Category Archives: Math

π

3.
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Happy π Day!

Dijkstra's algorithm

Dijkstra's algorithm for finding the shortest paths in a graph is a classical one that most students of computer science get to learn about, although I suspect few have actually read the original paper. Published in the very first volume of the journal Numerische Mathematik in 1959, an official copy of the three-page paper A Note on Two Problems in Connexion with Graphs is available from SpringerLink, although you would have to be at an academic institution with a subscription or have a personal subscription to SpringerLink to download the paper.

Continue reading Dijkstra's algorithm

Blog carnivals

With the elections on November 4th in the United States being over, the special election edition of the Carnival of the Liberals is up at The Lay Scientist. It includes articles that focus on the election, organized by whether an article was written before or after. My punditry as to what went wrong with McCain's presidential campaign is included in the latter category.

In the same vein, the 43rd edition of the Carnival of Mathematics is up at The Number Warrior, which has a preponderance of puzzles this time around. Among them is my explanation of a puzzle of chance presented at the Shores of the Dirac Sea.

The probability of a probability

The Shores of the Dirac Sea has a somewhat head-scratching puzzle about probabilities:

Let us say that someone gives you a lopsided bet. Say that with probability r one gets heads, and with probability 1-r one gets tails, and you have to pick heads or tails. You only know the outcome of the first event. Let's say after the first toss it came out heads. What is the probability that r > \frac{1}{2}?

Continue reading The probability of a probability