Stony Brook University 3 credits MAT
Basic definitions and examples. Holomorphic differential forms. Riemann-Hurwitz Theorem. The Riemann-Roch Theroem. The Dirichlet Problem. The Hodge Theorem for Riemann surfaces. Embeddings into Projective Space. Uniformization theorem(s). Abel’s Theorem and Jacobi’s inversion theorem. Further topics may include: Sheaves and cohomology. Fields of meromorphic functions, valuations and connections with algebraic number theory. Monodromy and classification of branched covers. Note: This course was previously known as MAT 538 and is not to be repeated for additional credit. 3 credits Prerequisite: MAT 533 , MAT 536 & MAT 549 Grading Letter graded (A, A-, B+, etc.)
Our subject experts help with essays, research papers, case studies, discussion posts, and capstone projects for these programs — written from scratch to your course requirements.
Program and course information is reproduced from each university's published academic catalog for informational purposes and may change. Always confirm current requirements with your university. We are an independent academic support service and are not affiliated with or endorsed by the universities listed.
Expert guides on essay writing, citation styles, study skills, and academic success.
View All Articles
Learn how to write a good research question for a paper. Narrow your topic, identify a research problem, and create a focused question with practical examples.
Learn how to choose a research topic you can actually research. Discover how to narrow broad ideas, find reliable sources, and develop a focused research question.
Learn how to cite sources in a research paper using APA, MLA, and Chicago styles, with in-text citation examples and reference-list tips.