# DISCRETE MATHEMATICS

MAT1DIS

2017

Credit points: 15

## Subject outline

In Discrete Mathematics you will explore some important mathematical ideas that play a key role in modern computing. Topics include number bases, logic, sets, relations, recursion, Boolean algebra and cryptography. Although Discrete Mathematics is designed in particular for those who are studying information technology, the subject is relevant and useful for any person with an interest in contemporary mathematics and its applications.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorMumtaz Hussain

Subject year levelYear Level 1 - UG

Exchange StudentsYes

## Subject particulars

### Subject rules

PrerequisitesN/A

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Special conditionsN/A

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsDiscrete mathematics for computing.PrescribedGrossman, P.3RD EDN. PALGRAVE MACMILLAN, BASINGSTOKE, 2009.

## Graduate capabilities & intended learning outcomes

01. By the end of this subject, students will be able to convert numbers between bases, carry out arithmetic in non-decimal bases, and apply some of the mathematical ideas involved in storing and manipulating numbers in a computer.

Activities:
Students are required to convert numbers between bases, carry out arithmetic in non-decimal bases, and solve mathematical problems related to the storage and manipulation of numbers in computers, in Test 1 and the exam.

02. Apply the laws of logic and truth tables to establish and verify equivalences in propositional and simple predicate logic.

Activities:
Students are required to solve a variety of problems in propositional and simple predicate logic, supported by appropriate explanations, in Tests 1 and 2 and the exam.

03. Demonstrate an understanding of basic concepts of set theory, and use the laws of sets to establish set equalities.

Activities:
Students are required to solve problems in elementary set theory, and to use the laws of sets to simplify a given expression, in Test 2 and the exam.

04. Classify, and construct examples of, binary relations according to key properties that they may or may not possess, and determine structures (e.g. partitions) that equivalence and partial order relations generate in their underlying sets.

Activities:
Students are required to solve problems on binary relations, and to construct examples of relations with specific properties, supported by appropriate explanations, in Test 2 and the exam.

05. Analyze and design simple iterative and recursive algorithms.

Activities:
Students are required to solve problems related to recursion (particularly recursively-defined sequences) and simple recursive algorithms in Test 2 and the exam.

06. Apply the laws of Boolean algebra to the simplification of Boolean expressions and design of digital circuits.

Activities:
Students are required to solve problems in Boolean algebra and its applications in the exam.

07. Encrypt and decrypt messages using fundamental secret key and public key methods.

Activities:
Students are required to encrypt and decrypt short messages in the exam.

08. Demonstrate effective written communication skills by presenting mathematical ideas and solutions to problems in a clear and logical fashion, supported by appropriate explanations and correct use of mathematical notation.

Activities:
Students are required to demonstrate effective communication skills in Tests 1 and 2 and the exam. In all assessment items, communication is one of the factors taken into account when awarding marks to question responses.

## Subject options

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Start date between: and    Key dates

## Bendigo, 2017, Semester 2, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorMumtaz Hussain

### Class requirements

Tutorial Week: 31 - 43
One 1.0 hours tutorial per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

Lecture Week: 31 - 43
Three 1.0 hours lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.