Students

MATH288 – Advanced Topics in Mathematics II

2015 – S1 Day

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Lecturer
Stuart Hawkins
Unit convenor
Xuan Duong
Credit points Credit points
3
Prerequisites Prerequisites
(MATH133 or MATH136(HD)) and permission of Executive Dean of Faculty
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description
This unit is designed for students enrolled in the Bachelor of Advanced Science in Mathematics, and for strong Mathematics majors seeking to widen their mathematical background. Topics are chosen from accessible areas of current research to excite and challenge talented students.

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:

  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment Tasks

Name Weighting Due
Four assignments 10% As advised in lectures
Four assignments 10% as per unit website
Class test 20% Week 11
Final examination 60% Exam period

Four assignments

Due: As advised in lectures
Weighting: 10%

Four assignments on Lebesgue integration.


On successful completion you will be able to:
  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Four assignments

Due: as per unit website
Weighting: 10%

Four assignments on Computational Mathematics.


On successful completion you will be able to:
  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Class test

Due: Week 11
Weighting: 20%

Class test conducted in lecture.


On successful completion you will be able to:
  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Final examination

Due: Exam period
Weighting: 60%

Final examination.


On successful completion you will be able to:
  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Delivery and Resources

Classes

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

Technology Used and Required

Students are expected to have access to an internet enabled computer with a web browser and Adobe Reader software. Accounts are available for all students in the Mathematics/Physics computing laboratory (E7B 209) — this will be the location of laboratory sessions and some lectures. Students are expected to work here on assignments and other assessment tasks.

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

BEGINNING

TOPOLOGY, COVERINGS

Diophantine Analysis

1

03/03/2014

 

 Metric spaces Diophantine analysis

 

2

10/03/2014

 Topological spaces  

3

17/03/2014

 Compact spaces  

4

24/03/2014

 Groups and actions  

5

31/03/2014

 Topological groups

 

6

07/04/2014

 Coverings

 

     Mid-semester break  
7 28/04/2014

Homotopy type

 

8

05/05/2014

 Fundamental group  

9

12/05/2014

 Fundamental group  

10

19/05/2014

 Classification of coverings  

11

26/05/2014

 Galois correspondence  

12

02/06/2014

 Applications  

13

09/06/2014

Revision

 

 

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/

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.

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

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

  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment tasks

  • Class test
  • Final examination

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

  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment tasks

  • Four assignments
  • Four assignments
  • Class test
  • Final examination

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 outcomes

  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment tasks

  • Four assignments
  • Four assignments
  • Class test
  • Final examination

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

  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment tasks

  • Four assignments
  • Four assignments
  • Class test
  • Final examination

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

  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment tasks

  • Four assignments
  • Four assignments
  • Class test
  • Final examination

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

  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment tasks

  • Four assignments
  • Four assignments
  • Class test
  • Final examination

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 a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment tasks

  • Four assignments
  • Four assignments
  • Class test
  • Final examination

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

  • demonstrate a well-developed knowledge of the principles, concepts and techniques of the topics covered.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning, in the areas of the topics covered.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment task

  • Four assignments

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 outcome

  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in the topics covered.

Assessment task

  • Four assignments

Extra Requirements

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. 

 

There may be assignment questions directed specifically toward students enrolled in Math 388. Also, students in 388 can expect to have their work judged against a higher standard than students in 288.