tel: 736-2100 Ext 33968
e-mail: bergeron@mathstat.yorku.ca
Office: 2029 TEL BUILDING.

Books

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]

Classification of finitely generated abelian groups
[Class Jan 19 [JC]]

rational canonical form

Jordan canonical form

Further ring and module theory:
[ see D&F 10.5]

injective and projective modules

Fields theory and Galois theorems:

Fields extensions

splitting fields

automorphism group of Fields

Galois correspondence

Galois groups of polynomials

solving polynomials with radicals

Further ring and module theory (We may skip this?):

semisimple ring and Wedderburn Theorem

Introduction to algebraic geometry:

Varieties

radical ideals

Hilbert's nullstellensatz

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)

Wedderburn Theorem

Hilbert's nullstellensatz

Newton's Theorem on Symmetric functions.

...

Program a canonical form

Compute discriminant of any degree

Propose a relevant topic or project.

Evaluation:

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%.
Nantel Bergeron
Office: 2029 TEL Building
email address: bergeron at yorku dot ca
Department of Mathematics and Statistics.
2029 TEL Building
York University
North York, Ontario M3J 1P3, Canada
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