Unit convenor and teaching staff |
Unit convenor and teaching staff
Lecturer
Michael Batanin
Contact via Email
12 Wally's Walk 706
by appointment
Steve Lack
Michael Batanin
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Credit points |
Credit points
3
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Prerequisites |
Prerequisites
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Corequisites |
Corequisites
MATH337
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Co-badged status |
Co-badged status
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Unit description |
Unit description
This unit further develops the theory of algebraic structures commenced in MATH337, and involves the study of a selection of topics in field theory as well as a study of algorithms used in the application of linear algebra to the practical computational solution of real-world problems. The field theory strand develops the basic theory, including the notion of irreducibility of polynomials, simple, algebraic and transcendental extensions, and the tower law. The ideas of group theory studied in MATH337 are then applied to the study of field extensions via the notion of automorphisms, culminating in the study of the Galois correspondence theorem. The numerical linear algebra strand focuses on the study of large matrices and the use of matrix decomposition techniques appropriate to the computation of approximate solutions of the kinds of differential equations with specified boundary conditions that commonly arise in problems in science and engineering.
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Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
On successful completion of this unit, you will be able to:
HURDLES: This unit has no hurdle requirements.
ATTENDANCE and PARTICIPATION: Please contact the unit convenor as soon as possible if you have difficulty attending and participating in any classes. There may be alternatives available to make up the work. If there are circumstances that mean you miss a class, you can apply for a Special Consideration.
ASSIGNMENT SUBMISSION: Assignment submission will be online through the iLearn page.
Submit assignments online via the appropriate assignment link on the iLearn page. A personalised cover sheet is not required with online submissions. Read the submission statement carefully before accepting it as there are substantial penalties for making a false declaration.
• Assignment submission is via iLearn. You should upload this as a single scanned PDF file.
• Please note the quick guide on how to upload your assignments provided on the iLearn page.
• Please make sure that each page in your uploaded assignment corresponds to only one A4 page (do not upload an A3 page worth of content as an A4 page in landscape). If you are using an app like Clear Scanner, please make sure that the photos you are using are clear and shadow-free.
• It is your responsibility to make sure your assignment submission is legible.
• If there are technical obstructions to your submitting online, please email us to let us know.
You may submit as often as required prior to the due date/time. Please note that each submission will completely replace any previous submissions. It is in your interests to make frequent submissions of your partially completed work as insurance against technical or other problems near the submission deadline.
LATE SUBMISSION OF WORK: All assignments or assessments must be submitted by the official due date and time. No marks will be given to late work unless an extension has been granted following a successful application for Special Consideration. Please contact the unit convenor for advice as soon as you become aware that you may have difficulty meeting any of the assignment deadlines. It is in your interests to make frequent submissions of your partially completed work. Note that later submissions completely replace any earlier submission, and so only the final submission made before the due date will be marked.
FINAL EXAM POLICY: examinations for individuals or groups of students. All students are expected to ensure that they are available until the end of the teaching semester, that is, the final day of the official examination period. The only excuse for not sitting an examination at the designated time is because of documented illness or unavoidable disruption. In these special circumstances, you may apply for special consideration via ask.mq.edu.au.
SUPPLEMENTARY EXAMINATIONS:
IMPORTANT: If you receive special consideration for the final exam, a supplementary exam will be scheduled in the interval between the regular exam period and the start of the next session. If you apply for special consideration, you must give the supplementary examination priority over any other pre-existing commitments, as such commitments will not usually be considered an acceptable basis for a second application for special consideration. Please ensure you are familiar with the policy prior to submitting an application. You can check the supplementary exam information page on FSE101 in iLearn (https://bit.ly/FSESupp) for dates, and approved applicants will receive an individual notification sometime in the week prior to the exam with the exact date and time of their supplementary examination.
Name | Weighting | Hurdle | Due |
---|---|---|---|
Assignment 1 | 10% | No | see iLearn |
Assignment 2 | 10% | No | see iLearn |
Assignment 3 | 10% | No | see iLearn |
Project | 10% | No | see iLearn |
Final examination | 60% | No | Formal University Examination Period |
Due: see iLearn
Weighting: 10%
Assignment based on both components of the unit.
Due: see iLearn
Weighting: 10%
Assignment based on both components of the unit.
Due: see iLearn
Weighting: 10%
Assignment based on both components of the unit.
Due: see iLearn
Weighting: 10%
In this project the student will apply the techniques of Galois to the study of two specific polynomial equations.
Due: Formal University Examination Period
Weighting: 60%
Two hour (plus 10 min reading time) exam covering all course material/topics.
Lectures: you should attend two hours of each lecture stream each week, making a total of four hours per week.
The required text for the Galois Theory part of MATH338 is Ian Stewart, Galois Theory Chapman and Hall 4th Edition. Lecture notes will be provided for the Advanced Linear Algebra part of MATH338.
ADDITIONAL TEXTS
Galois Theory
Advanced Linear Algebra
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.
The following table gives an approximate timetable for the topics covered week-by-week.
Week | Advanced Linear Algebra | Galois Theory |
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1 | Overview and review of basic Linear Algebra | Rings and Fields |
2 | The group GL_n of invertible matrices | Rings and Fields |
3 | The group GL_n of invertible matrices | Polynomials |
4 | Computation with Matrices | Polynomials (Galois Theory) |
5 | Singular Value Decomposition (Adv Linear Algebra) | Polynomials |
6 | Rings and Modules | Field Extensions |
7 | Invertible matrics over Euclidean domains | Field Extensions |
Mid Session Break | ||
8 | Invertible matrices over more general rings | Field Extensions |
9 | Further theory of modules | Field Maps |
10 | Structure theorem for modules over a Euclidean domain | Fundamental Theorem of Galois Theory |
11 | Structure theorem for modules over a Euclidean domain | Fundamental Theorem of Galois Theory |
12 | Rank and dimension for modules over a general ring | Solvability in Radicals |
13 | Revision |
Macquarie University policies and procedures are accessible from Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central). Students should be aware of the following policies in particular with regard to Learning and Teaching:
Undergraduate students seeking more policy resources can visit the Student Policy Gateway (https://students.mq.edu.au/support/study/student-policy-gateway). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.
If you would like to see all the policies relevant to Learning and Teaching visit Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central).
Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/study/getting-started/student-conduct
Results published on platform other than eStudent, (eg. iLearn, Coursera etc.) 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 or if you are a Global MBA student contact globalmba.support@mq.edu.au
Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/
Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.
Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.
For all student enquiries, visit Student Connect at ask.mq.edu.au
If you are a Global MBA student contact globalmba.support@mq.edu.au
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.
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