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Email Matthew K.

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Mathematics is not a subject to be understood only by a select few. As such, it is important for mathematics to be presented in a way that makes sense to each student. My time spent as a private tutor, mathematics teaching assistant at Stony Brook University, and instructor of mathematics at Stony Brook University, has given me the opportunity to establish versatility in instruction. I have worked with students at all grade levels, coming from a variety of educational backgrounds. Whether in a class room setting or one on one, I have had success making mathematics understandable to my students.

Beginning with a conversation, we establish where you are currently, mathematically-speaking, and set a course to grow your understanding of mathematics. On our journey we will fill in background details to make you comfortable with your current your workload and move forward with confidence as we complete new assignments.

Given my firm belief that each student is unique, it is important to establish our starting point and build a learning plan that maximizes your growth as a student of mathematics. Your potential is a formidable resource just waiting to be utilized. By working together, we will tap into your mathematical potential, making you aware of your abilities as an effective student of mathematics. Now aware of your mathematical capabilities, over time you will learn to trust your instincts and thought-process when tackling mathematical problems. Our goal will be to make you an independent mathematical thinker. With that said, I look forward to exploring mathematics with you.

Please feel free to send any questions to my WyzAnt email address concerning my tutoring approach and how it will help you strengthen your understanding of mathematics.

Best,

Matthew

Corporate Training:

C++, General Computer, GMAT, Java, Microsoft Excel, Microsoft Word, Networking (Computer), Statistics

Homeschool:

Computer:

C++, Computer Programming, DOS, General Computer, Java, Linux, Macintosh, Microsoft Excel, Microsoft PowerPoint, Microsoft Windows, Microsoft Word, Networking (Computer)

In preparation for ACT Math questions, we will focus on:

1. Pre-Algebra: basic operations using whole numbers, decimals, fractions, and integers; place value; square roots and approximations; the concept of exponents; scientific notation; factors; ratio, proportion, and percent; linear equations in one variable; absolute value and ordering numbers by value; elementary counting techniques and simple probability; data collection, representation, and interpretation; and understanding simple descriptive statistics.

2. Elementary Algebra: properties of exponents and square roots, evaluation of algebraic expressions through substitution, using variables to express functional relationships, understanding algebraic operations, and the solution of quadratic equations by factoring.

3. Intermediate Algebra: an understanding of the quadratic formula, rational and radical expressions, absolute value equations and inequalities, sequences and patterns, systems of equations, quadratic inequalities, functions, modeling, matrices, roots of polynomials, and complex numbers.

4. Coordinate Geometry: graphing and the relations between equations and graphs, including points, lines, polynomials, circles, and other curves; graphing inequalities; slope; parallel and perpendicular lines; distance; midpoints; and conics.

5. Plane Geometry: properties and relations of plane figures, including angles and relations among perpendicular and parallel lines; properties of circles, triangles, rectangles, parallelograms, and trapezoids; transformations; the concept of proof and proof techniques; volume; and applications of geometry to three dimensions.

6. Trigonometry: understanding trigonometric relations in right triangles; values and properties of trigonometric functions; graphing trigonometric functions; modeling using trigonometric functions; use of trigonometric identities; and solving trigonometric equations.

[Algebra 1] An introduction and familiarization with the following topics, where we will cover:

1. Number Theory

2. Operations

3. Variables and Expressions

4. Equations and Inequalities

5. Patterns, Functions, and Relations

6. Trigonometric Functions

7. Coordinate Geometry

8. Shapes

9. Measurement

10. Working with Data

11. Probability

[Algebra 2] Focus is placed on familiarization with the following topics, where we will cover:

1. Operations

2. Variables and Expressions

3. Equations and Inequalities

4. Patterns, Functions, and Relations

5. Coordinate Geometry

6. Trigonometric Functions

7. Measurement

8. Statistics and Probability

I have successfully completed coursework at Polytechnic Institute of NYU with an overall GPA of 4.00 out of 4.00. At Polytechnic Institute of NYU, the following coursework (pertaining to Computer Programming) was covered in detail: Introduction to Programming (C++), Data Structures and Algorithms (C++). Most importantly, I work professionally as a Software Engineer where I regularly use C++ to provide customized solutions to customers.

In Calculus we explore the world of counting/measurement as we cover topics such as:

1. Functions

2. Limits

3. Derivatives and their applications

4. Integrals and their applications

5. Proofs addressing concepts of Calculus

I have successfully completed coursework at Polytechnic Institute of NYU with an overall GPA of 4.00 out of 4.00. At Polytechnic Institute of NYU, the following coursework (pertaining to Computer Programming) was covered in detail:

Introduction to Programming (C++)

Data Structures and Algorithms (C++)

In addition, I have successfully completed training courses, offered by Learning Tree International, in the following focus areas:

Java Programming: A Comprehensive Hands-On Introduction

Building XML Web Services with Java: Hands-On

Most importantly, I work professionally as a Software Engineer where I regularly use Java and C++ to provide customized solutions to customers.

Topics that we will cover together are:

1. Geometric Relationships

a. Lines and Planes

b. Prisms, Pyramids, Cylinders, Cones, Spheres, Platonic Solids

c. Polygons - Interior and Exterior Angles

2. Constructions

a. Constructions: Copy, Bisect, Perpendicular, Parallel, Isosceles, Equilateral

b. Concurrence of Medians, Altitudes, Angle Bisectors, Perpendicular Bisectors *

3. Locus

a. The Basic Locus Theorems

b. Compound Loci

4. Informal and Formal Proof Why Study Proofs?

a. Logic - Negation, Conjunction, Disjunction, Conditional , Biconditional, Truth

b. Related Conditionals -- Converse, Inverse, Contrapositive

c. Writing a Proof - Direct Euclidean Proofs

d. Writing a Proof - Indirect Euclidean Proofs

e. Congruence of Triangles

f. Angles and Triangles

g. Isosceles Triangle Theorems

h. Triangle Inequality Theorems

i. Parallel Lines and Angles

j. Quadrilaterals

k. Mid-Segment (Mid-Line)of a Triangle

l. Similarity of Triangles

m. Mean Proportional in a Right Triangle *

n. Pythagorean Theorem and Converse

o. Circles: Chords, Secants and Tangents

p. Circles: Angles and Arcs

q. Circles: Area of Sectors and Segments

5. Transformational Geometry

a. Symmetry - Line, Plane, Point, Rotational - Intuitive

b. Reflections - Line, Point

c. Translations

d. Dilations and Similarity

e. Rotations

f. Review of Transformation Information

g. Compositions and Glide Reflections

h. Using the Graphing Calculator to Examine Reflections, Translations, Dilations

i. Using the Graphing Calculator to Examine Rotations

6. Coordinate Geometry

a. Slopes and Equations of Lines

b. Midpoint of a Line Segment

c. Distance Formula

d. Direct Analytic Proofs (Coordinate Geometry Proofs)

e. Linear - Quadratic Systems

f. Circles

We will focus on the Quantitative-based sections of the GMAT which measures the ability to reason mathematically, solve mathematical problems, and interpret graphic data.

Problem-Solving and Data-Sufficiency questions found on the GMAT require knowledge of:

1. Arithmetic

2. Elementary algebra

3. Commonly known concepts of geometry

Problem-Solving questions are designed to test:

1. Basic mathematical skills

2. Understanding of elementary mathematical concepts

3. The ability to reason quantitatively and solve quantitative problems.

Data-Sufficiency questions are designed to measure your ability to:

1. Analyze a quantitative problem

2. Recognize which information is relevant

3. Determine at what point there is sufficient information to solve a problem

We will focus our attention on the following areas of study:

1. Arithmetic topics that include properties and types of integers, such as divisibility, factorization, prime numbers, remainders and odd and even integers; arithmetic operations, exponents and roots; and concepts such as estimation, percent, ratio, rate, absolute value, the number line, decimal representation and sequences of numbers.

2. Algebra topics that include operations with exponents; factoring and simplifying algebraic expressions; relations, functions, equations and inequalities; solving linear and quadratic equations and inequalities; solving simultaneous equations and inequalities; setting up equations to solve word problems; and coordinate geometry, including graphs of functions, equations and inequalities, intercepts and slopes of lines.

3. Geometry topics that include parallel and perpendicular lines, circles, triangles — including isosceles, equilateral and 30°-60°-90° triangles — quadrilaterals, other polygons, congruent and similar figures, three-dimensional figures, area, perimeter, volume, the Pythagorean theorem and angle measurement in degrees.

4. Data analysis topics that include basic descriptive statistics, such as mean, median, mode, range, standard deviation, interquartile range, quartiles and percentiles; interpretation of data in tables and graphs, such as line graphs, bar graphs, circle graphs, boxplots, scatterplots and frequency distributions; elementary probability, such as probabilities of compound events and independent events; random variables and probability distributions, including normal distributions; and counting methods, such as combinations, permutations and Venn diagrams.

As an instructor (during graduate school) at Stony Brook University in the Department of Applied Mathematics and Statistics, I have:

1. Designed and led undergraduate lectures in Linear Algebra

2. Examined applications of Linear Algebra to engineering and business with my students

3. Fostered critical thinking of students during class time and during office hours

In the exploration of Linear Algebra we will introduce the theory and use of vectors and matrices; Matrix theory including systems of linear equations; Theory of Euclidean and abstract vector spaces; Eigenvectors and eigenvalues; as well as Linear transformations.

We will cover topics such as:

1. Number Theory

• Properties of Real Numbers

2. Operations

• Radicals

• Scientific Notation

• Fractions, Percents, Ratios, Proportions

• Direct/Indirect Variation

• Exponents (Powers)

• Factorials

• Absolute value

• Rational and Irrational Numbers

• Order of Operations

• Signed Numbers

We will focus on the following topics:

1. Functions

2. Inverse Functions

3. Trigonometric Functions

4. Solving Trigonometric Equations

5. Exponential Functions

6. Logarithmic Functions

7. Solving Exponential and Logarithm Equations

8. Common Graphs

We will place an emphasis on the following topics:

1. Probability spaces

2. Random variables

3. Moment generating functions

4. Algebra of expectations

5. Conditional and marginal distributions

6. Multivariate distributions

7. Order statistics

8. Law of large numbers.

As a graduate of Oceanside High School, I successfully completed New York State Regents track courses in:

Mathematics

Science

History

English

Foreign Language Study (Italian)

I received my New York State Regents Diploma from Oceanside High School in June of 1999. Following receipt of my diploma, I have served as a tutor of mathematics where students of mine have successfully raised their scores a full letter grade.

In preparation for SAT Math questions, we will focus on:

1. Number and Operations:

- Arithmetic word problems (including percent, ratio, and proportion)

- Properties of integers (even, odd, prime numbers, divisibility, etc.)

- Rational numbers

- Sets (union, intersection, elements)

- Counting techniques

- Sequences and series (including exponential growth)

- Elementary number theory

2. Algebra and Functions

- Substitution and simplifying algebraic expressions

- Properties of exponents

- Algebraic word problems

- Solutions of linear equations and inequalities

- Systems of equations and inequalities

- Quadratic equations

- Rational and radical equations

- Equations of lines

- Absolute value

- Direct and inverse variation

- Concepts of algebraic functions

- Newly defined symbols based on commonly used operations

3. Geometry and Measurement

- Area and perimeter of a polygon

- Area and circumference of a circle

- Volume of a box, cube, and cylinder

- Pythagorean Theorem and special properties of isosceles, equilateral, and right triangles

- Properties of parallel and perpendicular lines

- Coordinate geometry

- Geometric visualization

- Slope

- Similarity

- Transformations

4. Data Analysis, Statistics and Probability

- Data interpretation (tables and graphs)

- Descriptive statistics (mean, median, and mode)

- Probability

A survey of data analysis, probability theory, and statistics. Stem and leaf displays, box plots, schematic plots, fitting straight line relationships, discrete and continuous probability distributions, conditional distributions, binomial distribution, normal and t distributions, confidence intervals, and significance tests.

[Trigonometry] Focus is placed on familiarization with the following topics, where we will cover:

1. Operations

2. Variables and Expressions

3. Equations and Inequalities

4. Patterns, Functions, and Relations

5. Coordinate Geometry

6. Trigonometric Functions

7. Measurement

8. Statistics and Probability

A Brilliant Tutor — Matthew K. was able to break down complex subjects in statistics and present them in an easy to understand format until I reached the level of understanding that was needed. Matt thinks out of the box and always tries to explain the matter at hand with examples from other disciplines, which makes it all the more relevant and more easily acquired. I recommend Matthew highly: he is patient, and li ...

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