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My name is Bela S. I am Research Faculty at Caltech, working on computer modeling of black holes, neutron stars, and how these cause space and time to shake and wobble as they collide.
I have children of my own (the eldest being a 10th grader), who give me lots of opportunity to practice tutoring. They need plenty of help but it pays off really well. During the few years we lived in the South Pasadena School District they all become honors students. My daughter has been straight A throughout the middle school, and the boys are not that different either. Except for being boys...
As a side note, I have held various level teaching appointments in two Universities -- I've had a Teaching Faculty position in Romania, and I've been teaching (as part of my PhD program) at the Univ of Pittsburgh.
I can help with a variety of subjects. We can work together on Math, Physics, get familiar with the various components of Microsoft Office, or write Software in all kinds of programming languages. I can help you learn use your Windows computer or your Linux laptop.
As a summary, if you need help with Math, Physics, or Computers, let me know. I should be available mostly in the afternoons/evenings, weekends, or even in the early morning hours (if this is what you prefer).
Get it touch with me if you are interested.
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.
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.
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.
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.
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++.
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 on these is more or less straightforward. Given the central role of the type of differential equations one uses in the business of modeling black holes, I have worked with these from very early on in my science career.
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.
Besides being a scientist myself, I have been tutoring my children from elementary school through high school.
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.
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.
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 for modeling the type of equations one has to deal with for a particular problem. Given the central role of Linear Algebra in numerical work, I have been using it, starting with my Graduate studies, either for construction of new numerical schemes or studying the properties of the numerical methods we've been sometimes struggling to get to work properly.
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. My daily work is done on Linux computers. And this has been the case for the past 15+ years.
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, asking Mathematical do simplify all it can, whichever way it can.
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 organization. With these applications under my belt, I am confident tutoring in this subject is well within reach.
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.
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 confident I am able to tutor students at various levels of this language.
Very nice tutor — Bela was very patient with my son. It was very important for us to find someone who is very knowledgeable in respect to Astronomy, which is my son's favorite subject. I needed someone to take on the Socratic method of teaching, which would allow my son to critical think and learn through dialogue. I am looking forward to more sessions with Bela, and hope that he can continue to inspire and nurtu ...
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