MAS 4301 Abstract Algebra 1 — Homework assignments

Every day

• Master sections already covered in class.
• Do the homework assigned bellow.
• Read the section scheduled in the calendar to be discussed in the following class.

Minimum Homework by Due Date

• Due August 26. Do the problems in Homework 1.
• Due August 31. Calculate the Cayley table of the dihedral group D₄.
• Due September 2. Section 1, numbers 10, 13 and 15.
• Due September 4. Section 2, numbers 2, and 3. (Note: The book may be wrong when it says that some of these are binary operations.)
• Due September 9. Section 2, numbers 6, 7 and 10.
• Due September 11. Section 2, numbers 14, 16 and 18.
• Due September 14. Section 2, numbers 20, 24 and 26.
• Due September 14. Section 2, numbers 28, 30, and 31.
• Due September 21. 1) Let E be the set of even integers. Prove that E is a subgroup of the additive group of all integers.
  
  2) Let O be the set of all odd integers. Prove that O is not a subgroup of the additive group of all integers.
  
  3) Is the set of integers a subgroup of the additive group of all real numbers?
  
  4) Is the empty set a subgroup of the additive group of all integers?
• Due September 23 Section 3, numbers 26, 28, 48, and 51.
• Due September 25. Section 4, numbers 1 -7 odd and 11.
• Due October 2. Section 5, numbers 1 – 5.
• Due October 8. Section 5, numbers 6, 7, 36 and 41.
• Due October 14. Section 6, numbers 3, 6, 7, 12, 16, and 27.
• Due October 16. Section 7, numbers 1, 2, 3, 6, 7, 8, and 9.
• Due October 19. Section 7, numbers 19, 21, 26, and 28.
• Due October 21. Section 8, numbers 14, 16, and 18.
• Due October 23. Section 8, numbers 17, 19, 23, and 26.
• Due October 26. Section 10, numbers 2, 6, 26, and 36.
• Due October 28. Section 10, numbers 8, 22, and 25.
• Due October 30. Section 9, numbers 1, 2, 3, and 4.
• Due November 2. Section 9, numbers 6, 7, 10, and 25.
• Due November 9. Section 11, numbers 16, 34, and 36.
• Due November 16. Section 12, numbers 2, 3, 6, and 7.
• Due November 18. Section 12, numbers 18, 44, 52, and 53.
• Due November 20. Section 13, numbers 9, 10, 18, and 27.
• Due November 30. Section 15, numbers 17, 18, 25, 27, and 35.
• Due December 2. Section 14, numbers 4, 5, 15, and 18.

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