college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography
26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math
Also an Expert in Oceanography
Mathematics enables us to apply abstract principals to provide solutions to everyday problems as well as extend our understanding of the Universe. Being able to provide a mathematical solution that bridges the gap between intuition and a solid appication is very fulfilling.
I hope to acquire more thorough understanding of the many aspects of math and their relation to real world problems. I enjoy helping people understand the often deep results of mathematics and how they can reveal underlying relationships.
Integrating functions of real numbers (basically summing the values of a process to reveal its behaviour), uses several techniques taught in calculus. For complex numbers, combining real and imaginary numbers (square root of -1), the approach relies on powerful, elegant theorems to transform the function and its domain to obtain the value of the integral in a completely different way.
Humor: The famous mathematician Erdos once quipped that a mathematician is a machine that turns coffe into theorems.
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I think the trace of X should be zero. Here's my derivation: Traces have some simple and useful properties, such as (for a matrices A and B) 1. Tr(A +B) = Tr(A) + Tr(B) 2. Tr(A) = Tr(A^t) 3
For A and B are in Mnxn, the form S = AB - BA, is called a commutator, made famous by the Heisenberg Principal (just FYI). As you probably know, the dimension of the vector space of matrices
We can take as an example of an infinite Hilbert space the space of complex functions f of a complex argument, z, which are square integrable (integral of square < ∞) and which has an inner product
I think your conceptual difficulties arise from trying to define the function g in terms of x instead of h. Let me try to clarify. If I have a function, say g, it operates on an argument, which I'll
Defining h(x) = 1+x is a good start. Now we want to end up with f(x) = 1/(x+1) which would be f(x) = 1/h(x). This would define the function g by g⚬h = 1/h. When I work with compositions of
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