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Apr
30
asked First to note/document the relation between permutohedra and multiplicative inversion
Apr
26
comment intuitive connection between The KdV equations and the Virasoro bott group
Could it somehow be related to the central extension involving the Schwarzian through a cocyle and the connection between the Schwarzian and the velocity of soliton solutions of the KdV equation, a velocity which is related to deviation of the solns from Moebius transformations? mathoverflow.net/questions/38105/… and mathoverflow.net/questions/145555/…
Apr
19
comment What is the structure of the space of solutions of a non linear ODE?
@L.Spice. tandfonline.com/doi/abs/10.1142/S1402925110000635
Apr
14
comment Compositional inversion and generating functions in algebraic geometry
Alm and Petersen, "Brown's dihedral moduli space and freedom of the gravity operad" arxiv.org/abs/1509.09274
Apr
14
comment Compositional inversion and generating functions in algebraic geometry
See also "Brown's moduli spaces of curves and the gravity operad" by Dupont and Vallette. arxiv.org/abs/1509.08840
Mar
24
comment Why do we teach calculus students the derivative as a limit?
So they have at least an implicit knowledge (and most likely explicit knowledge from books on quantitative vs. fundamental analysis of the market) of when and how to fit a curve (a function) to sections of massaged data, in agreement with my first point. Btw, I taught freshman calculus and physics without calculus during graduate studies at an engineering university. No motivated student had a problem with the courses, in particular with concepts involving ratios of changes.
Mar
22
comment Why do we teach calculus students the derivative as a limit?
I can only suppose that you would ensure that they think of the problem geometrically in terms of a graph of the dependent and independent variables of suitably averaged prices, which would be the natural line of thinking if one started from the physics approach first. I can appreciate how difficult it might be to come up with a derivative from the real data that would have predictive value. What should be the window for the time-averaging, ..., etc.?
Mar
22
comment Why do we teach calculus students the derivative as a limit?
Students have an implicit, working understanding of functions. They know that given any group of people they can assign a unique height (mod units in feet and inches or centimeters) to each person but given a height they might not be able to assign only one person to it. If they are confused, it can only be by an obfuscating formalism.
Mar
22
comment Why do we teach calculus students the derivative as a limit?
Look at Morse and Feshbach's Methods for Theoretical Physics for an intuitive explanation of the form of the Schrodinger equation for the wave function for a free particle.
Mar
22
comment Why do we teach calculus students the derivative as a limit?
The use of the term sensitivity for the derivative is incredibly silly to me, especially for physics majors. The natural introduction is through the Newton quotient, velocity, and trajectories of balls. Then generalize to limiting rates or ratios of changes of other quantities.
Mar
20
comment Dao's theorem on six circumcenters associated with a cyclic hexagon
Sorry, even my last comment is full of idioms difficult for most Asians to understand.
Mar
20
comment Dao's theorem on six circumcenters associated with a cyclic hexagon
Oai, it's just a matter of translation. Most Americans don't understand how difficult it can be for non-native English speakers to express their sentiments in English and often jump to the wrong conclusion. Hard to explain. Don't worry about it.
Mar
19
comment Dao's theorem on six circumcenters associated with a cyclic hexagon
@Oai, OP = original poster = the original author of the question = you
Mar
19
comment Dao's theorem on six circumcenters associated with a cyclic hexagon
@Jon, I'm sure that's exactly the sentiment the OP intended to convey.
Mar
19
comment Dao's theorem on six circumcenters associated with a cyclic hexagon
@Jon, cut her some slack. Most foreign speakers aren't familiar with linguistic etiquette in English--how to assume the proper tone. "I published a theorem illustrating the remarkable / beautiful connections between ..." would be perfectly acceptable.
Mar
19
comment Mathematical habits of thought and action which would be of use to non-mathematicians
On MO itself, there are comments and answers made by famous mathematicians on fundamental topics that are both highly upvoted and simply wrong. History is replete with examples of authority trumping careful, conscientious analysis in various fields of math, science, and engineering. MO is not exempt from social dynamics.
Mar
17
comment Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
Related: arxiv.org/abs/1502.05771
Mar
11
comment What are fixed points of the Fourier Transform
math.stackexchange.com/questions/118078/…
Mar
11
comment What is Lagrange Inversion good for?
For 1) see mathoverflow.net/questions/60478/…
Mar
8
comment Guises of the Stasheff polytopes, associahedra for the Coxeter $A_n$ root system?
Dwight is referenced in Mathworld under 'series reversion' and also the classic book by Morse and Feshbach, which is frequently a great ref for geometric insights behind the analytics of the topics they discuss.