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Mathematics

A Survey of Knot Theory

A Survey of Knot Theory PDF Author: Akio Kawauchi
Publisher: Birkhäuser
ISBN: 3034892276
Category : Mathematics
Languages : en
Pages : 423

Book Description
Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

A Survey of Knot Theory

A Survey of Knot Theory PDF Author: Akio Kawauchi
Publisher: Birkhäuser
ISBN: 3034892276
Category : Mathematics
Languages : en
Pages : 423

Book Description
Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

A Survey of Knot Theory and Invariants of a Twelve-crossing Knot

A Survey of Knot Theory and Invariants of a Twelve-crossing Knot PDF Author: Kausha C. Miller
Publisher:
ISBN:
Category :
Languages : en
Pages : 182

Book Description


Knot Theory and Its Applications

Knot Theory and Its Applications PDF Author: Krishnendu Gongopadhyay
Publisher: American Mathematical Soc.
ISBN: 1470422573
Category : Knot theory
Languages : en
Pages : 357

Book Description
This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10–20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.

Introductory Lectures on Knot Theory

Introductory Lectures on Knot Theory PDF Author:
Publisher:
ISBN: 9814464740
Category :
Languages : en
Pages :

Book Description


Encyclopedia of Knot Theory

Encyclopedia of Knot Theory PDF Author: Colin Adams
Publisher: CRC Press
ISBN: 100022242X
Category : Mathematics
Languages : en
Pages : 941

Book Description
"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory

Handbook of Knot Theory

Handbook of Knot Theory PDF Author: William Menasco
Publisher: Elsevier
ISBN: 9780080459547
Category : Mathematics
Languages : en
Pages : 502

Book Description
This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics

Knot Theory

Knot Theory PDF Author: J. C. Hausmann
Publisher: Springer
ISBN: 354035705X
Category : Mathematics
Languages : en
Pages : 311

Book Description
Dedicated to the Memory of Christos Demetriou Papakyriakopoulos, 1914-1976

Teaching and Learning of Knot Theory in School Mathematics

Teaching and Learning of Knot Theory in School Mathematics PDF Author: Akio Kawauchi
Publisher: Springer Science & Business Media
ISBN: 4431541381
Category : Mathematics
Languages : en
Pages : 188

Book Description
​This book is the result of a joint venture between Professor Akio Kawauchi, Osaka City University, well-known for his research in knot theory, and the Osaka study group of mathematics education, founded by Professor Hirokazu Okamori and now chaired by his successor Professor Tomoko Yanagimoto, Osaka Kyoiku University. The seven chapters address the teaching and learning of knot theory from several perspectives. Readers will find an extremely clear and concise introduction to the fundamentals of knot theory, an overview of curricular developments in Japan, and in particular a series of teaching experiments at all levels which not only demonstrate the creativity and the professional expertise of the members of the study group, but also give a lively impression of students’ learning processes. In addition the reports show that elementary knot theory is not just a preparation for advanced knot theory but also an excellent means to develop spatial thinking. The book can be highly recommended for several reasons: First of all, and that is the main intention of the book, it serves as a comprehensive text for teaching and learning knot theory. Moreover it provides a model for cooperation between mathematicians and mathematics educators based on substantial mathematics. And finally it is a thorough introduction to the Japanese art of lesson studies–again in the context of substantial mathematics.

Knots In Hellas '98 - Proceedings Of The International Conference On Knot Theory And Its Ramifications

Knots In Hellas '98 - Proceedings Of The International Conference On Knot Theory And Its Ramifications PDF Author: Cameron Mca Gordon
Publisher: World Scientific
ISBN: 9814492876
Category : Mathematics
Languages : en
Pages : 580

Book Description
There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon-Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected by the following path: hyperbolic structures, PSL(2,C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.

Braid and Knot Theory in Dimension Four

Braid and Knot Theory in Dimension Four PDF Author: Seiichi Kamada
Publisher: American Mathematical Soc.
ISBN: 0821829696
Category : Mathematics
Languages : en
Pages : 313

Book Description
Braid theory and knot theory are related via two famous results due to Alexander and Markov. Alexander's theorem states that any knot or link can be put into braid form. Markov's theorem gives necessary and sufficient conditions to conclude that two braids represent the same knot or link. Thus, one can use braid theory to study knot theory and vice versa. In this book, the author generalizes braid theory to dimension four. He develops the theory of surface braids and applies it to study surface links. In particular, the generalized Alexander and Markov theorems in dimension four are given. This book is the first to contain a complete proof of the generalized Markov theorem. Surface links are studied via the motion picture method, and some important techniques of this method are studied.For surface braids, various methods to describe them are introduced and developed: the motion picture method, the chart description, the braid monodromy, and the braid system. These tools are fundamental to understanding and computing invariants of surface braids and surface links. Included is a table of knotted surfaces with a computation of Alexander polynomials. Braid techniques are extended to represent link homotopy classes. The book is geared toward a wide audience, from graduate students to specialists. It would make a suitable text for a graduate course and a valuable resource for researchers.