Day 22, Mat385

Last time Next time

Announcements
- From Trump's science attacks trigger urgent warning from leading researchers: More than 1,900 scientists write letter in 'SOS' over Trump's attacks on science
  For over 80 years, wise investments by the US government have built up the nation's research enterprise, making it the envy of the world. Astoundingly, the Trump administration is destabilizing this enterprise by gutting funding for research, firing thousands of scientists, removing public access to scientific data, and pressuring researchers to alter or abandon their work on ideological grounds.
  The undersigned are elected members of the National Academies of Sciences, Engineering, and Medicine, representing some of the nation's top scientists, engineers, and medical researchers. We are speaking out as individuals. We see real danger in this moment. We hold diverse political beliefs, but we are united as researchers in wanting to protect independent scientific inquiry. We are sending this SOS to sound a clear warning: the nation's scientific enterprise is being decimated.
  ...
  We call on the administration to cease its wholesale assault on U.S. science, and we urge the public to join this call. Share this statement with others, contact your representatives in Congress, and help your community understand what is at risk. The voice of science must not be silenced. We all benefit from science, and we all stand to lose if the nation's research enterprise is destroyed.
- Per our quiz:
  - The quiz
  - The key
  - Some comments:
    1. I like problems like this, because it's important that we learn to capture all cases. We must know definitions, however, and that was a problem. Some of you didn't know the definition of simple. Some of you didn't respect the "four nodes" part....
    2. There is only one tree, unless you allow prescribing left versus right branches of a tree.
      Our author's inorder algorithm assumes the first branch is left. If one allows the first to be a right, then there is a second tree that works.
    3. Because the graph is simple, you only need one bijection, between the nodes of the two graphs. If you don't choose well, you might conclude that they're not isomorphic. But if you choose well, you will reach the right conclusion.
- Wednesday we have our second midterm exam. It will cover everything we've covered from 4.1 through 7.3.
  You will be allowed a cheat sheet, as before. It will be stapled to the exam, as before.
- Here are some old exams:
  - First Exams
  - Second Exams
  The course has changed over the years, so some things were emphasized in the past that may not be emphasized today (or vice versa). Some topics were coverd in the past that are no longer covered (e.g. Prolog). So don't necessarily panic if you don't recognize something!
  Also the topics covered on the "Second" exam may not have overlapped well with what we'll cover.
- Next Monday we'll start on section 8.1; we have four more sections to cover and we're done!
- RE projects: make sure that you send things to me via the correct email: some of you have been sending things to another Andrew Long....
  Issues?
Last time:
- We covered several examples of two algorithms for Section 7.3 (Shortest Paths and Minimal Spanning Trees).
- We saw that Dijkstra's algorithm is a recursive algorithm, and represented it visually (as pruned graphs); and then used the author's algorithm to determine the shortest distance (and path) between two given nodes in a larger graph.
- Then we studied Bellman-Ford's algorithm for determining the shortest distances and paths between two nodes, noting that the algorithm effectively constructs a "minimal spanning tree" between nodes, with the start node as root.
- Then we had a quiz.
Today:
- Any questions about what we did last time?
- We'll hit a final algorithm (Floyd's) from Section 7.3 (Shortest Paths and Minimal Spanning Trees).
- Then have a review, featuring any questions you may have. Here's an overview of the material we've covered since the previous exam.
- Review your quizzes and their keys.
- What questions do you have?

Links:

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\[ S(n)=c^{n-1}S(1)+\sum_{i=2}^{n}c^{n-i}g(i) \]