Math 416 (Sections 200/500) -- Spring 2013

Modern Algebra II

Tuesday & Thursday 12:45-2:00
BLOC 121


Final paper (Section 200 only)

Course Description:

This is a second course in abstract algebra and is a continuation of the topics covered in Math 415, including rings and ideals, field theory, Galois theory, and advanced topics in group theory. The course material will include the following topics, and additional ones will be covered as time permits.
  • Rings and ideals
  • Field theory
  • Algebraic extensions of fields
  • Finite fields
  • Isomorphism theoerems
  • Sylow theorems
  • Free abelian groups
  • Group actions
  • Free groups and presentations
  • Field automorphisms
  • Fundamental Theorem of Galois Theory
  • Insolvability of the quintic
  • Unique factorization domains and Euclidean domains

Course Information:

Instructor: Matthew Papanikolas

Office Hours: Wed. & Thurs. 3:00-4:00; also by appointment.

Office: 321 Milner


Textbook: The required textbook is A First Course in Abstract Algebra, 7th ed., by John B. Fraleigh, Addison-Wesley, 2003, ISBN 0-201-76390-7.

Course Syllabus: The course covers most of Chapters V, VI, VII, and X, with additional topics from Chapter IX if time permits.

Prerequisites: Math 415 or the equivalent. Students will be expected to be proficient at writing proofs.

Course Webpage:

Exam Schedule:

There will be 2 in-class exams during the semester, as well as a cumulative final exam. The dates and times are listed below.

Exam 1

Exam 2

Final Exam


Feb. 19 (Tues.)

Apr. 4 (Thurs.)

May 8 (Wed.)
8:00-10:00 AM


BLOC 121

BLOC 121

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Your final grade will be determined by your performance on exams, homework, and your final paper (if you are in the honors section). The contributions of the graded parts of the course are weighted as follows:


Sec. 200 Percentages

Sec. 500 Percentages







Exam 1



Exam 2



Final Exam



The following grade distribution will be used in determining final course grades:


Percentage of Total Points












Homework will be collected roughly once per week for a grade. Late homework will not be accepted, except as allowed by university policies on missed work (see below). Your lowest homework score will be dropped at the end of the semester. It is fine to work together to solve the homework problems, but you are expected to write up your solutions on your own. Consulting web sites or other problem solution sources (other than the textbook) is not allowed.

Honors Information:

Students enrolled in the honors section of this course (Section 200) will be assigned additional problems each week, and they will also be assigned a 5 page paper on an extra topic to be determined through consultation with the instructor. These papers will be due in class on Thursday, April 25. Further information will be provided after the second exam.

Detailed Syllabus:

We will use the following schedule for lectures, covering material out of the given sections of Fraleigh. We will adhere to this schedule as closely as possible, though changes may be necessary as the semester progresses.

Week 1 (1/15, 1/17): Sections 26, 27
Week 2 (1/22, 1/24): Sections 27, 29
Week 3 (1/29, 1/31): Sections 29, 30
Week 4 (2/5, 2/7): Sections 31
Week 5 (2/12, 2/14): Sections 31, 33
Week 6 (2/19, 2/21): Section 33; Exam 1 on Tues. 2/19
Week 7 (2/26, 2/28): Sections 34, 16
Week 8 (3/5, 3/7): Sections 16, 17
Week 9 (3/19, 3/21): Sections 35, 36
Week 10 (3/26, 3/28): Sections 37, 48
Week 11 (4/2, 4/4): Section 49; Exam 2 on Thurs. 4/4
Week 12 (4/9, 4/11): Section 50, 51
Week 13 (4/16, 4/18): Sections 53, 54
Week 14 (4/23, 4/25): Sections 55, 56.
Wed., 5/8, 8:00-10:00 AM: Final Exam

Course Policies:

Missed Work: Making up missed work (including missed exams, quizzes, and homework) will be arranged according to University policies only. A university approved excuse must be provided to the instructor in writing (e-mail is sufficient) within 1 working day for exams and within 2 working days for other work.

Academic Dishonesty: "An Aggie does not lie, cheat, or steal or tolerate those who do." It is not permissible to hand in the work of others for a grade, including work on exams, quizzes, and homework. You are allowed to discuss homework with others, but your write-ups are expected to be done on your own and in your own words. Copying the work of others will be prosecuted to the full extent possible under University policies. Please see the Honor Council Rules and Procedures on the web at

Disability Assistance: 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. Students seeking speical considerations for an exam must contact this office several weeks in advance of the exam. For more information, visit

Copyright Information: All printed handouts and web materials are protected by US Copyright Laws. No multiple copies can be made without written permission of the instructor.

Contact Information: Course announcements may occasionally be made via e-mail (e.g. in case of a change to office hours or to clarify problems in homework sets). Students should regularly check their neo e-mail accounts.

Page maintained by Matt Papanikolas, Dept. of Mathematics, Texas A&M University.