Unit convenor and teaching staff |
Unit convenor and teaching staff
Lecturer
Gerry Myerson
Contact via x8952
AHH 2.639
By appointment
Paul Smith
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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:
Name | Weighting | Due |
---|---|---|
Ten assignments | 40% | Weeks 4 through 13 |
MATLAB computation | 0% | weeks 6-13 |
Final examination | 60% | University Examination Period |
Due: Weeks 4 through 13
Weighting: 40%
Assignments.
Due: weeks 6-13
Weighting: 0%
included as integral part of numerical linear algebra assessments
Due: University Examination Period
Weighting: 60%
Lectures: you should attend two hours of each lecture stream each week, making a total of four hours.
The required text for the Galois Theory part of MATH338 is Ian Stewart, Galois Theory Chapman and Hall 4th Edition. The numerical linear algebra part of MATH338 is strongly based on the material in Lloyd Trefethen and David Bau, Numerical Linear Algebra, SIAM, 1977.
ADDITIONAL TEXTS
Galois Theory
Numerical 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 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.
WEEK |
Monday (Galois Theory) |
Wednesday (Numerical Linear Algebra) |
TASK DUE |
1 |
Fields, characteristic, vector spaces |
Motivation for Numerical Linear Algebra |
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2 |
Polynomials, Division Theorem, Euclid's Algorithm |
Motivation (ctd.) |
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3 |
Polynomials, ctd. |
Unitary matrices; norms for vectors and matrices |
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4 |
Extension fields, degree, Tower Law |
The Singular Value Decomposition |
Assignment 1 |
5 |
Simple and algebraic extensions, minimal polynomial |
The Singular Value Decomposition, ctd. |
Assignment 2 |
6 |
Splitting fields, separability |
Introduction to MATLAB |
Assignment 3 |
7 |
Groups of field automorphisms |
QR Decomposition and Householder reflectors |
Assignment 4 |
MID-SEMESTER BREAK |
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8 |
Normal extensions |
QR Decomposition and Householder reflectors, ctd. |
Assignment 5 |
9 |
[Labor Day public holiday] |
Least squares |
Assignment 6 |
10 |
The Fundamental Theorem of Galois Theory |
LU Decomposition; pivoting and condition number |
Assignment 7 |
11 |
The Fundamental Theorem of Galois Theory, ctd. |
LU Decomposition; pivoting and condition number, ctd. |
Assignment 8 |
12 |
Solution by radicals, unsolvability of the quintic |
Ill-conditioned systems and regularisation |
Assignment 9 |
13 |
Revision |
Revision |
Assignment 10 |
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Assessment Policy http://mq.edu.au/policy/docs/assessment/policy.html
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In addition, a number of other policies can be found in the Learning and Teaching Category of Policy Central.
Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/support/student_conduct/
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.
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.
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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.