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020 _a9780387747255
_99780387747255
024 7 _a10.1007/9780387747255
_2doi
035 _avtls000332531
039 9 _a201509030230
_bVLOAD
_c201404122155
_dVLOAD
_c201404091926
_dVLOAD
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040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA150-272
100 1 _aChilds, Lindsay N.
_eeditor.
_9303285
245 1 2 _aA Concrete Introduction to Higher Algebra /
_cedited by Lindsay N. Childs.
264 1 _aNew York, NY :
_bSpringer New York,
_c2009.
300 _axiv, 603 páginas
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aUndergraduate Texts in Mathematics,
_x0172-6056
500 _aSpringer eBooks
505 0 _aNumbers -- 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.
520 _aThis 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 finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, error correction, integration, and especially to elementary and computational number theory. The later chapters include expositions of Rabin's probabilistic primality test, quadratic reciprocity, the classification of finite fields, and factoring polynomials over the integers. Over 1000 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix. The new edition includes topics such as Luhn's formula, Karatsuba multiplication, quotient groups and homomorphisms, Blum-Blum-Shub pseudorandom numbers, root bounds for polynomials, Montgomery multiplication, and more. "At every stage, a wide variety of applications is presented...The user-friendly exposition is appropriate for the intended audience" - T.W. Hungerford, Mathematical Reviews "The style is leisurely and informal, a guided tour through the foothills, the guide unable to resist numerous side paths and return visits to favorite spots..." - Michael Rosen, American Mathematical Monthly
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9780387745275
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-0-387-74725-5
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942 _c14
999 _c279129
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