Introduction to Discrete Mathematics (MAST20036)

This subject explores the study of finite mathematical structures, focusing on counting, constructing, and analysing discrete objects. A key aspect is the development of efficient methods and algorithms for enumeration and computation. 

The subject provides greater depth in foundational topics, covering set theory, logic, functions, and methods of proof. Using this foundation, the subject covers enumeration, introducing fundamental counting principles, binomial and multinomial coefficients, combinatorial identities, Fibonacci numbers, and Catalan numbers; graph algorithms, including spanning trees, depth-first search, breadth-first search, and shortest path algorithms; and combinatorial structures such as Latin squares, combinatorial designs, and projective planes. To support the construction and analysis of combinatorial structures with desired properties, especially in areas such as finite geometry and error-correcting codes, key algebraic structures, including groups, rings, fields, and permutation groups, are introduced. 

This subject is designed for students interested in both the theoretical foundations and practical applications of discrete mathematics, with relevance to fields such as computer science, operations research, mathematical physics, and algebraic structures.