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A Concrete Introduction to Higher Algebra
This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strong emphasis on congruence classes leads in a natural way to finite groups and f...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2009.
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| Edición: | 3rd ed. 2009. |
| Colección: | Undergraduate Texts in Mathematics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- Numbers
- Numbers
- Induction
- Euclid's Algorithm
- Unique Factorization
- Congruence
- Congruence classes and rings
- Congruence Classes
- Rings and Fields
- Matrices and Codes
- Congruences and Groups
- Fermat's and Euler's Theorems
- Applications of Euler's Theorem
- Groups
- The Chinese Remainder Theorem
- Polynomials
- Polynomials
- Unique Factorization
- The Fundamental Theorem of Algebra
- Polynomials in ?[x]
- Congruences and the Chinese Remainder Theorem
- Fast Polynomial Multiplication
- Primitive Roots
- Cyclic Groups and Cryptography
- Carmichael Numbers
- Quadratic Reciprocity
- Quadratic Applications
- Finite Fields
- Congruence Classes Modulo a Polynomial
- Homomorphisms and Finite Fields
- BCH Codes
- Factoring Polynomials
- Factoring in ?[x]
- Irreducible Polynomials.