PURE MTH 7066 - Pure Mathematics Topic E
North Terrace Campus - Semester 2 - 2024
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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.
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Learning Outcomes
Course Learning Outcomes
In 2024, 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) 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.
3 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.
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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/1612.09375Recommended 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.
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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.Workload
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
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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
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.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:
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.
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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
- International Student Support
- Library Services for Students
- 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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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’s disciplinary procedures.
The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.
