Day 23, Mat385

Last time

Next time

Announcements:
- Our quiz this week will cover section 6.2 and 6.3
- I was exposed to someone with Covid over the weekend, so I'll be masking for several sessions. If anything ugly should arise, I may be switching to Zoom....
Today:
- Let's look at the quiz from last week:
  - Key
  - Some comments:
    1. Perhaps the recursive definition of trees helps; or work by depth.
      In any event, some sort of organization is essential so that you don't get lost in the forest! Breadcrumbs....
    2. Trouble with induction:
      1. we need a base case (in this case depth 0),
      2. and then 1st principle works: show that \(P(k) \rightarrow P(k+1)\)
- Last time: We started Section 7.2 (Euler Paths and Hamiltonian Circuits).
  We'll continue with that, and then jump into Section 7.3: Shortest Path and Minimal Spanning Tree.
- A couple of handouts to help with today's stuff:
  1. Euler/Hamiltonian/Floyd
  2. Shortest Paths (Dijkstra's and Bellman-Ford
Links:
- Rooted Trees
- Euler Path algorithm
- Using a directed, acyclic graph to represent an algebraic operation: Supplementary Material On-line

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