Start of GeneratingFunctions: basic idea, finding generating functions for a^{n} and n^{k}, 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.)