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PreTeXt Sample Book:
Abstract Algebra (SAMPLE ONLY)
Thomas W. Judson, Isaac Newton (Editor)
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Front Matter
Colophon
Author Biography
About Robert A. Beezer
Dedication
Acknowledgements
Preface
Contributors to the 4
\(^\mathrm{th}\)
Edition
I
Basics
1
Preliminaries
1.1
A Short Note on Proofs
1.1.1
Some Cautions and Suggestions
1.2
Sets and Equivalence Relations
1.2.1
Set Theory
1.2.2
Cartesian Products and Mappings
1.2.3
Equivalence Relations and Partitions
1.3
Sage
1.3.1
Executing Sage Commands
1.3.2
Immediate Help
1.3.3
Annotating Your Work
1.3.4
Lists
1.3.5
Lists of Integers
1.3.6
Saving and Sharing Your Work
1.4
Exercises
1.5
Sage Exercises
1.6
References and Suggested Readings
2
The Integers
2.1
Mathematical Induction and Math in a Title
\(A\notsubset B\)
2.2
The Division Algorithm
2.2.1
The Euclidean Algorithm
2.2.2
Prime Numbers
2.2.3
Historical Note
2.3
Sage
2.3.1
Division Algorithm
2.3.2
Greatest Common Divisor
2.3.3
Primes and Factoring
2.4
Exercises
2.5
Programming Exercises
2.6
Sage Exercises
2.7
References and Suggested Readings
II
Algebra
1
Groups
1.1
Integer Equivalence Classes and Symmetries
1.1.1
The Integers mod
\(n\)
1.1.2
Symmetries
1.2
Definitions and Examples
1.2.1
Definition of a Group
1.2.2
Examples of Groups
1.2.3
Basic Properties of Groups
1.2.4
Historical Note
1.3
Subgroups
1.3.1
Definitions and Examples
1.3.2
Some Subgroup Theorems
1.4
Sage
1.4.1
Integers mod n
1.4.2
Groups of symmetries
1.4.3
Quaternions
1.4.4
Subgroups
1.5
Exercises
1.6
Additional Exercises: Detecting Errors
1.7
Sage Exercises
1.8
References and Suggested Readings
2
Cyclicity
2.1
Cyclic groups
2.2
Subgroups of a Cyclic Group
2.3
Cyclic Groups of Complex Numbers
2.4
Large Powers of Integers
2.5
Exercises
2.6
Programming Exercises
2.7
Sage Exercises
2.8
References and Suggested Readings
3
Runestone Testing
3.1
ActiveCode
3.2
Code Lens
3.3
Coding Exercises
3.4
Data Files
3.5
YouTube Videos
3.6
Deeper
3.6.1
Subsection One
3.6.2
Subsection Two
3.7
True/False Exercises
3.8
Multiple Choice Exercises
3.9
Parsons Exercises
3.10
Horizontal Parsons Exercises
3.11
Matching Exercises
3.12
Clickable Area Exercises
3.13
Select Exercises
3.14
Short Answer Exercises
3.15
Fill-In Exercises
3.16
Hodgepodge>
3.17
Exercises that are Timed
3.17
Timed Exercises
3.18
Projects and Friends
3.19
Expedited Samples
3.20
Reading Questions
3.21
YouTube Video Embedding
3.22
Runestone Assignment Testing
3.22
Exercises
Back Matter
A
Notation
B
Hints and Answers to Selected Odd Exercises
C
Hints and Answers to Selected Even Exercises
D
Hints and Answers to Selected Exercises
E
A Structured Appendix
E.1
A Section in an Appendix
E.1.1
A Subsection in a Section in an Appendix
E.1.1.1
A Subsubsection in a Subsection in a Section in an Appendix
E.2
Numbering in the Back Matter
F
GNU Free Documentation License
Index
Colophon
Colophon
Colophon
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This book was authored in MathBook XML.
