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Note: You are looking at a static copy of the former PineWiki site, used for class notes by James Aspnes from 2003 to 2012. Many mathematical formulas are broken, and there are likely to be other bugs as well. These will most likely not be fixed. You may be able to find more up-to-date versions of some of these notes at http://www.cs.yale.edu/homes/aspnes/#classes.

Start of GeneratingFunctions: basic idea, finding generating functions for an and nk, extracting sums of coefficients, extracting individual coefficients, solving recurrences, and simplification using partial fraction expansions. Readings: Sections 25.4, 25.1 and 25.2.

In reading these sections, don't worry too much about rings and fields; when BiggsBook talks about a power series over a field, think of this as just meaning a power series with arbitrary numbers (not necessarily integers) for coefficients. (We'll come back to rings and fields later when we talk about AlgebraicStructures.)

2014-06-17 11:57