MATH4033 Advanced Topics in Pure Mathematics

Credit
6 points
Offering
(see Timetable)

If this unit does not have an online alternative, then 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.

AvailabilityLocationMode
Semester 2UWA (Perth)Face to face Predominantly face-to-face. On campus attendance required to complete this unit. May have accompanying resources online.
Details for undergraduate courses
  • Honours option in Mathematics and Statistics [Bachelor of Science (Honours)]
Content
This unit covers topics from either combinatorics or analysis, typically alternating from year to year depending on student background and needs and lecturer availability. Topics from combinatorics may include graph theory, algebraic combinatorics, and finite geometry. These may include structural theory of graphs, matroid theory, Cayley graphs, highly symmetrical graphs, symmetrical block designs, projective geometry, projective planes, and generalised polygons. Topics from analysis and algebraic topology may include the contraction mapping principle, elements of linear analysis and spectral theory, unique solvability of ordinary differential equations, inverse and implicit function theorem, critical points and regular values, winding numbers, simplicial or singular homology, differential forms, integration on manifolds and de Rham cohomology.
Outcomes
Students are able to (1) develop mathematical intuitions and the ability to articulate these intuitions within a formalism at an appropriate level; (2) prove results about mathematical structures and construct examples demonstrating key concepts; and (3) demonstrate a deep understanding of the structures and techniques involved in proving the main results in the field.
Assessment
Indicative assessments in this unit are as follows: (1) assignments; (2) mid-semester test; and (3) a final examination. Further information is available in the unit outline.

Supplementary assessment is not available in this unit.
Unit Coordinator(s)
Associate Professor Michael Giudici
Unit rules
Prerequisites:
MATH3031 Algebraic Structures and Symmetry (ID 375) or MATH3032 Topology and Analysis (ID 372) or MATH3033 Geometry (ID 6597)
Contact hours
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 one week prior the commencement of study. Reading lists and essential textbooks are subject to change each semester. Information on essential textbooks will also be made available on the Essential Textbooks. This website is updated regularly in the lead up to semester so content may change. It is recommended that students purchase essential textbooks for convenience due to the frequency with which they will be required during the unit. A limited number of textbooks will be made available from the Library in print and will also be made available online wherever possible. 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.