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Kostyantyn M.

Highland Park, NJ

$52/hr

Master of Mathematics

Background check passed as of 2/28/14
Usually responds in about 3 hours

Master of Mathematics

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For the last four years, I have tutored mathematics at a university. The job required me to help any student who comes into the office. Each tutoring session would be with a different student, which meant that students have asked me about a wide range of mathematics courses, ranging from from their pre-calculus course (a condensed review of topics from basic algebra to trigonometry), to certain beginning graduate courses. I have tutored people in Pre-Calculus, Calculus I, Calculus II, Liner Algebra, Differential Equations, Multi-Variable Calculus, Data Analysis (a probability and statistics course), Complex Variables, Partial Differential Equations, and Real Analysis for at least one extended (2-3 hours) session each - and most of these topics for at least several sessions.

From there, I learned that it is significantly easier to solve a problem than to teach someone else how to solve a problem. It is easy to parrot out some memorized facts - and in some areas of study, this is unfortunately required. Mathematics, however, is very different: memorizing facts does not get one far at all. For instance, one could memorize the quadratic formula. The next time one encounters a quadratic equation, one can apply the quadratic formula to solve it. However, what of the related problems about conic sections: finding the vertex of a parabola or the center of an ellipse? The quadratic formula will not help with that. However, knowing how the quadratic formula is derived does help solve these related problems.

This observation is crucial to my methods of tutoring. When someone asks for help with a topic, I aim to instill a thorough understanding of that topic. To that end, if I find that the student has gaps in material that is necessary to understand the material asked about, then I would start by explaining that prerequisite material. If I am only there for a limited amount of time, that means I might never get to the actual question - but that is better than just having the student commit the procedure for this question to memory. In the same vein, I aim to show the reasoning behind material, and that usually means proving the crucial results that are necessary for this problem. More than that, it means helping the student himself or herself figure out a proof. If I succeed in explaining the topic, I may ask a nonroutine problem involving what was just learned. All these approaches are just means to the end of a fuller understanding of the topic asked about.

Testimonials

"So very brilliant!"

- Renee, New Brunswick, NJ on 6/13/14

"Doing a Great Job"

- Patience, Bronx, NY on 4/22/14
Math:
ACT Math, Algebra 1, Algebra 2, Calculus,
Discrete Math,
Finite Math,
Geometry, Linear Algebra,
Logic, Prealgebra, Precalculus, Probability,
SAT Math, Statistics,
Trigonometry
English:
Grammar
Science:
Chemistry
Computer:
C++, Computer Science,
Microsoft Excel
Language:
French
History:
European History
Elementary Education:
Elementary Math, Grammar
Business:
Microsoft Excel
Homeschool:
Algebra 1, Algebra 2, Calculus,
Chemistry, French, Geometry, Prealgebra, Precalculus, SAT Math, Statistics
Test Preparation:
ACT Math, SAT Math
Corporate Training:
C++, French, Grammar, Microsoft Excel, Statistics

Approved subjects are in bold.

Approved subjects

In most cases, tutors gain approval in a subject by passing a proficiency exam. For some subject areas, like music and art, tutors submit written requests to demonstrate their proficiency to potential students. If a tutor is interested but not yet approved in a subject, the subject will appear in non-bold font. Tutors need to be approved in a subject prior to beginning lessons.

Calculus

I have taken Calculus AB and BC, and later tutored Calculus I and II. Additionally, I took a slew of subjects that crucially depend on knowledge of the material in calculus - differential equations, multivariable calculus, data analysis complex variables, and real analysis. I have experience tutoring all these subjects, and the calculus topics came up directly - especially integration techniques and limits.

Computer Science

I have taken two computer language courses, Python and C++ (the C++ course included a detailed lecture on pointers). I have also taken a range of courses in theoretical computer science: data structures (which include the C++ standard template library), artificial intelligence, algorithm analysis, theory of computation, and machine learning. I have also taken a numerical analysis course that required writing programs to solve problems. I have had the occasion to tutor algorithm analysis.

Discrete Math

I have taken a discrete math course covering: logic, sets, proofs (including induction), quantifiers, big-O notation, recurrence relations, graph theory and automata theory. I have also used all of these topics in more advanced classes - real analysis (big-O notation is defined the same way as limits), topology (where quantifier manipulation is essential), algorithm analysis (big-O notation is essential, and the runtime of an algorithm is often the solution of a recurrence relation, and which also included topics like graph-traversal algorithms), and theory of computation (proofs about automata). I have had occasion tutoring real analysis and algorithm analysis, and some of these topics came up directly - for instance, use of Master's theorem and supremum definition (using quantifiers).

Finite Math

I have taken advanced courses which cover the finite mathematics topics in greater detail. I took linear algebra at the graduate level, which rigorously covered matrices. I took discrete mathematics, which covered logic and finite differences. In real analysis and topology, there were lots of proofs that used manipulation of quantifiers (such as epsilon-delta definitions). I took an advanced course in probability, which covered topics such as two-dimensional probability density functions and conditional expectation and variance. I had occasion to help students in all these higher level classes. The topics that would be covered in finite mathematics occasionally appeared directly: proofs with quantifiers, combinations and permutations, and determinants of matrices are just a few such topics. They also appeared as topics necessary to understand to solve more difficult problems.

Linear Algebra

I have taken a graduate course in Linear Algebra, covering the standard topics (vector spaces, linear transformations (and ranges and kernels of them), determinant, inverse matrices, eigenvalues, diagonalizability) in detail, and then proceeding to inner product spaces and then to properties of symmetric matrices. I also took differential equations, which used linear algebra topics - eigenvalues and eigenvectors and diagonalization - to solve systems of first-order linear differential equations. I gained more experience with Hermitian linear operators in a quantum chemistry class. I had occasion to directly tutor most of the linear algebra topics mentioned above.

Probability

I have taken an advanced probability course covering two-dimensional probability-density functions, conditional expectation and variance, multivariable normal distribuitons, modes of convergence of random variables, the law of large numbers, the central limit theorem (both being proved), moment-generating and characteristic functions, Markov chains, random processes and simulation. Such topics use topics found in a standard probability course extensively - one-dimensional distributions, expectation and variance, dependence between events. For the combinatorial aspects of a typical probability course, I have taken an advanced course in combinatorics - culminating in generating functions that reduce problems about finding the number of ways to distribute indistinguishable objects into finding coefficients of a polynomial.

Statistics

I have taken two statistics courses, covering: combinatorics, definition of probability, probability mass and probability density functions, expectation, variance, the normal, t, and chi-square distributions, moment-generating functions, estimators, confidence intervals, and hypothesis testing. I have also used those topics in more advanced classes - advanced probability, advanced combinatorics, and machine learning. In advanced probability, two-dimensional probability density functions, conditional expectation and variance, and moment-generating functions were covered; in advanced combinatorics, additional methods of counting arrangements were covered - one such topic is distributing indistinguishable objects in distinguishable piles; the machine learning course made use of estimators and the probability density function of the normal distribution. I had occasion to tutor combinatorics topics, probability density functions, expectation and variance, and use of normal tables in the context of a probability or data-analysis class.

Trigonometry

I have taken numerous courses that require knowledge of trigonometry: calculus, linear algebra, differential equations, complex variables, and partial differential equations. Some integrals require a technique known as trigonometric substitution, which requires knowledge of several trigonometric identities. Additionally, changes of variables of multiple integrals occasionally require trigonometric functions. In linear algebra, rotation matrices use trigonometric functions directly. In complex variables, trigonometric functions appear as real and imaginary parts of complex exponentials. In differential equations and partial differential equations, trigonometric functions appear as solutions to problems.

Kostyantyn’s Resources

Tutors have the ability to create educational resources and share them with the WyzAnt community. Here are some of the resources created by Kostyantyn. View all of Kostyantyn’s resources

Using the Ideal Gas Law, PV = nRT:   n = PV/RT = (101.3 kPA*22.4L)/(8.31 J/(mol K) * 273 K) = = (101.3 * 1000 N/m^2 * 22.4/1000 m^3)/(8.31 N m/(mol K) * 273 K) = = (101.3 * 22.4 N m)/(8.31 * 273 N m/mol) = = (101.3 * 22.4/(8.31*273)) mol = = 1.00022 mol   Number...

sin(theta)*cos(theta) = cos(theta) sin(theta)*cos(theta) - cos(theta) = 0 cos(theta)*(sin(theta) - 1) = 0   cos(theta) = 0 OR sin(theta) = 1   cos(theta) = 0: pi/2, 3pi/2 sin(theta) = 1: pi/2   Final answer: {pi/2, 3*pi/2}

4*cos^2(x) + 2*sin^2(x) = 3 2*cos^2(x) + 2*cos^2(x) + 2*sin^2(x) = 3 2*cos^2(x) + 2*(cos^2(x) + sin^2(x)) = 3 2*cos^2(x) + 2*1 = 3 2*cos^2(x) = 1 cos^2(x) = 1/2 cos(x) = +- sqrt(2)/2   Solutions with the + sign: pi/4, 7pi/4   Solutions...

Polytechnic Institute of New York University
Mathematics
Polytechnic Institute of New York University
Master's

Education

Polytechnic Institute of New York University (Mathematics)

Polytechnic Institute of New York University (Master's)

So very brilliant! — Nice guy, great tutor, very professional. He tutors my college daughter and I feel like Harvard is in my family room. ...

— Renee, New Brunswick, NJ on 6/13/14

Hourly fee

Standard Hourly Fee: $52.00

Cancellation: 24 hours notice required

I do not offer any free sample sessions. For long sessions, as long as we agree beforehand, my rate is lower: $45/hour for a 2-3 hour session; $35/hour for a session at least 3 hours long.

Travel policy

Kostyantyn will travel within 5 miles of Highland Park, NJ 08904.


About Kostyantyn

For the last four years, I have tutored mathematics at a university. The job required me to help any student who comes into the office. Each tutoring session would be with a different student, which meant that students have asked me about a wide range of mathematics courses, ranging from from their pre-calculus course (a condensed review of topics from basic algebra to trigonometry), to certain beginning graduate courses. I have tutored people in Pre-Calculus, Calculus I, Calculus II, Liner Algebra, Differential Equations, Multi-Variable Calculus, Data Analysis (a probability and statistics course), Complex Variables, Partial Differential Equations, and Real Analysis for at least one extended (2-3 hours) session each - and most of these topics for at least several sessions.

From there, I learned that it is significantly easier to solve a problem than to teach someone else how to solve a problem. It is easy to parrot out some memorized facts - and in some areas of study, this is unfortunately required. Mathematics, however, is very different: memorizing facts does not get one far at all. For instance, one could memorize the quadratic formula. The next time one encounters a quadratic equation, one can apply the quadratic formula to solve it. However, what of the related problems about conic sections: finding the vertex of a parabola or the center of an ellipse? The quadratic formula will not help with that. However, knowing how the quadratic formula is derived does help solve these related problems.

This observation is crucial to my methods of tutoring. When someone asks for help with a topic, I aim to instill a thorough understanding of that topic. To that end, if I find that the student has gaps in material that is necessary to understand the material asked about, then I would start by explaining that prerequisite material. If I am only there for a limited amount of time, that means I might never get to the actual question - but that is better than just having the student commit the procedure for this question to memory. In the same vein, I aim to show the reasoning behind material, and that usually means proving the crucial results that are necessary for this problem. More than that, it means helping the student himself or herself figure out a proof. If I succeed in explaining the topic, I may ask a nonroutine problem involving what was just learned. All these approaches are just means to the end of a fuller understanding of the topic asked about.

Testimonials

"So very brilliant!"

- Renee, New Brunswick, NJ on 6/13/14

"Doing a Great Job"

- Patience, Bronx, NY on 4/22/14
}

Education

Polytechnic Institute of New York University
Mathematics
Polytechnic Institute of New York University
Master's

Education

Polytechnic Institute of New York University (Mathematics)

Polytechnic Institute of New York University (Master's)


Tutor Policies

Cancellation
24 hours notice required

I do not offer any free sample sessions. For long sessions, as long as we agree beforehand, my rate is lower: $45/hour for a 2-3 hour session; $35/hour for a session at least 3 hours long.

Travel Radius
Travels within 5 miles of Highland Park, NJ 08904

Kostyantyn’s Subjects

Math:
ACT Math, Algebra 1, Algebra 2, Calculus,
Discrete Math,
Finite Math,
Geometry, Linear Algebra,
Logic, Prealgebra, Precalculus, Probability,
SAT Math, Statistics,
Trigonometry
English:
Grammar
Science:
Chemistry
Computer:
C++, Computer Science,
Microsoft Excel
Language:
French
History:
European History
Elementary Education:
Elementary Math, Grammar
Business:
Microsoft Excel
Homeschool:
Algebra 1, Algebra 2, Calculus,
Chemistry, French, Geometry, Prealgebra, Precalculus, SAT Math, Statistics
Test Preparation:
ACT Math, SAT Math
Corporate Training:
C++, French, Grammar, Microsoft Excel, Statistics

Approved subjects are in bold.

Approved subjects

In most cases, tutors gain approval in a subject by passing a proficiency exam. For some subject areas, like music and art, tutors submit written requests to demonstrate their proficiency to potential students. If a tutor is interested but not yet approved in a subject, the subject will appear in non-bold font. Tutors need to be approved in a subject prior to beginning lessons.


Kostyantyn’s Resources

Tutors have the ability to create educational resources and share them with the WyzAnt community. Here are some of the resources created by Kostyantyn. View all of Kostyantyn’s resources

Using the Ideal Gas Law, PV = nRT:   n = PV/RT = (101.3 kPA*22.4L)/(8.31 J/(mol K) * 273 K) = = (101.3 * 1000 N/m^2 * 22.4/1000 m^3)/(8.31 N m/(mol K) * 273 K) = = (101.3 * 22.4 N m)/(8.31 * 273 N m/mol) = = (101.3 * 22.4/(8.31*273)) mol = = 1.00022 mol   Number...

sin(theta)*cos(theta) = cos(theta) sin(theta)*cos(theta) - cos(theta) = 0 cos(theta)*(sin(theta) - 1) = 0   cos(theta) = 0 OR sin(theta) = 1   cos(theta) = 0: pi/2, 3pi/2 sin(theta) = 1: pi/2   Final answer: {pi/2, 3*pi/2}

4*cos^2(x) + 2*sin^2(x) = 3 2*cos^2(x) + 2*cos^2(x) + 2*sin^2(x) = 3 2*cos^2(x) + 2*(cos^2(x) + sin^2(x)) = 3 2*cos^2(x) + 2*1 = 3 2*cos^2(x) = 1 cos^2(x) = 1/2 cos(x) = +- sqrt(2)/2   Solutions with the + sign: pi/4, 7pi/4   Solutions...


Background Check Status for Kostyantyn M.

Kostyantyn M. passed a background check on 2/28/14. The check was ordered by Kostyantyn through First Advantage. For more information, please review the background check information page.

After sending a message to Kostyantyn, you will be able to order a new background check for $7.99. As part of your tutor selection process, we encourage you to run updated background checks. Please also review the safety tips for hiring tutors.