PURE MTH 4107 - Groups and Rings - Honours
North Terrace Campus - Semester 1 - 2019
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General Course Information
Course Details
Course Code PURE MTH 4107 Course Groups and Rings - Honours Coordinating Unit Mathematical Sciences Term Semester 1 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Available for Study Abroad and Exchange Y Prerequisites MATHS 1012 Assumed Knowledge PURE MTH 2106 Restrictions Honours students only Assessment ongoing assessments, exam Course Staff
Course Coordinator: Associate Professor Thomas Leistner
Course Timetable
The full timetable of all activities for this course can be accessed from Course Planner.
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Learning Outcomes
Course Learning Outcomes
1. Demonstrate understanding of the idea of a group, a ring and an integral domain, and be aware of examples of these structures in mathematics. 2. Appreciate and be able to prove the basic results of group theory and ring theory. 3. Understand and be able to apply the fundamental theorem of finite abelian groups. 4. Understand Sylow's theorems and be able to apply them to prove elementary results about finite groups. 5. Appreciate the significance of unique factorization in rings and integral domains. 6. Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty. 7. Demonstrate skills in communicating mathematics orally and in writing. University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
1,2,3,4,5,6 Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
all Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
7 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
7 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
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Learning Resources
Required Resources
None.Recommended Resources
J. B. Fraleigh, “A first course in abstract algebra", Addison-Wesley, 7th edition, 2002; covers most of the material in the course in a similar manner to that presented in lectures.
M. A. Armstrong, "Groups and Symmetry", Springer, 1988; covers most of the material about groups in the course, but in addition has many geometric applications and examples.
There are many other introductory texts on abstract algebra in the library which students may find useful as references.Online Learning
Assignments, tutorial exercises, handouts, and course announcements will be posted on MyUni. -
Learning & Teaching Activities
Learning & Teaching Modes
Lecture notes for the course will be made available to students, students will be expected to read over this material in advance. The lecturer guides the students through the course material in the lectures, working through proofs and examples. In particular students will have opportunity to raise any points of difficulty arising from their own reading of the notes. Whilst they will be recorded, students will not
gain the full benefit if not able to attend in person. Fortnightly homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.
Workload
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lectures/Tutorials 33 99 Assignments 5 20 Test 1 11 Group Project 1 26 Total 156 Learning Activities Summary
In weeks 2,4,6,8,10 and 12 there will be a tutorial in the Friday class.Lecture Schedule Week 1 Groups Groups and subgroups. Week 2 Groups Permutation groups, isomorphisms, cosets and normal subgroups, conjugation. Week 3 Groups Simple groups, homomorphisms and factor groups. Week 4 Groups The first isomorphism theorem, the Jordan-Hölder theorem. Week 5 Groups Products of groups Week 6 Groups Finitely Generated Abelian groups. Week 7 Groups Groups acting on sets. Week 8 Groups The Sylow theorems and applications. Week 9 Rings Introduction to rings. Week 10 Rings Integral domains, polynomial rings. Week 11 Rings Factorisation in integral domains, ideals, eudlidean domains. Week 12 Rings Principal Ideal Domains, Unique Factorisation Domains.
There will be a mid semester test, most likely in the Wednesday class in week 7 after the mid semester break. There will be one meeting during one of the classes for discussions about the group project.Small Group Discovery Experience
A group project with a written report develops research skills, teamwork skills, and communication skills. -
Assessment
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Summary
Assessment task Task type Due Weighting Learning outcomes Examination Summative Examination period 60% All Homework assignments Formative and summative Weeks 3,5,7,9,11 15% All Mid semester test Summative Weeks 7 15% All Group Project Formative and summative Week 11 10% All Assessment Related Requirements
An aggregate score of 50% is required to pass the course.Assessment Detail
Assessment task Set Due Weighting Assignment 1 Week 1 Week 3 3% Assignment 2 Week 3 Week 5 3% Assignment 3 Week 5 Week 7 3% Assignment 4 Week 7 Week 9 3% Assignment 5 Week 9 Week 11 3% Mid semeseter test Week 7 Week 7 15% Group Project Week 3 Week 11 10%
Submission
Homework assignments must be given to the lecturer in person or emailed as a pdf. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty for that assignment. Assignments will be returned within two weeks.
Students may be elegible for an extension or exemption from an assignment for medical or compassionate reasons. Documentation is required and the lecturer must be notified as soon as possible.
Course Grading
Grades for your performance in this course will be awarded in accordance with the following scheme:
M11 (Honours Mark Scheme) Grade Grade reflects following criteria for allocation of grade Reported on Official Transcript Fail A mark between 1-49 F Third Class A mark between 50-59 3 Second Class Div B A mark between 60-69 2B Second Class Div A A mark between 70-79 2A First Class A mark between 80-100 1 Result Pending An interim result RP Continuing Continuing CN Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
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Student Feedback
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
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Student Support
- Academic Integrity for Students
- Academic Support with Maths
- Academic Support with writing and study skills
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- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
- YouX Student Care - Advocacy, confidential counselling, welfare support and advice
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Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangements Policy
- Academic Integrity Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs Policy
- Copyright Compliance Policy
- Coursework Academic Programs Policy
- Elder Conservatorium of Music Noise Management Plan
- Intellectual Property Policy
- IT Acceptable Use and Security Policy
- Modified Arrangements for Coursework Assessment Policy
- Reasonable Adjustments to Learning, Teaching & Assessment for Students with a Disability Policy
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
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