A Concrete Introduction to Higher Algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1995
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is written as an introduction to higher algebra for students with a background of a year of calculus. The first edition of this book emerged from a set of notes written in the 1970sfor a sophomore-junior level course at the University at Albany entitled "Classical Algebra." The objective of the course, and the book, is to give students enough experience in the algebraic theory of the integers and polynomials to appre ciate the basic concepts of abstract algebra. The main theoretical thread is to develop algebraic properties of the ring of integers: unique factorization into primes, congruences and congruence classes, Fermat's theorem, the Chinese remainder theorem; and then again for the ring of polynomials. Doing so leads to the study of simple field extensions, and, in particular, to an exposition of finite fields. Elementary properties of rings, fields, groups, and homomorphisms of these objects are introduced and used as needed in the development. Concurrently with the theoretical development, the book presents a broad variety of applications, to cryptography, error-correcting codes, Latin squares, tournaments, techniques of integration, and especially to elemen tary and computational number theory. A student who asks, "Why am I learning this?," willfind answers usually within a chapter or two. For a first course in algebra, the book offers a couple of advantages. • By building the algebra out of numbers and polynomials, the book takes maximal advantage of the student's prior experience in algebra and arithmetic. New concepts arise in a familiar context |
| Beschreibung: | 1 Online-Ressource (XV, 522 p) |
| ISBN: | 9781441987020 9780387989990 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4419-8702-0 |
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| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4419-8702-0 |
| edition | Second Edition |
| format | Electronic eBook |
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| isbn | 9781441987020 9780387989990 |
| issn | 0172-6056 |
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| spelling | Childs, Lindsay 1940- Verfasser (DE-588)1055770054 aut A Concrete Introduction to Higher Algebra by Lindsay N. Childs Second Edition New York, NY Springer New York 1995 1 Online-Ressource (XV, 522 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 This book is written as an introduction to higher algebra for students with a background of a year of calculus. The first edition of this book emerged from a set of notes written in the 1970sfor a sophomore-junior level course at the University at Albany entitled "Classical Algebra." The objective of the course, and the book, is to give students enough experience in the algebraic theory of the integers and polynomials to appre ciate the basic concepts of abstract algebra. The main theoretical thread is to develop algebraic properties of the ring of integers: unique factorization into primes, congruences and congruence classes, Fermat's theorem, the Chinese remainder theorem; and then again for the ring of polynomials. Doing so leads to the study of simple field extensions, and, in particular, to an exposition of finite fields. Elementary properties of rings, fields, groups, and homomorphisms of these objects are introduced and used as needed in the development. Concurrently with the theoretical development, the book presents a broad variety of applications, to cryptography, error-correcting codes, Latin squares, tournaments, techniques of integration, and especially to elemen tary and computational number theory. A student who asks, "Why am I learning this?," willfind answers usually within a chapter or two. For a first course in algebra, the book offers a couple of advantages. • By building the algebra out of numbers and polynomials, the book takes maximal advantage of the student's prior experience in algebra and arithmetic. New concepts arise in a familiar context Mathematics Algebra Mathematik Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Algebra (DE-588)4001156-2 s DE-604 https://doi.org/10.1007/978-1-4419-8702-0 Verlag Volltext |
| spellingShingle | Childs, Lindsay 1940- A Concrete Introduction to Higher Algebra Mathematics Algebra Mathematik Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4123623-3 |
| title | A Concrete Introduction to Higher Algebra |
| title_auth | A Concrete Introduction to Higher Algebra |
| title_exact_search | A Concrete Introduction to Higher Algebra |
| title_full | A Concrete Introduction to Higher Algebra by Lindsay N. Childs |
| title_fullStr | A Concrete Introduction to Higher Algebra by Lindsay N. Childs |
| title_full_unstemmed | A Concrete Introduction to Higher Algebra by Lindsay N. Childs |
| title_short | A Concrete Introduction to Higher Algebra |
| title_sort | a concrete introduction to higher algebra |
| topic | Mathematics Algebra Mathematik Algebra (DE-588)4001156-2 gnd |
| topic_facet | Mathematics Algebra Mathematik Lehrbuch |
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