Advanced Discrete Mathematics

This subject has the following teaching availabilities in 2016:

170 hours

None

It is recommended that students have completed third year subjects in graph theory and/or discrete mathematics equivalent to one of the following

None.

For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry.

The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/

The subject consists of three main topics. The bijective principle with applications to maps, permutations, lattice paths, trees and partitions. Algebraic combinatorics with applications rings, symmetric functions and tableaux. Ordered sets with applications to generating functions and the structure of combinatorial objects.

After completing the subject students will gain:

• an advanced knowledge of advanced discrete mathematics topics drawn from: Ramsey theory, graph theory, posets and lattices, enumeration, integer partitions, combinatorial designs, and finite geometries;
• the ability to pursue further studies in this and related areas.

Up to 36 pages of written assignments (36%: four assignments worth 12% each, due during the semester), a 3-hour written examination (64%, in the examination period).

None

TBA

This subject is not available as a breadth subject.

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

• problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
• analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
• collaborative skills: the ability to work in a team;
• time-management skills: the ability to meet regular deadlines while balancing competing commitments.