An Introduction to Ordinary
Mathematics and Statistics
DescriptionThis book is a short introduction to generating functions from a a computational perspective. It is an experiment with new technology.
My goal is to cover only the topic of ordinary generating functions and only a quick introduction. It does not extend beyond the computational aspects and does not cover more combinatorial applications of generating functions. These are topics that I hope to cover in other short books.
Below I include the video summaries of the text which accompany each section.
Chapter 1: Introduction
|Section 1.1: About this
||Section 1.2: Notes about
recommended background of the reader
Chapter 2: Generating functions neither generate nor are they
The three W's of generating functions (what, when
||Section 2.2: Examples
Chapter 3: Getting the most out of your generating functions
Back and forth
||Section 3.2: Examples
Chapter 4: Examples and exercises
Exercises to help build strong generating functions
||Section 4.2: Using
generating functions to prove summation formulas
Section 4.3: Solutions
Chapter 5: Final words
After you have finished this book I hope that you have the
basic tools to manipulate generating functions for sequences and
that you are able to use them to prove basic identities.
This is a very good starting point, but you will find that what
I have presented here only a very small part of the subject and
you will need to find other references to learn more advanced