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I have 22 years of experience in astrophysics. My specialty - theoretical astrophysics. I have 6 papers published in internationally recognozed magazines.

I have 14 years of teaching experience. Courses I have taught - Physical Science, …
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This test measures mathematical skills students are expected to gain in courses taken up to the beginning of the graduation year. It contains 60 problems to be solved in 60 minutes, and covers six content areas: Pre-Algebra, Elementary Algebra, Intermediate Algebra, Coordinate Geometry, Plane Geometry, and Trigonometry.

This course study includes evaluation of algebraic expressions, solving linear and quadratic equations, analysis and graphing of linear and quadratic functions, finding equations of straight lines and parabolas by given parameters and points they are passing through, operations with simple exponential functions such as those related to the processes of growth and decay, solving linear and quadratic inequalities, operations with rational expressions, presentation of numbers in the standard form as well as using scientific notations. The course also includes methods of solving systems of two linear equations, recognizing number patterns, proportions, properties and operations with rational and irrational numbers, basic ideas and concepts of mathematical statistics, finding lines of best fit. Word problems showing the connection of key concepts with real life situations will be a significant part of study in this program.

This course is a study of linear, quadratic, exponential, logarithmic, polynomial and rational functions, as well as functions with radicals. Students have to be able to identify functions by their graphs, analyze their behavior, find critical points, solve equations involving the functions. While solving word problems they have to be able to convert word statements into mathematical

statements. In doing so they will understand the connection between basic ideas and concepts they learn with real-life situations.

Another part of this program is a solving systems of two and three linear equations using various methods , including the method of matrices. Students will learn algebraic operations with matrices, complex numbers, what are arithmetic and geometric series and how to apply them in practical situations.

The course study also includes fundamentals of analytic geometry (describe and recognize conic shapes by their equations), discrete mathematics (permutations and combinations of elements), their simple applications in theory of probability.

The last topics of the program include triangle trigonometry and trigonometric functions, their equations and reciprocal trigonometric functions, applications in geometry.

Astronomy is the one of ancient sciences. It refers to study of planets and their motion, small bodies of the solar system, stars and their motion as well as their physical properties (temperature, atmosphere, mass, luminosity, spectra, etc.), the origin and evolution of stars.

Motion and dynamics of many astronomical objects in the Milky Way and the Universe can be described within the Newton's theory of gravitation.

One of important branches of astronomy is called "galactic astronomy" which is dealing with the districbution and motion of stars and their systems (such as multiple stars, groups and clusters, open and globular) in the Milky Way, evolution of stellar systems, formatiion of stars in the interstellar medium (includes nebulae and molecular clouds).

In this course students will learn what are variable stars, nova and supernova stars, white dwarfs, neutron stars (pulsars), black holes, and they relate to initial masses of evolving stars.

Extragalactic astronomy and Cosmology are other two exciting branches of astronomy. The first one is a study of galaxies, their groups and clusters, as welll as superclusters of galaxies, their origin and evolution. Cosmology is a study of the Universe as one whole system, its origin and evolution. Cosmological studies are based on Big Bang theory.

Historical aspects of astronomy are very important. Students will learn how people developed different models of the universe in the course of history.

This course is a study of limits of number sequences and functions, classification of functions (such as continuous, discontinuous, monotonic, etc.), study of derivatives and integrals of the functions, divergency or convergency infinite numerical and functional series, polynomial approximations of the functions, differentiation and integration techniques.

These methods help to analyze behavior of different types of functions, their maximum and minimum points, their curvature in different intervals, solve optimization problems, calculate lengths of curved lines, areas and volumes of 2- and 3- dimensional regions and shapes using cartesian, polar spherical and cylindrical coordinate systems. Methods of Calculus show how to integrate proper and improper integrals using Jacobian matrix, transforming integration variables from one system to another, how to solve different types of differential equations (method of separation of variables, Bernulli's method, Laplas transform, etc.). Methods of Calculus include also vector analysis, their applications in analytical geometry, partial differentiation (for functions with multiple variables), integration of multiple integrals.

Geometry is a branch of mathematics concerned with properties of objects such as points, lines, angles, circles and other shapes, either 2 or 3 - dimensional. The word 'geometry" is a combination of two greek words - "geo" (means "land", 'earth")and "metron" (measure). Thus, geometry includes calcuations of such characteristics of geometric shapes as perimeters, areas and volumes.

High School geometrty is a Euclidean Geometry in which the distance between two points in the plane or space (metrics) is defined by Pythagorean theorem for right triangles.

Euclidean geometry is based on a set of axioms - statements without proof, taken for granted as true statements. Any other statement in geometry must be proven. Those statemnets are called theorems. Students will learn what are inductive and deductive reasonoing, and how to apply them to prove geometric statements.

The course of geometry can be divided into two areas: plane geometry (2-dimensional) and space geometry (3-dimensional).

In the plane geometry we are dealing with objects such as points, lines (curved and parallel), their disposition with respect to each other, circles, coordinate plane, triangles and quadrilaterals, polygons, Pythagorean theorem, definitions of basic trogonometric functions and their simple applications in problems involving triangles and regular polygons. The plane geometry is also dealing with transformations of a palne such as rigid motion and translation, reflection and rotation as well as their combinations (composite transformations).

In the plane geometry students will learn what are vectors, what are similar triangles and polygons, dilations, how to calculate areas of different shapes, sine and cosine theorems.

In space geometry students will learn the classifcation of solids (spheres, cylinders, cones,pyramids, prisms, polyhedrons) and how to calculate their areas and volumes,

Study of physics comprises the following areas:

1. Mechanics (study of motion). It includes description of a moving particle(s) or body(s)and explanation of its/their motion. The first part is called kinematics and refers to calculating velocity of motion, distance traveled, accelertaion of motion, time elapsed, trajectory of motion. The second part refers to dynamics which is dealing with Newton's three laws of motion, different types of forces of nature,linear momentum, the law of conservation of linear momentum in isolated systems. Students have to know definitions of all physical quantities they study, their Metric (international)units alongside with English units they used to apply in everyday life.

Students will learn what is work, energy, what is the law of conservation of energy, what are forms of energy and how they can be transformed one into another, how to measure work and energy, and what are their Metric units of measurement.

Mechanics also includes the study of the Universal Law of Gravitation and rotational motion, the concept of torque and its application in statics (examples - constructions). The last topics of mechanics include study of motion of liquids (hydrostatics and hydrodynamics - Pascal's law, buoyant force, Bernulli's principle).

2. Thermodynamics. This part of physics is dealing with transfer and exchange of thermal energy (heat) between physical systems and their environment. It includes the study of laws of thermodynamics (the law of conservation of energy (in more generic form), increase of entropy in closed physical systems), gas laws and and their application in real life situations,theremodynamic processes and energy exchange associated with them.

3. Physics of sound ways. Transfer of sound ways is not a purely mechanical process, but also refers to thermodybnamic characteristics of a transfering medium. Students will learn what types of sound waves we observe in nature, what are the physical characteristics of sound waves (which are the characteristics of any types of waves) such as amplitude,wavelength, frequency, speed, how sound the frequency of sound waves changes with the speed of source of sound (Doppler effect).

4. Optics - study of intercation of light and matter. It refers to refraction and reflection of light in different media and optical devices, constructing optical images in lenses, defining their focal distances and other characteristics (geometric optics), study of diffraction and interference of light (wave optics).

5. Electricity and magnetism - study of various physical phenomena associated with motion of electrically charged particles and their relation with the existence and the origin of magnetic fields. Students will learn basic definitions and equations regarding characteristics of electric and magnetic fields (Coulomb force,strength, potential, current,voltage, elecgtrostatic and magnetic induction), characteristics of electric circuits and magnetic properties of materials, and how they are used in physical devices, what are electromagnetic waves and their practical use for our everyday needs.

6. Atomic physics - study of structure of atoms and atomic nucleui, their relation to quantum mechanics, structure of the periodic table of chemical elements,and elementary particle physics, discovery and properties of elementary particles, their importance for understanding the structure and evolution of the Universe today.

Precalculus emphsizes many topics studied in the course of Algebra 2, but does it in more profound basis. It is more focused on graphing and analysing behavior of quadrtaic, exponential, logarithmic, polymomial and rational functions, as well as functions with radicals, calculating their critical points, solving equations involving these functions, finding horizontal and vertical asymptots. In a Precalculus course students will study in more details properties of polynomial functions, how to find their roots and factors, methods of long and sysnthetic division.

In a Precalculus program the method of matrix algebra is used to solve systems of linear equations. Systems of quadratic equations and inequalities are also part of the program, as well as concepts of mathematical statistics and probability (such as binomial and normal distribution). Students will have more practice with trigonometric fucntions and their reciprocals, their graphical representations, trigonometric transformations (identities) and their applications in solving trigonometric equations and inequalities.

SAT Math tests problem solving and thinking skills for students who have covered 10- grade math program. Problem solving tests contain 10 multiple choice questions each. Grid ins test contains 10 questions of student response. Each of them is given 12 minutes for completion. In this program we will use sample tests from available books as well as websites.

The course of Trigonometry is based on study of properties and graphs of basic trigonometric functions, such as sin, cos, tan, cot and their reciprocals, their characterristics (such as amplitude, period, phase, frequency), trigonometric relationships (identities), methods of solving trigonometric equations. Students will learn the connection between Trigonometry and the theory of complex numbers, applications of triconometric concepts in real-life situations, involving 2- and 3- dimensional geometry problems as well as problems of physics and astronomy.

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Certified Physics and Math Teacher G.S.