Course Title: Design complex algorithms using mathematical and scientific principles

Part B: Course Detail

Teaching Period: Term1 2011

Course Code: MATH7039

Course Title: Design complex algorithms using mathematical and scientific principles

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C6068 - Advanced Diploma of Computer Science

Course Contact: Raymond Rozen

Course Contact Phone: +61 3 9925 4699

Course Contact Email: rar@rmit.edu.au


Name and Contact Details of All Other Relevant Staff

Michael Cobucci
Building 51, level 06, Room 04
+61 3 9925 4898
michael.cobucci@rmit.edu.au

Nominal Hours: 60

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites

MATH 7012C

Course Description

A selection of topics including,
Matrices and Simultaneous Equations
Vectors
Integral Calculus
Numerical Methods
Laboratory Techniques
Differential Equations


National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

VBP029 Design complex algorithms using mathematical and scientific principles

Element:

Apply mathematical/scientific method to the process

Performance Criteria:

3.1 OH&S requirements for carrying out the work are followed.

3.2 Model of the process is created.

3.3 Appropriate computations are performed.

3.4 If appropriate, relevant computer application software is used to aid solution.

3.5 Decisions for dealing with unexpected situations are made from discussions with appropriate personnel, job specifications and enterprise procedures.

3.6 Methods for dealing with unexpected situations are selected on the basis of safety and specified work outcomes.

Element:

Identify the process for applying mathematical/scientific principles

Performance Criteria:

1.1 OH&S and environmental requirements for a given work area are obtained and understood.

1.2 The process is determined through analysis of a real-life or laboratory situation.

1.3 The requests, design briefs or equivalent are clarified with the appropriate personnel.

1.4 Where appropriate, expert advice is sought with respect to the process and according to enterprise procedures.

Element:

Select appropriate mathematical/scientific method

Performance Criteria:

2.1 OH&S requirements for carrying out the work are followed.

2.2 Industry codes, regulations and technical documentation relevant to the process are interpreted and understood.

2.3 Where appropriate, tables, graphs and software packages are used to obtain computational data.

2.4 The appropriate assumptions underlying the solution are made and recorded.

2.5 Resources required are identified, obtained and checked as fit for purpose.

2.6 The most appropriate method of modelling is selected and can be justified.

Element:

Verify and interpret results

Performance Criteria:

4.1 OH&S requirements for completing the work are followed.

4.2 Results are verified, interpreted and discussed with appropriate personnel.

4.3 Results are documented, graphed or charted.


Learning Outcomes


Apply mathematical/scientific method to the process
Identify the process for applying mathematical/scientific principles
Select appropriate mathematical/scientific method
Verify and interpret results


Details of Learning Activities

Learning Activities for this course may include

• Teacher directed face-to face delivery of lessons
• Class discussions
• Pair/Group discussion
• Small group workshops
• Revision quizzes
• Worksheets
• Laboratory experiments
• Record keeping of experiments
• Presentations
• Research activities
• Mathematical problem solving
• Note taking / Data collection
• Graphing activities
• Problem solving
• Use of calculator
• Use of computer, eg software programs and the Internet

Topics
1. Matrices and Simultaneous equations

• Operation between matrices
• Determinants of a matrix
• Matrices and systems of linear equations

2. Vectors
• Vectors and scalars
• Vector notation
• Addition of vectors
• Subtraction of vectors
• Scalar multiplication of vectors
• The negative of a vector
• The zero vector
• Position vectors in 2 dimensions
• Algebra of vectors in two dimensions
• Use of unit vectors
• Scalar products and component forms
• Angle between vectors
• Projections
• Dot and cross products
• Complex numbers and vectors

3. Functions and Relations
• Set Notation
• Graphs (Functions and relations).
• Domain and range.
• Types of functions and relations.
• Function notation
• Further Types of functions -

4. Differential equations
• Limits
• First Principles
• Basic rules for differentiation
• Higher derivatives
• Chain rule
• Product rule and Quotient rule
• Derivatives of trigonometric and exponential functions

5. Integration
• Introduction to Integration
• Basic Integration
• Remember the C
• Definitive Integration
• Areas
• Integration of basic trigonometric and exponential functions.


Teaching Schedule

Week
Semester 1
2011
Performance Criteria Section Title Topic Problem Set
Week 1
(Class 1 - Semester 1)

1.1
2.1
2.2
3.1
4.1

Introduction to the Course and discussion of
OH & S
Matrices
Operation between matrices. Start
Set 1A
Set 1B


Week 1
(Class 2 - Semester 1) 






1.2
1.3
1.4
2.3
2.4
3.2
3.3
Matrices Operation between matrices. Determinants of a matrix.Set 1A
Set 1B
Week 2
(Class 1 - Semester 1)  




1.2
1.3
1.4
2.3
2.4
3.2
3.3
Matrices Operation between matrices.Determinants of a matrix.
Set 1A
Set 1B
Set 1C
Week 2
(Class 2 - Semester 1)
 1.2
1.3
1.4
2.3
2.4
3.2
3.3
Matrices Operation between matrices Determinants of a matrix.  



.
Set 1A
Set 1B
Set 1C
Week 3
(Class 1 - Semester 1)
1.2
1.3
2.3
2.4
3.2
3.3
 Matrices Matrices and systems of linear equationsSet 1D
Set 1E
Set 1F
 
Week 3
(Class 2 - Semester 1) 
 


1.2
1.3
2.3
2.4
2,6
3.2
3.3
 MatricesMatrices and systems of linear equationsSet 1D
Set 1E
Set 1F
 Week 4
(Class 1 - Semester 1) 






1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
3.6
  Vectors Vectors and Scalars

Vector notation

Addition of vectors

Subtraction of vector
Set 2A
Set 2B
 Week 4
(Class 2 - Semester 1)
1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
3.6
 Vectors Scalar multiplication of vectors

The negative of a vector

The zero vector
Set 2C
Set 2D
 Week 5
(Class 1 - Semester 1) 
 

  
 

1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
3.6
 Vectors

Position vectors in 2 dimensions

Algebra of vectors in two dimensions

Set 2E
Set 2F
Set 2G
 Week 5
(Class 2 - Semester 1)
 1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
 Vectors  Position vectors in 2 dimensions
Algebra of vectors in two dimensions
Set 2E
Set 2F
Set 2G
 Week 6
(Class 1 - Semester 1) 
1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
Vectors

 Scalar products and component forms Set 2H
Set 2I
Set 2J
Week 6
(Class 2 - Semester 1)
1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
 Vectors
Scalar products and component forms
Set 2H
Set 2I
Set 2J
 Week 7
(Class 1 - Semester 1)  
1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
 Vectors

Angle between vectors

 
Projections

Dot and cross products

Set 2K
Set 2L
Set 2M
 Week 7
(Class 2 - Semester 1)
1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
 Vectors Angle between vectors


Projections


Dot and cross products
Set 2K
Set 2L
Set 2M
 Week 8
(Class 1 - Semester 1) 


1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Vectors Complex numbers and vectors Set 2N
Set 2O

Week 8
(Class 2 - Semester 1)




1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
 Vectors  Complex numbers and vectorsSet 2N
Set 2O
 
Week 9
(Class 1 - Semester 1) 


 

1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Functions and Relations

 Set Notation

Graphs (Functions and relations).

Set 3A
Set 3B
Week 9
(Class 2 - Semester 1) 












1.2
1.3
2.3
2.4
2.5
2.6
3.2
3.3
3.4
3.5
4.2
4.3
Functions and Relations

Domain and range.

Types of functions and relations.

Set 3C
Set 3D
 Week 10
(Class 1 - Semester 1) 






1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Functions and Relations Function notationFurther Types of functions
Set 3E
Set 3F
Week 10
(Class 2 - Semester 1) 





1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
 

Differential equations




 Limits


First Principles
Set 4A
Set 4B
 Week 11
(Class 1 - Semester 1 



1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
 
Differential equations
 Limits

First Principles


Basic rules for differentiation
Set 4A
Set 4B
Set 4C 
 
 Week 11
(Class 2 - Semester 1
1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
 Differential equations Limits

First Principles


Basic rules for differentiation
Set 4A
Set 4B
Set 4C
 Week 12
(Class 1 - Semester 1) 



 




1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Differential equations Basic rules for differentiation


Higher derivatives
Set 4D
Set 4E
 Week 12
(Class 2 - Semester 1) 






1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Differential equations
Basic rules for differentiation

Higher derivatives

Chain rule 
 
Set 4D
Set 4E
 Week 13
(Class 1 - Semester 1) 



  




1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Differential equationsProduct rule and Quotient rule
Set 4F
Set 4G
 Week 13
(Class 2 - Semester 1) 






1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Differential equationsDerivatives of trigonometric
functions
Set 4H
Set 4I
 Week 14
(Class 1 - Semester 1)



1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Differential equations Derivatives of logarithmic and exponential functions Set 4J
Set 4K

Week 14
(Class 2 - Semester 1) 





1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
Integration

Introduction to Integration

Basic Integration

Set 5A
Set 5B
 Week 15
(Class 1 - Semester 1) 
 






1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
 IntegrationIntroduction to Integration


Basic Integration
 Set 5A

Set 5B
 Week 15
(Class 2 - Semester 1) 



1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
 Integration

Remember the C


Definitive Integration

Set 5C

Set 5D
Week 16
(Class 1 - Semester 1) 


1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
IntegrationRemember the C


Definitive Integration
Set 5C

Set 5D
Week 16
(Class 2 - Semester 1)
1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
IntegrationRemember the C


Definitive Integration
Set 5C

Set 5D
Week 17
(Class 1 - Semester 1) 
  




1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3
IntegrationAreas

Integration of basic trigonometric and exponential functions.
Set 5E

Set 5F
Week 17
(Class 2 - Semester 1)





1.2
1.3
2.3
2.4
2.5
3.2
3.3
3.4
3.5
4.2
4.3 
Revision .Areas


Integration of basic trigonometric and exponential functions
Set 5E

Set 5F
  REVIEW / REVISION  


Learning Resources

Prescribed Texts

There is no prescribed textbook for this course. Class notes and sets of problem booklets will be handed out to students.


References

Any first year text, or Mathematical Methods Year 11 or 12 textbook, or most first year texts on Algebra and Calculus. Thomas & Finney. Calculus and Analytical Geometry, Stewart J. Calculus. Students will be notified by their instructor in relation to any internet resources that may be helpful in their study.


Other Resources

Students should have a calculator, writing instruments, paper, a folder to organise and take down notes and an exercise book.
Access to a computer would be advantageous.


Overview of Assessment

The student must demonstrate an understanding of all elements of a particular competency to be deemed competent.
Assessment will incorporate a variety of methods including written tests. There will be a Module Assignment, Laboratory Work and Final Theory Exam.


Assessment Tasks

Assessment Tasks will consist of Tests, Exams & 1 Assignment

In class tests: 30%

Exam 1
End of Semester 1, June – Exam: 55%

Assignment : 15%

TOTAL=100%


Assessment Matrix

 Element 1Element 2Element 3Element 4
Test
Exam
Assignment

Other Information

Access to a computer would be advantageous.

Further Support
Additional RMIT study and support can be obtained from the Study and Learning Centre (SLC). Further information can be obtained via the following website:
www.rmit.edu.au/studyandlearningcentre

The SLC can also be contacted on 9925 3600.
The SLC can also be contacted via the E-mail learning query service.

University Plagiarism Statement
Students are reminded that cheating, whether by fabrication, falsification of data, or plagiarism, is an offence subject to University disciplinary procedures. Plagiarism in oral, written or visual presentations is the presentation of the work, idea or creation of another person, without appropriate referencing, as though it is one’s own. Plagiarism is not acceptable. The use of another person’s work or ideas must be acknowledged. Failure to do so may result in charges of academic misconduct, which carry a range of penalties including cancellation of results and exclusion from your course. Students are responsible for ensuring that their work is kept in a secure place. It is also a disciplinary offence for students to allow their work to be plagiarised by another student. Students should be aware of their rights and responsibilities regarding the use of copyright material.

Course Overview: Access Course Overview