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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
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
Curve-fitting using circles - Mathematics Stack Exchange Here is a Matlab program that generates this family of circles (changing the value of parameter c c changes the eccentricity of the generated ellipse): clear all;close all;axis equal;axis off;hold on c=1; u=0:0 01:2*pi; for z=-c:0 1:c; r=sqrt(1-(z c)^2); x=r*cos(u)+z; y=r*sin(u); plot(x,y); end; In fact there are two circles with radius 0, i e , points that are the foci of this ellipse This
How to propose a conjecture - Mathematics Stack Exchange Even when one is at the cutting edge of research, there is always a possibility that one's conjecture will be wrong, due (typically) to a misunderstanding of or lack of knowledge of certain phenomena and (counter-)examples (This is an occupational hazard of making conjectures!)
Introduction to the replica trick - Mathematics Stack Exchange I think it is also self-contained (might assume some basic probability theory familiarity with statistical mechanics) Once again they also cover replica method cavity method message passing They also show derivations for some cutting-edge research (as of 2020ish) on representing teacher-student models in machine learning as spin glass
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
calculus - Can a function have a inflection point at somewhere non . . . For such nuances you have to know what your instructor thinks the right definition is It's not an important enough thing for most people to care about, honestly (No one is doing cutting edge research in Calculus or analysis that would suddenly be invalidated if someone had a different definition of inflection point )
What algebraic topology book to read after Hatchers? 9 J Peter May and Kate Ponto's More Concise Course In Algebraic Topology is a follow-up to May's introductory book containing cutting edge topics such as spectral sequences, model categories,basic homotopy theory,localization and completion of spaces and more I haven't seen the whole book,but what I have seen looks terrific