Fibonacci and Lucas Numbers with Applications 1st Edition

There's nothing wrong with this book, exactly, but it suffers from being too technical to be a popular book on Fibonacci and too breezy and gimmicky to be a mathematics text. It flits and floats and flies from sub-topic to sub-topic, sometimes visiting the same sub-topic more than once, without discernable pattern. While I have no doubt that that Koshy knows his stuff and his discussion in each sub-chapter is more or less correct, I wish I had a better sense of what's left out.Fibonacci has always been a dilettante's heaven, and dilettantes need books, like Koshy's could have been, that give them a sense of what's known and what's not. If you're staring into the fire some winter night and suddenly go, Hark!, you need an easy way to decide if your Hark! is worth pursuing, and if so what's already been done. You don't need mathematical rigor, at least not beyond some bare minimum. You need to know if anyone ever bothered to work out a general formula, for general k, for the coefficients of a(0)F(i)^k + a(1)F(i+1)^k + a(2)F(i+2)^k + . . . + a(m)F(i+m)^k = 0. (someone did: see Lewis, More Power to Fibonacci, Mathematics Gazette July 2003.)A one-volume (affordable) Fibonacci encyclopedia reliably answering the breadth question would be nearly priceless. Koshy's book is not it. You have to buy this book; there's nothing else out there, that I know about, anyway, matching its breadth or depth. And, I suppose Koshy deserves his royalties simply for stepping into the market niche where I was waiting. But there's something missing.PS. People who know their stuff have warned us about the many typos in this book. I have found a few myself. So, test those Fibonacci identities before you use them, the same way you would test thin ice.

Too Hard to read

The author has collected a lot of facts about these numbers and a decent bibliography. The book can help senior math students (with student projects, capstone papers) as well as professional scholars who need a reference.Here and there one finds mistakes and typos. For example, the conclusion of Theorem 12.6 on page 159 is wrong - the factor (-1)^n should not be there. The mistake is in the middle of the proof, where erroneously 1-alpha = -beta instead of 1-alpha = beta.

Overall, this is a good book, covering many aspects of the fibonacci numbers, however, at about a 100USD, the potential buyer should be warned that there is a lot a typographical errors in the book.While it is frequent to find a few notation's mistakes in every mathematics book, this one is way over average, most of them fortunately are quite obvious and easy to correct, but, in some cases, it simply makes the demonstration unreadable and the reader is better off working out the proof by himself; luckily, most of the proofs are quite elementary.For the reader patient enough to go through this book simultaneously reading and correcting it, it definitely is a worthy repository of results involving Fibonacci and Lucas numbers.