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Hi, my name is Philip; although, I usually am called by my Orthodox Name, which is Michael. I studied Mathematics at Georgia College and State University (now simply Georgia College) in Milledgeville, Georgia. I really enjoyed learning more about and going deeper into not only the subject of Mathematics, but how to apply math to various applications in real-life.
I am extremely passionate regarding my area of expertise. One of my strong suits is my passion, and love for the subject matter, and I embody that by thoroughly enjoying tutoring young people in this sometimes difficult subject. When I was getting my core classes taken care of at Middle Georgia College in my hometown of Cochran I tutored many students (both through the school and privately) in a wide area of levels of maths; ranging from basic Algebra to Calculus, and Linear Algebra. Many of the students liked my passion and zeal for helping them, and if at that time I did not know (or perhaps forgot) how to do a certain formula or solve a particular equation type, I would use my reference sources to find out the answer, and would not rest until the student and I were both satisfied with the result.
I believe that not only do I know the subject matter well, but really and truly possess a care and concern for the student understanding what is going on in each particular situation. I do not simply want them to learn by 'rote', but want them to understand what is going on, why, and how (if applicable and time permits) this particular equation or formula is used in 'real-life' applications. Simply 'plugging-in' to a formula and 'memorizing' the formula is not enough - the student eventually will forget this; whereas if they learn the why, and how; they (more than likely) will remember how to solve a particular equation in the future when it comes up.
Additionally, I will soon be substitute teaching - primarily to gain teaching experience. Eventually, the goal is for me to go back to school; obtain a Master's in Mathematics; and work towards teaching college. I look forward to the ability to help your students/children learn, attain your/their goals, and succeed!
Algebra I is the study of basic algebra, including rational and radical expressions, as well as polynomials. Here, a student learns how to solve linear equations,and then moves on to learning how to solve quadratic, other polynomial equations, and radical equations by factoring. Additionally, for quadratic equations, the quadratic formula is taught here. Also, the concept of complex numbers is taught and the idea of absolute value.
Students will also learn about the Cartesian or Rectangular coordinate system, how to graph lines, and polynomial functions. They will learn about the concept of a function itself, and deal with the notion of quadratic functions, as well as general polynomial functions, rational functions, and inverse functions.
Additionally, many applications of these ideas will be 'sprinkled' throughout these lessons.
Algebra II is a continuation of the topics taught in Algebra I. Here the student goes on to learn the ideas of inverse functions, and then to apply those ideas to exponential functions, and their inverse - the logarithmic function.
Also, they are taught how to solve systems of linear equations, by substitution, and elimination. Then those same systems are solved by a technique using what is known as a matrix (think of an array of numbers/variables). Next, matrix algebra is taught, as well as the notion of determinants, and the idea of partial fractions.
Then, they will learn to graph linear and quadratic inequalities. And finally, there is a whole chapter devoted to conic sections such as the circle, hyperbola, parabola, and the ellipse. Additional topics that may or may not be covered include sequences, series, and basic probability.
Calculus is the essentially the study of the infinite. The basis of the calculus is the limit, which allows us to approach something (typically a point, line, or plane) infinitely close and then observe the behavior at that infinitely close position.
Using the notion of limits and the limiting process as the basis of the calculus, we arrive at the two pillars or foundations of the calculus - namely the derivative and the integral.
In the case of the former (the derivative), the student learns that the derivative is essentially the slope of the line tangent to a given line (or later on to a given plane for calculus 3). The student should be able to recall how to find the slop of the secant line, and now we employ the limiting process to enable us to find the slope of the tangent line. Many applications are to be found, especially in Engineering and Psychics. We will also be teaching the students the notion of a linear approximation to a curve, that is if given an equation of a line, and a point on that line, how can we approximate the value of the curve at that point.
Now on to the integral. The integral is basically the area under a curve (or later on in Calculus 3, the volume under a curve). Here, we use 'little' rectangles to approximate the area, then find the limit of these areas as the number of rectangles goes to infinity.
Of course, the calculus contains much more than this, such as a much more in depth explanation (than that received in Algebra) of sequence and series, and many, many applications. I received my certification and credentials in this area by successfully completing the calculus sequence at GA College - Calculus 1, 2, and 3.
Mathematical Logic is - at a somewhat lower level - a branch of mathematics that deals with what might be called variously as the Foundations of Mathematics or the Fundamentals of Mathematics. This branch of mathematics initially the study of mathematical propositions, theorems, logical connectives, logical implications, and all of the basic language needed in order to understand the essence of and how to prove mathematical theorems.
After learning the basic logic mentioned above, basic proof theory is taught - including direct proof, proof by contrapositive, and proof by contradiction. Sometimes, fundamental ideas such as set theory, the concepts of functions relations, and cardinality are also taught in this type of mathematics. Basically, this subject prepares a student for higher math classes and allows him/her to develop a foundation in mathematics.
Mathematical logic or Foundations can be taught at the Undergraduate Level in a class called simply Foundations, or Fundamentals of Mathematics, and that is where I received my training and credentials in this subject. There, I learned about basic mathematical logic, connectives, disjunctions, implications, if and only if statements, and conditional clauses. I then learned various proof methods, including direct proof, proof by contrapositive, proof by contradiction, and proof by mathematical induction.
Pharmacology is the study of medications (drugs) and their action in the human body. This course is a requirement for a Nursing license and for a license as a Pharmacology Technician.
My expertise in this area comes from when I was studying to be an LPN. I was required to pass [among other things] a Pharmacology test in order to obtain my LPN license.
Pre-Algebra is basically a transition from the 'concreteness' of arithmetic (which to some extent can be done with the hands - or at least can be visualized more readily) to a bit of abstraction. In this gradual step towards abstraction, symbols (letters usually) are gradually used to replace numbers.
So, for instance, while the student begins adding, subtracting, multiplying, and diving numbers, he/she will eventually be adding, subtracting, multiplying, and dividing algebraic expression (combinations of numbers and letters). They are taught that these letter (know as variables) are used essentially as place-holders to represent a specific number. They then go on to solve basic algebraic equations and are prepared for Algebra 1.
Precalculus is essentially the study of Algebra and Trigonometry. I am certified in this subject because I have taken this class in college and passed it successfully.
In this course, students will study things such as solving linear equations and inequalities, and solving polynomial equations and inequalities. Also, they will be taught the concept of functions, and then the idea of inverse functions which will lead them into the notions of the exponential and logarithmic functions.
In the trigonometry section, the student will be taught the basic trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant-both from the perspective of a right triangle and using the unit circle. They will also be taught basic trigonomtric identities such as the Pythagorean identities, and the sum and difference formulas. Additionally, the graphs of those trig functions will be presented.
Additionally, the student learns the inverse trigonometric functions, and how to solve trigonometric equations. Also, the students will be learning rules such as the Law of Sines and the Law of Cosines and how to apply them.
Additional topics may be taught including sequences, series, matrices, some basic linear algebra, and basic probability.
Sight-singing is the art and skill of being able to use systems such as solfege, or movable do in order to see a new piece of vocal music and be able to apply the taught system (solfege, for example) and use that system in order to sing that piece of music once given the starting pitch.
Once training is begun, the singer learns to associate things such as intervals with different syllables in the various systems; thus enabling him/her to be able to translate this into a relative pitch recognition. As with any skill/ability, practice increases not only the ability of a singer to master this technique, but will also enable the singer to learn to sight-read more and more difficult and more and more chromatic pieces of music as time goes by.
In order for me to gain competence in this area of study, I took 3 semesters of sight-singing that covered this topic from basic scales, and rhythms in the common practice period, up to atonal music.
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