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MATH133 – Mathematics IB (Advanced)

2017 – S2 Day

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Lecturer
Michael Batanin
Contact via 9850 8926
12 Wally's Walk (E7A) 706
Wednesday 9-10
Convenor
Paul Smith
Contact via 9850 8944
12 Wally's Walk (E7A) 726
Tuesday 5-6
Michael Batanin
Credit points Credit points
3
Prerequisites Prerequisites
MATH132 or MATH135(HD)
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description
The notion of linearity is developed in this unit through the introduction of the abstract notion of vector spaces. The new ideas are then used to further study systems of linear equations. 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. The topics in this unit are studied with a degree of rigour and sophistication appropriate to better prepared students with a strong interest in the theoretical underpinnings of the subject. An alternative treatment of the same material from a less sophisticated point of view can be obtained by taking MATH136.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at http://students.mq.edu.au/student_admin/enrolmentguide/academicdates/

Learning Outcomes

  1. Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  2. Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  3. Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  4. Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  5. Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  6. Appropriate interpretation of information communicated in mathematical form. In particular, interpreting the solutions of ordinary differential equations and linear systems.
  7. Appropriate presentation of information, reasoning and conclusions in written form.
  8. Ethical application of mathematical approaches to solving problems
  9. Ability to work effectively, responsibly and safely in an individual or team context.

General Assessment Information

HURDLES: This unit has no hurdle requirements. This means that there are no second chance examinations and assessments if you happen to fail at your first attempt, and your final grade is determined by adding the marks obtained for your examinations and assessments. Students should aim to get at least 60% for the course work in order to be reasonably confident of passing the unit.

IMPORTANT: If you apply for Disruption to Study for your final examination, you must make yourself available for the week of December 11 – 15, 2017.  If you are not available at that time, there is no guarantee an additional examination time will be offered. Specific examination dates and times will be determined at a later date

Assessment Tasks

Name Weighting Due
Three assignments 30% See iLearn
One test 10% See iLearn
Final examination 60% University Examination Period

Three assignments

Due: See iLearn
Weighting: 30%

-


This Assessment Task relates to the following Learning Outcomes:
  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  • Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate interpretation of information communicated in mathematical form. In particular, interpreting the solutions of ordinary differential equations and linear systems.
  • Appropriate presentation of information, reasoning and conclusions in written form.
  • Ethical application of mathematical approaches to solving problems
  • Ability to work effectively, responsibly and safely in an individual or team context.

One test

Due: See iLearn
Weighting: 10%

-


This Assessment Task relates to the following Learning Outcomes:
  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  • Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate interpretation of information communicated in mathematical form. In particular, interpreting the solutions of ordinary differential equations and linear systems.
  • Appropriate presentation of information, reasoning and conclusions in written form.
  • Ethical application of mathematical approaches to solving problems
  • Ability to work effectively, responsibly and safely in an individual or team context.

Final examination

Due: University Examination Period
Weighting: 60%
-
This Assessment Task relates to the following Learning Outcomes:
  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  • Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate interpretation of information communicated in mathematical form. In particular, interpreting the solutions of ordinary differential equations and linear systems.
  • Appropriate presentation of information, reasoning and conclusions in written form.
  • Ethical application of mathematical approaches to solving problems
  • Ability to work effectively, responsibly and safely in an individual or team context.

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.

Required and Recommended Texts and/or Materials

The following texts are recommended for this unit, and are available from the CO-OP Bookshop on campus, and are in the reference section of the Library.

  • Stewart; Calculus
  • Trim: Calculus
  • Anton and Rorres: Linear Algebra and its Applications
  • David C. Lay: Linear Algebra and its Applications

Other similar texts are available in the Library, and for reference in the Numeracy Centre.

Additional notes Notes for Markov chains

http://www.sosmath.com/matrix/markov/markov.html http://aix1.uottawa.ca/~jkhoury/markov.htm Most books on linear algebra with applications will cover Markov chains. Some references have the columns summing to 1, others have the rows summing to 1 (depending on which way the state table is constructed). We will adopt the convention that the future state is on the vertical axis, so the columns sum to 1.

 

Technology Used and Required

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.

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

ALGEBRA

CALCULUS

1

Vector spaces (Introduction, proofs, subspaces)

Sequences and series, convergence of sequences

2

Vector spaces (Span, Linear Independence)

Convergence Tests of series

3

Vector spaces (Basis, Dimension)

Power series  

4

Vector spaces associated with matrices

Taylor series

5

 

Functions of several real variables, Limits

6

Orthogonality

Continuity, partial derivatives

7

 Projections, Least Squares

Tangent planes, chain rule

  MID-SEMESTER BREAK  

8

Eigenvectors nd Eigenvalues

Maxima and minima, Lagrange multipliers

9

Diagonalization

First order ordinary differential equations

10

Applications: Markov Chains, Discrete Dynamical Systems

Applications of first order ordinary differential equations

11

Applications: Systems of linear differential equations

Higher order ordinary differential equations

12

 Applications: Quadratic Forms

Applications of ordinary differential equations

13

Revision

Revision

Learning and Teaching Activities

Lectures

4 one hour lectures per week

Tutorial

1 one hour tutorial per week

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_2016.html

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

Complaint Management Procedure for Students and Members of the Public http://www.mq.edu.au/policy/docs/complaint_management/procedure.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/

Results

Results shown in iLearn, or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit ask.mq.edu.au.

Late Assignments

No extensions will be granted. Students who have not submitted the task prior to the deadline will be awarded a mark of 0 for the task, except for cases in which an application for special consideration is made and approved.

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 Enquiry Service

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

Equity 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.

IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/

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

Graduate Capabilities

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

  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  • Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate interpretation of information communicated in mathematical form. In particular, interpreting the solutions of ordinary differential equations and linear systems.
  • Appropriate presentation of information, reasoning and conclusions in written form.

Assessment tasks

  • Three assignments
  • One test
  • Final examination

Learning and teaching activities

  • 4 one hour lectures per week
  • 1 one hour tutorial per week

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

  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  • Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate presentation of information, reasoning and conclusions in written form.
  • Ethical application of mathematical approaches to solving problems
  • Ability to work effectively, responsibly and safely in an individual or team context.

Assessment tasks

  • Three assignments
  • One test
  • Final examination

Learning and teaching activities

  • 4 one hour lectures per week
  • 1 one hour tutorial per week

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

  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  • Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate interpretation of information communicated in mathematical form. In particular, interpreting the solutions of ordinary differential equations and linear systems.
  • Appropriate presentation of information, reasoning and conclusions in written form.
  • Ethical application of mathematical approaches to solving problems
  • Ability to work effectively, responsibly and safely in an individual or team context.

Assessment tasks

  • Three assignments
  • One test
  • Final examination

Learning and teaching activities

  • 4 one hour lectures per week
  • 1 one hour tutorial per week

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 outcomes

  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate presentation of information, reasoning and conclusions in written form.
  • Ethical application of mathematical approaches to solving problems
  • Ability to work effectively, responsibly and safely in an individual or team context.

Assessment task

  • Three assignments

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

  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  • Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate interpretation of information communicated in mathematical form. In particular, interpreting the solutions of ordinary differential equations and linear systems.
  • Appropriate presentation of information, reasoning and conclusions in written form.

Assessment tasks

  • Three assignments
  • One test
  • Final examination

Learning and teaching activities

  • 4 one hour lectures per week
  • 1 one hour tutorial per week

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 outcomes

  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, including arguments concerning convergence and linear independence.
  • Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods including models based on ordinary differential equations and linear systems.
  • Application of mathematical principles, concepts, techniques and technology to solve practical and abstract problems.
  • Appropriate interpretation of information communicated in mathematical form. In particular, interpreting the solutions of ordinary differential equations and linear systems.
  • Appropriate presentation of information, reasoning and conclusions in written form.
  • Ability to work effectively, responsibly and safely in an individual or team context.

Assessment tasks

  • Three assignments
  • One test
  • Final examination

Learning and teaching activities

  • 4 one hour lectures per week
  • 1 one hour tutorial per week

Engaged and Ethical Local and Global citizens

As local citizens our graduates will be aware of indigenous perspectives and of the nation's historical context. They will be engaged with the challenges of contemporary society and with knowledge and ideas. We want our graduates to have respect for diversity, to be open-minded, sensitive to others and inclusive, and to be open to other cultures and perspectives: they should have a level of cultural literacy. Our graduates should be aware of disadvantage and social justice, and be willing to participate to help create a wiser and better society.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to the development of the mathematical sciences. In particular, applications of differential equations and linear algebra in other fields.
  • Ethical application of mathematical approaches to solving problems
  • Ability to work effectively, responsibly and safely in an individual or team context.

Socially and Environmentally Active and Responsible

We want our graduates to be aware of and have respect for self and others; to be able to work with others as a leader and a team player; to have a sense of connectedness with others and country; and to have a sense of mutual obligation. Our graduates should be informed and active participants in moving society towards sustainability.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of infinite series, partial derivatives, ordinary differential equations, vector spaces, linear transformations, matrix theory, and eigenvectors.
  • Ability to work effectively, responsibly and safely in an individual or team context.

Changes since First Published

Date Description
28/07/2017 Changes to the Resources Section.