A Gentle Introduction to the Art of Mathematics
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A Gentle Introduction to the Art of Mathematics
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Re: A Gentle Introduction to the Art of Mathematics
#2The quality of writing in this book is fantastic. If you're studying math or have a recreational interest I really recommend it.
Re: A Gentle Introduction to the Art of Mathematics
#3Seems very student-friendly and accessible which is good. A quick browse shows that it covers Set Theory, Logic and Proofs i.e. the absolute basics for "Modern Mathematics". One of the biggest difficulties for the student i.e "Mathematical Notations" (which are merely a shorthand language) are explained from the ground up which is great.
Re: A Gentle Introduction to the Art of Mathematics
#4At the very start of the book:
> It has been said that “God invented the integers, all else is the work of Man.” This is a mistranslation. The term “integers” should actually be “whole numbers.” The concepts of zero and negative values seem (to many people) to be unnatural constructs.
It is not a mistranslation. In German "ganze zahlen" actually means "integers". It is just if you translate it word for word, "ganze" -> "whole", "zahl" -> "number", that you get whole numbers, which would be a mistranslation, because in English whole numbers mean 0, 1, 2, ...
Re: A Gentle Introduction to the Art of Mathematics
#5At the very start of the book: > It has been said that “God invented the integers, all else is the work of Man.” This is a mistranslation. The term “integers” should actually be “whole numbers.” The concepts of zero and negative values seem (to many people) to be unnatural constructs. It is not a mistranslation. In German "ganze zahlen" actually means "integers". It is just if you translate it word for word, "ganze"…
> in English whole numbers mean 0, 1, 2, ...
According to Wikipedia [1], the term is ambiguous. Its talk page [2] has plenty discussion about it though.
Re: A Gentle Introduction to the Art of Mathematics
#6At the very start of the book: > It has been said that “God invented the integers, all else is the work of Man.” This is a mistranslation. The term “integers” should actually be “whole numbers.” The concepts of zero and negative values seem (to many people) to be unnatural constructs. It is not a mistranslation. In German "ganze zahlen" actually means "integers". It is just if you translate it word for word, "ganze"…
I can't seem to find a reference for it now, but a math professor once told us that some early cultures didn't even have a proper word/symbol for the number "one", and the act of counting didn't kick in until there were two items.
Re: A Gentle Introduction to the Art of Mathematics
#7At the very start of the book: > It has been said that “God invented the integers, all else is the work of Man.” This is a mistranslation. The term “integers” should actually be “whole numbers.” The concepts of zero and negative values seem (to many people) to be unnatural constructs. It is not a mistranslation. In German "ganze zahlen" actually means "integers". It is just if you translate it word for word, "ganze"…
> in English whole numbers mean 0, 1, 2, ... According to Wikipedia [1], the term is ambiguous. Its talk page [2] has plenty discussion about it though. [1] https://en.wikipedia.org/wiki/Whole_number [2] https://en.wikipedia.org/wiki/Talk:Whole_number
In German though "Ganze Zahlen" is not ambiguous. At least in my entire life I have not seen any other understanding of it and every child at school learns about them and that they include 0 and negative numbers, in contrast to natural numbers ("Natürliche Zahlen").
Re: A Gentle Introduction to the Art of Mathematics
#8Would be nice if we could see experienced mathematicians endorse this, please. It would help to decide whether to put time into it. At first glance it looks really nice.
Re: A Gentle Introduction to the Art of Mathematics
#9Earlier quoted context omitted.
> in English whole numbers mean 0, 1, 2, ... According to Wikipedia [1], the term is ambiguous. Its talk page [2] has plenty discussion about it though. [1] https://en.wikipedia.org/wiki/Whole_number [2] https://en.wikipedia.org/wiki/Talk:Whole_number
In German though "Ganze Zahlen" is not ambiguous. At least in my entire life I have not seen any other understanding of it and every child at school learns about them and that they include 0 and negative numbers, in contrast to natural numbers ("Natürliche Zahlen").
As a German, this is exactly what whole numbers means - numbers such as -1, 0, 1. Natural numbers are whole numbers > 0.
Re: A Gentle Introduction to the Art of Mathematics
#10Would be nice if we could see experienced mathematicians endorse this, please. It would help to decide whether to put time into it. At first glance it looks really nice.
I'm a mathematician (PhD in numnber theory...) and I took a look. It's a basic textbook about some concepts like functions, relations, and basic proof techniques. It seems okay. I was expecting something different from the title, though. It's not too different from many basic books introducing such concepts but obviously a lot of effort was put into it.
Personally, I think if you want an introduction to the "art" of mathematics, it would be a lot better to pick up a more idiosyncratic book that doesn't aim to cover the basics of the standard curriculum in a textbook-style way, which in my opinion is rather tedious. That could either be a more high-level book like Ian Stewart's "From Here to Infinity" or one of Raymond Smullyan's fun texts on logic.
Or for a more basic book, something like "The Mathematical Universe" by William W. Dunham is a much more interesting introduction to the "art" of mathematics than a textbook-style intro.