MATH-4320A (CRN 2243) Spring 2019 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.

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.

In-class discussion

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

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 Weight
Discussion 15%
Worksheets 25%
Homework 60%

Grading scale

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

Other policies

AUM COVID-19 updates. Please follow guidelines detailed in the AUM pandemic plan relating to the COVID-19 pandemic.

Technology equipment expectation. Access to computers and stable Internet connection are expected. Students who do not have their own equipment can use AUM open labs including labs found in the first floor of the Taylor center and the second floor of the library.

Syllabus contingency plan. Should the Alabama Department of Public Health, the Governor, or Chancellor determine the university discontinue face-to-face (in-person) instruction in the interest of safety, this course would be converted to a virtual-only format. If normal class and/or lab activities are disrupted due to illness, emergency, or crisis situation (such as a COVID-19 outbreak), the syllabus and other course plans and assignments may be modified to allow completion of the course. If this occurs, an addendum to the syllabus and/or course assignments will replace the original materials.

In case the instructor cannot attend due to COVID-related matter, a back-up instructor will be arranged by the Department of Mathematics.

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. If you do, you will receive an “F” in the course. 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

Academic support. Student Success Advising in the WASC can be scheduled through Advisor Trac, email at wasc@aum.edu, or by calling our front desk at 334.244.3230. ISL: Tutoring appointments can be scheduled online by filling out the form at http://www.aum.edu/tutoringapp.

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 reviews
  • Day 2: Definition of rings, homomorphism, isomorphism, ideals, and quotient rings
  • Day 3: Different kinds of ideals: maximal ideals and prime ideals
  • Day 4: Case study: ring of integers
  • Day 5: Case study: polynomial rings and power series rings
  • Day 6: Case study: complex numbers
  • Day 7: Different kinds of rings: UFD and PID
  • Day 8: Euclidean domains
  • Day 9: Case study: Gauss integers
  • Day 10: Definition of fields and fields of fractions
  • Day 11: Case study: rational numbers, real number, complex numbers, and Laurent power series
  • Day 12: Baby steps in algebraic geometry
  • Day 13: Applications of algebraic geometry
  • Day 14: Modules
  • Day 15: Module over PID
  • Day 16: Discussions
  • Day 17: Algebraic and transcendental elements
  • Day 18: Field extensions
  • Day 19: Algebraically close fields
  • Day 20: Case study: complex numbers
  • Day 21: Case study: finite fields
  • Day 22: Case study: Puiseux series
  • Day 23: Nullstensatz
  • Day 24: Discussions