Mystery Of Knots, The: Computer Programming For Knot Tabulation

Inbunden, Engelska, 1999

Del 20 i serien Series on Knots & Everything

2 255 kr

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Beskrivning

One of the most significant unsolved problems in mathematics is the complete classification of knots. The main purpose of this book is to introduce the reader to the use of computer programming to obtain the table of knots. The author presents this problem as clearly and methodically as possible, starting from the very basics. Mathematical ideas and concepts are extensively discussed, and no advanced background is required.

Produktinformation

Utgivningsdatum:1999-12-14
Mått:156 x 221 x 26 mm
Vikt:672 g
Format:Inbunden
Språk:Engelska
Serie:Series on Knots & Everything
Antal sidor:408
Förlag:World Scientific Publishing Co Pte Ltd
ISBN:9789810238780

Utforska kategorier

Systemvetenskap och AI inom Data och IT
Topologi inom Naturvetenskap och teknik

Innehållsförteckning

A knot theory primer - a general understanding of topology; knot theory as a branch of topology; the regular representations of knots; the equivalence moves; the knot invariants; elements of group theory; the fundamental group; the knot group; the colourization invariants; the Alexander polynomial; the theory of linear homogeneous systems; calculating the Alexander polynomial; the "minor" Alexander polynomials; the Meridian-longitude invariants; proving a knot's chirality; braid theory - skein invariants; calculating the HOMFLYPT polynomials; knot theory after the HOMFLYPT; the problem of knot tabulation - basic concepts of computer programming; the Dowker notation; drawing the knot; when is a notation drawable?; the "equal drawability" moves; multiple notations for equivalent knots; ordering the Dowker notations; calculating the notation invariants; a few examples; the knot tabulation algorithm; the pseudocode; the flowchart; actual results; the table of knots.