Abstract Algebra

Kevin Hopkins

Files that could be used in teaching Abstract Algebra. Some are also used in other classes, (like the Complex Number files), so the section numbers may not match the sections from Abstract Algebra. As of Spring 2016, I have started using a new Abstract Algebra book. The book by Pinter doesn't include as many concrete examples for students to work with, so I hope to expand the worksheets. I will also have to alter the Chapter number as the course proceeds. [b][color=#b20ea8]If you find what you think is an error, please take a screen shot and email that to me (khopkins@sbuniv.edu) so I can investigate.[/color][/b]

Table of Contents

  1. Pinter's Book
    1. Appendix-Set Operations
    2. New Operations
    3. Z_n Under Addition-An example of operations from Chapter 2
    4. Z_n Under Multiplication-An example of operations-Chapter 2
    5. Ordered Pair, Group Example-Chapter 3
    6. Chapter 7-Permutations
    7. Chapter 7-Permutations
    8. Chapter 7-Permutations
    9. Chapter 7-Permutations
    10. Chapter 8-Permutations of a Finite Set
    11. Chapter 8-Permutations of a Finite Set
    12. Chapter 10 and 11-Cyclic Groups and Subgroups
    13. Chapter 10 & 11-Multiplication-Hopefully now working
    14. Identifying Rational vs Irrationals
  2. Gilbert's book
    1. Section 2.4
    2. Section 2.5-2.6: Solving equations modulo n.
    3. Section 2.6-Inverses in Z sub n
    4. Section 8.4-Polynomials
    5. Section 8.4-Addition of Complex Numbers
    6. Section 8.4-Multiplication of Complex Numbers
    7. Section 8.4-Division of Complex Numbers
    8. Polar Form of Complex Numbers-Section 7.2
    9. Complex Numbers in Rectangular Form-Section 7.2
    10. Complex Products using Polar Form
    11. Complex Powers
    12. Section 7.3-Roots of Complex Numbers
    13. Mandelbrot Set-Extension of Use of Complex Numbers.

1.

Pinter's Book

Files that have been created or updated (title at least) for Pinter's book used first in Spring 2016

  • 1. Appendix-Set Operations
  • 2. New Operations
  • 3. Z_n Under Addition-An example of operations from Chapter 2
  • 4. Z_n Under Multiplication-An example of operations-Chapter 2
  • 5. Ordered Pair, Group Example-Chapter 3
  • 6. Chapter 7-Permutations
  • 7. Chapter 7-Permutations
  • 8. Chapter 7-Permutations
  • 9. Chapter 7-Permutations
  • 10. Chapter 8-Permutations of a Finite Set
  • 11. Chapter 8-Permutations of a Finite Set
  • 12. Chapter 10 and 11-Cyclic Groups and Subgroups
  • 13. Chapter 10 & 11-Multiplication-Hopefully now working
  • 14. Identifying Rational vs Irrationals

1.1.

Appendix-Set Operations

Set operations.
– Kevin Hopkins

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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2.

Gilbert's book

Files used with Gilbert's book. The files may eventually be updated and renamed to use with Pinter's book.

  • 1. Section 2.4
  • 2. Section 2.5-2.6: Solving equations modulo n.
  • 3. Section 2.6-Inverses in Z sub n
  • 4. Section 8.4-Polynomials
  • 5. Section 8.4-Addition of Complex Numbers
  • 6. Section 8.4-Multiplication of Complex Numbers
  • 7. Section 8.4-Division of Complex Numbers
  • 8. Polar Form of Complex Numbers-Section 7.2
  • 9. Complex Numbers in Rectangular Form-Section 7.2
  • 10. Complex Products using Polar Form
  • 11. Complex Powers
  • 12. Section 7.3-Roots of Complex Numbers
  • 13. Mandelbrot Set-Extension of Use of Complex Numbers.

2.1.

Section 2.4

Finding greatest common divisor
Section 2.4
– Kevin Hopkins

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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Information