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Discrete mathematics underpins many areas of modern-day science. In MATH320, we explore selected topics in discrete mathematics in greater depth and detail. In particular, we investigate some technical methods that allow for elegant solutions to more advanced enumeration questions, and explore the structural properties of directed graphs and partially-ordered sets (posets). Topics covered: Term 1: Combinatorial enumeration: Binomial identities and direct enumeration. Principle of Inclusion and Exclusion; Generating functions (ordinary and exponential). Lagrange inversion and applications. Term 2: Directed graphs and posets: Basic Ramsey theory, theory of directed graphs (structural results, algorithms, algebraic methods, phase transitions) and partially-ordered sets (Möbius inversion, Dilworth Theorem).
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Employable, innovative and enterprising
Students will develop key skills and attributes sought by employers that can be used in a range of applications.
Engaged with the community
Students will have observed and understood a culture within a community by reflecting on their own performance and experiences within that community.
30 points from MATH201, MATH202, MATH203, MATH220, MATH240, EMTH210, EMTH211.
Students must attend one activity from each section.
Domestic fee $824.00
International fee $4,750.00
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
This course will not be offered if fewer than 15 people apply to enrol.
For further information see
Mathematics and Statistics