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Reflection On Studied Topics and Intuition

Mathematics, The Student Life · May 30, 2013, Thursday

When you study, don’t just stop to the concepts you’re trying to fixate in your mind.

Discuss the concept with yourself, bring on some deep reflection.

Not just when you do it the topic will come up easier to learn and memorize, but you could come up with interesting ideas that will further your studies and make you advance in your curriculum.

Back in 2009, I was deeply involved with Discrete Mathematics as I was prepping for the exam. As I was relaxing in the afternoon, watching a Disney movie on DVD, I came up with an idea that I had to put down on paper.

The idea linked together two topics in Discrete Mathematics I was studying that day, relations and graphs.

Here is the exact copy from my note sheet from that very productive afternoon:

Let G=(V,E) be a connected, non-oriented graph, and let’s define a ρ b the relation between two nodes a and b, with ρ the relation symbol:

a ρ b ⇔ there exists at least one walk between a and b

R: a ρ a ⇔ there exists a walk from a to a (it’s the size 0 walk)

S: a ρ bb ρ a, a ρ b if there exists a walk from a to b; b ρ a if there exists a walk from b to a

T: a ρ b ∧ b ρ ca ρ c, with

  • a ρ b: there exists a walk from a to b
  • b ρ c: there exists a walk from b to c
  • a ρ c: there exists a walk from a to c

mathidea

(Graph created with http://dl.dropboxusercontent.com/u/4189520/GraphJS/graphjs.html and a bit of hand-drawing. It’s not great, I know… ^^”)

Luana Spinetti