Abstract Algebraic Systems – MATH 520

CG • Section 8WK • 11/08/2019 to 04/16/2020 • Modified 07/28/2020

Course Description

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

Prerequisite

Math 510

Rationale

A basic understanding of algebraic systems, built on the fundamental axioms, is necessary to understand and effectively explain the processes 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.

Measurable Learning Outcomes

Upon successful completion of this course, the student will be able to:

  1. Write definitions of terms associated with abstract algebra.
  2. Classify groups of small order.
  3. Construct proofs of both previously demonstrated and newly formed theorems and exercises.
  4. Apply abstract concepts to concrete examples.
  5. Generalize specific examples to focus on abstract properties.
  6. Analyze various sets and operations to determine algebraic structure. Explain differences between the set of real numbers under basic operations and general abstract algebraic systems.

Course Assignment

Textbook Readings and Lecture Presentations

Course Requirements Checklist

After reading the Course Syllabus and Student Expectations, the student will complete the related checklist found in Module/Week 1.

Introduction Video

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 Demonstrations

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

Homework Portfolios (2)

Homework will be assigned weekly.  Weeks 1 – 4 will be scanned into a single document and sent as a homework portfolio before the Midterm Exam in week 4.  Homework from weeks 5 – 8 will be scanned into a single document and sent as a homework portfolio before the Final Exam in week 8.  Many exam problems will come from the assigned homework.

Quizzes (7)

Each quiz will be timed, handwritten, and open-book/open-notes/open-video and will cover material from the videos in the assigned modules/weeks. 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.

Exams (2)

Each exam will be timed, handwritten, and open-book/open-notes/open-video and will cover the Reading & Study material for the assigned modules/weeks. The time limit for the Midterm Exam is 1 hour and 30 minutes, while the time limit for the Final Exam is 2 hours. On all written work, the student is expected to write correct mathematics to avoid point deductions.