Christopher E. Heil

• Office: Skiles 109.
  
  
• Please fill out the Course/Instructor Opinion Survey
  
  
• Course Syllabus
  
  
• Background and supplementary materials:
  • Writing Proofs
  • Materials used in Math 4107 in Spring 2007
  
  
  
• LECTURE NOTES:
  
  Lecture notes follow the text "Abstract Algebra," Third Edition, by I. N. Herstein, Wiley, 1999. Notes may be updated throughout the semester.
  
  
  • Chapter 1
    
    
  • Chapter 2, Sections 2.1-2.4
    • Some practice problems with solutions
  • Chapter 2, Sections 2.5-2.6
    • Some practice problems with solutions
    • Solution to Problem 2.5 #15 from the text
    • Example of cosets in the dihedral group of order 8
  • Chapter 2, Section 2.7
    • Some practice problems with solutions
  • Chapter 2, Section 2.8
  • Chapter 2, Section 2.9
    • Some practice problems with solutions
    
    
  • Chapter 3, Sections 3.1-3.2
    • Some practice problems with solutions
  • Chapter 3, Section 3.3
    • Notes on functions that map functions to functions
    • Proof that A_n is simple for n >= 5
    
    
  • Chapter 4, Section 4.1
  • Chapter 4, Sections 4.2-4.3 through ideals
  • Chapter 4, Section 4.3 on quotient rings
    • Some practice problems with solutions
  • Chapter 4, Section 4.4
  • Chapter 4, Section 4.5 through the Division Algorithm
  • Chapter 4, Section 4.5 on divisors through factorization
    • Some practice problems with solutions
  • Chapter 4, Section 4.6
  • Chapter 4, Section 4.7
  
  
  
• HOMEWORK:
  • Homework 1 (due February 1, 2010).
  • Homework 2 (due February 12, 2010).
  • Homework 3 (due March 5, 2010).
  • Homework 4 (due March 15, 2010).
  • Homework 5 (due April 12, 2010).
  • Homework 6 (due April 23, 2010).
  
  
  
• EXAMS:
  • Exam 1 will take place on Friday, February 19, 2010 (in class). You are allowed to bring one 8.5x11 sheet of notes to the exam (you can write on both sides). The exam will cover the material through Section 2.6 of our text.
  • Exam 2 will take place on Friday, March 19, 2010 (in class). You are allowed to bring one 8.5x11 sheet of notes to the exam (you can write on both sides). The exam will cover the material through Section 2.9 of our text.
  • Our Final Exam is scheduled for 11:30 a.m. - 2:20 p.m., Monday, May 3 (in our usual classroom). You are allowed to bring one 8.5x11 sheet of notes to the exam (you can write on both sides). The exam is comprehensive, covering through 4.6 of our text.
  
  
  
• 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, 38, 40(use #38), 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