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Higher arithmetic : an algorithmic introduction to number theory / Harold M Edwards

By: Contributor(s): Material type: TextTextSeries: Student mathematical library, v. 45Publication details: Providence, R.I. : American Mathematical Society, ©2008Description: xii, 210 pages : illustrations ; 22 cmISBN:
  • 9781470454814
Subject(s): DDC classification:
  • 512.7 EDW
Contents:
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.
Summary: "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.
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Holdings
Item type Current library Call number Status Barcode
Mathematics Departmental Library Mathematics Departmental Library SNU LIBRARY 512.7 EDW (Browse shelf(Opens below)) Available M033
Total holds: 0

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.

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