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MTH129 Discrete Mathematics

Discrete mathematics explores finite mathematic objects such as the integers, graphs, and logical statements which assume distinct and separated values. The importance of discrete mathematics has greatly increased with the development of digital computers which themselves operate in discrete steps and store data in discrete units (bits). Students will learn the concepts and notation which are fundamental in studying several areas of computer science, including computer algorithms, data structures, programming languages, cryptography, and software development.

Availability

The subject is available in Session 2, with 60 students on campus at the Bathurst Campus and online at the Bathurst Campus.

Subject Information

Grading System

The grading system for this subject is HD/FL.

Duration

The duration of this subject is one session.

School

The subject is offered by the School of Computing and Mathematics.

Learning Outcomes

Upon successful completion of this subject, students should:

• be able to recognise and use mathematical notation and operations to simplify expressions and prove properties of sets, formal logic, and computer circuits and other discrete objects;
• be able to follow and apply simple mathematical statements and proofs;
• be able to understand that numbers can be represented in several bases, and be able to reason in non-decimal bases such as binary and hexadecimal;
• be able to work with discrete probabilities, and the related statistics such as expectations and variances;
• be able to understand the basic algorithms for analysing graphs, apply them to examples, and to estimate running times;
• be able to analyse growth rates in terms of recursions and recurrence equations;

Syllabus

This subject will cover the following topics:

• Sets: operations on sets, algebra of sets, and Venn diagrams.
• Logic: truth tables, propositional calculus, and types of proof.
• Number systems: binary and hexadecimal systems, and principles of counting.
• Discrete probability functions, expected value and variance, conditional probability, and independence.
• Binomial and Poisson distributions, bi-variate distributions, and random numbers.
• Graphs: types of graphs, traversibility, planarity, digraphs, and trees. Adjacency matrices, maximal flow, and minimum spanning algorithms.
• Recursion, recursive definitions, and algorithms, solution of recurrence equations, big "O" notation, and complexity of algorithms.
• Boolean algebra and logic circuits.