New York University 4 credits Mathematics
This course is a transition from vector calculus to differential geometry, the study of curved spaces. The course plan is to move from a study of extrinsic geometry of curves and surfaces in space, familiar from multivariable calculus, to the intrinsic geometry of manifolds. This includes the study of tangent spaces and vector fields and the concept of Riemannian manifolds and leading to explicit characterizations of metrics, connections, and curvatures. Computational tools will include tensor algebra and differential forms. Using these, derivatives on manifolds and integration on manifolds will generalize the corresponding notions from multivariable calculus. Further topics also include the Euler characteristic, The Gauss-Bonnet theorem, symmetry, homogeneous spaces, and applications such as Electromagnetism and General Relativity. Prerequisites: MATH-UH 1020 or MATH-UH 1021 and MATH-UH 1022.
Our subject experts help with essays, research papers, case studies, discussion posts, and capstone projects for these programs β 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.