最新糖心Vlog

PURE MTH 4123 - Fields and Modules - Honours

North Terrace Campus - Semester 2 - 2023

This subject presents the foundational material for the last of the basic algebraic 最新糖心Vlog pervading contemporary pure mathematics, namely fields and modules. The basic definitions and elementary results are given, followed by two important applications of the theory: to the classification of finitely generated abelian groups, and to Jordan canonical form for matrices. The subject concludes by returning to fields to present interesting applications of the theory. Fields: vector spaces, matrices, characteristic values; extension fields. Modules: finitely generated modules over a PID; canonical forms for matrices; Jordan canonical form. Applications of fields to algebraic and geometric problems.

  • General Course Information
    Course Details
    Course Code PURE MTH 4123
    Course Fields and Modules - Honours
    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
    Restrictions Honours students only
    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 .

  • 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 最新糖心Vlog.
    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 the theory in the course to solve a variety of problems at an appropriate level of difficulty.
    6 Demonstrate skills in communicating mathematics orally and in writing.
    最新糖心Vlog Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    最新糖心Vlog 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.

    6
  • 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.


  • 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 groups and rings.  Fields: basic definitions and examples.
    Week 2 Fields Vector spaces, polynomials over a field, field extensions, algebraic elements.
    Week 3 Fields Embeddings, primitive elements, splitting fields.
    Week 4 Fields Galois theory.
    Week 5 Fields Algebraic closure, finite fields.
    Week 6 Fields, Modules Finite fields (cont.).  Modules: basic definitions and examples, submodules, quotient modules.
    Week 7 Modules Module homomorphisms, isomorphism theorems, torsion, free modules, cyclic modules, direct sums.
    Week 8 Modules Finitely generated modules over a principal ring.
    Week 9 Modules Applications to abelian groups and matrices.
    Week 10 Modules Applications to matrices (cont.).  The exponential of a matrix.  The axiom of choice and Zorn's lemma.
    Week 11 Modules Applications of the axiom of choice and Zorn's lemma.  Tensor products.
    Week 12 Modules, Review Tensor products (cont.).  Review.


    Tutorials in Weeks 2, 4, 6, 8, 10 and 12 cover the material of the previous two weeks.
  • Assessment

    The 最新糖心Vlog's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Assessment taskTask typeDueWeightingLearning 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
    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 Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    Assessment taskSetDue
    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
    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.
    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 最新糖心Vlog'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:

    M11 (Honours Mark Scheme)
    GradeGrade reflects following criteria for allocation of gradeReported 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 .

  • Student Feedback

    The 最新糖心Vlog 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 最新糖心Vlog 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.

  • Student Support
  • Policies & Guidelines
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