实例介绍
【实例简介】
群论的可视化，英文版： If you are interested in learning about group theory in a relaxed, intuitive way, then this book is for you.
master”-2011/1018-17:10— page 1-#2 c 2009 by the Mathematical association of america, Inc Library of Congress Catalog Card Number 2009923532 Print edition isbn 978-0-88385-757-1 Electronic edition isbn 978-1-61444-102-1 Printed in the United states of merica Current Printing (last digit) 10987654321 master”-2011/10/1817:10— page lll# Visual Group Theory Nathan C. Carter Bentley university Published and distributed by he Mathematical association of america master”-2011/10/18—17:10— page IV-#4 Council on publications Paul Zorn Chair Classroom Resource materials Editorial board Gerald m. bryce editor William c. bauldrv Diane l. herrmann Loren d. pitt Wayne roberts p Philip d. Straffi Holly S. zullo master 20110/18-17:10— page v-#5 CLASSROOM RESOURCE MATERIALS Classroom Resource Materials is intended to provide supplementary classroom material for students--laboratory exercises, projects, historical information, textbooks with unusual approaches for presenting mathematical ideas, career information, etc 101 Careers in Mathematics, 2nd edition edited by Andrew Sterrett Archimedes. What Did He Do Besides Cry Eureka? Sherman Stein and Thrillers. R. Grant Wood Conjecture and Proof, Miklos Laczkovich Creative Mathematics. H.S. Wall Environmental Mathematics in the Classroom edited by b. A. Fusaro and P. C. Kenschaft Exploratory Examples for Real Analysis, Joanne E. Snow and Kirk e. Weller Geometry From Africa. Mathematical and Educational Explorations, Paulus gerdes Historical Modules for the Teaching and Learning of Mathematics (CD), edited by Victor Katz and Karen dee michalowicz Identification Numbers and Check Digit Schemes, Joseph Kirtland Lively Application Projects, edited by chris a Inverse Problems: Activities for Undergraduates, Charles W. Groelsch Laboratory Experiences in Group Theory, Ellen Maycock Parker Learn from the Masters, Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor atz Math Made visual: Creating Images for Understanding Mathematics, Claudi Alsina and roger b Nelsen Ordinary Differential Equations: A Brief Eclectic Tour, David A S anchez Oval track and Other permutation puzzles john o, Kiltinen A Primer of abstract Mathematics, robert b. ash Proofs Without Words, Roger B. Nelsen Proofs Without Words lL, Roger B. Nelsen She Does math!, edited hy Marla Parker Solve This. Math Activities for Students and Clubs, James S. Tanton Student Manual for Mathematics for Business Decisions Part 1: Probability and Simulation, David Williamson Marilou mendel. Julie Tarr. and Deborah Yoklic Student Manual for Mathematics for Business Decisions Part 2: Calculus and Optimization, David Williamson Marilou mendel. Julie tarr. and Deborah Yoklic Teaching Statistics Using Baseball, Jim Albert Visual Group Theory, Nathan C. Carter Writing Projects for Mathematics Courses: Crushed Clowns, Cars, and Coffee to Go, Annali Crannell, Gavin LaRose, Thomas Ratliff, Elyn Rykken MAA Service Center P O. Box 91112 Washington. DC 20090-1112 1-800-331-1 MAA FAX:1-3012069789 master”-2011/10/18-17:10— page vI—#6 master 2011/1018—17:10— page vll一#7 Acknowledgments I am grateful to God for life and breath and mathematics, as well as my ability to write it, draw it, and enjoy it. I am grateful to my family, especially Lydia, who put up with my absence during times I needed to work on this manuscript Many thanks to Doug Hofstadter, who showed me the power of group theory visu- alization and supported my work on it in several ways, including much good advice Many thanks to Charlie Hadlock, who kept me away from not-so-good advice(such as Don't write a book before you get tenure?) and who guided many of the early steps of this project. I also thank Don Albers, the MAa, and Bentley University(particularly Rick Cleary and Kate Davy), all of whom encouraged, supported, and took a chance on a first-time author I must also thank those whose mathematical work helped me in mine. One of my early exposures to group theory visualization techniques was Magnus and Grossman's Groups and Their Graphs. In writing this book I made frequent reference to the excellent texts by Michael Artin, John Fraleigh, Charles Hadlock, and Thomas Hungerford. The powerful and well-designed software Asymptote by John Bowman helped me make the more than 300 figures herein. Thank you! Lastly, there are many people who read early chapters and drafts and provided much helpful feedback. These include Doug Hofstadter, Jon Zivan, an anonymous referee, my parents, and my Fall 2006 Discrete Mathematics class, especially Kathryn Ogorzalek Thank you for helping me see my work through your eyes, and improve it master 2011/10/18 17:10— page vi #8 maste r”-2011/10/18-17:10- page Ix-#9 Preface If you are interested in learning about group theory in a relaxed, intuitive way, then this book is for you. I say learning about group theory because this book does not aim to cover group theory comprehensively. Herein you will find clear, illustrated exposition about the basics of the subject, which will give you a solid foundation of intuitions, images, and examples on which you can build with further study This book is ideal for a student beginning a first course in group theory It can be used in place of a traditional textbook, or as a supplement to one, but its aim is quite different than that of a traditional text. Most textbooks present the theory of groups using theorems proofs, and examples. Their exercises teach you how to make conjectures about groups and prove or refute them. This book, however, teaches you to know groups. You will see them, experiment with them and understand their significance. The mental library of images and intuitions you gain from reading this book will enable you to appreciate far better the facts and proofs in a traditional text This book is also appropriate for recreational reading. If you want an overview of the theory of groups, or to learn key principles without going as deep as some upper-level undergraduate mathematics courses, you can read this book by itself. Only a typical high school mathematics education is assumed, but you should have a willingness to think My work on this book stems from Group Explorer, a software package I wrote that creates illustrations for finite groups, and allows the user to interact and experiment with them. Many of the illustrations in this text were generated with the help of Group Explorer, and the investigations possible in Group Explorer can help you with some of this book’ s exercises You do not need Group Explorer to benefit from this book; very few exercises specif- ically direct you to Group Explorer. But I recommend taking full advantage of hands-on, interactive learning experiences when theyre available; the more involved we are, the Inore we tend to learn. Group Explorer is free software, available for all major operating systems. You can find it online at http://groupexplorer.sourceforge.et 【实例截图】
【核心代码】
群论的可视化，英文版： If you are interested in learning about group theory in a relaxed, intuitive way, then this book is for you.
master”-2011/1018-17:10— page 1-#2 c 2009 by the Mathematical association of america, Inc Library of Congress Catalog Card Number 2009923532 Print edition isbn 978-0-88385-757-1 Electronic edition isbn 978-1-61444-102-1 Printed in the United states of merica Current Printing (last digit) 10987654321 master”-2011/10/1817:10— page lll# Visual Group Theory Nathan C. Carter Bentley university Published and distributed by he Mathematical association of america master”-2011/10/18—17:10— page IV-#4 Council on publications Paul Zorn Chair Classroom Resource materials Editorial board Gerald m. bryce editor William c. bauldrv Diane l. herrmann Loren d. pitt Wayne roberts p Philip d. Straffi Holly S. zullo master 20110/18-17:10— page v-#5 CLASSROOM RESOURCE MATERIALS Classroom Resource Materials is intended to provide supplementary classroom material for students--laboratory exercises, projects, historical information, textbooks with unusual approaches for presenting mathematical ideas, career information, etc 101 Careers in Mathematics, 2nd edition edited by Andrew Sterrett Archimedes. What Did He Do Besides Cry Eureka? Sherman Stein and Thrillers. R. Grant Wood Conjecture and Proof, Miklos Laczkovich Creative Mathematics. H.S. Wall Environmental Mathematics in the Classroom edited by b. A. Fusaro and P. C. Kenschaft Exploratory Examples for Real Analysis, Joanne E. Snow and Kirk e. Weller Geometry From Africa. Mathematical and Educational Explorations, Paulus gerdes Historical Modules for the Teaching and Learning of Mathematics (CD), edited by Victor Katz and Karen dee michalowicz Identification Numbers and Check Digit Schemes, Joseph Kirtland Lively Application Projects, edited by chris a Inverse Problems: Activities for Undergraduates, Charles W. Groelsch Laboratory Experiences in Group Theory, Ellen Maycock Parker Learn from the Masters, Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor atz Math Made visual: Creating Images for Understanding Mathematics, Claudi Alsina and roger b Nelsen Ordinary Differential Equations: A Brief Eclectic Tour, David A S anchez Oval track and Other permutation puzzles john o, Kiltinen A Primer of abstract Mathematics, robert b. ash Proofs Without Words, Roger B. Nelsen Proofs Without Words lL, Roger B. Nelsen She Does math!, edited hy Marla Parker Solve This. Math Activities for Students and Clubs, James S. Tanton Student Manual for Mathematics for Business Decisions Part 1: Probability and Simulation, David Williamson Marilou mendel. Julie Tarr. and Deborah Yoklic Student Manual for Mathematics for Business Decisions Part 2: Calculus and Optimization, David Williamson Marilou mendel. Julie tarr. and Deborah Yoklic Teaching Statistics Using Baseball, Jim Albert Visual Group Theory, Nathan C. Carter Writing Projects for Mathematics Courses: Crushed Clowns, Cars, and Coffee to Go, Annali Crannell, Gavin LaRose, Thomas Ratliff, Elyn Rykken MAA Service Center P O. Box 91112 Washington. DC 20090-1112 1-800-331-1 MAA FAX:1-3012069789 master”-2011/10/18-17:10— page vI—#6 master 2011/1018—17:10— page vll一#7 Acknowledgments I am grateful to God for life and breath and mathematics, as well as my ability to write it, draw it, and enjoy it. I am grateful to my family, especially Lydia, who put up with my absence during times I needed to work on this manuscript Many thanks to Doug Hofstadter, who showed me the power of group theory visu- alization and supported my work on it in several ways, including much good advice Many thanks to Charlie Hadlock, who kept me away from not-so-good advice(such as Don't write a book before you get tenure?) and who guided many of the early steps of this project. I also thank Don Albers, the MAa, and Bentley University(particularly Rick Cleary and Kate Davy), all of whom encouraged, supported, and took a chance on a first-time author I must also thank those whose mathematical work helped me in mine. One of my early exposures to group theory visualization techniques was Magnus and Grossman's Groups and Their Graphs. In writing this book I made frequent reference to the excellent texts by Michael Artin, John Fraleigh, Charles Hadlock, and Thomas Hungerford. The powerful and well-designed software Asymptote by John Bowman helped me make the more than 300 figures herein. Thank you! Lastly, there are many people who read early chapters and drafts and provided much helpful feedback. These include Doug Hofstadter, Jon Zivan, an anonymous referee, my parents, and my Fall 2006 Discrete Mathematics class, especially Kathryn Ogorzalek Thank you for helping me see my work through your eyes, and improve it master 2011/10/18 17:10— page vi #8 maste r”-2011/10/18-17:10- page Ix-#9 Preface If you are interested in learning about group theory in a relaxed, intuitive way, then this book is for you. I say learning about group theory because this book does not aim to cover group theory comprehensively. Herein you will find clear, illustrated exposition about the basics of the subject, which will give you a solid foundation of intuitions, images, and examples on which you can build with further study This book is ideal for a student beginning a first course in group theory It can be used in place of a traditional textbook, or as a supplement to one, but its aim is quite different than that of a traditional text. Most textbooks present the theory of groups using theorems proofs, and examples. Their exercises teach you how to make conjectures about groups and prove or refute them. This book, however, teaches you to know groups. You will see them, experiment with them and understand their significance. The mental library of images and intuitions you gain from reading this book will enable you to appreciate far better the facts and proofs in a traditional text This book is also appropriate for recreational reading. If you want an overview of the theory of groups, or to learn key principles without going as deep as some upper-level undergraduate mathematics courses, you can read this book by itself. Only a typical high school mathematics education is assumed, but you should have a willingness to think My work on this book stems from Group Explorer, a software package I wrote that creates illustrations for finite groups, and allows the user to interact and experiment with them. Many of the illustrations in this text were generated with the help of Group Explorer, and the investigations possible in Group Explorer can help you with some of this book’ s exercises You do not need Group Explorer to benefit from this book; very few exercises specif- ically direct you to Group Explorer. But I recommend taking full advantage of hands-on, interactive learning experiences when theyre available; the more involved we are, the Inore we tend to learn. Group Explorer is free software, available for all major operating systems. You can find it online at http://groupexplorer.sourceforge.et 【实例截图】
【核心代码】
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