tel: 736-2100 Ext 33968
Office: 2029 TEL BUILDING.
Algebra, T. W. Hungerford, GTM Springer. (recommended but not required) Abstract Algebra, Dummit and Foote, Willey. (Highly recommended but not required) An Introduction to Computational Algebraic Geometry and Commutative Algebra, D. A. Cox,
J. Little and D. O'shea, UTM Springer (Highly recommended but not required)
I plan as follow:
[I will add links to notes (from John Campbell[JC] or others) when available]
Fields theory and Galois theorems:
[ see D&F all Chap. 13 and Chap. 14 Sec. 1--8 ]
automorphism group of Fields
Galois groups of polynomials
solving polynomials with radicals
we stopped here.
Further ring and module theory (We may skip this?):
semisimple ring and Wedderburn Theorem
Introduction to algebraic geometry:
More on Categories
Proposed Presentation or Projects (let me know in advance your intent so that we can coordinate when to present it and if it is relevant):
My list is not inclusive and is just suggestions
Pick a Theorem above and present it in class (let me know in advance to coordinate when to present it)
Newton's Theorem on Symmetric functions.
Program a canonical form
Compute discriminant of any degree
Propose a relevant topic or project.
Students will be evaluated on five aspects (which are parts of the life of any living mathematician). The final grade will be base on the average of the best three of the following four:.
1 Project/Homework (working on an extended project or working on exercises)
2 Midterms (Writing exams).
3 Oral Presentation (Presenting some special topic or long proofs).
4 Comprehensive exam (writing the comprehensive exam at the end, Note that for some of you it is one of your Ph. D. requirements).
5 Participation in class (Being there, asking questions, being curious, etc.) is ALSO an important aspect of the evaluation. It may help increase any of your average above by up to 10%.
Office: 2029 TEL Building
email address: bergeron at yorku dot ca
Department of Mathematics and Statistics.
2029 TEL Building
North York, Ontario M3J 1P3, Canada
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