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This subject is concerned with the study of objects, which are finite in number and typically computable. At a computational level one seeks efficient algorithms and methods for construction and counting of the objects.
The main topics to be covered are: enumeration, permutations, designs, finite geometry, words, Ramsey theory and physical combinatorics. Designs are relevant to statistics, Ramsey theory to computer science, and physical combinatorics to mathematical physics. Words are useful for representing and constructing objects and relating combinatorial objects to algebraic structures.
Intended learning outcomes
On completion of this subject, the student should:
- comprehend the features characterizing problems in discrete combinatorial mathematics;
- develop skills required to analyze and solve problems in discrete combinatorial mathematics;
- appreciate the overlap between discrete mathematics and other areas of applied and pure mathematics.
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 andexpress 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.
Last updated: 3 March 2021