PURE MTH 7066 - Pure Mathematics Topic E
North Terrace Campus - Semester 2 - 2021
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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: Professor Finnur Larusson
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 2021, 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
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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".
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Learning & Teaching Activities
Learning & Teaching Modes
Students work through the textbook with support from the lecturer in weekly workshops. 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
Weekly study and workshop 12 96
Assignments 6 60
Total 156
Learning Activities Summary
Lectures
Categories, functors and natural transformations
Adjoints
Sets
Representables
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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 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:
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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