Higher arithmetic
Edwards, Harold M.
Higher arithmetic : an algorithmic introduction to number theory / Harold M Edwards - Providence, R.I. : American Mathematical Society, ©2008 - xii, 210 pages : illustrations ; 22 cm. - Student mathematical library, v. 45. .
Numbers --
The problem A + B = --
Congruences --
Double congruences and the Euclidean algorithm --
The augmented Euclidean algorithm --
Simultaneous congruences --
The fundamental theorem of arithmetic --
Exponentiation and orders --
Euler's 0-funtion --
Finding the order of a mod c --
Primality testing --
The RSA Cipher system --
Primitive roots mod p --
Polynomials --
Tables of indices mod p. Brahmagupta's Formule and hypernumbers --
Modules of hypernumbers --
A canonical form for modules of hypernumbers --
Solution of A + B = --
Proof of the theorem of chapter 19 --
Euler's remarkable discovery --
Stable modules --
Equivalence of modules --
Signatures of equivalence classes --
The Main theorem --
Modules that become principal when squared --
The possible signatures for certain values of A --
The Law of Quadratic Reciprocity --
Proof of the Main theorem --
The theory of binary quadratic forms --
Composition of binary quadratic forms.
"Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory."--Jacket.
9781470454814
Mathematics
Algebra
Number theory.
Zahlentheorie.
Talteori.
512.7 EDW
Higher arithmetic : an algorithmic introduction to number theory / Harold M Edwards - Providence, R.I. : American Mathematical Society, ©2008 - xii, 210 pages : illustrations ; 22 cm. - Student mathematical library, v. 45. .
Numbers --
The problem A + B = --
Congruences --
Double congruences and the Euclidean algorithm --
The augmented Euclidean algorithm --
Simultaneous congruences --
The fundamental theorem of arithmetic --
Exponentiation and orders --
Euler's 0-funtion --
Finding the order of a mod c --
Primality testing --
The RSA Cipher system --
Primitive roots mod p --
Polynomials --
Tables of indices mod p. Brahmagupta's Formule and hypernumbers --
Modules of hypernumbers --
A canonical form for modules of hypernumbers --
Solution of A + B = --
Proof of the theorem of chapter 19 --
Euler's remarkable discovery --
Stable modules --
Equivalence of modules --
Signatures of equivalence classes --
The Main theorem --
Modules that become principal when squared --
The possible signatures for certain values of A --
The Law of Quadratic Reciprocity --
Proof of the Main theorem --
The theory of binary quadratic forms --
Composition of binary quadratic forms.
"Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory."--Jacket.
9781470454814
Mathematics
Algebra
Number theory.
Zahlentheorie.
Talteori.
512.7 EDW
