The Art of Proving Binomial Identities is Now Available

A couple of months ago I posted that my book, The Art of Proving Binomial Identities, would soon be finished.  Well, it’s out now, and you can buy it straight from the publisher (CRC Press).  It’s up on Amazon as well.

The March blog post summarizes the contents of the book, but there is one other feature of it I’d like to highlight.  In addition to the usual index of topics, I added an index of identities and theorems.  Every identity and theorem in the book appears in this index, with page numbers indicating exactly where.  My intent was for this to facilitate one of my main goals with the book: Understanding particular binomial identities better by looking at them through multiple lenses.  For example, the references to Identity 24, \sum_{k=0}^n \binom{n}{k} \frac{(-1)^k}{k+1} = \frac{1}{n+1} (which I used in my last post), lead you to proofs of it that involve the absorption identity, integration, the beta function, probability, generating functions, finite differences, and mechanical summation.  Each proof gives another perspective on why Identity 24 is true.

Also, at some point within the past couple of months I needed to find a particular binomial identity.  Sure enough, it was in the index!  That was gratifying.

(There are a couple of small errors on the CRC site.  First, I am no longer department chair, as I finished my three-year term in 2018.  I was department chair when I submitted the book proposal, and I corrected it on the info sheet I was sent a couple of months back, but for some reason it didn’t get updated on the CRC site.  Second, there is a chapter on mechanical summation that didn’t make it into the site’s description of the Table of Contents.  I suspect this is because the TOC list is from the original draft of the book I sent CRC, and the mechanical summation chapter was added later.)

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