10,084 reputation
14469
bio website vmm.math.uci.edu
location Univ. of California at Irvine
age 82
visits member for 3 years, 9 months
seen Apr 8 at 22:40
I'm a Professor at UC Irvine, but spent most of my career at Brandeis. My research areas: Differential Topology, Transformation Groups, and Global Analysis. Recently I developed a math visualization program, 3D-XplorMath, freely available at http://3D-XplorMath.org) and a companion website, the Virtual Math Museum at http://VirtualMathMuseum.org. Last year I co-authored a differential equations text with my son Bob, most of which is downloadable from http://ode-math.com .

Dec
7
answered Notes for Bott's 1963 lectures on Morse theory
Nov
7
answered Any good books on numerical methods for ordinary differential equations?
Oct
16
comment Proof synopsis collection
@mathahada Where do you see a geometric series in my proof? (One of the points I had in publishing the above proof was to show that the geometric series argument (used since Banach's original proof) is really not necessary.
Oct
14
comment Can the level set of a critical value be a regular submanifold?
You probably should say amend the statement of the theorem to say that a non-empty level set of a regular value of a smooth function f:M→ℝ on a smooth manifold is a regular submanifold of codimension one. (That takes care of the problem with f identically zero.)
Oct
11
answered Proofs for doubly ruled surfaces
Sep
21
revised Definition of Sobolev spaces as a space of sections of certain type
Added a link to a copy of referenced work; deleted 1 characters in body; added 1 characters in body
Sep
20
answered Definition of Sobolev spaces as a space of sections of certain type
Sep
19
comment Collapsing of Riemannian manifolds with a group action
"...Consider the fixed point set F, it is of course a submanifold of M by the slice theorem". Note that it is really simpler than that; in geodesic coordinates at a point p of F, the fixed point set is locally the linear subspace left fixed by the linearized action at p.
Sep
15
comment First known proof of $\sqrt 2$ is irrational with prime factorization?
Your right Franz, it doesn't. It's just that there seems to be a belief that you NEED unique prime factorization to prove the irrationality of non-square integers, and when I first saw this (much more elementary) proof I found it an eye-opening experience.
Sep
14
answered First known proof of $\sqrt 2$ is irrational with prime factorization?
Sep
3
comment Area of union of random circles in a plane
You will probably get a more "natural" answer if you choose a "torus", i.e., identify opposite edges of a square, to eliminate edge effects.
Aug
31
awarded  Good Answer
Aug
29
awarded  Nice Answer
Aug
25
awarded  Enlightened
Aug
25
awarded  Nice Answer
Aug
25
revised Square root of a positive $C^\infty$ function.
improved citation
Aug
25
comment Square root of a positive $C^\infty$ function.
Yes, and functions of this type are discussed in section 2 of the reference I gave in my answer.
Aug
25
answered Square root of a positive $C^\infty$ function.
Aug
24
answered Measure theory treatment geared toward the Riesz representation theorem
Aug
16
awarded  Guru