MATH3032 Topology and Analysis

Credit
6 points
Offering
(see Timetable)
AvailabilityLocationMode
Semester 2UWA (Perth)Face to face
Details for undergraduate courses
  • Level 3 option in the Mathematics and Statistics major sequence
  • The area of knowledge for this unit is Mathematical and Physical Sciences
  • Category A broadening unit for Bachelor of Science students where relevant according to the broadening requirements for each student
  • Level 3 elective
Content
This unit provides an introduction to abstract methods in a continuous setting. Topics include topology and geometry from a constructive perspective in dimensions two, three and four. Students investigate, via concrete examples, homeomorphisms and diffeomorphisms of manifolds; curvature; vector bundles; and elements of the machinery for describing space-time in physics. Alternatively, topics may include Banach spaces, Hilbert spaces, projections, compact, self-adjoint, normal and unitary operators, Riesz representation theorem, the Fredholm alternative and applications to solving integral and differential equations from physics.
Outcomes
Students are able to (1) demonstrate intuition and skills in analysis and geometry and (2) understand how these geometry techniques can be applied to mechanics and physics.
Assessment
Indicative assessments in this unit are as follows: (1) assignments and (2) a final examination. Further information is available in the unit outline.

Supplementary assessment is not available in this unit except in the case of a bachelor's pass degree student who has obtained a mark of 45 to 49 overall and is currently enrolled in this unit, and it is the only remaining unit that the student must pass in order to complete their course.
Unit Coordinator(s)
Professor Luchezar Stoyanov
Unit rules
Prerequisites:
MATH2031 Introduction to Pure Mathematics
Contact hours
lectures: 3 hours per week
  • The availability of units in Semester 1, 2, etc. was correct at the time of publication but may be subject to change.
  • All students are responsible for identifying when they need assistance to improve their academic learning, research, English language and numeracy skills; seeking out the services and resources available to help them; and applying what they learn. Students are encouraged to register for free online support through GETSmart; to help themselves to the extensive range of resources on UWA's STUDYSmarter website; and to participate in WRITESmart and (ma+hs)Smart drop-ins and workshops.
  • Unit readings, including any essential textbooks, are listed in the unit outline for each unit one week prior the commencement of study. The unit outline will be available via the LMS and the UWA Handbook. Reading lists and essential textbooks are subject to change each semester. Essential textbooks can be purchased from the commercial vendors to secure the best deal. The Student Guild can provide assistance on where to purchase books if required. Books can be purchased second hand at the Guild Secondhand bookshop (second floor, Guild Village), which is located on campus. Copies of textbooks and other readings will be made available for students to access from the Library, online wherever possible as well as in print.
  • If this unit is offered as on-campus face-to-face study only, students who are presently unable to enter Western Australia and whose studies would be delayed by an inability to complete this unit, should contact the unit coordinator (details given on this page) to ascertain, on an individual case-by-case basis, if alternate arrangements can be made to support their study in this unit.