Abstract Algebraic Structures – MATH 423

CG • Section 8WK • 07/01/2018 to 12/31/2199 • Modified 04/06/2022

Course Description

This course focuses on developing an understanding of basic algebraic concepts and the structures of groups, group homomorphisms, rings, and ring homomorphisms through both examples and proofs.

For information regarding prerequisites for this course, please refer to the Academic Course Catalog.

Rationale

A basic understanding of algebraic systems, built on fundamental axioms, it is necessary to understand and effectively explain the process used when "doing" algebra. This course is designed to provide an axiomatic understanding of the structure of general algebraic systems which can then be applied to subsets of the real numbers. 

Course Assignment

Textbook Readings and Presentations

Course Requirements Checklist

After reading the Course Syllabus and Student Expectations, the student will complete the related checklist found in the Course Overview.

Prerequisite Quiz

The Prerequisite Quiz is a low stakes, high reward refresher quiz that should have you consider
many of the prerequisite tools and prior mathematical concepts that are required to be successful
in the course. After reading the Prerequisite Quiz Instructions, the student will complete the Prerequisite Quiz.

(CLO: A, E. FSLO: A, B)

This is a short video introduction of each student to the class and the instructor. The student must make sure that he or she can be seen and heard in the video. This assignment also acts as a trial run for the required Video Demonstrations.

Video Demonstration Assignments (2)

Each demonstration is a concise, precise, well-practiced presentation of the proof of some given proposition in abstract algebra. They serve as a way of demonstrating knowledge and practicing correct presentation of mathematical proofs in a simulated classroom setting.

(CLO: A-F, FSLO: A, B, D)

Homework Assignments (7)

Homework problems are essential to this course and students will be assigned homework problems to complete throughout the course. One homework problem out of the assigned problems will be submitted for grading in Modules 1–7.

(CLO: A-F, FSLO: A, B, D)

Homework Portfolio Assignments (2)

Homework will be assigned weekly. Module: Weeks 1–4 will be scanned into a single pdf document and sent as a homework portfolio before the Midterm Exam in Module: Week 4. Homework Assignments from Module: Weeks 5–7 will then be scanned into a single pdf document and sent as a homework portfolio. Many exam problems will come from the assigned homework.

(CLO: A-F, FSLO: A, B, D)

Quizzes: Module Video Presentation (7)

Each quiz will be timed and open-book/open-notes/open-video and will cover material from the videos in the assigned modules. The time limit for each quiz is 30 minutes.  The quizzes are some combination of T/F, multiple choice and/or fill in the blank questions.

(CLO: A-F, FSLO: A, B, D)

Exam Assignments (2)

Each exam will be timed, handwritten, and open-book/open-notes/open-video and will cover the Learn material for the assigned modules: weeks. The time limit for the Midterm Exam is 90 minutes and for the Final Exam is 2 hours. On all written work, the student is expected to write correct mathematics to avoid point deductions.

(CLO: A-F, FSLO: A, B, D)