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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
When you randomly shuffle a deck of cards, what is the probability that . . . The situation is not the same as in the birthday paradox The birthday paradox works because the two identical birthdays may appear between any two of the persons However, in your experiment, you demand that you are one of the two persons involved in the same card deck A situation analogous to the birthday paradox would be given by the question "what is the chance that over the last 600
combinatorics - A visual solution to the cube cutting problem . . . You will find that each tetrahedron is made by piecing together two isosceles right triangles with edge lengths 1 1, 1 1, 2–√ 2, and two right triangles with edge lengths 1 1, 2–√ 2, 3–√ 3 This is something you can actually build by cutting the pieces from card stock and taping them together
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
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
For someone who loves mathematics - Mathematics Stack Exchange Specializing towards communications on the broad sense (network traffic problems, information theory, silicon chip design and logic, filter design, control ) can get pretty cutting edge mathematically How deep you go depends on what a particular department might specialize in as far as research goes
combinatorics - Let G be a connected graph in which every vertex has . . . The edge v v - v1 v 1 (or v v - v2 v 2 or v v - v3 v 3) was a bridge when V V was removed, connecting v1 v 1 to that component Therefore the deletion of v v - v1 v 1 disconnects G G But this is a contradiction since we said G G has no cut-edge Another method is to first see that G G has no loops; if it did, it would contain a cut-edge
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 × 2–√ 1 × 2 It is the intersection of the cube and the plane
What is the difference between elementary and advanced math? Pell's equation is quite easy to solve, Pythagorean triples were known to the Babylonians, Fermat's Last Marginalium lasted hundreds of years and requires cutting-edge work on general elliptic curves Bisecting an angle is easy with straightedge and compass, trisecting an angle is impossible without neusis The area of a cirle is πr2 π r 2