Master Abstract Algebra: Course Syllabus and Key Outcomes
School
Southern New Hampshire University**We aren't endorsed by this school
Course
MAT 415
Subject
Mathematics
Date
Dec 11, 2024
Pages
6
Uploaded by Dejahnc1998
P a g e | 1Syllabus Last Updated 8/17/2024Undergraduate Course Syllabus MAT 415: Abstract Algebra Course Prerequisites MAT 299 with a grade of C or better Course Description Algebra is concerned with sets of objects and operations on these sets. This course will take students beyond the real number and polynomials to groups and other algebraic structures. In a modern, or abstract algebra course, one assumes a small number of basic properties as axioms and then proves many other properties from the axioms. This will assist the student in becoming more proficient at proof-writing. Course Outcomes •Analyze the structure of common types of groups and their subgroups •Generate permutation groups and cyclic groups •Determine the cosets of a group and apply Lagrange's theorem •Compare structures of groups by studying the characteristics of homomorphisms between groups •Identify factor groups and isomorphic groups using the fundamental theorem •Analyze the properties and structures of common types of rings, fields, and integral domains •Investigate rings of polynomials, ideals, factor rings, extension fields, and finite fields Required Materials Using your learning resources is critical to your success as a student. For this course, you will not need to purchase any materials through the SNHU Online Bookstore. Access your resources through the links provided in your course.Codio This course uses Codio, a cloud-based integrated development environment (IDE). For further information on using this resource, review the Codio Student Guide. Technical Requirements Make sure you’ve met the technical requirements to complete this course. Diversity, Equity, and Inclusion As indicated in our core values, SNHU is committed to “embrace diversity where we encourage and respect diverse identities, ideas, and perspectives by honoring difference, amplifying belonging, engaging civilly, and breaking down barriers to bring our mission to life.”
P a g e | 2Syllabus Last Updated 8/17/2024This may or will be reflected in SNHU’s curriculum as we embrace and practice diversity, equity, and inclusion (DEI) to provide the most transformative experience for our students, faculty, and staff. Because topics pertaining to DEI can be sensitive, please remember that embodying and practicing diversity, equity, and inclusion is one of our core values that you will encounter throughout the academic experience. In higher education, we are expected to think and engage critically. Use a growth mindset to embrace the diverse readings, course assignments, and experiences of your peers and faculty. For more information about DEI at SNHU, please visit our website at the Office of Diversity and Inclusion. Instructor Availability and Response Time Your class interaction with the instructor and your classmates will take place on a regular, ongoing basis. Your instructor will be actively engaged within the course throughout the week. You will normally communicate with your instructor in the weekly discussions or the General Questions discussion topic so that your questions and the instructor’s answers benefit the entire class. You should feel free, however, to communicate with your instructor via SNHU email at any time, particularly when you want to discuss something of a personal or sensitive nature. Your instructor will generally provide a response within 24 hours. Instructors will post grades and feedback (as applicable) within seven days of an assignment’s due date, or within seven days of a late submission.Grade Distribution Assignment Category Number of Graded Items Point Value per Item Total Points Discussion: Getting Started 1 50 50 Discussion: Applications 1 50 50 Exercises 7 50 350 Quiz 2 125 250 Final Exam 1 300 300 Total Course Points:1,000This course may also contain non-graded activities. The purpose of these non-graded activities is to assist you in mastering the learning outcomes in the graded activity items listed above. University Grading System: Undergraduate Grade Numerical Equivalent Points A 93–100 4 A˗90–92 3.67 B+ 87–89 3.33 B 83–86 3 B˗80–82 2.67 C+ 77–79 2.33 C 73–76 2 C˗70–72 1.67
P a g e | 3Syllabus Last Updated 8/17/2024Grade Numerical Equivalent Points D+ 67–69 1.33 D 60–66 1 F 0–59 0 I Incomplete IF Incomplete/Failure * IP In Progress (past end of term) W Withdrawn * Please refer to the policy page for information on the incomplete grade process. Grading Guides Specific activity directions, grading guides, posting requirements, and additional deadlines can be found in the Assignment Information section of the course. Weekly Assignment Schedule All readings can be found within each module of the course, and assignment instructions can be found in the Assignment Information section of the course. Assignments and discussion posts during the first week of each term are due by 11:59 p.m. Eastern Time. Assignments and discussion posts for the remainder of the term are due by 11:59 p.m. of the student’s local time zone.Module Topics and Assignments One Groups, Part I Abstract Algebra: Theory and Applications, Chapters 3 and 4 1-1 Discussion: Getting Started 1-2 Exercises Two Groups, Part II Abstract Algebra: Theory and Applications, Chapters 5, 6, and 9 2-1 Exercises Three Groups, Part III Abstract Algebra: Theory and Applications, Chapters 10, 11, and 13 3-1 Exercises 3-2 Quiz: Modules 1–3 Four Rings Abstract Algebra: Theory and Applications, Chapters 16, 17, and 18 4-1 Exercises Five Fields, Part I Abstract Algebra: Theory and Applications, Chapters 20 and 21 5-1 Exercises
P a g e | 4Syllabus Last Updated 8/17/2024Module Topics and Assignments Six Fields, Part II Abstract Algebra: Theory and Applications, Chapters 22 and 23 6-1 Exercises 6-2 Quiz: Modules 4–6 Seven Sylow Theorems Abstract Algebra: Theory and Applications, Chapter 15 7-1 Final Exam Eight Applications Abstract Algebra: Theory and Applications, Chapters 7 and 8 8-1 Discussion: Applications 8-2 Exercises Course Participation Course participation is required within the first week of the term for all online courses. Participationin this context is defined as completing one graded assignment during the first week of the course. Otherwise, students will be administratively removed for nonparticipation. Students who do not participate during the first week may forfeit their rights to be reinstated into the course. Students who stop attending a course after the first week and who do not officially withdraw will receive a grade calculated based on all submitted and missed graded assignments for the course. Missed assignments will earn a grade of zero. See the course withdrawal policy and the full attendance policy for further information. Late Assignments Students who need extra time may submit assignments (excluding discussion board postings) up to one week after the assignment due date. Discussion board submissions will not be accepted for credit after the deadline except in extenuating circumstances. •A penalty of 10 percent of the total value of the assignment will be applied to the grade achieved on the late assignment regardless of the day of the week on which the work is submitted. •Students who submit assignments more than one week late will receive a grade of zero on the assignment unless they have made prior arrangements with the instructor. Students must submit all assignments no later than 11:59 p.m. (in their own time zone) on the last day of the term. No assignments are accepted after the last day of the term unless an incomplete has been submitted. See the incomplete grades policy. There may be times an instructor makes an exception to the late assignment policy. Instructors may accept late work, including discussion board posts, with or without prior arrangement. •Exceptions to the late policy on these grounds are left to the instructor’s discretion, including whether the late penalty is applied or waived. Students should not assume that they will be allowed to submit assignments after the due dates.
P a g e | 5Syllabus Last Updated 8/17/2024•If an instructor finds that they are unable to determine whether an exception to the late policy would be appropriate without documentation, the collection and review of student documentation should be handled through the Dispute Resolution team in order to protect the student’s privacy. In these cases, students should file a Student Concern Dispute form to have the circumstances reviewed. If a student is experiencing (or knows they will experience) a circumstance, including pregnancy, that is protected under the Americans with Disabilities Act or Title IX, they are encouraged to contact the Online Accessibility Center (OAC) as soon as possible to explore what academic accommodations might be offered. Instructors must honor all deadlines established through the OAC. Student Handbook Review the student handbook. ADA/504 Compliance Statement Southern New Hampshire University (SNHU) is dedicated to providing equal access to individuals with disabilities in accordance with Section 504 of the Rehabilitation Act of 1973 and with Title III of the Americans with Disabilities Act (ADA) of 1990, as amended by the Americans with Disabilities Act Amendments Act (ADAAA) of 2008. SNHU prohibits unlawful discrimination on the basis of disability and takes action to prevent such discrimination by providing reasonable accommodations to eligible individuals with disabilities. The university has adopted the ADA/504 Grievances Policy (version 1.2 effective October 16, 2017), providing for prompt and equitable resolution of complaints regarding any action prohibited by Section 504 or the ADA. For further information on accessibility support and services, visit the Disability and Accessibility Services webpage. Academic Integrity Policy Southern New Hampshire University requires all students to adhere to high standards of integrity in their academic work. Activities such as plagiarism and cheating are not condoned by the university. Review the full academic integrity policy. AI Usage Guidelines We recognize there are a variety of generative AI programs available to assist in your work. Generative AI programs are not a replacement for human creativity, originality, or critical thinking. However, within limited circumstances, and with proper citation, generative AI may be used as a tool in this course. For further guidance, review this student guide to generative AI. Copyright Policy Southern New Hampshire University abides by the provisions of United States Copyright Act (Title 17 of the United States Code). Any person who infringes the copyright law is liable. Review the full copyright policy. Use of Open Educational Materials Students may encounter openly licensed learning materials such as open access (OA) publications and open educational resources (OERs) in their courses. Southern New Hampshire University uses these openly licensed
P a g e | 6Syllabus Last Updated 8/17/2024materials in compliance with the stated license terms on the material. Students must also ensure that any uses outside of this course follow the license terms of the material. The selection of these materials adheres to SNHU’s accepted guidelines on course material adoption. Withdrawal Policy Review the full withdrawal policy. Southern New Hampshire University Policies More information about SNHU policies can be found on the policy page.