Modern Algebra I Honors

Math 415-200

Fall 2005

Instructor: Peter F. Stiller
Office: Blocker Bldg. 634B
Office Phone: 862-2905
E-mail: stiller@math.tamu.edu
Office Hours: Fall Schedule

Course Information

Time: TTh 2:20 to 3:35
Place: BLOC 624

Text: A First Course in Abstract Algebra 7th Edition by John B. Fraleigh
Supplementary Material: See the bibliography below

Prerequisites: Some experience with proofs - for example Math 304.

Grades: We will have three major exams. Two will each count for 15% of the grade and the final will count for 20%. The exams will include an in class, as well as a take home, portion. We will have six problem sets that will count 30% (5% each). The remaining 20% will be based on an independent project. The usual scale will apply 100-90 A, 89-80 B, 79-70 C, 69-60 D, 59 and below F.

Overview: This course will give students an introduction to abstract algebra and will include the study of a number of fundamental algebraic objects such as groups, rings and fields.

Syllabus

Detailed Description: We will cover a portion of the book in Math 415 and most of the remainder in Math 416. Since this is an honors section, we will use a number of supplementary books and papers.

Topics

Groups and Subgroups
Isomorphism
Cyclic Groups
Generators and Relations
Permutation Groups, Alternating Groups
Cosets
Finitely Generated Abelian Groups
Homomorphisms, Normal Subgroups
Factor (or Quotient) Groups, Simple Groups
Groups Actions on a Set
Sylow Theorems and Classification
Rings and Fileds
Integral Domains
Fields of Fractions, Localization
Polynomial Rings
Factoring Polynomials over a Field

Bibliography:

Symmetry by Hermann Weyl
Genius and Biographers: The Fictionalization of Evariste Galois

Week #1 August 29 - Septmember 2

Read: Section 0, pages 1-10 and Sections 1 and 2 pages 11-28. Try the following exercises:

Page 8-10, Exercises 11,12,19,27,29,31.
Page 19-20, Exercises 6,7,9,19,23,32,33.
Page 25-28, Exercises 2,4,12,13,16,29-34.

Assignment #1 Due Tuesday September 6th in class.

Do the following exercises: Exercise 10 page 36, Exercises 35-38 page 19, and Exercises 5,23 pages 26-27.

Week #2 September 5 - September 9

Read: Sections 3 and 4 pages 28-49. Try the following exercises:

Page 34-36, Exercises 3,7,11-15,18.
Page 45-49, Exercises 2,4,8,10,13,18,23,25.

Assignment #2 Due Tuesday September 13 in class.

Do the following exercises: Exercises 26,27,28,33,34 pages 34-36 and Exercises 19,20,21,29,32,34,41 pages 45-49

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