This book has been growing over the years out of several resources. Firstly, the courses in number theory and modern algebra I had occasionally been teaching at UNC Charlotte. Secondly, my interest to invent mathematical problems for competitions, and invent and pose problems for individual work with gifted students.After being forced to retire about two years ago because of health reasons, I did continue to occupy myself with these topics, and I learned more substantially from the work of Gauss on quadratic reciprocity and on the construction of Fermat polygons. Too, I did take up numerical computation with the computer language of Dr. Racket, which is based on Lisp and freely available on the internet.
This book has been growing over the years out of several resources. Firstly, the courses in number theory and modern algebra I had occasionally been teaching at UNC Charlotte. Secondly, my interest to invent mathematical problems for competitions, and invent and pose problems for individual work with gifted students.After being forced to retire about two years ago because of health reasons, I did continue to occupy myself with these topics, and I learned more substantially from the work of Gauss on quadratic reciprocity and on the construction of Fermat polygons. Too, I did take up numerical computation with the computer language of Dr. Racket, which is based on Lisp and freely available on the internet.
For a regular 17-gon, the formulas above give the x-coordinate of the first vertex in the upper half plane.The first formula goes back to Gauss. The second formula is obtained by a more elementary...
Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and...
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the...
The branch of pure mathematics devoted primarily to the study of integers and integer-valued functions is known as number theory. The concepts of prime numbers as well as the properties of...
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