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Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Nov
13
revised f(f(x))=exp(x)-1 and other functions “just in the middle” between linear and exponential.
edited tags; edited tags
Nov
13
comment f(f(x))=exp(x)-1 and other functions “just in the middle” between linear and exponential.
I suppose we do not know if an entire function (or something close to entire) with such an intermediate growth function is possible, and also are such functions related to any mathematics. (Maybe they are related to formal groups.)
Nov
13
comment Fundamental Examples
The wiki entry is en.wikipedia.org/wiki/Tsirelson_space . See also a discussion on Gowers's blog gowers.wordpress.com/2009/02/17/…
Nov
13
answered Fundamental Examples
Nov
13
comment Fundamental Examples
Here is a nice link for the figure eight knot mathworld.wolfram.com/FigureEightKnot.html . The trefoil knot en.wikipedia.org/wiki/Trefoil_knot is a basic example in knot theory.
Nov
13
comment What precisely Is “Categorification”?
Moving from "Euler characteristic" to "homology" was mentioned as a basic example. Moving from "Betti numbers" to "homology groups" is claimed as an even better example of categorification but I do not understand this claim.
Nov
13
answered Fundamental Examples
Nov
12
answered Fundamental Examples
Nov
12
comment Fundamental Examples
I agree. I would also add the Fibonacci numbers en.wikipedia.org/wiki/Fibonacci_number . Fibonacci numbers lead to rational generating functions and Catalan numbers to rational generating functions. The Catalan numbers appear in an amazing number of different problems.
Nov
12
answered What is the first interesting theorem in (insert subject here)?
Nov
12
comment Fundamental Examples
Dear Andrew, I see your point; In any case, now that it is a community wiki some explenation for why an example is fundamental can be added by other participants.
Nov
12
answered Free, high quality mathematical writing online?
Nov
12
revised How Does Random Noise Typically Look?
edited tags
Nov
12
revised How Does Random Noise Typically Look?
edited tags; edited tags
Nov
12
answered Fundamental Examples
Nov
12
awarded  Self-Learner
Nov
12
comment Groupoid of moves on trivalent fatgraph
i did not understand the second move. But first what is a fatgraph?
Nov
12
revised Fundamental Examples
edited tags
Nov
12
answered Fundamental Examples
Nov
12
answered Fundamental Examples