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. |
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. |
Element: |
Select appropriate mathematical/scientific method |
Performance Criteria: |
2.1 OH&S requirements for carrying out the work are followed. |
Element: |
Verify and interpret results |
Performance Criteria: |
4.1 OH&S requirements for completing the work are followed. |
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 equations | Set 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 | Matrices | Matrices and systems of linear equations | Set 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 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 vectors | Set 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 notation | Further 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 equations | Product 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 equations | Derivatives 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 | Integration | Introduction 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
| 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 | Integration | Remember 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 | Integration | Remember 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 | Integration | Areas 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 1 | Element 2 | Element 3 | Element 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