Question on Elements of Algebra by Euler

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Discussion Overview

The discussion revolves around Euler's "Elements of Algebra," particularly focusing on the binomial theorem and its connections to combinatorics and advanced mathematics. Participants express their experiences with the book and seek guidance on understanding the material and related topics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant appreciates Euler's exposition but feels challenged by unfamiliar topics, particularly the theory of combinations, and questions its importance for understanding the book.
  • Another participant identifies the binomial theorem as a key topic and notes its connection to combinatorics, suggesting that it is essential to study it well.
  • A participant mentions the elegance of combinatorial proofs for the binomial theorem while acknowledging the existence of other proof methods, including induction.
  • Concerns about the difficulty of accessing classical texts on combinatorics, such as those by Bernoulli and De Montmort, are raised, along with a request for recommendations on accessible resources.
  • Suggestions for modern resources are provided, including websites and books that cover combinatorics and discrete mathematics, with an emphasis on their relevance to understanding the binomial theorem.
  • One participant expresses gratitude for the recommendations and indicates openness to modern sources of information.

Areas of Agreement / Disagreement

Participants express a mix of agreement on the importance of the binomial theorem and its connection to combinatorics, but there is no consensus on the necessity of understanding these topics immediately or the best resources to use.

Contextual Notes

Some participants express uncertainty about the classification of the binomial theorem within advanced mathematics and its relationship to probability and statistics, indicating a lack of clarity on these connections.

fde645
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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.)
 
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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.
 
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.
 
fde645 said:
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
 
Last edited by a moderator:
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 :)
 

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