Christopher E. Heil

• Office Hours: MWF 10:00-11:00 and 11:30-12:00, and by appointment.
  
  
• Course Syllabus
• Handout on Writing Proofs
  
  
• Lecture notes following the text "Abstract Algebra," Third Edition, by I. N. Herstein, Wiley, 1999:
  • Chapter 1 (posted 1/8/07).
  • Chapter 2, Sections 2.1-2.4 (posted 1/10/07).
    • Some practice problems with solutions (posted 1/19/07).
  • Chapter 2, Sections 2.5-2.6 (posted 1/22/07).
    • Some practice problems with solutions (posted 1/31/07).
    • Solution to Problem 2.5 #15 from the text (posted 2/6/07).
    • Example of cosets in the dihedral group of order 8 (posted 2/7/07).
  • Chapter 2, Section 2.7 (posted 2/5/07).
    • Some practice problems with solutions (posted 2/24/07).
  • Chapter 2, Section 2.8 (posted 2/12/07).
  • Chapter 2, Section 2.9 (posted 2/26/07).
    • Some practice problems with solutions (posted 3/2/07).
  • Chapter 3, Sections 3.1-3.2 (posted 3/2/07).
    • Some practice problems with solutions (posted 3/5/07).
  • Chapter 3, Section 3.3 (posted 3/5/07).
    • Notes on functions that map functions to functions (posted 3/5/07).
    • Proof that A_n is simple for n >= 5 (posted 3/7/07).
  • Chapter 4, Section 4.1 (posted 3/26/07).
  • Chapter 4, Sections 4.2-4.3 through ideals (posted 3/28/07).
  • Chapter 4, Section 4.3 on quotient rings (posted 4/2/07).
    • Some practice problems with solutions (posted 4/1/07).
  • Chapter 4, Section 4.4 (posted 4/2/07).
  • Chapter 4, Section 4.5 through the Division Algorithm (posted 4/6/07).
  • Chapter 4, Section 4.5 on divisors through factorization (posted 4/13/07).
    • Some practice problems with solutions (posted 4/15/07).
  • Chapter 4, Section 4.6 (posted 4/17/07).
  • Chapter 4, Section 4.7 (posted 4/23/07).
  
  
• Homework 1 (due January 29, 2007).
• Homework 2 (due February 9, 2007).
• Homework 3 (due March 9, 2007).
• Homework 4 (due April 9, 2007).
• Homework 5 (due April 23, 2007).
  
  
• Exam 1 has been rescheduled for February 16, 2007. The exam will cover sections 1.3, 1.4, 1.6, and 2.1-2.6 in the text. You are allowed to bring one 8.5x11 sheet of notes to the exam (you can write on both sides).
• Exam 2 has been rescheduled for March 16, 2007. The exam will cover sections 2.7-2.9 and 3.1-3.3 in the text. You are allowed to bring one 8.5x11 sheet of notes to the exam (you can write on both sides).
• Our Final Exam is scheduled for Friday, May 4, 8:00-10:50 a.m. The final is comprehensive. You are allowed to bring one 8.5x11 sheet of notes to the exam (you can write on both sides).
  
  
• Recommended Practice Homework Problems:
  • Section 1.3: #3, 6, 7, 13, 23, 24, 27
  • Section 1.4: #1, 2, 3, 4, 5, 8, 9, 15, 16, 21
  • Section 1.6: #1, 2, 7, 13
  • Section 2.1: #1, 2, 8, 9, 13, 14, 15, 16, 18, 19, 25, 28, 31
  • Section 2.2: #3, 5
  • Section 2.3: #1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 19, 20, 21, 22
  • Section 2.4: #2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 15, 16, 17, 18, 26, 28, 31, 32, 34, 43
  • Section 2.5: #1, 2, 3, 5, 6, 9, 12, 14, 15, 16, 18, 19, 20, 26, 28, 37, 40, 41
  • Section 2.6: #1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 15, 16, 18
  • Section 2.7: #2, 3, 4, 5, 6
  • Section 2.8: #2, 4, 5, 6, 7, 8, 11, 12, 13, 15
  • Section 2.9: #1, 2, 3, 4, 5, 6
  • Section 3.1: #1, 2, 3, 4, 5
  • Section 3.2: #1, 2, 3, 5, 8, 9, 10, 11,12, 13, 14, 15, 17, 18, 19, 20, 21
  • Section 3.3: #1, 2, 3, 5, 6, 7, 8, 9(challenge)
  • Section 4.1: #1, 2, 3, 5, 11, 21, 26, 27, 28, 29, 30, 31, 32, 34
  • Section 4.2: #1, 2, 3, 5, 6, 8
  • Section 4.3: #1, 2, 3, 4, 5, 6, 7, 9, 11, 14, 15, 18, 19, 20, 21, 22, 23, 26
  • Section 4.4: #2, 3, 4, 5, 6, 7, 8
  • Section 4.5: #1, 2, 3, 4, 5, 6, 8, 10, 11, 14, 15, 16, 18, 20, 23, 24, 27
  • Section 4.6: #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
  
  
• Sample Exams: Below are the exams given in this course in Fall 2002. Please keep in mind that a different text was used that semester, so the content, emphasis, and notation is different from that of this semester.
  • Exam 1.
  • Exam 2.
  • Final Exam.