Continuous mappings | Differential topology | Algebraic topology
In topology, the degree of a continuous mapping between two compact oriented manifolds of the same dimension is a number that represents the number of times that the domain manifold wraps around the range manifold under the mapping. The degree is always an integer, but may be positive or negative depending on the orientations. The degree of a map was first defined by Brouwer, who showed that the degree is homotopy invariant (invariant among homotopies), and used it to prove the Brouwer fixed point theorem. In modern mathematics, the degree of a map plays an important role in topology and geometry. In physics, the degree of a continuous map (for instance a map from space to some order parameter set) is one example of a topological quantum number. (Wikipedia).
BM8.2. Mappings 2: Basic Properties
Basic Methods: We continue with properties of mappings. We define domain, range, image, and inverse image. Some rules for set operations and noted, and then the notions of one-one and onto are introduced. Examples are given, and finally we further identify equivalence relations and par
From playlist Math Major Basics
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Determine the Interval of Continuity of a Function (quad/trig)
This video explains how to determine the interval of continuity for a given function.
From playlist Continuity Using Limits
BM8.3. Mappings 3: Composition and Inverse Mappings
Basic Methods: We define composition of mappings and draw parallels to multiplication of real numbers. Items include associativity, identity, and commutativity. Consideration of multiplicative inverses leads to the definition of an inverse mapping, and we give conditions for its existenc
From playlist Math Major Basics
This video explains the idea behind the Intermediate Value Theorem and then illustrated the Intermediate Value Theorem. Site: http://mathispower4u.com
From playlist Continuity Using Limits
Topology Proof The Constant Function is Continuous
Topology Proof The Constant Function is Continuous If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Topology
Basic Methods: We define mappings (or functions) between sets and consider various examples. These include binary operations, projections, and quotient maps. We show how to construct the rational numbers from the integers and explain why division by zero is a forbidden operation.
From playlist Math Major Basics
Old-New Perspectives on the Winding Number - Haim Brezis
Analysis and Beyond - Celebrating Jean Bourgain's Work and Impact May 22, 2016 More videos on http://video.ias.edu
From playlist Analysis and Beyond
AlgTop13: More applications of winding numbers
We define the degree of a function from the circle to the circle, and use that to show that there is no retraction from the disk to the circle, the Brouwer fixed point theorem, and a Lemma of Borsuk. This is the 13th lecture of this beginner's course in Algebraic Topology, given by Assoc
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Michael Drmota: Vertex degrees in planar maps
Abstract: We consider the family of rooted planar maps MΩ where the vertex degrees belong to a (possibly infinite) set of positive integers Ω. Using a classical bijection with mobiles and some refined analytic tools in order to deal with the systems of equations that arise, we recover a un
From playlist Probability and Statistics
Stefan Sauter: A Family of Crouzeix-Raviart Non-Conforming Finite ...
Stefan Sauter: A Family of Crouzeix-Raviart Non-Conforming Finite Elements in Two- and Three Spatial Dimensions The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Numerical Inverse and Stochastic Homogenization. (17.02.2017) In t
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
AlgTop14: The Ham Sandwich theorem and the continuum
In this video we give the Borsuk Ulam theorem: a continuous map from the sphere to the plane takes equal values for some pair of antipodal points. This is then used to prove the Ham Sandwich theorem (you can slice a sandwich with three parts (bread, ham, bread) with a straight planar cut
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Topology Proof The Composition of Continuous Functions is Continuous
Topology Proof The Composition of Continuous Functions is Continuous If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Topology
Parallel session 7 by Chris Connell
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part2)
Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, name
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Proof that every Differentiable Function is Continuous
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A proof that every differentiable function is continuous.
From playlist Calculus
Lecture 16: TC of perfect rings
In this video, we compute TC, CT^- and TP of perfect rings of characteristic p. In order to do that we also have to discuss the Witt vectors and their universal property. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=t
From playlist Topological Cyclic Homology
Lecture 13: Smooth Surfaces II (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Calculus - Application of Differentiation (3 of 60) Max/Min Values: Ex. 2 f(x)=x^2-5x+6
Visit http://ilectureonline.com for more math and science lectures! In this video I will find max/min, where f(x) is increasing/decreasing of f(x)=x^2-5x+6.
From playlist CALCULUS 1 CH x APPLICATIONS OF DIFFERENTIATION
Solvability in Polynomials of Pell Equations in a Pencil and a Conjecture of Pink - Umberto Zannier
Umberto Zannier Scuola Normale Superiore de Pisa, Italy April 10, 2013 The classical Pell equation X2−DY2=1X2−DY2=1, to be solved in integers X,Y≠0X,Y≠0, has a variant for function fields (studied already by Abel), where now D=D(t)D=D(t) is a complex polynomial of even degree and we seek s
From playlist Mathematics