Math 415 (Section 502) -- Fall 2010

Modern Algebra I

Tuesday & Thursday 3:55-5:10
BLOC 161

Math 415 Homework

Exam 1 Solutions

Exam 2 Solutions

Course Description:

This is a first course in abstract algebra. The main topics the course will cover are the introductory theories and applications of groups, rings, and fields. There will be an emphasis placed on rigorous proofs throughout the semester, including during class and on homework and exams. Topics we will cover this semester include
  • Binary operations
  • Groups and subgroups
  • Lagrange's Theorem
  • Homomorphisms and isomorphisms
  • Normal subgroups and factor groups
  • The Fundamental Homomorphism Theorem
  • Rings and fields
  • Fermat's and Euler's Theorems
  • Integral domains and fields of quotients
  • Polynomial rings
  • Factoring polynomials over finite fields
  • Ideals and factor rings

Course Information:

Instructor: Dr. Matthew Papanikolas

Office Hours: Tues. 11-12, Thurs. 1-2; also by appointment.

Office: 321 Milner

Office Phone: 845-1615


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 I-IV and part of Chapter V. Additional topics will be covered as time permits. Please be sure you are familiar with topics covered in Section 0 (review from Math 220), which we will not cover in class. See below for a detailed weekly syllabus.

Calculators: Calculators are not generally needed for this course and will not be permitted on exams.

Prerequisites: Math 323 (Linear algebra with 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


Oct. 5 (Tues)

Nov. 16 (Tues)

Dec. 14 (Tues)


BLOC 161

BLOC 161

BLOC 161


Your final grade will be determined by the total number of points obtained on exams and homework. Out of 450 total points, each component contributes to your grade as follows:





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. They must be turned in on time, and late homeworks will not be accepted. Working together on problems is perfectly fine (and encouraged!), *but* students are expected to turn in their solutions in their own words. Students turning in identical solutions for problems will be penalized on those problems. Homework assignments will be posted on this web page (check the link at the top of the page or click here), so check back frequently!

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 (8/31, 9/2): Sections 1-3
Week 2 (9/7, 9/9): Sections 3-5
Week 3 (9/14, 9/16): Sections 5-6
Week 4 (9/21, 9/23): Sections 7-9
Week 5 (9/28,9/30): Sections 9-10
Week 6 (10/5, 10/7): Exam 1 on 10/5; Sections 10-11
Week 7 (10/12, 10/14): Sections 11, 13
Week 8 (10/19, 10/21): Sections 13-14
Week 9 (10/26, 10/28): Sections 14-15
Week 10 (11/2, 11/4): Sections 18-20
Week 11 (11/9, 11/11): Sections 20-21
Week 12 (11/16, 11/18): Exam 2 on 11/16; Sections 21-22
Week 13 (11/23): Section 22
Week 14 (11/30, 12/2): Sections 23, 26-27
Week 15 (12/7): Section 27 and Review
Tues., 12/14, 1:00-3:00: 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 correct potential errors in homework problem sets). Students should regularly check their neo e-mail accounts.

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