PURE MTH 4066 - Pure Mathematics Topic E - Honours
North Terrace Campus - Semester 2 - 2021
General Course Information
Course Code PURE MTH 4066 Course Pure Mathematics Topic E - Honours Coordinating Unit 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 Coordinator: Professor Finnur Larusson
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesIn 2021, 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.
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
Required ResourcesTom Leinster's book "Basic Category Theory", freely available from arxiv.org.
Recommended ResourcesWe 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 ModesStudents 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.
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
Learning Activities SummaryTopics
Categories, functors and natural transformations
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 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 RequirementsA mark of 50 is required to pass the course.
Assessment DetailThere will be six homework assignments, due in Weeks 3, 5, 7, 9, 11, and 13, and set at least 7 days earlier.
SubmissionHomework assignments should be submitted via MyUni.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M11 (Honours Mark Scheme) Grade Grade reflects following criteria for allocation of grade Reported 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.
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