# Discrete Mathematics

Course code MATH1510
Available in 2016

## Description

Discrete mathematics is the study of mathematical structures that are discrete, separated or distinct; in contrast with calculus which deals with continuous change. It is an important area of pure and applied mathematics, as well as providing the mathematical basis for the understanding of computers and modern computation. Discrete Mathematics is important in the sciences, where it has increasing application in many areas, an exemplar of which is the understanding of DNA sequences in molecular biology. The Discrete Mathematics course introduces first year students to the basic concepts of discrete mathematics, covering topics such as sets, logic, enumeration methods, probability, recurrence relations, induction and graph theory. The course provides important background for students pursuing a BMath degree. It covers much of the mathematics essential for students majoring in Computer Science or Software Engineering, and is a compulsory course in those degree programs.

### Availability

#### Ourimbah

• Semester 2 - 2016
• Semester 2 - 2017

#### Callaghan

• Semester 2 - 2016
• Semester 2 - 2017

### Learning Outcomes

On successful completion of the course students will be able to:

1. Be able to read, interpret and write some basic mathematical notation

2. Be able to recognise and/or construct examples of mathematical objects introduced during the course, such as sets and functions

3. Have been introduced to several mathematical models, (e.g. propositional logic, trees) including some of those underlying computing and information technology

4. Have had the opportunity to develop capacity in knowing what constitutes a valid argument, and in constructing valid arguments/proofs

5. Have had opportunity to develop problem solving skills; and been introduced to ways of thinking useful for simplifying complex situations

### Content

• Elementary set theory
• Relations and functions
• Graph theory
• Modular arithmetic
• Logic and proofs
• Enumeration techniques
• Elementary probability theory
• Recurrence relations

### Assumed Knowledge

HSC Mathematics (Bands 5 or 6), or equivalent.

### Assessment Items

Quiz: Quiz

Formal Examination: Formal examination

Written Assignment: Written Assignments

### Contact Hours

#### Callaghan

##### Lecture

Face to Face On Campus 4 hour(s) per Week for Full Term

##### Workshop

Face to Face On Campus 2 hour(s) per Week for Full Term

#### Ourimbah

##### Lecture

Online 4 hour(s) per Week for Full Term

##### Self-Directed Learning

Face to Face On Campus 1 hour(s) per Week for Full Term

##### Workshop

Face to Face On Campus 2 hour(s) per Week for Full Term