PURE MTH 3023 - Fields and Modules III
North Terrace Campus - Semester 2 - 2023
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General Course Information
Course Details
Course Code PURE MTH 3023 Course Fields and Modules III Coordinating Unit Mathematical Sciences Term Semester 2 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 and (PURE MTH 2106 or PURE MTH 3007) Assumed Knowledge PURE MTH 2106, PURE MTH 3007 Biennial Course Offered in odd years Assessment Ongoing assessment, exam Course Staff
Course Coordinator: Dr Daniel Stevenson
Course Timetable
The full timetable of all activities for this course can be accessed from .
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Learning Outcomes
Course Learning Outcomes
1 Demonstrate understanding of the concepts of a field and a module and their role in mathematics. 2 Demonstrate familiarity with a range of examples of these structures. 3 Prove the basic results of field theory and module theory. 4 Explain the structure theorem for finitely generated modules over a principal ring and its applications to abelian groups and matrices. 5 Apply Galois theory to the theory of polynomial equations 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) Attribute 1: Deep discipline knowledge and intellectual breadth
Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.
1, 2, 3, 4, 5 Attribute 2: Creative and critical thinking, and problem solving
Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.
1, 2, 3, 4, 5, 6 Attribute 3: Teamwork and communication skills
Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.
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Learning Resources
Required Resources
None.Recommended Resources
J. B. Fraleigh, `A first course in abstract algebra'.
S. Lang, `Undergraduate Algebra' (available in the library as an e-book).Online Learning
Assignments, tutorial exercises, handouts, and course announcements will be posted on MyUni.
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Learning & Teaching Activities
Learning & Teaching Modes
The course will be taught as a sequence of topics and managed via My-Uni.
Each topic will be presented through a series of short topic videos, followed by quizzes to test student understanding and provide instantaneous feedback.
Each week a face-to-face active learning session will be offered together with a weekly face-to-face tutorial.
Students are expected to engage with all material on My-Uni.
Fortnightly homework assignments help students strenghten their understanding of course material, and help them gauge their progress.Workload
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Workload hours Topic videos 66 Active learning sessions 12 Tutorials 12 Online quizzes 30 Assignments 30 Mid-semester test 6 Total 156 Learning Activities Summary
Lecture Schedule Week 1 Review, Fields Review of rings. Fields: basic definitions and examples. Week 2 Fields Vector spaces, polynomials over a field, algebraic elements. Week 3 Fields Finite extensions and algebraic extensions, embeddings, algebraically closed fields. Week 4 Fields Splitting fields and normal extensions, finite fields. Week 5 Fields Galois Theory. Week 6 Fields, Modules Galois Theory (cont.). Modules: basic definitions and examples, submodules, quotient modules. Week 7 Modules Module homomorphisms, isomorphism theorems, direct sums. Week 8 Modules Finitely generated modules and free modules. Week 9 Modules Finitely generated modules over a principal ring. Week 10 Modules Finitely generated modules over a principal ring (cont.), Applications to matrices. Week 11 Modules Applications to matrices (cont.). Week 12 Modules, Review Review.
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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
It is anticipated that the examination will be invigilated and held at Wayville for students in Adelaide. Alternative arrangements will be made for remote students.Assessment task Task type Due Weighting Learning outcomes Examination Summative Examination period 50% All Homework assignments Formative and summative Weeks 3, 5, 7, 9, 11 15% All Mid-semester Test Formative and summative Week 6 20% All Quizzes Formative and summative ongoing 10% All Participation Formative and summative ongoing 5% All Assessment Related Requirements
An aggregate score of 50% is required to pass the course.Assessment Detail
Each assignment will count for 3% of the final grade. The participation grade will be determined by participation in tutorials and/or active participation in discussion. Online quizzes will be set on an ongoing basis. The mid-semester test will be held in Week 6.Assessment task Set Due Assignment 1 Week 2 Week 3 Assignment 2 Week 4 Week 5 Assignment 3 Week 6 Week 7 Assignment 4 Week 8 Week 9 Assignment 5 Week 10 Week 11 Submission
Homework assignments must be submitted on time with a signed assessment cover sheet. Assignments will be returned within two weeks. Students may be excused from an assignment for medical or compassionate reasons in accordance with the University's Modified Arrangements for Coursework Assessment Policy.Course Grading
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending 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 .
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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
- Careers Services
- Library Services for Students
- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
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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
- 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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Fraud Awareness
Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student鈥檚 disciplinary procedures.
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