PURE MTH 7066 - Pure Mathematics Topic E

North Terrace Campus - Semester 2 - 2024

This course is available for students taking a Masters degree in Mathematical Sciences. The course will cover an advanced topic in pure mathematics. For details of the topic offered this year please refer to the Course Outline.

  • General Course Information
    Course Details
    Course Code PURE MTH 7066
    Course Pure Mathematics Topic E
    Coordinating Unit Mathematical Sciences
    Term Semester 2
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Available for Study Abroad and Exchange Y
    Course Staff

    Course Coordinator: Dr Daniel Stevenson

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    In 2024, the title of this course is Category Theory.

    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.

    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)

    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

    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

    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.


    Attribute 8: Self-awareness and emotional intelligence

    Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.

  • Learning Resources
    Required Resources
    This is a reading course. The course will make use of the following textbook

    T. Leinster, Basic Category Theory

    which is available online at: https://arxiv.org/abs/1612.09375
    Recommended Resources
    There are several other excellent references for category theory. The most suitable ones for this course are:

    E. Riehl, Category Theory in Context, available from the authors webpage at https://math.jhu.edu/~eriehl/context.pdf

    S. Mac Lane, Categories for the Working Mathematician, available online through the Barr Smith Library 

    F. W. Lawvere, S. H. Schanuel, Conceptual Mathematics: a first introduction to category theory, available in the Barr Smith Library 

    Online Learning
    Course information and resources will be posted on MyUni.

  • Learning & Teaching Activities
    Learning & Teaching Modes
    Students are expected to read and engage with the assigned reading material. There will be a weekly workshop with a mix of lecturing, students working on problems, together and with guidance from the lecturer, and consulting. Fortnightly homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    Activity Quantity Workload Hours
    Workshops 12 24
    Assignments 5 50
    Self-study 82
    Total 156
    Learning Activities Summary
    1. Categories, functors and natural transformations
    2. Adjunctions 
    3. Representables and the Yoneda Lemma
    4. Limits and colimits
    5. Adjoints, representables and 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 60% all
    Homework assignments Formative and summative Weeks 3,5,7,9,11 40% all
    Assessment Related Requirements
    A mark of 50 is required to pass the course.
    Assessment Detail
    There will be five homework assignments, due in Weeks 3, 5, 7, 9 and 11.
    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:

    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 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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