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.

##### 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
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...