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Thursday, February 24, 2011

The concrete tetrahedron

I once wrote that I rated Concrete Mathematics 6 out of 5 stars. Unfortunately the book was published in the pre LaTeX era. To the eyes or 21st century readers the book simply looks ugly. If you look a bit deeper though you'll notice that you struck gold as far as content is concerned. But... what we can do today on a laptop with Mathematica installed on it was beyond the possibilities of the super computers in the days CM was written. In that respect the book looks out-dated.

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

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