2013-01-15

Some basic mathematical notation

I started out today reading up on the "binomial coefficient," and proceded to drill into the definition of its terms, so the "factorial," came up. From there, the related concepts I wasn't familiar with were "double factorial," "multi factorial," and "gamma function." The notation for these involves a lot of '!'s and the capital Greek letter Gamma.

Thereafter, I had to go revise the notion of "summation," whose "capital-Sigma notation," I have always found confusing. Why can't these things be required to for some sort of geometric sense, instead of being arbitary arrangements of symbols, whose relative placement must be remembered for semantic context?

So I also learnt the capital-Pi notation for the product of a series, which corresponds to capital-Sigma notation's use to represent the sum of a series.

On we then go, to "finite differences," and a review of the classic topic of "mathematical induction." "Recurrence relations," and "seed values," round off the evening. Time for bed, at 0306 hours.

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