Dear Nez77,
Hello. My name is Carissa and I'm 16 years old. I'm doing a project for pre-calculus and I need some information on Gauss' book, Disquisitiones Arithmeticae. I've searched the net but I haven't found anything. If you have any links about this book or information not included on your page your help would be greatly appreaciated.
Sincerly,
Carissa
FOLLOW-UP:
Carissa,
Of course I'll help you out!
I'm sure that on my page I have basic information about the Disquisitiones Arithmeticae, such as when it first came out in print, some other information regarding it. What else are you looking for?
If you don't mind me asking, when is this project due? I think I can get a copy of the book on Sunday, so if you need exerpts or whatever. Perhaps just a certain formula or property that you are looking into? If it's not too long, I wouldn't mind typing it up for you. Or worst comes to worst, I can scan the pages if you would like.
I apologize for not being able to provide any links. That's the main reason I created this page, because there weren't any good pages on Gauss on the Web (in English anyways).
Sincerely,
Nelly "Nez" Cung
FOLLOW-UP:
Nelly,
Thanks for your help. The project is almost done, I'm just having a little trouble understanding the contents of Gauss's book. From the biography section of your page, you wrote "Number theory (coined "higher arithmetic") is a branch of mathematics that seems least amenable to generalities. In the late eighteenth century, it consisted of a large collection of isolated results. In his Disquisitiones arithmetucae, Gauss summarized previous work in a systematic way, solved some of the most difficult outstanding questions, and formulated concepts and questions that set the pattern of research that is still in effect today. He introduced congruence of integers with respect to a modulus, the first significant algebraic example of the now ubiquitous concept of equivalence relation. He proved the law of quadratic reciprocity, developed the theory of composition of quadratic forms, and completely analyzed the cyclotomic equation. Disquisitiones arithmetucae almost instantly won gauss recognition by mathematicians as their prince, but readership was small and the full understanding required for further development came only through the less austere exposition in Dirichlet's Vorlesungen�ber Zahlentheorie (Lecture on Counted Theory) of 1863. "
I interpret that to mean that Number theory, which cannot be generalized very easily, consists of a large collection of mathematical solutions (or were they results not all the way proved?). In Gauss' book, Disquisitiones arithmeticae, he summarized the Number theory and solved some more problems. He also helped set up a pattern of research that is still used today. He introduced congruence of integers, which was the first example of a concept (equivalence relation) that is now widely used. He proved the law of quadratic reciprocity, developed the theory of composition of quadratic forms, and completely analyzed the cyclotomic equation.
Because of the book, other mathematicians greatly respected him, but very few people read the book because they couldn't understand it. Then when Dirichlet released 'Vorlesungen�ber Zahlentheorie (Lecture on Counted Theory)', which wasn't as stern as Gauss's, people began to understand.
Is that about right?
There is no specific formula or property I need, unless there's somthing you suggest I should use.
Your web page was great. How did you find out all that information? I'd been looking for a couple hours before I found your page.
Thanks again, I really appreaciate your help.
-Carissa
FOLLOW-UP: Carissa,
WOW.........
how old are you, I was EXTREMELY impressed with your statement... it sounded so, perfect! I don't think I could improve on that at all! As a matter of fact, I've learned from it... great job on your research, I haven't done much with the book, but thanks! You're e-mail will be in the commentary for sure! Thanks, and Good Luck on your project, but I'm sure you don't really need it!
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