MATH 3230 Abstract Algebra I (Spring 2019)

Math 3230 Abstract Algebra I Fall 2018
Instructor: Ralf Schiffler
Office: Mont 336
Office hours: TT 2:00-3:00 or by appointment
Email: schiffler at math dot uconn dot edu

Lectures: MCHU 309, TT 9:30-10:45

Exam schedule :
Tu Mar 12 6-8 pm in Monteith 419
Tu Apr 30 6-8 pm in Monteith 419
Material covered: Sections 3.6., 3.7, 3.8, 4.1, 4.2, 5.1.

Description: This is the first part of a two-semester course on Abstract Algebra. It gives an introduction to the theory of groups with an emphasis on the development of careful mathematical reasoning. Among the topics covered in the course are groups, subgroups, factor groups, cyclic groups, permutation groups, linear groups, isomorphism theorems. We will cover chapter 3 and sections 1.4,2.3 of the textbook and then continue either with more group theory (chapter 7) or with ring theory (chapters 4,5). Each topic will be illustrated and explored through examples.

This course will be quite different from other math courses you have taken so far. We will work through many new definitions and concepts and most of them are rather abstract. We will develop many theorems and their proofs, and you will write plenty of proofs yourself in homework assignments and exams.

It is essential that you work on the material outside the classroom. Carefully read the textbook before coming to the lecture and use pencil and paper to work through the material, study the examples and fill in omitted steps in the text.

Textbook: Beachy and Blair, Abstract Algebra, third edition, Waveland Press.

Homework: Homework will be assigned on Thursdays and collected the following Thursday. Homework must be on letter-size paper only and multiple pages must be stapled together. I will NOT accept any LATE HOMEWORK, but I will drop the two problem sets with the lowest grades when I compute the final homework grade.

Exams: We will have two exams. Each of them will be a two-hour exam and will take place in the evening (see tentative schedule above and please let me know as soon as possible if you have a time conflict). The morning class on the day of the exam will be a review session.
Each exam will cover the material seen in class since the previous exam. There will be no final exam. In exchange for the evening exams, I will cancel two regular classes during the semester.

Course Grade:

Exam 1: 35%
Exam 2: 35%
Homework: 30%

Homework Problems:

  1. HW1: Due Jan 31
    Section 2.3 # 1,2,3,6 (ignore the parts about transpositions)
    Section 3.1 # 1, 2 (b)(c)
    Read Sections 2.3 and 3.1.
  2. HW2: Due Feb 7
    Section 1.4 # 1 (a)(b), 2(a)(b)
    Section 2.3 # 13
    Section 3.1 # 8,11,17
    Read Sections 1.4 and 3.1.
  3. HW3: Due Feb 14
    Section 3.1 # 22,23
    Section 3.2 # 4,6(a),9,11
    Read Section 3.2.
  4. HW4: Due Feb 21
    Section 1.4 # 13(a)
    Section 3.2 # 5(b)(d), 15, 21(a), 27 [Hint: Use the group GL_2(R). ]
    Read Section 3.3.
  5. HW5: Due Feb 28
    Section 3.3 # 5, 11
    Section 3.4 # 2, 6
    Read Section 3.4.
  6. HW6: Due Mar 7
    Section 3.4 # 11, 15
    Section 3.5 # 2, 3(a), 12
    Read Section 3.5.
  7. HW7: Due Apr 11
    Section 3.6 # 15
    Section 3.7 # 1(a),7,14, 20
    Read Sections 3.6 & 3.7.
  8. HW8: Due Apr 18
    Section 3.8 # 2, 6, 7, 12, 23
    Read Sections 3.8, 4.1 & 4.2.
  9. HW9: Due Apr 25
    Section 4.2 # 1(b), 2(d), 12
    Section 5.1 # 16, 17
    Read Section 5.1, & 5.2.