PURE MTH 7023 - Pure Mathematics Topic D
North Terrace Campus - Semester 2 - 2022
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General Course Information
Course Details
Course Code PURE MTH 7023 Course Pure Mathematics Topic D Coordinating Unit Mathematical Sciences Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Available for Study Abroad and Exchange Y Assessment Ongoing assessment, exam Course Staff
Course Coordinator: Associate Professor Sanjeeva Balasuriya
Course Timetable
The full timetable of all activities for this course can be accessed from .
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Learning Outcomes
Course Learning Outcomes
In 2016, the topic of this course is Differential and Algebraic Topology.
Syllabus
This course is part of the geometry/topology sequence. However, its methods also underlie part of the basic theory of partial differential equations, which appears, roughly speaking, as an infinite-dimensional extension of these ideas.
Aims:
* To define the degree of a smooth map and give standard topological applications
* To show existence of embeddings of compact smooth manifolds into Euclidean space
* To define and study transversality results
* To study regular and singular values of smooth maps and Sard's theorem
* brief introduction to Morse theory
* brief introduction to surgery theory
* brief introduction to K-theory
Other topics not covered in Topic A eg some Riemannian geometry, Inverse and implicit function theorems etc
Advanced topics if time permits:
* brief introduction to the Dirac operator and index theory
(here is where Topic B is required)
Assumed knowledge:
Topic A (Murray's course in semester 1)
Topic B (Rosenberg's course in semester 1)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
Video recordings, short writeups, research publications and other ancillary material will all be provided via the course's MyUni site.Recommended Resources
Online Learning
This course will have an active MyUni website. -
Learning & Teaching Activities
Learning & Teaching Modes
The learning in this course will be governed by modern pedagogical techniques, with no traditional lectures. A combination of the concepts of flipped classrooms, active learning, discovery-based learning, peer evaluations, and assessments for learning will be employed.Workload
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Workshops (includes presentations, and prior work) 24 90 Problem sets 4 36 Final project 1 30 Total 156 Learning Activities Summary
The course material will be associated with the following sections, each of which will be of roughly two weeks duration:
1. Theoretical preliminaries: existence, uniqueness, continuity in initial conditions
2. Phase space: invariant sets, Lasalle invariance, Hamiltonian systems, Lyapunov functions, alpha and omega limits sets
3. Critical points and local behaviour: stability, Hartman-Grobman theorem, stable and unstable manifolds, centre manifolds
4. Poincare maps: critical points for maps, Poincare maps, Poincare-Bendixson theorem, van der Pol oscillator
5. Local bifurcations: saddle-node, transcritical, pitchfork, Hopf, period-doubling, establishment via the implicit function theorem
6. Chaos: Smale horseshoe map, symbolic dynamics, Smale-Birkhoff theorem, Melnikov methods
The delivery of these sections will be via the two workshop sessions per week, run in student-centred mode, coupledwith prior readings/viewings. -
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 Type Weighting Learning Outcomes Problem sets (4) Formative and Summative 44% All Presentations (instructor-reviewed) Formative and Summative 16% All Presentations (peer-reviewed) Formative and Summative 6% All Active participation (instructor+peer-reviewed) Formative and Summative 10% All Final project Summative 24% All Assessment Detail
No information currently available.
Submission
No information currently available.
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 .
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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
- Library Services for Students
- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
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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
- 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鈥檚 disciplinary procedures.
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