MATH4033 Advanced Topics in Pure Mathematics

Credit
6 points
Offering
(see Timetable)
AvailabilityLocationMode
Semester 2UWA (Perth)Face to face
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:
MATH2031 Introduction to Pure Mathematics
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.
  • Books and other material wherever listed may be subject to change. Book lists relating to 'Preliminary reading', 'Recommended reading' and 'Textbooks' are, in most cases, available at the University Co-operative Bookshop (from early January) and appropriate administrative offices for students to consult. Where texts are listed in the unit description above, an asterisk (*) indicates that the book is available in paperback.