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Introduction to Discrete Mathematics (MAST20036)
Undergraduate level 2Points: 12.5On Campus (Parkville)
Overview
| Availability | Semester 1 - On Campus |
|---|---|
| Fees | Look up fees |
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.
Intended learning outcomes
On completion of this subject, students should be able to:
- reason using fundamental combinatorial concepts, including enumeration techniques, permutations, and graph algorithms;
- apply counting principles, bijective arguments, and algebraic methods to solve combinatorial problems;
- construct and analyse combinatorial proofs, demonstrating logical reasoning and mathematical rigour; and
- implement combinatorial techniques to solve problems related to research and industry.
Generic skills
- 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.
Last updated: 8 December 2025