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Saturday, January 30, 2010

MT365 - Introductory Chapter online

I was unfair to the course coordinator. He managed to scan and upload the first chapter of MT365. Still, the book is a nice complement to the course. Graph Theory started with a paper of Euler about the bridges in Konigsberg. That fact is mentioned in practically all books on graph theory and discrete mathematics I have seen sofar but I hadn't seen the actual article written by Euler yet. Well, there is translation of that article added to the introductory chapter of MT365 as an appendix. The more I learn and hear about Euler his statue grows. I am beginning to understand why he is considered ( one of ) the greatest mathematicians of all time.

Fibonacci introduced his famous series 1,1,2,3,5,8,13,21,34, etc. in 1202, Binet published his formula around 1850 or so. A problem that was unsolved for more than six hundred years. Today, I learned that Binet's formula was known to Euler ( ... ) , de Moivre and Bernouilli over a hundred years earlier. I can prove Binet's formula using a technique in Linear Algebra called 'change of basis'. I wonder how Euler found the solution because that particular technique was not yet known when Euler still lived.

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