Math 331: Abstract Algebra

Professor: Jonah Blasiak

Fall 2019

Monday, Wednesday, Friday 4:00pm - 4:50pm, University Crossings 153
Course Description: Covers the theory of groups, including homomorphisms, cosets, group actions, the structure theorem of finite abelian groups, and Sylow theorems. Emphasis on proof writing.
Prerequisites: (MATH 220 Minimum Grade: C- or CS 270 Minimum Grade: C-) and (MATH 201 Minimum Grade: D or MATH 261 Minimum Grade: D or ENGR 231 Minimum Grade: D)
Office Hours: Korman 275, Wednesday 11:00am-12:30pm, Friday 11:30am-12:30pm.
Textbooks: We will mostly use the following text. I will be using the 6th edition, but other editions should be okay.
  • A First Course in Abstract Algebra 6th Edition, by John B. Fraleigh
    • Grade Breakdown:
  • 20% Homework
  • 20% Quizzes
  • 25% Midterm
  • 35% Final
    • Grading Policy:
  • A: 80-100%
  • B: 60-80%
  • C: 40-60%
  • D-F: 0-40%
    • Exam Policy: No books or electronic devices are allowed on the midterm or exam. No collaboration is permitted at the midterm or exam. THERE WILL BE NO MAKE-UPS FOR EXAMS.
    The midterm will be in-class on Wednesday, October 23; it will be 50 minutes long.
    Students with special exam-taking requirements or time conflicts should contact me by October 4.
    Quiz Policy: Quizzes will be given in recitation every week. They will be about 15 minutes long. There will be about 8 quizzes total and the lowest quiz grade will be dropped to compute the quiz grade. No books or electronic devices are allowed on quizzes. No collaboration is permitted on quizzes. THERE WILL BE NO MAKE-UPS FOR QUIZZES.
    Homework Policy: You may consult each other and the textbook above. List all people and sources who aided you and whom you aided, and write up the solutions independently, in your own language. It is easy nowadays to find solutions to almost anything online. DO NOT consult such solutions until after turning your homework. Solutions to homeworks will be handed out in class and/or discussed in class. Late homeworks will not be accepted.
    Please visit this site frequently for new information. Updates to the syllabus and reading assignments, and homeworks will be posted here as the course progresses.

    Syllabus

    Week 1: Sep 23, Sep 25, Sep 27
    Definitions and examples of groups, matrix groups, subgroups.
    Read 1.3--1.5 in Fraleigh. Homework 1 due Oct 2.
    For problem 1(a), use the definition N = {0,1,2,...}.

    Week 2: Sep 30, Oct 2, Oct 4
    Cyclic groups, Cosets.
    Read 1.5, 0.2.15--0.2.21, 2.3 in Fraleigh.
    No Quiz this week. The first quiz will be in recitation Oct 7 or 9.
    Homework 2 due Friday Oct 11.
    Homeworks will be due on Fridays from now on, including Homework 2.

    Week 3: Oct 7, Oct 9, Oct 11
    Lagrange's Theorem, classification of groups of order 6, group homomorphisms, image, kernel
    Read 2.3,3.1 in Fraleigh. Homework 3 due Oct 18

    Week 4: Oct 16, Oct 18
    Normal subgroups, product groups, isomorphisms
    Read 3.1 and the beginning of 2.4 through Example 2.4.11 in Fraleigh.
    The quiz will be in class this week instead of recitation since we didn't have class Monday.
    Homework 4 due Nov 01 (no homework due October 25 because of the midterm)

    Week 5: Oct 21, Oct 23, Oct 25
    Read 3.2 in Fraleigh.
    Quotient groups
    Midterm: October 23. It will be in-class and 50 minutes long.
    Try to arrive a couple minutes early to class if possible so we can start exactly on the hour. The midterm will cover all the material from class up through Monday Oct 21 and homeworks 1-4 (I won't give a problem as hard as 4.7--4.9, but something like problems 4.1--4.6 is possible). The relevant book sections are those listed above for weeks 1--5. In general I will try to make the questions related to the more recent material easier.

    Week 6: Oct 28, Oct 30, Nov 01
    Read 3.2, 2.1, 0.2.15--0.2.21 in Fraleigh.
    First isomorphism theorem, the symmetric group
    Homework 5 due Nov 08
    The quiz on Nov 4/6 will focus on Homework 4.

    Week 7: Nov 4, Nov 6, Nov 8
    Read 2.1, 3.5 in Fraleigh.
    The symmetric group, conjugacy classes, group actions
    Homework 6 due Nov 15

    Week 8: Nov 11, Nov 13, Nov 15
    Read 3.5 in Fraleigh.
    Group actions
    Homework 7 due Nov 22

    Week 9: Nov 18, Nov 20, Nov 22
    Read 3.6, 4.2-4.3 in Fraleigh.
    Burnside's Theorem, p-groups, Sylow theorems
    There will be no quiz the week of November 25.

    Week 10: Nov 25
    Read 4.2-4.3 in Fraleigh.
    Applications of Sylow theorems, proof of Cauchy's Thm
    Homework 8 due Dec 06

    Week 11: Dec 02, Dec 04, Dec 06
    Read 4.3, 2.4 Fraleigh.
    Applications of Sylow theorems, groups of order 12, abelian groups, final review
    I will be gone December 2-4 and Felix will cover class. There will be a quiz in class on December 4, not in recitation. I will not have office hours on Dec 4th, but office hours will be 11:30-12:30 as usual on Dec 6th.

    The Final Exam is on Thursday, December 12, in PISB 108, from 1pm to 3pm. It will cover all the material from class and on the homeworks, with more emphasis on the material from weeks 5-11. The format of the final will be similar to the midterm but about two times as long.
    Extra Office Hours: Monday December 09, 1:30 - 3:00pm.

    Homework Help: Math Resource Center (Korman 247)
    Important University Policies:

    Academic Dishonesty

    Course Drop Policy

    Code of Conduct

    Disability Resources:
    Students requesting accommodations due to a disability at Drexel University need to request a current Accommodations Verification Letter (AVL) in the ClockWork database before accommodations can be made. These requests are received by Disability Resources (DR), who then issues the AVL to the appropriate contacts. For additional information, visit the DR website at drexel.edu/oed/disabilityResources/overview/, or contact DR for more information by phone at 215.895.1401, or by email at disability@drexel.edu.
    Outcomes: Students should be able to read and write clear proofs at an advanced undergraduate level. Students will be well-versed in the language of group theory, including an understanding of groups, homomorphisms, group actions, and Sylow theorems.