Question on Elements of Algebra by Euler

[fde645]

I like this book very much. Euler is a brilliant mathematician no doubt. He explains everything very well without holding back significant information with his exposition. However, I bump into an unfamiliar topic. I do believe it has something to do with advanced mathematics. I googled it, and I believe it has some relation to the theory of combinations, to which unfortunately I am ignorant of. I don't know which branch of mathematics it falls into. Regardless of the title elements of algebra, this book is certainly not just any ordinary book, for which I like very well. Although, I am worried since I can't understand it, is it important to understand it now, or should I take it just to have a different set of perspective on things? (Since he uses this to explain the powers of a binomial, which I understand, but his method is somehow, I think it has something to do with other branch of mathematics.)

 

[fde645]

Just to define it precisely, It has something to do with the Binomial theorem. This is the first time I heard of such theorem. I didn't know there was a brilliant theorem, that aids in getting the powers of a binomial. So, the way Euler explained it, he invoked theory of combinations and permutations. If my intuition is correct this is for advanced mathematics, I just don't where it belongs. Should I just absorb it at this current time just to have a some knowledge of it since I am just broadening my knowledge on algebra, and after this book I would jump to Euclid's Elements.

 

[micromass]

The binomial theorem is of extreme importance. So I suggest you study it well. It seems like Euler explains it using combinatorics, which I think is the most elegant proof. There are other proofs as well. A common proof is by induction: http://en.wikipedia.org/wiki/Binomial_theorem#Inductive_proof

 

[fde645]

Given my ignorance of combinatorics, and it seems that it is very difficult to obtain the books of Bernoulli and De Montmort on the subject matter. Does anyone have any advice on the books that explain the subject at hand? This has something to do with probability I suppose, So maybe this will be a good introduction to statistics.

 

[micromass]

Given my ignorance of combinatorics, and it seems that it is very difficult to obtain the books of Bernoulli and De Montmort on the subject matter. Does anyone have any advice on the books that explain the subject at hand? This has something to do with probability I suppose, So maybe this will be a good introduction to statistics.

You seem to be very interested in old books, so forgive me if I recommend newer sources instead. Anyway, I am really intrigued by the following website:
http://www.math.uah.edu/stat/foundations/Counting.html
http://www.math.uah.edu/stat/foundations/Structures.html

It is everything you will need on the topic to understand the binomail theorem.

If you want more information, then you should consider the excellent book Concrete Mathematics: https://www.amazon.com/dp/0201558025/?tag=pfamazon01-20
It has computer science on the cover, but don't let that fool you! The book is truly mathematical and extremely good!

Other sources would consist of discrete mathematics books. I don't know many of those, but I always liked Grimaldi: https://www.amazon.com/dp/0201726343/?tag=pfamazon01-20

 

[fde645]

Just the books I am looking for thank you! I don't mind modern books at all. I don't know maybe I am old deep inside :)