knot theory mathematical association of america textbooks

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Knot Theory

Author : Charles Livingston
ISBN : 0883850273
Genre : Mathematics
File Size : 43. 20 MB
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This book uses only linear algebra and basic group theory to study the properties of knots.

An Invitation To Knot Theory

Author : Heather A. Dye
ISBN : 9781498701655
Genre : Mathematics
File Size : 37. 13 MB
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The 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.

The Knot Book

Author : Colin Conrad Adams
ISBN : 9780821836781
Genre : Mathematics
File Size : 25. 54 MB
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Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. The Knot Book is an introduction to this rich theory, starting from our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research. The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in The Knot Book.

Applications Of Knot Theory

Author : American Mathematical Society. Short course
ISBN : 9780821844663
Genre : Mathematics
File Size : 20. 78 MB
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Over the past 20-30 years, knot theory has rekindled its historic ties with biology, chemistry, and physics as a means of creating more sophisticated descriptions of the entanglements and properties of natural phenomena--from strings to organic compounds to DNA. This volume is based on the 2008 AMS Short Course, Applications of Knot Theory. The aim of the Short Course and this volume, while not covering all aspects of applied knot theory, is to provide the reader with a mathematical appetizer, in order to stimulate the mathematical appetite for further study of this exciting field. No prior knowledge of topology, biology, chemistry, or physics is assumed. In particular, the first three chapters of this volume introduce the reader to knot theory (by Colin Adams), topological chirality and molecular symmetry (by Erica Flapan), and DNA topology (by Dorothy Buck). The second half of this volume is focused on three particular applications of knot theory. Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology.

Teaching And Learning Of Knot Theory In School Mathematics

Author : Akio Kawauchi
ISBN : 9784431541387
Genre : Mathematics
File Size : 40. 38 MB
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​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 And Links

Author : Dale Rolfsen
ISBN : 9780821834367
Genre : Mathematics
File Size : 72. 75 MB
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Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book"".

An Index Of A Graph With Applications To Knot Theory

Author : Kunio Murasugi
ISBN : 9780821825709
Genre : Mathematics
File Size : 65. 71 MB
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This book presents a remarkable application of graph theory to knot theory. In knot theory, there are a number of easily defined geometric invariants that are extremely difficult to compute; the braid index of a knot or link is one example. The authors evaluate the braid index for many knots and links using the generalized Jones polynomial and the index of a graph, a new invariant introduced here. This invariant, which is determined algorithmically, is likely to be of particular interest to computer scientists.

Parametrized Knot Theory

Author : Stanley Ocken
ISBN : 9780821818701
Genre : Mathematics
File Size : 61. 9 MB
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Knots And Surfaces

Author : David W. Farmer
ISBN : 9780821804513
Genre : Mathematics
File Size : 42. 97 MB
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In most mathematics textbooks, the most exciting part of mathematics - the process of invention and discovery - is completely hidden from the reader. The aim of ""Knots and Surfaces"" is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequisites for understanding the text. Any college student interested in discovering the beauty of mathematics will enjoy a course taught from this book. The book has also been used successfully with non science students who want to fulfill a science requirement. Also available from the AMS by David W. Farmer is ""Groups and Symmetry: A Guide to Discovering Mathematics"".

Why Knot

Author : Colin Conrad Adams
ISBN : 1931914222
Genre : Mathematics
File Size : 77. 83 MB
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Presents an introduction to knot theory along with a variety of exercises using the "tangle" rope.

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