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What is cutting edge maths? - Mathematics Stack Exchange My maths teacher always keeps telling me about this 'cutting edge maths' that is going on in the world, amazing maths research, etc A lot of the google searches I've done for 'Cutting Edge Mathematics' hasn't returned much useful information, so I've taken to mathematics stack exchange
Cut vertices and cut edges - did I answer these correctly? Problem Find the cut vertices and cut edges for the following graphs My understanding of the definitions: A cut vertex is a vertex that when removed (with its boundary edges) from a graph creates
number theory - Undergraduate roadmap for Langlands program and its . . . This is like a person who is just learning to count asking for a roadmap to integral calculus Focus on completing the core graduate material in analysis, geometry, and algebra -- the cutting-edge stuff will come in due time
Why can algebraic geometry be applied into theoretical physics? As I progressed in math graduate school specializing in number theory and algebraic geometry, it was astounding to discover a certain class of researchers who were doing very serious and nontrivial cutting-edge stuff connecting algebraic geometry and mathematical physics
What is a proper face of a graph? - Mathematics Stack Exchange The paper On the Cutting Edge: Simplified O(n) Planarity by Edge Addition by John Boyer and Wendy Myrvold uses the term quot;proper face quot; I do not know what this term means At a guess, perh
Slicing edges out of a high dimensional polytope. The original cone was $123$ and after cutting it it became $12p3$ because $12$ is a valid edge, so are $2p, p3, 31$ In 4D our plane generates 3 new edges, we know that it intersects the planes $2,3,4$
Finding the spherical coordinates for the edge obtained by cutting a . . . What I am now interested in is finding the parametrization of the cutting edge, however not as parametrization of a circle, but instead in spherical coordinates of the sphere This means I want to find the coordinates of every point on the cut, expressed in the spherical coordinate system
Cutting a cube with a plane - Mathematics Stack Exchange That would be the same as just cutting a square with a line What the questions asks for, is the shape of the two new internal faces that appears after the cut For example, if you cut along an edge to the opposite edge, you would get a rectangle of dimensions $1\times\sqrt2$ It is the intersection of the cube and the plane I speak Danish by
general topology - Examples of the difference between Topological . . . 33 There is apparently cutting-edge research by Dustin Clausen Peter Scholze (and probably others) under the name Condensed Mathematics, which is meant to show that the notion of Topological Space is not so well-chosen, and that Condensed Sets lead to better behaved structures What is a simple low-tech example to see the difference?