The following course will be offered in the Fall term of 2013-2014

Mathematics 4123A/9023A

Rings and Modules

 

Instructor:

Professor David Riley
Department of Mathematics 
Middlesex College 136
Email: DMRiley@uwo.ca

Time and Location:

Tuesdays and Thursdays 12:30-12:00 pm in MC 108 (starting on Tuesday, September 10)

Textbook:

An Introduction to Ring Theory, by Paul M. Cohn (Springer, 2000)

Prerequisites:

Math 3020A/B for Math 4123A. Special permission of the instructor is required for to enroll in Math 9023A. This course assumes a basic background in linear algebra and one introductory course in abstract algebra. Please note the following point, which is required to be stated in this outline by Senate regulation: "Unless you have either the prerequisites for this course or the written special permission of your Dean to enroll in it, you may be remove from this course and it will be deleted from your record. This decision may not be appealed. You will receive no adjustment to your fees in the event you are dropped from a course for failing to have the necessary prerequisites."

Synopsis:

The object of this course is to introduce the fundamental algebraic concept of a module over a ring. Theory will be developed in order to solve such problems as how to classify finitely generated Abelian groups and how to choose a basis to represent linear transformations as matrices with in easy and manageable canonical forms.

Main Topics (as time permits):

·  Cartesian products and Zorn's Lemma

·  A quick review of introductory ring theory 

·  Euclidean domains, principal ideal domains and unique factorization domains

·  Polynomial rings

·  Introduction to module theory

·  Tensor algebras, symmetric and exterior algebras

·  Modules over principal ideal domains

·  Depending on time and interest, other topics may include basic category theory, Noetherian rings, Artinian rings, discrete valuation rings, and Dedekind domains     

Evaluation of Student Performance:

·  Five assignments, one roughly every two weeks, worth 10% of the final mark each

·  One in-class midterm examination worth 20% of the final mark

·  One final examination worth 30% of the final mark

·  Performance expectations are significantly higher in Math 9023A than in Math 4123A

Senate Regulations on Scholastic Offences 
(Plagiarism and Cheating):

Please note the following points, which are required to be stated in this outline by Senate regulation:
"Plagiarism is a major academic offence (see Scholastic Offence Policy in the Western Academic Calendar). The University of Western Ontario uses software for plagiarism checking. Students may be required to submit their written work in electronic form for plagiarism checking. In addition, if any computer-marked multiple-choice tests and/or exams are given, software to check for unusual coincidences in answer patterns that may indicate cheating may be used."

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