The exact content of the course will be adapted to those participating in it and will be determined during the first meeting, Wednesday September 7, Topics will likely include: basic notions of affine and projective varieties the notions of rational maps between varieties differentials and singularities function fields Divisors, the Riemann-Roch theorem classification of algebraic curves.
Algebraic geometry is a topic central to pure mathematics, and its ideas and results play an ever increasing role in all fields of mathematics. This makes it a very worthwhile topic to learn about if you are interested in mathematics. Shafarevich, I.
William Fulton, Algebraic Curves , freely available, see: Fulton's homepage. Reid, Miles. Undergraduate algebraic geometry. This service is more advanced with JavaScript available. Basic Notions of Algebra. Authors view affiliations Igor R. Front Matter Pages I What is Algebra?
Pages Commutative Rings. Homomorphisms and Ideals. Algebraic Aspects of Dimension. The Algebraic View of Infinitesimal Notions. Noncommutative Rings. Modules over Noncommutative Rings.
Semisimple Modules and Rings. Division Algebras of Finite Rank. The Notion of a Group. Examples of Groups: Finite Groups. Examples of Groups: Infinite Discrete Groups. General Results of Group Theory. Group Representations. Some Applications of Groups. Lie Algebras and Nonassociative Algebra.
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