Year: 2004 Language: English Author: Adams C. Genre: Knots Publisher: W.H. Freeman and Company ISBN: 978-0-8218-3678-1 Format: PDF Quality: Scanned pages Pages count: 308 Description: Mathematics is an incredibly exciting and creative field of endeavor. Yet most people never see it that way. Nonmathematicians too often assume that we mathematicians sit around talking about what Newton did three hundred years ago or calculating a couple of extra million digits of tt. They do not realize that more new mathematics is being created now than at any other time in the history of humankind. Explaining the field of knot theory is a particularly effective way to dispel this misconception. Here is a field that is over one hundred years old, and yet some of the most exciting results have occurred in the last fifteen years. Easily stated open questions still abound, and one can get a taste for what it is like to do research very quickly. The other tremendous advantage that knot theory has over many other fields of mathematics is that much of the theory can be explained at an elementary level. One does not need to understand the complicated machinery of advanced areas of mathematics to prove interesting results. My hope is that this book will excite people about mathematics that it will motivate them to continue to explore other related areas of mathematics and to proceed to such topics as topology, algebra, differential geometry, and algebraic topology. Unfortunately, mathematics is often taught as if the only goal were to pass a body of information from one person to the next. Although this is certainly an important goal, it is essential to teach an appreciation for the beauty of mathematics and a sense of the excitement of doing mathematics. Once readers are hooked, they will fill in the details themselves, arid they will go a lot farther and learn a lot more. Who, then, is this book for? It is aimed at anyone with a curiosity about mathematics. I hope people will pick up this book and start reading it on their own. I also hope that they will do the exercises: the only way to learn mathematics is to do it. Some of the exercises are straightforward; others take some thought. The very hardest are starred and can be a bit more challenging. Scientists with primary interests in physics or biochemistry should find the applications of knot theory to these fields particularly fascinating. Although these applications have only been discovered recently, already they have had a huge impact. This book can be and has been used effectively as a textbook in classes. With the exception of a few spots, the book assumes only a familiarity with high school algebra. I have also given talks on selected topics from this book to high school students and teachers, college students, and students as young as seventh graders. The first six chapters of the book are designed to be read sequentially. With the exception that Section 8.3 depends on Section 7.4, the remaining four chapters are independent and can be read in any order. The topics chosen for this book are not the standard topics that one would see in a more advanced treatise on knot theory. Certainly the most glaring omission is any discussion of the fundamental group. My desire to make this book more interesting and accessible to an audience without advanced background has precluded such topics. The choice of topics has been made by looking for areas that are easy to understand without much background, are exciting, and provide opportunities for new research. Some of the topics such as almost alternating knots are so new that little research has yet been done on them, leaving numerous open questions.
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Adams C. Адамс К.- The Knot book Книга узлов [2004, PDF, ENG]
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The Knot Book
Language: English
Author: Adams C.
Genre: Knots
Publisher: W.H. Freeman and Company
ISBN: 978-0-8218-3678-1
Format: PDF
Quality: Scanned pages
Pages count: 308
Description: Mathematics is an incredibly exciting and creative field of endeavor. Yet most people never see it that way. Nonmathematicians too often assume that we mathematicians sit around talking about what Newton did three hundred years ago or calculating a couple of extra million digits of tt. They do not realize that more new mathematics is being created now than at any other time in the history of humankind.
Explaining the field of knot theory is a particularly effective way to dispel this misconception. Here is a field that is over one hundred years old, and yet some of the most exciting results have occurred in the last fifteen years. Easily stated open questions still abound, and one can get a taste for what it is like to do research very quickly. The other tremendous advantage that knot theory has over many other fields of mathematics is that much of the theory can be explained at an elementary level. One does not need to understand the complicated machinery of advanced areas of mathematics to prove interesting results.
My hope is that this book will excite people about mathematics that it will motivate them to continue to explore other related areas of mathematics and to proceed to such topics as topology, algebra, differential geometry, and algebraic topology.
Unfortunately, mathematics is often taught as if the only goal were to pass a body of information from one person to the next. Although this is certainly an important goal, it is essential to teach an appreciation for the beauty of mathematics and a sense of the excitement of doing mathematics. Once readers are hooked, they will fill in the details themselves, arid they will go a lot farther and learn a lot more.
Who, then, is this book for? It is aimed at anyone with a curiosity about mathematics. I hope people will pick up this book and start reading it on their own. I also hope that they will do the exercises: the only way to learn mathematics is to do it. Some of the exercises are straightforward; others take some thought. The very hardest are starred and can be a bit more challenging.
Scientists with primary interests in physics or biochemistry should find the applications of knot theory to these fields particularly fascinating. Although these applications have only been discovered recently, already they have had a huge impact.
This book can be and has been used effectively as a textbook in classes. With the exception of a few spots, the book assumes only a familiarity with high school algebra. I have also given talks on selected topics from this book to high school students and teachers, college students, and students as young as seventh graders.
The first six chapters of the book are designed to be read sequentially. With the exception that Section 8.3 depends on Section 7.4, the remaining four chapters are independent and can be read in any order. The topics chosen for this book are not the standard topics that one would see in a more advanced treatise on knot theory. Certainly the most glaring omission is any discussion of the fundamental group. My desire to make this book more interesting and accessible to an audience without advanced background has precluded such topics.
The choice of topics has been made by looking for areas that are easy to understand without much background, are exciting, and provide opportunities for new research. Some of the topics such as almost alternating knots are so new that little research has yet been done on them, leaving numerous open questions.
Contents
Screenshots
Adams C. Адамс К.- The Knot book Книга узлов [2004, PDF, ENG]
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