PURE MTH 4066 - Pure Mathematics Topic E - Honours

North Terrace Campus - Semester 2 - 2020

Please contact the School of Mathematical Sciences for further details.

  • General Course Information
    Course Details
    Course Code PURE MTH 4066
    Course Pure Mathematics Topic E - Honours
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Available for Study Abroad and Exchange Y
    Restrictions Honours students only
    Course Description Please contact the School of Mathematical Sciences for further details.
    Course Staff

    Course Coordinator: Professor Finnur Larusson

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    In 2020, the title of this course is Category Theory.

    Overview
    This course is an introduction to category theory.  Category theory is a kind of algebra that studies the fundamental structures that occur everywhere in mathematics: objects, relationships between them, relationships between relationships, and so on.  Knowledge of basic category theory is useful to all mathematicians and essential to many.  For example, modern algebraic geometry and algebraic topology could not exist without category theory.  The categorical way of thinking enables us to see common patterns in diverse areas of mathematics and guides us in our search for appropriate definitions and fruitful conjectures.  We will pay particular attention to categorical structures in the areas of mathematics that the students in the course have studied previously.

    Prerequisites
    No strict prerequisites, but the more third-year pure mathematics you have done, the better.

    Learning Outcomes
    1.  Demonstrate understanding of and ability to apply the basic concepts and theorems of category theory.
    2.  Demonstrate awareness and understanding of categorical structures in diverse areas of mathematics.
    3.  Demonstrate skills in formulating, solving, and communicating mathematical problems.

    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
    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
    1, 2, 3
    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
    3
    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
    3
  • Learning Resources
    Required Resources
    Tom Leinster's book "Basic Category Theory", freely available from arxiv.org.
    Recommended Resources
    We will follow Tom Leinster's book "Basic Category Theory", freely available from arxiv.org.  We will cover chapters 1-5 of the book.

    Other introductory books on category theory that students might want to have a look at:
    Steve Awodey, "Category Theory".
    Saunders Mac Lane, "Categories for the Working Mathematician".
    Emily Riehl, "Category Theory in Context".

  • Learning & Teaching Activities
    Learning & Teaching Modes
    Students work through the textbook with support from the lecturer.  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

    Study                                               30                                                  90 
    Assignments                                      6                                                   66
    Total                                                                                                    156



    Learning Activities Summary
    Topics

    Categories, functors and natural transformations
    Adjoints
    Sets
    Representables
    Limits


  • Assessment

    The University'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 task Task type Due Weighting Learning outcomes
    Examination Summative Examination period 70% all
    Homework assignments Formative and summative Weeks 3, 5, 7, 9, 11, 13 30% all
    Assessment Related Requirements
    A mark of 50 is required to pass the course.
    Assessment Detail
    There will be six homework assignments, due in Weeks 3, 5, 7, 9, 11, and 13, and set at least 7 days earlier.

    Submission
    Homework assignments should be submitted via MyUni.
    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 Access Adelaide.

  • 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.

  • Student Support
  • Policies & Guidelines
  • Fraud Awareness

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