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MATH6205 Differential Geometry

Offered By Department of Maths
Academic Career Graduate Coursework
Course Subject Mathematics
Offered in First Semester, 2010, Second Semester, 2010, First Semester, 2011, and Second Semester, 2011
Unit Value 6 units
Course Description

This course introduces students to the key concepts and techniques of Differential Geometry. Possible topics include:

  • Surfaces in Euclidean space
  • General differentiable manifolds
  • Tangent spaces and vector fields
  • Differential forms
  • Riemannian manifolds
  • Gauss-Bonnet theorem

Note: Graduate students attend joint classes with undergraduates but are assessed separately.

Learning Outcomes

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the concepts and language of differential geometry and its role in modern mathematics
2. Analyse and solve complex problems using appropriate techniques from differential geometry
3. Apply problem-solving with differential geometry to diverse situations in physics, engineering or other mathematical contexts
4. Apply differential geometry techniques to specific research problems in mathematics or other fields
Indicative Assessment 4-5 written assignments involving problem-solving, proofs of theorems and extension of theory (20-25% each; LO 1, 2, 3, 4)

 

Course Classification(s) AdvancedAdvanced courses are designed for students having reached 'first degree' level of assumed knowledge, which provide a deep understanding of contemporary issues; or 'second degree' and higher levels of knowledge; or for transition to research training programs. and SpecialistSpecialist courses are designed for students having reached 'first degree' level of assumed knowledge, which provide for the acquisition of specialist skills; or 'second degree' and higher level of knowledge; or for transition to research training programs; or knowledge associated with professional accreditation.
Areas of Interest Mathematics
Eligibility Bachelor degree; with second year Mathematics. 
Requisite Statement Second year Mathematics is required. 
Consent Required Please contact admin.teaching.msi@anu.edu.au for consent to enrol in this course.
Programs Master of Mathematical Sciences
Academic Contact Dr John Urbas

The information published on the Study at ANU 2010 website applies to the 2010 academic year only. All information provided on this website replaces the information contained in the Study at ANU 2009 website.

Updated:   13 Nov 2015 / Responsible Officer:   The Registrar / Page Contact:   Student Business Solutions