This module extends the ideas of discrete mathematics introduced in Sequences and Patterns (MATH07002). Below is a list of the topics that will be covered.
Sequences:
Recurrence relations, first and second order linear difference equations, stability of solutions, one dimensional maps, fixed points and their stability, logistic map, orbit diagram, period doubling to chaos, bifurcations
Number theory:
Divisibility, Euclid’s lemma, Euclid’s algorithm, linear Diophantine equations; definition of a prime, fundamental theorem of arithmetic, Sieve of Eratosthenes, Fermat’s factorisation method, congruences and their properties, special divisibility tests, linear congruences, Chinese remainder theorem, Fermat’s little theorem, Wilson’s theorem
Graphs, digraphs, networks, and flows:
Definition and representations of graphs, valency, paths and cycles, Hamiltonian cycle, trees, Euler’s formula, weighted graph, shortest path problem, Djikstra’s algorithm, definitions of digraph and network, flows and cuts, sources and sinks, max-flow min-cut theorem
The Graduate Attributes relevant to this module are given below:
- Academic: Critical thinker; Analytical; Inquiring; Knowledgeable; Problem-solver; Autonomous.
- Personal: Motivated; Resilient
- Professional: Ambitious; Driven.
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