MTH745P / MTH745U: Further Topics in Algebra (2013–14)
(Fields and Galois Theory variant)
Basic Info |
Lectures and Classes |
News |
Exercises |
Solutions |
General Comments |
Notes |
Past Papers
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Lecturer:
Dr J. N. Bray.
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Office: Room B54 in the Mathematics Building.
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Office hours: Please see my main webpage.
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Module text (NOT essential): I. Stewart. Galois Theory (Third Edition).
Chapman and Hall/CRC, 2004.
There is no requirement for you to buy the said text.
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Course information:
See here (slightly updated). Please note that the QM “+” address
(http://qmplus.qmul.ac.uk/course/view.php?id=2498) in the paper versions of this is wrong
despite this being what was on module website; the correct version (at least at the moment) is
http://qmplus.qmul.ac.uk/course/view.php?id=3521.
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One more PDF-file:
Description, Syllabus and Learning Outcomes.
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Prerequisite(s): At least MTH5100: Algebraic Structures I; other modules very helpful.
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Parameters: Level 7, Semester A, 15 Credits.
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Assessment: 100% Final Exam (in May/June).
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Lectures: Monday 1:00–3:00pm in Maths 203.
Since this is Level 7 lectures can run in Week 7. I have not yet decided whether to
use this possibility.
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Classes: Monday 3:00–4:00pm in Maths 203.
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Assignments: These are for feedback only.
Please hand them into me if you want them marking.
23-ix-2013: None yet.
- The definitive content of this module is contained in the lecture notes,
and so the module text is not essential. However, you may find the module text useful in
supplying some additional examples, diagrams and explanations.
- Students are expected to be quiet during lectures.
Mobile phones must be switched OFF in lectures and in exercise classes.
- Exercise classes start in Week 2 (though I may run a class in Week 1).
- Use of calculators is not permitted in the final examination.
- Being a student is full-time job. Thus should you aim to spend 9–10 hours a week on
each of the four modules you currently studying. Note that only about 4 hours of
this is timetabled work.
- It is my job to try to educate you to produce independent learners:
employers are seeking people who can think for themselves, not merely
follow recipes. I will help you achieve this.
Note that the word ‘educate’ comes from the Latin word educare
meaning ‘to rear’ or ‘to bring up’; it does not mean
‘to spoon-feed’!
(The word educare is a compound word, with parts e (ex) ‘from’
and ducere ‘to lead’.)
Some notes may eventually appear here, but do not count on it.
You take notes in lectures, basically writing down what I write on the board.
The theorem numbers and examples are likely to be different from what I
do in class. I have also included some notes here not included in lectures,
and vice-versa.
Some of the following may constitute suitable further reading. Some are quite introductory,
and some are at a more advanced level than this module.
- I. Stewart. Galois Theory (Third Edition).
Chapman and Hall/CRC, 2004. (Main module text.)
- E. Artin. Galois Theory. Dover Publications, 1998.
- P.J. Cameron. Introduction to Algebra (Second Edition). Oxford University Press, 2007.
- J.S. Milne. Fields and Galois Theory. Available at
http://www.jmilne.org/math/CourseNotes/FT.pdf.
- I.N. Herstein. Topics in Algebra (Second Edition). John Wiley and Sons, 1975.
- D.J.H. Garling. A Course in Galois Theory. Cambridge University Press, 1986.
- L.H. Soicher. The Computation of Galois Groups. M.Comp.Sci. Thesis, Concordia University,
Montreal, 1981. Scanned copy (as PDF).
Solutions to past papers will NOT be made available. Please come to see me
during my office hours if you have problems with the questions. This year’s paper is
likely to be in the format of Answer ALL questions. These papers are for various
versions of past modules in Galois Theory, which may have different emphases and/or syllabuses
from the current version. MAS316 was a Level 6 module entitled Galois Theory, while
MTH733U/MTHM733 and MTH745U/MTH745P were Level 7 versions of Fields and Galois Theory (though
MTH745U/MTH745P had the title Further Topics in Algebra).
- 2012 (PDF-format; MTH745U/MTH745P).
- 2010 (PDF-format; MTH733U/MTHM733).
- 2008 (PDF-format; MAS316).
- 2007 (PDF-format; MAS316).
- 2005 (PDF-format; MAS316).
- 2004 (PDF-format; MAS316).
- 2000 (PDF-format; MAS316).
- 1999 (PDF-format; MAS316).
- 1998 (PDF-format; MAS316).
- 1997 (PDF-format; MAS316).
Last updated: 15th April 2014.
Dr John N. Bray.