Recently a book by Kauers, Palle was published by Springer called 'The Concrete Tetrahedron'. In the book the concrete tetrahedron stands for:
- symbolic sums;
- recurrence equations;
- asymptotic estimates;
- generating functions.
The authors have the following to say about it.
... the present book is not meant to be merely a summary of “Concrete Mathematics”. We have a new twist to add to the matter, and this is computer algebra. In the last decade of the 20th century, many algorithms have been discovered by which much of the most tedious and error-prone work about the four vertices of the Concrete Tetrahedron can be performed by simply pressing a button. We believe that a mathematics student of the 21st century must be able to use these algorithms, and so we will devote a great part of this book to explaining what can and should be left to a computer, and what can and should be still better done the traditional way.
In Apostol's Analytic Number Theory formal power series and Dirichlet multiplication are among the topics. For me that was a reason to refresh, review my knowledge on formal power series and generating functions. ( One of my favorite subjects in mathematics. ) That is how I became aware of this new release.
Link: The Concrete Tetrahedron
Link: Video lectures about Concrete Mathematics