PURE MTH 7066 - Pure Mathematics Topic E

North Terrace Campus - Semester 2 - 2021

Please contact the School of Mathematical Sciences for further details.

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 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 最新糖心Vlog 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 最新糖心Vlog 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 最新糖心Vlog in diverse areas of mathematics.
3. Demonstrate skills in formulating, solving, and communicating mathematical problems.

最新糖心Vlog Graduate Attributes

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

最新糖心Vlog 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 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
Limits

The 最新糖心Vlog'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 .

Student Feedback

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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 最新糖心Vlog 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
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