Geometric Measure Theory - Histórico de revisão

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2017-02-14T13:56:29Z

Textbooks

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	=== Textbooks ===		=== Textbooks ===

	We will be following Herbert Federer's famously hard book as a guide, mainly learning his language and style through the first ~~few~~ chapters, then selecting topics for advancing right to the theory of currents (ch. 4.1) as fast as possible [https://drive.google.com/drive/u/0/folders/0B8Z1cZSIN8qyQTlJbXU1VTBBX0U]		We will be following Herbert Federer's famously hard book as a guide, mainly learning his language and style through the first couple of chapters, then selecting topics for advancing right to the theory of currents (ch. 4.1) as fast as possible [https://drive.google.com/drive/u/0/folders/0B8Z1cZSIN8qyQTlJbXU1VTBBX0U]
	* [https://www.amazon.com/Geometric-Measure-Theory-Classics-Mathematics/dp/3540606564/ref=sr_1_1?ie=UTF8&qid=1487018260&sr=8-1&keywords=geometric+measure+theory Geometric Measure Theory ], Herbert Federer, Springer-Verlag, 1969 (the text used at Brown)		* [https://www.amazon.com/Geometric-Measure-Theory-Classics-Mathematics/dp/3540606564/ref=sr_1_1?ie=UTF8&qid=1487018260&sr=8-1&keywords=geometric+measure+theory Geometric Measure Theory ], Herbert Federer, Springer-Verlag, 1969 (the text used at Brown)

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2017-02-14T13:56:02Z

Textbooks

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	=== Textbooks ===		=== Textbooks ===

	We will be following Herbert Federer's famously hard book as a guide, mainly learning his language and style through the first few chapters, then selecting topics for advancing right to the theory of currents as fast as possible [https://drive.google.com/drive/u/0/folders/0B8Z1cZSIN8qyQTlJbXU1VTBBX0U]		We will be following Herbert Federer's famously hard book as a guide, mainly learning his language and style through the first few chapters, then selecting topics for advancing right to the theory of currents (ch. 4.1) as fast as possible [https://drive.google.com/drive/u/0/folders/0B8Z1cZSIN8qyQTlJbXU1VTBBX0U]
	* [https://www.amazon.com/Geometric-Measure-Theory-Classics-Mathematics/dp/3540606564/ref=sr_1_1?ie=UTF8&qid=1487018260&sr=8-1&keywords=geometric+measure+theory Geometric Measure Theory ], Herbert Federer, Springer-Verlag, 1969 (the text used at Brown)		* [https://www.amazon.com/Geometric-Measure-Theory-Classics-Mathematics/dp/3540606564/ref=sr_1_1?ie=UTF8&qid=1487018260&sr=8-1&keywords=geometric+measure+theory Geometric Measure Theory ], Herbert Federer, Springer-Verlag, 1969 (the text used at Brown)

V1z em 23h51min de 13 de fevereiro de 2017

2017-02-13T23:51:34Z

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	The spaces dealt with in this course extend the theory of finite-dimensional		The spaces dealt with in this course extend the theory of finite-dimensional
	differentiable varieties, covered in a previous Differential Varieties course,		differentiable varieties, covered in a previous Differential Varieties course,
	to more general sets~~, at times infinite-dimensional and non-differentiable~~. Most importantly,		to more general sets. Most importantly,
	this course provides fundamental language for researchers using advanced mathematics in		this course provides fundamental language for researchers using advanced mathematics in
	many different fields, such as probability theory and machine learning in high dimensions.		many different fields, such as probability theory and machine learning in high dimensions.

V1z em 21h01min de 13 de fevereiro de 2017

2017-02-13T21:01:49Z

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	The public is interdisciplinary scientists and mathematicians. Emphasis is given to a conceptual and intuitive		The public is interdisciplinary scientists and mathematicians. Emphasis is given to a conceptual and intuitive
	understanding of this difficult but powerful subject, regarded as very hard within mathematics, while ~~studying~~ the ~~deepest~~ formalisms.		understanding of this difficult but powerful subject, regarded as very hard within mathematics, while working out the most fundamental formalisms.

	== General Info ==		== General Info ==

V1z em 21h01min de 13 de fevereiro de 2017

2017-02-13T21:01:00Z

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	many different fields, such as probability theory and machine learning in high dimensions.		many different fields, such as probability theory and machine learning in high dimensions.

	The public is interdisciplinary scientists and mathematicians. Emphasis ~~will be~~ given on a conceptual		The public is interdisciplinary scientists and mathematicians. Emphasis is given to a conceptual and intuitive
	understanding of this difficult but powerful subject, regarded as very hard within mathematics.		understanding of this difficult but powerful subject, regarded as very hard within mathematics, while studying the deepest formalisms.

	== General Info ==		== General Info ==

V1z em 20h59min de 13 de fevereiro de 2017

2017-02-13T20:59:33Z

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	differentiable varieties, covered in a previous Differential Varieties course,		differentiable varieties, covered in a previous Differential Varieties course,
	to more general sets, at times infinite-dimensional and non-differentiable. Most importantly,		to more general sets, at times infinite-dimensional and non-differentiable. Most importantly,
	it provides fundamental language for researchers using advanced mathematics in		this course provides fundamental language for researchers using advanced mathematics in
	many different fields, such as probability theory and machine learning in high dimensions.		many different fields, such as probability theory and machine learning in high dimensions.

V1z: /* Links */

2017-02-13T20:57:07Z

Links

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	== Links ==		== Links ==
	* [[~~Geometria_Riemaniana~~]]		* [[Geometria Riemaniana]]
	* [[Pattern Theory]]		* [[Pattern Theory]]

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2017-02-13T20:56:50Z

Textbooks

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	Complementary Textbooks on Differential Geometry, Manifolds and Tensors		Complementary Textbooks on Differential Geometry, Manifolds and Tensors
	* ''Foundations of Differentiable Manifolds and Lie Groupds'', Frank W. Warner		* ''Foundations of Differentiable Manifolds and Lie Groupds'', Frank W. Warner
	** A beautiful and modern intro to tensors on Chapter 2 provides an initial setting for Federer's beautiful Chapter 1.		** A beautiful and modern intro to tensors on Chapter 2 provides an initial setting for Federer's also beautiful Chapter 1.
	* See also [[~~Geometria_Riemaniana~~]].		* See also [[Geometria Riemaniana]].

	=== Lectures ===		=== Lectures ===

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2017-02-13T20:53:51Z

Approximate Content

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	== Approximate Content ==		== Approximate Content ==
	We will be reading sections of interest from ~~Mumford~~'s book together with complements from the others.		We will be reading sections of interest from Federer's book (starting with Ch 1), together with complements from the others. Focus may shift based on research demand and demand from student's individual projects.
	Focus may shift based on research demand and demand from student's individual projects.
	We plan to focus on the following topics.		We plan to focus on the following topics.


	== Main Resources ==		== Main Resources ==

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2017-02-13T20:52:57Z

Pre-requisites

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	* Strictly, one is expected to be familiar with traditional measure theory as seen in graduate-level real analysis or functional analysis (review will be provided for those coming from an engineering background)		* Strictly, one is expected to be familiar with traditional measure theory as seen in graduate-level real analysis or functional analysis (review will be provided for those coming from an engineering background)
	* Riemannian Geometry and Differential Varieties: we will review tensors at a deep level, from scratch, but your life will be a lot easier if you have already seen these concepts.		* Riemannian Geometry and Differential Varieties: we will review tensors at a deep level, from scratch, but your life will be a lot easier if you have already seen these concepts.
	* Linear Algebra: the only real pre-requisite. Students are expected to know linear algebra at the level of Hoffman and Kunze, and also in the context of its application to the theory of differentiable varieties and riemannian geometry.		* Linear Algebra: the only real pre-requisite. Students are expected to know linear algebra at the level of [https://www.amazon.com/Linear-Algebra-2nd-Hoffman-Kunze/dp/8120302702/ref=sr_1_1?ie=UTF8&qid=1487019089&sr=8-1&keywords=hoffman+kunze Hoffman and Kunze], and also in the context of its application to the theory of differentiable varieties and riemannian geometry.

	== Approximate Content ==		== Approximate Content ==