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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

Experience in the area

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

Past/Present Clients

Also an Expert in Oceanography

What do you like about this subject?

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.

What do you still hope to achieve/learn in this field?

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.

Something interesting about this subject that others may not know:

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.

Something controversial or provocative about this subject

Humor: The famous mathematician Erdos once quipped that a mathematician is a machine that turns coffe into theorems.

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Snehal01/15/17101010Great help
Carol12/20/16Hi Randy, Thanks for the help. These .....
Alexa12/03/16101010Thank you very much. Yes, I was .....

Recent Answers from randy patton

2017-01-13 linear algebra:

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

2017-01-02 linear algebra:

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

2016-11-21 Functional analysis:

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

2016-08-26 Composition of Functions:

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

2016-08-25 Composition of Functions:

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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