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Algebra 1

Algebra is part of my daily work as a Caltech Research Faculty. I've been using it on a regular basis for 25 years, throughout my undergrad/graduate studies as well as in my research.

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Algebra 2

Algebra 2, along with many other chapters of math, is part of my daily work at Caltech as Research Faculty. We work on numerical modeling of black hole collisions, basing our models in Einstein's Theory. This would not be doable without an in-depth knowledge of many chapters of math, including algebra 2.

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Geometry

Geometry is a chapter of math that is essential for numerical modeling of astrophysical systems such as black holes. Einstein's Theory (which is what describes black holes) is a very high level geometry. As such, geometry is part of my daily life. Starting with the level at which I am tutoring my children through their various geometry related classes, and to the level I need at my work.

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Trigonometry

I am using Trigonometry as part of my daily research at Caltech. I have spent a number of years working on software capable of modeling the coalescence of black holes. In this research area an essential element of the modeling accuracy is construction of a proper mesh -- this will then be used as the basis of the numerical approximations in your model. These meshes can get really complex, and their construction involves a lot of mathematics, primarily Trigonometry.

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Elementary Math

Math (well beyond elementary level) is part of my daily work as a Caltech Research Faculty. Our work involves re-writing the equations Einstein wrote down in a way suitable for numerical modeling. This involves lots of mathematics. I also have children of my own whom I have been tutoring through all grades of math.

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Elementary Science

Besides being a scientist myself, I have been tutoring my children from elementary school through high school.

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Differential Equations

My work as a researcher consists of modeling black hole collisions. Creating a software able to accurately model such a phenomena requires several steps. One of the first of these is casting of the Einstein Equations (a set of quasi-linear partial differential equations) into a form suitable for numerical evolution. It turns out that when one casts equations into what is known as 'symmetric hyperbolic system of partial differential equations', then implementation of an evolution algorithm based...
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C++

I have used C++ for a number of projects during my Research Career. The very first complete research software I wrote was a 2-D hydrodynamics software (using the Lattice Boltzmann approximation). This was 3-4000 lines of C++. As a check on my code, one of my colleagues wrote an equivalent algorithm in Fortran, and has reproduced my results. The agreement was a practical proof of both codes being valid.

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C

I have been using the C programming language for 25 years. I have taught C at the West University of Timisoara, Romania. As part of my course work, I wrote a 150 page introductory book, to be used by my own students, describing the basic elements of this language.

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Computer Programming

I have spent maybe two decades with Computer Programming. My very first program computed a representation of the various electron shells around an atom. Later on I wrote code for two-dimensional hydrodynamics, then software to model black holes. I have also written database software for various applications. I have used a number of programming languages, such as Pascal, Basic, Fortran, C, C++.

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Fortran

Fortran is one of the programming languages I use for my research. I have first used this language 15 years ago (back then it was called Fortran 77). My PhD work was also based on software written in Fortran. In addition, part of the code we use for black hole modeling at Caltech is written in Fortran. I have recently spent some weeks working on this code, improving the way it interfaces with the rest of the software (written in C++). With all of this, I should be able to help one learn this language...
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Linear Algebra

My first encounter with linear algebra was during my studies at the West Univ. of Timisoara, Romania, as a physics major. As it turns out, this same chapter of math is essential when one constructs a numerical representation of a differential operator, or a system of partial differential equations. Linear Algebra is not only essential in defining numerical differentiation operators, but also it is a crucial tool in proving theorems about the extent to which a particular numerical scheme is suitable...
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Linux

My first contact with the Linux operating system was in the early 90's. At that time, as a University Assistant Professor at the West Univ of Timisoara, Romania, we were exploring ways to utilize computer resources that were slowly becoming accessible to us in Eastern Europe. It turns out that Linux is the main operating system used in my field, throughout the World. It provides a powerful command line interface as well as networking capabilities that have become an absolute must in much of science...
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Microsoft Access

I have written 2-3 database applications (of various magnitudes) within Microsoft Access. The smallest of these was a personal banking tool which I had built / customized as my concept of personal banking has evolved. I have also written two large scale Microsoft Access applications, both with hundreds of forms, queries, reports, dozens of tables. The larger of these was a student database at a small college. The smaller (still in use) is an essential tool in the everyday life of a non-profit...
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Visual Basic

I have used Visual Basic as the programming language underneath the various Forms, Reports and Modules of Microsoft Access. I have probably written 1000 pages worth of code in this language, most of it within a database application that served as the student- and fundraising-database in a small educational institute numbering a few hundred students. Given the amount of years spent with this language (starting with 1996) as well as the shear number of code lines I wrote using Visual Basic, I am...
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Mathematica

Mathematica was an essential tool for my Master's Degree project. The task was something on the order of "electron mass renormalization" (or a similar, very theoretical, quantum mechanics title.) After having managed to freeze my work station a few times with overly complex demands on this algebraic manipulation software, eventually I learned enough about using computer algebra to understand how one must wrestle smaller parts of the main expression to simple forms before putting it all in one,...
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