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 9:35-10:50am

 Office hours: Wednesday 10-11am, Tuesday 2-3pm or by appointment (or drop in!)

 

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 2 Midterms (28pts each), Homework (15pts), and a Final (29pts) 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. 

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. Forming study groups is encouraged, but homework is to be done individually and be your own work.  Homework counts as 15pts, and will be posted below.  Some problems will be assigned only to students in the honors section and others to regular section students only.  Each honors section student will be asked to present some material to the class.

Exams: There are three exams. Calculators are not allowed (or needed) on the exams. Honors students' exams will include more challenging problems.

Course Policies: Make-ups for missed exams will only be guaranteed for a university approved excuse in writing, other situtations (interviews etc.) will be considered on a case-by-case basis, but must always be supported with documentation. Wherever possible, students should inform the instructor before an exam or major assignment 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. Late homework is not accepted or graded.  If a homework cannot be completed due to a university approved excuse, that homework will be dropped.

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, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. 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 21
  
• Q-drop Deadline: April 15
  
• Exam II: March 28
  
• Final Exam: Thursday May 2 12:30-2:30
  

Homework Assignments/Syllabus (tentative)

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

• HW 1 Due Jan. 24 (9:35am)
  
  • 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 Jan. 31 (9:35am)
• 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. 7 (9:35am)
  
  • 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. 14 (9:35am)
  
  • E: Read Fraleigh Section 33. do: §33: 3,4,9,10 also:  X: Determine the number of fields (up to isomorphism) E containing GF(2) and contained in GF(64).
    
  • R: §33:1,2,5
  • H: §33: 11,13,14
• HW 5 Due Feb. 21 (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 Feb 28( 9:35am)
  
  • E: Read Fraleigh Section 16. do: §16: 9ab,12,13abc
    
  • R: §16:1,2,3
  • H: §16: 10,15
• HW 7 Due March 7 (9:35am)
  
  • E: Read Fraleigh Sections 36. do: §36: 5,6,11,13,17,18
    
  • R: §36: 2,3,4
  • H: §36: 16,19,20ab
• HW 8 Due March 21 (9:35am)
  
  • E: Read Fraleigh Sections 37. do: §37: 2,4,5,6 also: do your best to classify groups of order 28, 30 or 231 (pick one).
    
  • R: §37: 1,7
  • H: §37: 8
• HW 9 Due March 28(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 10 Due April 4(9:35pm)
  
  • E: Read Fraleigh Section 49 do: §49: 2,3,4,7a
  • R: §49: 1,10
  • H: §49: 6,13
  
  
• HW 11 Due April 11(9:35pm)
  
  • E: Read Fraleigh Section 50,51 do: §50: 2,4,5,10,18 §51: 15abc,16abc
    
  • R: §50: 8,9
  • H: §50: 17,24
  
  
• HW 12 Due April 18 (9:35am)
  
  • E: Read Fraleigh Section 51: Pick 5 problems to do (besides 15/16).
  
  
  
• HW 13 Due April 26 (9:35am)
  
  • E: Read Fraleigh Section 53,54 do: §53: 9,12,22ab §54: 4abcd,5,8
    
  • R: §53: 1,2 §54: 1
  • H: §53: 20 §54: 7