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I have over 30 years of experience in science and engineering, including a lot of math. My Ph.D. is in Electrophysics, which is a cross between Physics and Electrical Engineering. I've used that experience to tutor my own nieces and nephews, mostly through Intermediate and High School, a little in college. For seven years I was in a position where I had to tutor experienced scientists in areas outside their expertise, and help them write well. I'm best at Math (pre-Algebra, Algebra, Advanced Algebra, Trigonometry, Geometry, Analytic Geometry Calculus, and Statistics) and Physical Sciences (Physics, Chemistry, and general sciences), and I can do well in most other sciences as well (Biology, Geology, etc.). I can also help with English and Social Studies.
Algebra 1 is the base subject, introducing manipulation of variables. This was the class that first got me interested in math. I got my niece and her friends through this class at Palos Verdes Intermediate School; after learning mathematics of numbers for so long, using variables took a shift in thinking.
Algebra II is where algebra becomes more "rigorous"--which means there are a lot of proofs. I took this class when I was in 10th grade, and even then I helped the other students. The secret in this class is to be *organized* -- and that was really hard when I was a sophomore! Now I'm happy to help other people find their own ways to think in algebra terms.
I became interested in Astronomy in third grade, when a friend brought constellation flash cards to school. I have been both an amateur astronomer (using my own telescope, attending observing conferences, etc.) and a professional astronomer (running an observatory, developing experiments to search for planets around other stars, and adding computer controls to old telescopes). I'm still a member of Friends of the (Griffith) Observatory. This is one of my favorite subjects!
Calculus--the study of change and growth--was the class that convinced me to take a lot of advanced math in college. This is the basis for a lot of the work I do every day as a research scientist. My niece is taking Calculus this year, and at least once a week I help her through problem sets or test reviews.
Differential Equations is the next step in Math after Calculus. It is best described as the technique of solving for a function of one or more variables, given one or more equations involving the function itself, its derivatives of various orders, and other functions of the variables.
In both science and engineering I use differential equations to describe things I measure or observe. Solving these equations (and related mathematics, such as complex functions) is the basis of my job, and I enjoy helping others see the beauty of solving differential equations.
Electrical Engineering is the area of engineering having to do with electromagnetism. This includes simple circuits, components such as capacitors, inductors, resistors, diodes, transistors, and sources of current or voltage. By combining these components, more complex devices (amplifiers, lighting systems, power supplies) can be created.
I worked for over 10 years as an electrical engineer, and was certified by the State of California as a Professional Engineer. My expertise is in the normal (analog) circuits that will be covered in a typical Electrical Engineering class, and some basic digital circuits, rather than in complex digital and computer design.
Geometry makes it possible to visualize all the crazy things we learned about in Algebra! For many students (including my niece), this class is a revelation, finally making Algebra understandable, while simultaneously explaining everyday objects mathematically. It was very gratifying to see the sudden comprehension on both my daughter's and my niece's faces as I helped them understand Geometry.
Linear Algebra is the extension of Algebra to cover matrices and arrays. More correctly, it is a study of linear spaces (vector spaces) of at least two dimensions, which accept one vector as an input and return another vector as the output. In general, Linear Algebra includes matrix theory.
I have used Linear Algebra to solve sets of coupled equations. In my everyday work in optics and lasers, I use matrix theory constantly; I even use Linear Algebra to solve problems in quantum physics. I've found it is a lot easier to explain solutions in terms of Linear Algebra than in the raw equations of physics.
Physical Science is a combination of such sciences as Physics, Chemistry, Geology, Astronomy, and other "natural sciences." The combination actually makes more sense than trying to study each of these separately, because they are all closely related (development of stalactites in caves can be explained partially by chemistry, some parts of physics make no sense until they are used in astronomy). I have expertise in all the subsidiary areas and generally do a good job combining the fields into a single explanation.
Physics was my undergraduate minor and the basis of my PhD. It is the most fundamental science; all other natural and life sciences are based on Physics. I've been working as a physicist for more years than I want to count, and still use physics every day, both in my job and in understanding everyday life.
Prealgebra is the preparation for algebra. It introduces the concept of variables, which is a major concept shift that often makes it hard for students to understand algebra. I look at this class from the point of view of someone who uses a lot of algebra, and hope to help students be ready for the conceptual shift.
When I was in high school, we called this subject "Analytic Geometry." The purpose of this class is to prepare the student for calculus, and it is generally done through a combination of proofs (learned in Algebra II) and geometry, including trigonometry. Many students have trouble with the proofs (I know I did!), and I believe the main difficulty is the specific type of organization needed to deal with proofs. I got my niece through this class when she lived 1500 miles away; I can help anyone who is within driving distance!
Trigonometry is the study of triangles and circles. That sounds easy! But it is difficult, not just because of the weird relationships among the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent), but also because of the underlying concept that a periodic function can describe both triangles and circles. Trigonometry is surprisingly useful, critical for astronomy and navigation, for example. In my own work, trigonometric functions are often the solutions to equations I need to solve, so I keep very familiar with the subject.
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