LEADER 03158nam 22005412 450 001 9910821350503321 005 20151002020706.0 010 $a1-61444-023-9 035 $a(CKB)2670000000386407 035 $a(EBL)3330352 035 $a(SSID)ssj0000577666 035 $a(PQKBManifestationID)12251675 035 $a(PQKBTitleCode)TC0000577666 035 $a(PQKBWorkID)10578413 035 $a(PQKB)11570719 035 $a(UkCbUP)CR9781614440239 035 $a(MiAaPQ)EBC3330352 035 $a(Au-PeEL)EBL3330352 035 $a(CaPaEBR)ebr10722463 035 $a(OCoLC)929120416 035 $a(RPAM)2527017 035 $a(EXLCZ)992670000000386407 100 $a20111024d1993|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKnot theory /$fCharles Livingston$b[electronic resource] 210 1$aWashington :$cMathematical Association of America,$d1993. 215 $a1 online resource (xviii, 240 pages) $cdigital, PDF file(s) 225 1 $aThe Carus mathematical monographs ;$vno. 24 300 $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015). 311 $a0-88385-027-3 320 $aIncludes bibliographical references (p. 233-237) and index. 327 $aA century of knot theory -- What is a knot? -- Combinatorial techniques -- Geometric techniques -- Algebraic techniques -- Geometry, algebra, and the Alexander polynomial -- Numerical invariants -- Symmetries of knots -- High-dimensional knot theory -- New combinatorial techniques -- Appendix 1. Knot table -- Appendix 2. Alexander polynomials. 330 $aKnot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented. The interplay between topology and algebra, known as algebraic topology, arises early in the book, when tools from linear algebra and from basic group theory are introduced to study the properties of knots. Livingston guides you through a general survey of the topic showing how to use the techniques of linear algebra to address some sophisticated problems, including one of mathematics' most beautiful topics, symmetry. The book closes with a discussion of high-dimensional knot theory and a presentation of some of the recent advances in the subject—the Conway, Jones, and Kauffman polynomials. A supplementary section presents the fundamental group, which is a centerpiece of algebraic topology. 410 0$aCarus mathematical monographs ;$vno. 24. 606 $aKnot theory 615 0$aKnot theory. 676 $a514/.224 700 $aLivingston$b Charles$0193735 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910821350503321 996 $aKnot theory$94047491 997 $aUNINA