Higher arithmetic : an algorithmic introduction to number theory / Harold M. Edwards.
By: Edwards, Harold M
.
Material type: ![materialTypeLabel](/opac-tmpl/lib/famfamfam/BK.png)
![](/opac-tmpl/bootstrap/images/filefind.png)
![](/opac-tmpl/bootstrap/images/filefind.png)
Item type | Current library | Call number | Copy number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|
General Lending | MTU Bishopstown Library Lending | 512.7 (Browse shelf(Opens below)) | 1 | Available | 00183688 |
Browsing MTU Bishopstown Library shelves, Shelving location: Lending Close shelf browser (Hides shelf browser)
Enhanced descriptions from Syndetics:
Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself.
Bibliography: (page 207) and index.
Numbers -- The problem A() + B = () -- Congruences -- Double congruences and euclidean algorithm -- The augmented euclidean algorithm -- Simultaneous congruences -- The fundamental theorem of arithmetic -- Exponentiation and orders -- Euler's function -- 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 formula 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.
Table of contents provided by Syndetics
- Introduction to Number Theory
- Numbers The problem $A\square + B = \square$ Congruences
- Double congruences and the Euclidean algorithm
- The augmented Euclidean algorithm
- Simultaneous congruences
- The fundamental theorem of arithmetic
- Exponentiation and orders
- Euler's $\phi$-function
- Finding the order of $a\bmod c$ Primality testing
- The RSA cipher system
- Primitive roots $\bmod\ p$
- Polynomials Tables of indices $\bmod\ p$
- Brahmagupta's formula and hypernumbers
- Modules of hypernumbers
- A canonical form for modules of hypernumbers
- Solution of $A\square + B = \square$
- Proof of the theorem of Chapter 19
- Euler's remarkable discovery
- Stable modules
- Equivalence of modules
- Signatures of equivalence classes
- The main theorem
- Which modules 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
- Cycles of stable modules
- Answers to exercises
- Bibliography
- Index