The exercise above is from the book
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I worked on this exercise for a great deal of the week.
I had considerably more time to do math this week. In a sense I even made some discoveries. At least for myself. I am going to try to document them in 'paper-format' during the weekend. If all goes well, I''ll publish them there.
I had time to go after new books as well. Too many topics fascinate me. I want to select a topic in math to which I could eventually contribute. That means that I must be good at it, i.e. find it easily accessible. Becoming 'current' is the first step, I suppose, being able to read the journals and understanding who is who in the world of mathematics. At the moment I am going in the direction of computational group theory, representation theory and combinatorics. Still much too broad, I know.
As far as computational tools are concerned up until now I have worked with GAP and Mathematica. Since a year or so GAP can be used as part of SAGE, a more or less complete math workbench, comparable with Mathematica. The philosophy of the SAGE team is 'best of breed', if I understood them correct. Where Mathematica has to develop all their tools with their own payrolled staff, SAGE draws the best of breed from the Open Source Community, i.e. GAP for Group Theory in SAGE. I don't see Mathematica overtaking the lead from GAP real soon and the same is true for other specialized areas like for example Commutative Algebra. But as a productivity tool Mathematica beats SAGE by far.
Did you get the answer (m-1 choose k-1) * (n+1 choose k) for this question?
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