Sir Tony Hoare on the future of Computing Science (CACM, March 2009):
I expect the future to be as wonderful as the past has been. There’s still an enormous amount of interesting work to do. As far as the fundamental science is concerned, we still certainly do not know how to prove programs correct. We need [...]
In graph theory, the degree of a vertex A, d.A, is the number of edges incident with the vertex A, counting loops twice. So, considering graph 0 below, we have d.A=3, d.B=3, d.C=1, d.D=3, and d.E=2.
A well-known property is that every undirected graph contains an even number of vertices with odd degree. The result first [...]
Also filed in Algorithms, Computing Science, Education, Mathematics
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Tagged calculational, goal-oriented, graph, graph theory, Mathematics, Methodology, Programming, proof, quantifiers, vertex
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I found the following problem on K. Rustan M. Leino’s puzzles page:
[Carroll Morgan told me this puzzle.]
Prove that for any positive K, every Kth number in the Fibonacci sequence is a multiple of the Kth number in the Fibonacci sequence.
More formally, for any natural number n, let F(n) denote Fibonacci number n. That is, F(0) [...]
Tuesday, January 22, 2008
A recent article written by Dr. Robert B.K. Dewar and Dr. Edmond Schonberg (both from AdaCore Inc.) is generating some discussion on the state of Computer Science (CS) education in the United States. In “Computer Science Education: Where Are the Software Engineers of Tomorrow?“, Dewar and Schonberg claim that U.S. universities are training unqualified and [...]
Also filed in Algorithms, Education, Mathematics, Opinion, Programming
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Tagged Algorithms, Education, Mathematics, Methodology, Opinion, Programming, university
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In the last post I have presented some historical context about programming and mathematical methodology. If you read it, then you should have an idea when and why programmers started to investigate on mathematical methodology. However, I haven’t mentioned any aspects of mathematical methodology that can help us to improve our programming or mathematical skills.
In [...]
Thursday, December 28, 2006
First of all, welcome to my new blog. Being this my first post, I will present myself, give you some background on what I am doing and explain what are my intentions about this blog. My name is João Fernando Ferreira and I am a research student at the Foundations of Programming research group at [...]
