Advanced Discrete Mathematics

This subject is not offered in 2013.

Three contact hours per week and seven hours private study.

None

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 four main topics. These are combinatorial logic by way of tilings and Sperner's lemma; combinatorics on words and Sturmian sequences; bijective enumeration with applications to maps, permutations, lattice paths and trees; integer partitions, symmetric functions and tableaux.

After completing the subject students will gain:

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

Up to 50 pages of written assignments (48%: four assignments worth 12% each, due during the semester), a 3-hour written examination (52%, 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.