PURE MTH 4013 - Pure Mathematics Topic D - Honours
North Terrace Campus - Semester 2 - 2025
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General Course Information
Course Details
Course Code PURE MTH 4013 Course Pure Mathematics Topic D - Honours Coordinating Unit Mathematical Sciences Term Semester 2 Level Undergraduate Location/s North Terrace Campus Units 3 Available for Study Abroad and Exchange Y Prerequisites At least 18 units of Mathematical Sciences courses at Level III Restrictions Honours students only Assessment Ongoing assessment, exam Course Staff
Course Coordinator: Dr Michael Albanese
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
The topic of this course in 2025 is Lie Groups and Lie Algebras.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.
all 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.
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Learning Resources
Required Resources
Notes will be provided.Recommended Resources
There are a lot of books about Lie groups and Lie algebras that you could use to supplement the notes and add to your learning. Here are just a few:
- Erdmann & Wildon - Introduction to Lie algebras
- Varadarajan - Lie Groups, Lie Algebras, and Their Representations
- Godement - Introduction to the Theory of Lie Groups
- Warner - Foundations of Differentiable Manifolds and Lie Groups
The following two books focus on matrix Lie groups, but are still worth your time:
- Hall - Lie Groups, Lie Algebras, and Representations
- Stillwell - Naive Lie Theory
- Kirillov - An introduction to Lie groups and Lie algebras
- Duistermaat & Kolk - Lie Groups
- Knapp - Lie Groups Beyond an Introduction
- Humphreys - Introduction to Lie Algebras and Representation Theory
- Adams - Lectures on Lie Groups
- Chevalley - Theory of Lie Groups I
Online Learning
This course will have an active MyUni website. -
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 76 Total 150 Learning Activities Summary
Week 1: Review of smooth manifolds
Week 2: Definitions of Lie groups and Lie algebras, examples
Week 3: Exponential map
Week 4: Lie subgroups and Cartan's Theorem
Week 5: Classical groups and the Lie group-Lie algebra correspondence
Week 6: Adjoint representation
Week 7: Solvable and nilpotent Lie algebras
Week 8: Engel's Lemma and Lie's Theorem
Week 9: Toral subalgebras
Week 10: Roots
Week 11: Dynkin diagrams
Week 12: Classification of complex semisimple Lie algebras -
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 One week after assigned 40% All Assessment Related Requirements
An aggregate score of 50% is required to pass the course.Assessment Detail
There will be five homework assignments distributed approximately once every two weeks across the semester. There will also be a final examination.Submission
Homework assignments must be submitted on MyUni as pdf files. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty for that assignment.Course Grading
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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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.
