Southern Utah University

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Southern Utah University
Southern Utah University
Fall Semester 2025

Abstract Algebra I (Face-to-Face)

MATH 4220-103

Course: MATH 4220-103
Credits: 3
Term: Fall Semester 2025
Department: MATH
CRN: 31677

Course Description

An introduction to the study of algebraic structures focusing on groups. Topics include subgroups, homomorphisms, factor groups, permutations, and a brief introduction to rings and fields. (Fall) [Graded (Standard Letter)] Prerequisite(s): MATH 3120 - Prerequisite Min. Grade: C Registration Restriction(s): None

Required Texts

Abstract Algebra (2025) by Andrew Misseldine

Learning Outcomes

By their efforts in this course, students should improve in the following course learning outcomes: sets, functions, equivalence relations, induction, integers, groups, Cayley tables, subgroups, Hasse diagrams, cyclic groups, roots of unity, permutation groups, dihedral groups, matrix groups, symmetry, isomorphisms, direct products, Chinese remainder theorem, cosets, Lagrange's theorem, normal subgroups, quotient groups, group homomorphisms, Cayley's theorem, kernels, isomorphism theorems, cryptography, algebraic coding theory, rings, fields, ring homomorphisms

Additionally, students will improve in the following university Essential Learning Outcomes: Quantitative Literacy, Problem Solving, Communication, and Critical Thinking.

Course Requirements

Your final grade will be determined by your acquisition of points throughout the course. Points are rewarded based upon your engagement in learning activities and positive performances on course assessments, as outlined below. If x is the number of points earned, then letter grades will be assigned based upon x according to the following bounds:
A: x ≥ 930 pts                A-: 900 ≤ x < 930 pts     
B+: 870 ≤ x < 900 pts    B:  830 ≤ x < 870 pts     B-: 800 ≤ x < 830 pts     
C+: 770 ≤ x < 800 pts    C: 730 ≤ x < 770 pts      C-: 700 ≤ x < 730 pts
D+: 670 ≤ x < 700 pts    D: 630 ≤ x < 670 pts      D-: 600 ≤ x < 630 pts     
F: x < 600 pts

A grade of UW (unofficial withdrawal) will be assigned to students who have no course engagement after the official withdrawal deadline for this course, which is 29 October 2025.

There will be three types of assignments collected in this course:
Homework - 200 points - typically three a week
Project - 200 points - semester long
Exams - 600 points - three unit exams

Course Outline

Topics by Week
  1. Sets, Functions
  2. Inverse Functions, Equivalence Relations
  3. Induction, Integers, Groups 
  4. Cayley Tables, Group Properties, Subgroups
  5. Hasse Diagrams, Cyclic Groups, Roots of Unity
  6.  Repeated Squares, Permutation Groups, Transpositions
  7.  Dihedral Groups, Cosets, Lagrange's Theorem
  8.  Symmetric Key Cryptography, Public Key Cryptography
  9.  Coding Theory, Hamming Metric, Linear Codes
  10.  Decoding, Isomorphisms, Cayley's Theorem
  11. Chinese Remainder Theorem, Direct Products, Normal Subgroups
  12. Quotient Groups, Group Homomorphisms, Kernels
  13. Isomorphism Theorems, Matrix Groups, Symmetry
  14. Rings, Fields, Ring Homomorphisms

Instructor's policies on late assignments and/or makeup work

All graded assignments have a due date posted on Canvas. Students are expected to submit all of their work by these due dates. All assignments, other than exams, will be submitted via Canvas. After each due date, Canvas will lock the submission of that assignment. For this reason, it is important to submit all assignments on time.

Understanding there is a need for reasonable accommodations to strict due dates, the following late policy applies to all course assignments. If a foreseeable event prohibits your ability to submit an assignment by its due date, then it is your responsibility to email Dr. Misseldine before the assignment's due date to explain the situation and request an extension. If requested before the due date, then nearly all extensions will be granted. If requested after the due date, the extension is most likely to be denied. Of course, in the situation of an unforeseeable event, such as illness or emergency, you are expected to email Dr. Misseldine as soon as you reasonably can to expect the situation and request an extension. All university-approved absences will be approved for extension if requested prompted. Late work submitted without approval will receive no credit.

Note that the above procedure should only be used rarely, as there is no substitute for timely submission of work. Students who need to submit more than occasional late work will need to schedule a conference with Dr. Misseldine to discuss the concern and design an accommodation and responsibility schedule to serve the best needs of the student within university policies. 

Attendance Policy

Attendance is expected but not required. If you miss class for any reason, you are responsible for the material and information, including  announcements, presented during lecture. Office hours cannot be used to teach materials which were missed from lecture.

Course Fees

$204.75

ADA Statement

Students with medical, psychological, learning, or other disabilities desiring academic adjustments, accommodations, or auxiliary aids will need to contact the Disability Resource Center, located in Room 206F of the Sharwan Smith Center or by phone at (435) 865-8042. The Disability Resource Center determines eligibility for and authorizes the provision of services.

If your instructor requires attendance, you may need to seek an ADA accommodation to request an exception to this attendance policy. Please contact the Disability Resource Center to determine what, if any, ADA accommodations are reasonable and appropriate.

Academic Credit

According to the federal definition of a Carnegie credit hour: A credit hour of work is the equivalent of approximately 60 minutes of class time or independent study work. A minimum of 45 hours of work by each student is required for each unit of credit. Credit is earned only when course requirements are met. One (1) credit hour is equivalent to 15 contact hours of lecture, discussion, testing, evaluation, or seminar, as well as 30 hours of student homework. An equivalent amount of work is expected for laboratory work, internships, practica, studio, and other academic work leading to the awarding of credit hours. Credit granted for individual courses, labs, or studio classes ranges from 0.5 to 15 credit hours per semester.

Academic Freedom

SUU is operated for the common good of the greater community it serves. The common good depends upon the free search for truth and its free exposition. Academic Freedom is the right of faculty to study, discuss, investigate, teach, and publish. Academic Freedom is essential to these purposes and applies to both teaching and research.

Academic Freedom in the realm of teaching is fundamental for the protection of the rights of the faculty member and of you, the student, with respect to the free pursuit of learning and discovery. Faculty members possess the right to full freedom in the classroom in discussing their subjects. They may present any controversial material relevant to their courses and their intended learning outcomes, but they shall take care not to introduce into their teaching controversial materials which have no relation to the subject being taught or the intended learning outcomes for the course.

As such, students enrolled in any course at SUU may encounter topics, perspectives, and ideas that are unfamiliar or controversial, with the educational intent of providing a meaningful learning environment that fosters your growth and development. These parameters related to Academic Freedom are included in SUU Policy 6.6.

Academic Misconduct

Scholastic honesty is expected of all students. Dishonesty will not be tolerated and will be prosecuted to the fullest extent (see SUU Policy 6.33). You are expected to have read and understood the current SUU student conduct code (SUU Policy 11.2) regarding student responsibilities and rights, the intellectual property policy (SUU Policy 5.52), information about procedures, and what constitutes acceptable behavior.

Please Note: The use of websites or services that sell essays is a violation of these policies; likewise, the use of websites or services that provide answers to assignments, quizzes, or tests is also a violation of these policies. Regarding the use of Generative Artificial Intelligence (AI), you should check with your individual course instructor.

Emergency Management Statement

In case of an emergency, the University's Emergency Notification System (ENS) will be activated. Students are encouraged to maintain updated contact information using the link on the homepage of the mySUU portal. In addition, students are encouraged to familiarize themselves with the Emergency Response Protocols posted in each classroom. Detailed information about the University's emergency management plan can be found at https://www.suu.edu/emergency.

HEOA Compliance Statement

For a full set of Higher Education Opportunity Act (HEOA) compliance statements, please visit https://www.suu.edu/heoa. The sharing of copyrighted material through peer-to-peer (P2P) file sharing, except as provided under U.S. copyright law, is prohibited by law; additional information can be found at https://my.suu.edu/help/article/1096/heoa-compliance-plan.

You are also expected to comply with policies regarding intellectual property (SUU Policy 5.52) and copyright (SUU Policy 5.54).

Mandatory Reporting

University policy (SUU Policy 5.60) requires instructors to report disclosures received from students that indicate they have been subjected to sexual misconduct/harassment. The University defines sexual harassment consistent with Federal Regulations (34 C.F.R. Part 106, Subpart D) to include quid pro quo, hostile environment harassment, sexual assault, dating violence, domestic violence, and stalking. When students communicate this information to an instructor in-person, by email, or within writing assignments, the instructor will report that to the Title IX Coordinator to ensure students receive support from the Title IX Office. A reporting form is available at https://cm.maxient.com/reportingform.php?SouthernUtahUniv

Non-Discrimination Statement

SUU is committed to fostering an inclusive community of lifelong learners and believes our university's encompassing of different views, beliefs, and identities makes us stronger, more innovative, and better prepared for the global society.

SUU does not discriminate on the basis of race, religion, color, national origin, citizenship, sex (including sex discrimination and sexual harassment), sexual orientation, gender identity, age, ancestry, disability status, pregnancy, pregnancy-related conditions, genetic information, military status, veteran status, or other bases protected by applicable law in employment, treatment, admission, access to educational programs and activities, or other University benefits or services.

SUU strives to cultivate a campus environment that encourages freedom of expression from diverse viewpoints. We encourage all to dialogue within a spirit of respect, civility, and decency.

For additional information on non-discrimination, please see SUU Policy 5.27 and/or visit https://www.suu.edu/nondiscrimination.

Pregnancy

Students who are or become pregnant during this course may receive reasonable modifications to facilitate continued access and participation in the course. Pregnancy and related conditions are broadly defined to include pregnancy, childbirth, termination of pregnancy, lactation, related medical conditions, and recovery. To obtain reasonable modifications, please make a request to title9@suu.edu. To learn more visit: https://www.suu.edu/titleix/pregnancy.html.

Disclaimer Statement

Information contained in this syllabus, other than the grading, late assignments, makeup work, and attendance policies, may be subject to change with advance notice, as deemed appropriate by the instructor.