MATH 416 – Sections 500 and 200

CATALOG DESCRIPTION: A study of Groups, Rings and Fields, with an emphasis on the theoretical aspects and proofs. Prerequisites: Math 415.

Instructor: Dr. Eric Rowell. email: rowell@math.tamu.edu, webpage: www.math.tamu.edu/~rowell. Office BLOC 510B

Place and Time: This course meets TR 12:45-2:00pm in  BLOC 121.

 Office hours:  W 10:30-11:30am (or by appointment).

Course Objectives: The objectives are to learn advanced topics in modern algebra: ideals and quotients of rings, field extensions, Sylow theory, and Galois theory.

Text: Fraleigh, A first course in Abstact Algebra, 7th edition.

Material Covered/Syllabus: We will cover most of Chapters V, VI, VII, and X, with additional topics from Chapter VIII or IX if time permits.

Grading: Your grade will be based upon 3 Midterms (25pts each), Homework (10pts), and quizzes (15pts) for a total of 100 points. The grading scale is the usual one: 90-100% A, 80-89 % B, 70-79% C, 60-69 % D, 0-59% F.   Dates of exams/assignments will be posted below.  There will be no final exam.

Quizzes:  Every Tuesday there will be a short quiz, typically based on the previous week's lecutures. The lowest quiz score will be dropped.  Quizzes account for 15/100 of your grade.

Homework: Weekly homework sets will be turned in to be graded. Typically homework will be assigned on Thursdays and due the following Thursday.  As writing proofs takes considerable practice, the homework sets will likely be quite time-consuming. Your lowest homework score will be dropped. Late homeworks count as a 0, and may or may not be graded. Homework is to be done individually and be your own work.  Homework counts as 10pts, and will be posted below.

Exams: There are three midterm exams: February 19, April 2 and April 30.  These are worth 25pts each. Calculators are not allowed (or needed) on the exams.

Course Policies: Late homework and make-ups for missed exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam is missed. Consistent with University Student Rules, students are required to notify an instructor by the end of the next working day after missing an exam. Otherwise, they forfeit the right to a make-up.

An Aggie does not lie, cheat, or steal or tolerate those who do. Copying work that was done by others is an act of scholastic dishonesty and any instance of it will be prosecuted according to University Student Rules.

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, in Cain Hall, Room B118, or call 845-1637. For additional information visit http://disability.tamu.edu.

Copyright Policy: All printed materials disseminated in class or on the web are protected by Copyright laws. One photocopy (or printout from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

Important Announcements:

    Key Dates (tentative):

• Exam I: February 19
• Q-drop Deadline: April. 21
  
• Exam II: April 2
  
• Exam III: April 30
  

Homework Assignments/Syllabus (tentative)

Key: E means everyone, H means honors (section 200), R means regular (section 500).

• HW 1 Due Jan. 29 (12:45pm)
  
  • E: Read Fraleigh Sections 26 and 27.  do: §26: 1,22,26,37; §27: 2,5,25,31,37
    
  • R: §26: 18; §27: 18,19
    
  • H: §26: 20; §27:  17,24
    
• HW 2 Due Feb. 5 (12:45pm)
  
  • E: Read Fraleigh Sections 29,30. do: §29: 4,9,13,17; §30: 6,10
    
  • R: §29: 1,6; §30: 26
    
  • H: §29: 8, 32ab; §30: 27
  
  
• HW 3 Due Feb. 12 (12:45pm)
  
  • E: Read Fraleigh Section 31. do: §31: 2,22,23,24
    
  • R: §31: 3,5,6
  • H: (read pg 288-291 again!) §31: 27,30,38
  
  
• HW 4 Due Feb. 19 (12:45pm)
  
  • E: Read Fraleigh Section 33. do: §33: 3,4,9,10
    
  • R: §33:1,2,5
  • H: §33: 11,13,14
  
  
• HW 5 Due Feb. 26 (12:45pm)
  
  • E: Read Fraleigh Section 34. do: §34: 1abc,3abcd,7,9 and:
    Let N< S₄ be the (normal) subgroup: {e,(12)(34),(13)(24),(14)(23)} and H=<(1234)> the cyclic subgroup generated by (1234). Find |HN| using the second isomorphism theorem. Then try to write down all elements of HN.
• HW 6 Due March 5(12:45pm)
  
  • E: Read Fraleigh Section 16. do: §16: 9ab,12,13abc
    
  • R: §16:1,2,3
  • H: §16: 10,15
  
  
• HW 7 Due March 12 (12:45pm)
  
  • E: Read Fraleigh Sections 36,37 (omit Theorem 37.1). do: §36: 5,6,11,13,17,18 §37:1ab,5,7,8abcde,9
    
  • R: §36: 2,3,4
  • H: §36: 16,19,20ab
  
  
• HW 8 Due March 26(12:45pm)
  
  • E: Read Fraleigh Section 48. do: §48: 7,12,22abc,26,27,32,36abc,39
    
  • R: §48: 3,11,16
  • H: §48: 5,34,37
  
  
• HW 9 Due April 9(12:45pm)
  
  • E: Read Fraleigh Section 49,50,51 do: §49: 4,7a §50: 2,4,5,10,18 §51: 15abc,16abc
    
  • R: §50: 8,9
  • H: §50: 17,24
  
  
• HW 10 Due April 16(12:45pm)
  
  • E: Read Fraleigh Section 53 do: §53:9,12,16
    
  • R: §53: 1,2,13
  • H: §53: 14,17,20
  
  
• HW 11 Due April 23(12:45pm)
  
  • E: Read Fraleigh Sections 53 and 54 do: §53:10, 22ab; §54: 4abcd,5,8
    
  • R: §54: 1,7
  • H: §54: 10,11