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5: Additional Topics
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- 5.1: Generating Functions
- There is an extremely powerful tool in discrete mathematics used to manipulate sequences called the generating function. The idea is this: instead of an infinite sequence (for example: 2,3,5,8,12,… ) we look at a single function which encodes the sequence. But not a function which gives the n th term as output. Instead, a function whose power series (like from calculus) “displays” the terms of the sequence.
- 5.2: Introduction to Number Theory
- This is the main question of number theory: a huge, ancient, complex, and above all, beautiful branch of mathematics. Historically, number theory was known as the Queen of Mathematics and was very much a branch of pure mathematics, studied for its own sake instead of as a means to understanding real world applications. This has changed in recent years however, as applications of number theory have been unearthed.
- 5.3: Additional Topics (Exercises)