000			04534nam a2200601Ii 4500
001			9781315370750
003			FlBoTFG
005			20220711212216.0
006			m o d
007			cr
008			190122t20182016fluab ob 001 0 eng d
020			_a9781315370750 (e-book : PDF)
035			_a(OCoLC)958800440
040			_aFlBoTFG _cFlBoTFG _erda
041	1		_aeng
050		4	_aQA612.2
072		7	_aMAT _x000000 _2bisacsh
072		7	_aMAT _x012000 _2bisacsh
072		7	_aMAT _x025000 _2bisacsh
072		7	_aPBM _2bicscc
082	0	4	_a514.2242
100	1		_aDye, Heather A., _eauthor. _914299
245	1	3	_aAn Invitation to Knot Theory : _bVirtual and Classical / _cby Heather A. Dye.
250			_aFirst edition.
264		1	_aBoca Raton, FL : _bChapman and Hall/CRC, _c[2018].
264		4	_c©2016.
300			_a1 online resource (286 pages) : _b277 illustrations, text file, PDF
336			_atext _2rdacontent
337			_acomputer _2rdamedia
338			_aonline resource _2rdacarrier
505	0	0	_tKnots and crossingsVirtual knots and links CURVES IN THE PLANE VIRTUAL LINKS ORIENTED VIRTUAL LINK DIAGRAMS -- Linking invariants CONDITIONAL STATEMENTS WRITHE AND LINKING NUMBER DIFFERENCE NUMBER CROSSING WEIGHT NUMBERS -- A multiverse of knots FLAT AND FREE LINKS WELDED, SINGULAR, AND PSEUDO KNOTS NEW KNOT THEORIES -- Crossing invariants CROSSING NUMBERS UNKNOTTING NUMBERS UNKNOTTING SEQUENCE NUMBERS -- Constructing knots SYMMETRY TANGLES, MUTATION, AND PERIODIC LINKS PERIODIC LINKS AND SATELLITE KNOTS -- Knot polynomialsThe bracket polynomial THE NORMALIZED KAUFFMAN BRACKET POLYNOMIAL THE STATE SUM THE IMAGE OF THE F-POLYNOMIAL-- Surfaces SURFACES CONSTRUCTIONS OF VIRTUAL LINKS GENUS OF A VIRTUAL LINK -- Bracket polynomial II STATES AND THE BOUNDARY PROPERTY PROPER STATES DIAGRAMS WITH ONE VIRTUAL CROSSING -- The checkerboard framing CHECKERBOARD FRAMINGS CUT POINTS EXTENDING THE KAUFFMAN-MURASUGI-THISTLETHWAITE THEOREM-- Modifications of the bracket polynomial THE FLAT BRACKET THE ARROW POLYNOMIAL VASSILIEV INVARIANTS -- Algebraic structuresQuandles TRICOLORING QUANDLES KNOT QUANDLES -- Knots and quandles A LITTLE LINEAR ALGEBRA AND THE TREFOIL THE DETERMINANT OF A KNOT THE ALEXANDER POLYNOMIAL THE FUNDAMENTAL GROUP -- Biquandles THE BIQUANDLE STRUCTURE THE GENERALIZED ALEXANDER POLYNOMIAL -- Gauss diagrams GAUSS WORDS AND DIAGRAMS PARITY AND PARITY INVARIANTS CROSSING WEIGHT NUMBER -- Applications QUANTUM COMPUTATION TEXTILES -- Appendix A: Tables Appendix B: References by Chapter-- Open problems and projects appear at the end of each chapter.
520	3		_aThe Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory. An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.
530			_aAlso available in print format.
650		0	_aKnot theory. _914300
650		0	_aMATHEMATICS _xTopology. _914301
650		7	_aMATHEMATICS / Geometry / General. _2bisacsh _910959
650		7	_aMATHEMATICS / Recreations & Games. _2bisacsh _914302
650		7	_aclassical knots. _2bisacsh _914303
650		7	_af-polynomial. _2bisacsh _914304
650		7	_aJones Polynomial. _2bisacsh _914305
650		7	_aKnot invariants. _2bisacsh _914306
650		7	_aKnot theory textbook. _2bisacsh _914307
650		7	_aQuandles. _2bisacsh _914308
650		7	_aSurfaces. _2bisacsh _914309
650		7	_atopology. _2bisacsh _913470
650		7	_aVirtual knots. _2bisacsh _914310
650		7	_aVirtual links. _2bisacsh _914311
655		0	_aElectronic books. _93294
710	2		_aTaylor and Francis. _910719
776	0	8	_iPrint version: _z9781498701648
856	4	0	_uhttps://www.taylorfrancis.com/books/9781315370750 _zClick here to view.
942			_cEBK
999			_c70669 _d70669