Students

MATH136 – Mathematics IB

2014 – S2 Day

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Unit Convenor
Rod Yager
Contact via rod.yager@mq.edu.au
E7A 203
Credit points Credit points
3
Prerequisites Prerequisites
MATH132 or MATH135
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description
The notion of linearity first introduced in MATH135 is developed through the introduction of the abstract notion of vector spaces. The new ideas are then used to further study systems of linear equations. The unit also covers an introduction to group theory, one of the most fundamental concepts in modern mathematics. The study of differential and integral calculus is taken further by the introduction of functions of two real variables and the study of first-order and second-order ordinary differential equations. The notion of a limit is enhanced by the study of sequences and series. Ideas from power series are then used to revisit differential equations.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates

Learning Outcomes

On successful completion of this unit, you will be able to:

  • By the end of this unit, you should be able to demonstrate a well-developed knowledge of the properties of matrices and the role of eigenvectors and eigenvalues in the study of linear systems.
  • Demonstrate facility with a range of integration techniques and methods for solving ordinary differential equations.
  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables
  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Assessment Tasks

Name Weighting Due
Assignments 18% See unit website
Tutorial Work 20% Weekly
Online quizzes 7% See unit website
Class Test 15% See unit website
Final examination 40% University Examination Period

Assignments

Due: See unit website
Weighting: 18%

Three assignments


On successful completion you will be able to:
  • By the end of this unit, you should be able to demonstrate a well-developed knowledge of the properties of matrices and the role of eigenvectors and eigenvalues in the study of linear systems.
  • Demonstrate facility with a range of integration techniques and methods for solving ordinary differential equations.
  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables
  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Tutorial Work

Due: Weekly
Weighting: 20%

Submission of selected tutorial problems


On successful completion you will be able to:
  • By the end of this unit, you should be able to demonstrate a well-developed knowledge of the properties of matrices and the role of eigenvectors and eigenvalues in the study of linear systems.
  • Demonstrate facility with a range of integration techniques and methods for solving ordinary differential equations.
  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables
  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Online quizzes

Due: See unit website
Weighting: 7%

Several online quizzes


On successful completion you will be able to:
  • By the end of this unit, you should be able to demonstrate a well-developed knowledge of the properties of matrices and the role of eigenvectors and eigenvalues in the study of linear systems.
  • Demonstrate facility with a range of integration techniques and methods for solving ordinary differential equations.
  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables

Class Test

Due: See unit website
Weighting: 15%

Mid semester class test conducted in tutorials


On successful completion you will be able to:
  • By the end of this unit, you should be able to demonstrate a well-developed knowledge of the properties of matrices and the role of eigenvectors and eigenvalues in the study of linear systems.
  • Demonstrate facility with a range of integration techniques and methods for solving ordinary differential equations.
  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables
  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Final examination

Due: University Examination Period
Weighting: 40%

Final exam


On successful completion you will be able to:
  • By the end of this unit, you should be able to demonstrate a well-developed knowledge of the properties of matrices and the role of eigenvectors and eigenvalues in the study of linear systems.
  • Demonstrate facility with a range of integration techniques and methods for solving ordinary differential equations.
  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables
  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Delivery and Resources

Classes

Lectures: you should attend two hours of each lecture stream each week, making a total of four hours.

Tutorials: you should attend one tutorial each week.

Practicals: you are encouraged to attend one practical each week. 

Workshops: available for students wanting to see more examples and ask further questions. Attendance is strongly recommended.

Required and Recommended Texts and/or Materials

The required texts for MATH136 are 

  • Anton: Elementary Linear Algebra, Applications  Version ,  11th Edition,  Wiley 2014
  • Hughes Hallet : Calculus Single and Multivariable,  6th Edition, Wiley 2014  

Other useful material is available for download on

Required and Recommended Texts and/or Materials

Students are expected to have access to an internet enabled computer with a web browser and Adobe Reader software. Several areas of the university provide wireless access for portable computers. There are computers for student use in the Library and in the Numeracy Centre (C5A 255).

Difficulties with your home computer or internet connection do not constitute a reasonable excuse for lateness of, or failure to submit, assessment tasks.

 

 

Unit Schedule

Week

Topic

 

1

Complex Numbers

 
2 Matrices and matrix algebra  
3

Determinants, eigenvalues and eigenvectors

 
4 Diagonalization and applications  
5 Linear transformations in the plane  
6 Polynomials and rational functions; partial fractions  
7 Further techniques of integration  
8 Ordinary differential equations - first and second order linear equations  
9 Linear systems of differential equations  
10 Functions of several variables : limits, continuity and partial derivatives  
11 Gradients, directional derivatives, tangent planes and normals  
12 Sequences and series  
13  Revision  

Learning and Teaching Activities

Lectures

There will be three one hour lectures and one additional demonstration lecture per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Tutorials

There will be one two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

Workshop

There is a weekly optional workshop provided by the Numeracy Centre.

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central. Students should be aware of the following policies in particular with regard to Learning and Teaching:

Academic Honesty Policy http://mq.edu.au/policy/docs/academic_honesty/policy.html

Assessment Policy  http://mq.edu.au/policy/docs/assessment/policy.html

Grading Policy http://mq.edu.au/policy/docs/grading/policy.html

Grade Appeal Policy http://mq.edu.au/policy/docs/gradeappeal/policy.html

Grievance Management Policy http://mq.edu.au/policy/docs/grievance_management/policy.html

Disruption to Studies Policy http://www.mq.edu.au/policy/docs/disruption_studies/policy.html The Disruption to Studies Policy is effective from March 3 2014 and replaces the Special Consideration Policy.

In addition, a number of other policies can be found in the Learning and Teaching Category of Policy Central.

Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/support/student_conduct/

Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

Learning Skills

Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.

Student Services and Support

Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.

Student Enquiries

For all student enquiries, visit Student Connect at ask.mq.edu.au

IT Help

For help with University computer systems and technology, visit http://informatics.mq.edu.au/help/

When using the University's IT, you must adhere to the Acceptable Use Policy. The policy applies to all who connect to the MQ network including students.

Graduate Capabilities

Capable of Professional and Personal Judgement and Initiative

We want our graduates to have emotional intelligence and sound interpersonal skills and to demonstrate discernment and common sense in their professional and personal judgement. They will exercise initiative as needed. They will be capable of risk assessment, and be able to handle ambiguity and complexity, enabling them to be adaptable in diverse and changing environments.

This graduate capability is supported by:

Learning outcome

  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.

Assessment tasks

  • Assignments
  • Tutorial Work
  • Class Test
  • Final examination

Learning and teaching activities

  • There will be one two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

Commitment to Continuous Learning

Our graduates will have enquiring minds and a literate curiosity which will lead them to pursue knowledge for its own sake. They will continue to pursue learning in their careers and as they participate in the world. They will be capable of reflecting on their experiences and relationships with others and the environment, learning from them, and growing - personally, professionally and socially.

This graduate capability is supported by:

Learning and teaching activities

  • There will be one two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

Discipline Specific Knowledge and Skills

Our graduates will take with them the intellectual development, depth and breadth of knowledge, scholarly understanding, and specific subject content in their chosen fields to make them competent and confident in their subject or profession. They will be able to demonstrate, where relevant, professional technical competence and meet professional standards. They will be able to articulate the structure of knowledge of their discipline, be able to adapt discipline-specific knowledge to novel situations, and be able to contribute from their discipline to inter-disciplinary solutions to problems.

This graduate capability is supported by:

Learning outcomes

  • By the end of this unit, you should be able to demonstrate a well-developed knowledge of the properties of matrices and the role of eigenvectors and eigenvalues in the study of linear systems.
  • Demonstrate facility with a range of integration techniques and methods for solving ordinary differential equations.
  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables
  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Assessment tasks

  • Assignments
  • Tutorial Work
  • Online quizzes
  • Class Test
  • Final examination

Learning and teaching activities

  • There will be three one hour lectures and one additional demonstration lecture per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.
  • There will be one two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

Critical, Analytical and Integrative Thinking

We want our graduates to be capable of reasoning, questioning and analysing, and to integrate and synthesise learning and knowledge from a range of sources and environments; to be able to critique constraints, assumptions and limitations; to be able to think independently and systemically in relation to scholarly activity, in the workplace, and in the world. We want them to have a level of scientific and information technology literacy.

This graduate capability is supported by:

Learning outcomes

  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Assessment tasks

  • Assignments
  • Tutorial Work
  • Class Test
  • Final examination

Learning and teaching activities

  • There will be three one hour lectures and one additional demonstration lecture per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.
  • There will be one two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

Problem Solving and Research Capability

Our graduates should be capable of researching; of analysing, and interpreting and assessing data and information in various forms; of drawing connections across fields of knowledge; and they should be able to relate their knowledge to complex situations at work or in the world, in order to diagnose and solve problems. We want them to have the confidence to take the initiative in doing so, within an awareness of their own limitations.

This graduate capability is supported by:

Learning outcomes

  • By the end of this unit, you should be able to demonstrate a well-developed knowledge of the properties of matrices and the role of eigenvectors and eigenvalues in the study of linear systems.
  • Demonstrate facility with a range of integration techniques and methods for solving ordinary differential equations.
  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables
  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Assessment tasks

  • Assignments
  • Tutorial Work
  • Online quizzes
  • Class Test
  • Final examination

Learning and teaching activities

  • There will be three one hour lectures and one additional demonstration lecture per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.
  • There will be one two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

Creative and Innovative

Our graduates will also be capable of creative thinking and of creating knowledge. They will be imaginative and open to experience and capable of innovation at work and in the community. We want them to be engaged in applying their critical, creative thinking.

This graduate capability is supported by:

Learning and teaching activities

  • There will be one two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

Effective Communication

We want to develop in our students the ability to communicate and convey their views in forms effective with different audiences. We want our graduates to take with them the capability to read, listen, question, gather and evaluate information resources in a variety of formats, assess, write clearly, speak effectively, and to use visual communication and communication technologies as appropriate.

This graduate capability is supported by:

Learning outcomes

  • Demonstrate an understanding of the key concepts of limits, continuity and differentiation in the context of functions of several variables
  • Construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
  • Apply the concepts and techniques studied in this unit to a range of applications, particularly drawn from Physics and Engineering.
  • Express mathematical ideas clearly and logically, providing appropriate justification for conclusions.

Assessment tasks

  • Assignments
  • Tutorial Work
  • Online quizzes
  • Class Test
  • Final examination

Learning and teaching activities

  • There will be one two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

Changes from Previous Offering

The content and delivery of MATH136 has been substantially revised from previous offerings so that related material is studied in a large block; with more intensive tutorial work focused on students developing and demonstrating competence in applying skills related to current material. These changes build on and mirror the changes introduced in MATH135 in Session 1.

Extra requirements

In order to obtain a passing grade in this unit, students are required to demonstrate their mastery of the required basic skills and techniques by passing all five on-line quizzes. Students who do not meet this requirement will have their grade capped at F 49.

 

Satisfactory performance on supervised assessment tasks, such as tests and the final exam, is necessary to pass this unit. If there is a significant difference between a student's marks on supervised assessment tasks and on unsupervised assessment tasks, the scaling of these tasks may be adjusted when determining the final grade, to reflect more appropriately that student's performance on supervised tasks.

 

Students are expected to do satisfactory work in both the Calculus and the Linear Algebra stream in order to pass Math 136. 

Changes since First Published

Date Description
04/08/2014 Corrected heading line for the table in unit outline. (The heading Topic was incorrect).
04/08/2014 Updated textbooks and recommended reading from previous semesters details