theory: nodes, paths, circuits, degrees, circuits, coloring, planarity, etc. And there are classic problems of network theory that continue to be solved: The Traveling Salesman Problem, The Four-Color Problem, The Marriage Problem, etc.

Network theory is fundamentally concerned with the relationships between logical concepts called “nodes” and the paths between them. But it can also be considered about the empty spaces created by these nodes, and how they relate to each other. A node can be anything in real life that relates to anything else – humans, buildings, streets, classes, etc.

And that’s the gist of network theory: it’s the study of relationships between things.

The book, for its part, is one that you either have to have significant experience in math to appreciate, or you have to be willing to sit down and work through problems. Chapters build on one another, and there’s a lot of algebra in there. So, unless you’re willing to open the book up, and grab a paper and pencil, and spend time actually learning, then it’s not a light read.

But, in some ways, this is the best kind of book. It revealed a new world to me and I took many things away from it. Even if I don’t have all the answers, at least I now know that they exist.