Overview
- Explores an interesting sampling of groups typically not encountered until later in a student’s career
- Provides a concise and accessible introduction to more advanced topics in group theory
- Contains numerous exercises of varying difficulty to reinforce the material
Part of the book series: Compact Textbooks in Mathematics (CTM)
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Table of contents(6 chapters)
About this book
This textbook offers students with a basic understanding of group theory a preview of several interesting groups they would not typically encounter until later in their academic careers. By presenting these advanced concepts at this stage, they will gain a deeper understanding of the subject and be motivated to explore more of it.
Groups covered include Thompson’s groups, self-similar groups, Lamplighter groups, and Baumslag-Solitar groups. Each chapter focuses on one of these groups, and begins by discussing why they are interesting, how they originated, and why they are important mathematically. A collection of specific references for additional reading, topics for further research, and exercises are included at the end of every chapter to encourage students’ continued education.
With its accessible presentation and engaging style, A Sampling of Remarkable Groups is suitable for students in upper-level undergraduate or beginning graduate abstract algebra courses. It will also be of interest to researchers in mathematics, computer science, and related fields.
Reviews
“This delightful book is dedicated to introducing an advanced undergraduate student to the study of some aspects of infinite groups theory. … The whole book is enriched with beautiful and instructive illustrations.” (Enrico Jabara, zbMATH 1446.20001, 2020)
Authors and Affiliations
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Department of Math and Computer Science, New York City College of Technology, The City University of NewYork, Brooklyn, USA
Marianna C. Bonanome
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Department of Mathematics, Borough of Manhattan Community College, The City University of New York, New York, USA
Margaret H. Dean
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Department of Mathematics, Monroe Community College, Rochester, USA
Judith Putnam Dean
About the authors
Dr. Margaret H. Dean is an associate professor in mathematics at BMCC, CUNY. Her current research interest is in metabelian groups. In the area of undergraduate education, she is involved in various projects to study, disseminate and implement alternative learning methods in the classroom and to promote quantitative literacy across the curriculum.
Judith Putnam Dean is an associate professor in mathematics at Monroe Community College. As a Flipped Learning specialist, she helped develop a mastery flipped program for developmental math, designs flipped classes for upper level courses, creates instructional videos and shares her expertise through leading workshops. In addition she has created online, OER and writing intensive courses.
Bibliographic Information
Book Title: A Sampling of Remarkable Groups
Book Subtitle: Thompson's, Self-similar, Lamplighter, and Baumslag-Solitar
Authors: Marianna C. Bonanome, Margaret H. Dean, Judith Putnam Dean
Series Title: Compact Textbooks in Mathematics
DOI: https://doi.org/10.1007/978-3-030-01978-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-030-01976-1Published: 16 January 2019
eBook ISBN: 978-3-030-01978-5Published: 05 January 2019
Series ISSN: 2296-4568
Series E-ISSN: 2296-455X
Edition Number: 1
Number of Pages: XII, 188
Number of Illustrations: 157 b/w illustrations, 13 illustrations in colour
Topics: Group Theory and Generalizations