MATH-4320A (CRN 1734) Fall 2017 Course Syllabus

When, where, and who

My job is to help you to succeed in this class. I will be happy to discuss issues related to this course (or anything mathematical) in person or via email. In addition to the normal office hours listed above, alternative meeting time may be arranged (please give me at least 24hr advanced notice).

What we will learn

This is an undergraduate level course on abstract algebra that follows Modern Algebra I. Topics include rings, ideals, fields, modules, vector spaces, factorization, field extensions, and Galois theory.

Prerequisite

Modern Algebra I and certain level of “mathematical maturity”.

Textbook

  • [Required] Fundamentals of Modern Algebra: A Global Perspective by Robert Underwood (ISBN-13: 978-9814730297

Reading assignment and homework problems will be assigned from these textbook.

Attendance and participation

Participation in in-class discussions and activities is an important part of the learning process. Therefore class attendance is expected and will be recorded.

Code of conduct

Please be respectful of other people in the classroom and use common sense. In particular, please…

  • DO NOT use cell phones
  • DO NOT use social media
  • DO NOT take photos without permission
  • DO NOT sleep

Students who violate these rules will be asked to leave the classroom and will not be allowed to return until they have spoken privately with me.

Policy for calculators, computer programs, and smart devices

Scientific calculators or equivalent devices or software programs are neither required nor allowed in exams.

Homework problems

Practice is a crucial component in the learning process. Certain exercise problems will be assigned weekly. Each homework assignment is due the next Monday.

Reading assignments

You are expected to read the book in preparation of each class meetings. Reading assignments, i.e., sections (from the required textbook) are listed in the course schedule below. The reading assignments are to be completed before each class meeting.

In-class discussion

Participation in in-class discussion is an important component of the learning process. Your participation will be recorded.

Final exam

The mandatory final exam is scheduled at 9:30am–10:30am Dec. 7. It constitutes a major part of your course grade.

Grade composition

Your final grade is determined according to your overall performance on homework assignments, in-class discussions mid-term exam, and final exam. It is calculated according to the following weights.

Component Points
Homework 400
Discussion 400
Mid-term Exam 100
Final Exam 100

Grading scale

  • A: 90% - 100%
  • B: 80% - 89.9%
  • C: 70% - 79.9%
  • D: 60% - 69.9%
  • F: below 60%

Other policies

Academic dishonesty: Cheating of any kind will not be tolerated. In particular, you cannot copy (totally or partially) someone else’s solutions or allow someone else to copy your solutions on quizzes or exams. You will receive an “F” in the course if you are caught. Please consult Student Handbook for additional guidelines.

Disability accommodations: Students who need accommodations are asked to arrange a meeting during office hours to discuss your accommodations. If you have a conflict with my office hours, an alternate time can be arranged. To set up this meeting, please contact me by e-mail. If you have not registered for accommodation services through the Center for Disability Services (CDS), but need accommodations, make an appointment with CDS, 147 Taylor Center, or call 334-244-3631 or e-mail CDS at cds@aum.edu

Free academic support: All students have the opportunity to receive free academic support at AUM. Visit the Learning Center (LC) in the WASC on second floor Library or the Instructional Support Lab (ISL) in 203 Goodwyn Hall. The LC and ISL offers writing consulting as well as tutoring in almost every class through graduate school. The LC may be reached at 244-3470 (call or walk-in for a session), and the ISL may be reached at 244-3265. ISL tutoring is first-come-first served. Current operating hours can be found at http://www.aum.edu/learningcenter.

Student Privacy Policy: The Family Education Rights and Privacy Act of 1974, as amended, (FERPA) requires institutions receiving federal monies to protect the privacy of students’ educational records. For details go to the AUM’s FERPA website: http://www.aum.edu/academics/Registrars-office

Schedule

  • Day 1: Introduction and motivations
  • Day 2: Definition of rings
  • Day 3: Homomorphism and isomorphism of rings
  • Day 4: Ideals
  • Day 5: Quotient rings
  • Day 6: Different kinds of ideals: maximal ideals and prime ideals
  • Day 7: Case study: ring of integers
  • Day 8: Case study: polynomial rings
  • Day 9: Case study: complex numbers
  • Day 10: Case study: formal and convergent power series
  • Day 11: Different kinds of rings: UFD and PID
  • Day 12: Euclidean domains
  • Day 13: Case study: Gauss integers
  • Day 14: Modules
  • Day 15: (Optional) Module over PID
  • Day 16: Definition of fields
  • Day 17: Field of fractions
  • Day 18: Case study: rational numbers, real number, complex numbers, and Laurent power series
  • Day 19: Algebraic and transcendental elements
  • Day 20: Field extensions
  • Day 21: Algebraically close fields
  • Day 22: Case study: complex numbers
  • Day 23: Case study: finite fields
  • Day 24: Case study: Puiseux series
  • Day 25: (Optional) An invitation to algebraic geometry
  • Day 26: Galois theory