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I have more than 30-year experience teaching mathematics at several colleges (New York City College of Technology, formerly New York City Technical College, and Medgar Evers College, of the City University of New York, St. Francis College, Boricua College and College of New Rochelle). Presently, I am an adjunct lecturer at Boricua College. At this institution I teach the basic algebra prerequisites, including real numbers and their properties, exponents and radicals, polynomials, and special products, factoring polynomials, rational expressions, rectangular coordinate systems and graphs; equations, inequalities; functions and their graphs; polynomial, rational, exponential and logarithmic functions; trigonometry and analytic trigonometry; systems of equations and inequalities, and matrices and determinants.

Additionally,I have 7 years of experience tutoring math & ELA on individual one-on-one basis at students' homes throughout New York City five boroughs. My math teaching and tutoring methods involve an easy approach to learning remedial and advanced mathematics, stressing on practical solutions of problems in algebra, geometry, trigonometry, analytic geometry, infinitesimal calculus, and mathematics for the GED (High School Equivalency Diploma).

I currently teach mathematics at Boricua College. I teach algebra, trigonometry, matrices and determinants, among other subjects. I have taught math for more than thirty years at other high learning institutions in New York City, including New York City College of Technology (formerly New York City Technical College) and Medgar Evers College, of the City University of New York, St. Francis College and College of New Rochelle. I have also been an independent contractor for seven years, tutoring mathematics on individual one-on-one basis throughout New York City five boroughs.

I use an easy approach to learning remedial and advanced mathematics, stressing on practical solutions of problems and theory.

I will tutor, solve problems and go over the class homework assignments with the student.

The subjects and problems I wil work on with student in Algebra 1 include:

- Real or algebraic numbers.

- Addition, subtraction, multiplication & division of real numbers.

- Algebraic expressions.

- Addition, subtraction, multiplication & division of algebraic expressions.

- Factoring monomials, binomials, trinomials & polynomials.

- Additional methods of factorization.

- Fractional algebraic expressions.

- Complex fractions.

- First degree equations.

- Fractional equations.

- Introduction to Cartesian or rectangular coordinates & graphs.

- Systems of equations in two & several variables: analytical and graphical solutions.

- Radical expressions.

My academic credentials:

- B.S. in math and civil engineering from Brooklyn Polytech (1971).

- M.S. in civil engineering from Polytechnic Institute of New York University (1975).

- Ph. D. from Richardson University (1990).

- Teachers'license from The University of the State of New York, Education Department( 2010).

I have taught mathematics for over 30 years at several colleges in New York City, including New York City College of Technology (formerly New York City Technical College) and Medgar Evers College, of the City University of New York, St. Francis College and College of New Rochelle. Presently, I teach mathematics at Boricua College. I have also been tutoring math on individual one-on-one basis for the past seven years, as an independent contractor throughout New York City five boroughs.

I use an easy approach to learning remedial and advanced mathematics, stressing on practical solutions of problems in algebra, geometry, trigonometry, analytic geometry and calculus.

I will tutor, solve problems and go over the class homework assignments with the student. My tutoring subjects in algebra 2 will include:

- Review of Algebra 1 fundamentals.

- Quadratic equations.

- Radical equations.

- Inequalities: linear & quadratic inequalities.

- Long or conventional division of algebraic expressions.

- Synthetic division.

- Binomial expansion.

- Factor theorem: solution of equations of degree > 2.

- Logarithms.

My educational background:

- B.S. in math & civil engineering (Brooklyn Polytech).

- M.S. in civil engineering (Polytechnic Institute of New York University).

- Ph D in political science (Richardson University).

- Teachers' License (The University of the State of New York, Education Department).

I am qualified to tutor French. I am a polyglot (multi-language speaker), a writer, public speaker and language consultant. I have taught French (2001-2004) for the Department of Human Resources, Fairfax County, Springfield, Virginia. I have been a translator and interpreter (French/English/French, and English/Spanish/English for books, newsletters and political and religious institutions in the United States, Europe and Africa, including the World Council of Churches, Catholic Relief Services and the White House. I have written three books in French, English and Spanish. In addition, I have 7 years of experience as an independent contractor, tutoring students on individual one-on-one basis at their homes throughout New York City five boroughs. My teaching and tutoring methods involve an easy approach to learning French, stressing on grammar, reading, writing, translation and practical conversation. My educational background is a B.S. in math & civil engineering from Brooklyn Polytech, an M.S. in civil engineering from Polytechnic Institute of New York University, and a PhD in political science from Richardson University. I also have a Teachers’ License from the University of the State of New York, Education Department, Albany, N.Y.

I will tutor and go over the class homework assignments on the following topics:

1. Fundamentals & grammar:

- The noun: common and proper nouns.

- Genres.

- Feminine of nouns.

- Irregular feminine.

- Plural of nouns.

- The adjective.

- The article.

- The pronoun.

- Personal pronouns.

- Adjectives & possessive pronouns.

- Adjective & demonstrative pronouns.

- Pronouns & relative adjectives.

- Pronouns & interrogative adjectives.

- Pronouns & indefinite adjectives.

- Numeral adjectives.

- Verbs: conjugation of auxiliary verbs AVOIR (to have) and ÊTRE (to be).

- Conjugation of verb AIMER (to love) & FINIR (to finish).

- Conjugation of verb passive ÊTRE AIMÉ (to be loved).

- Conjugation of pro-nominal verb SE FLATTER (to claim or profess to be able)

- Particularities of verbs ending in -ER and -IR.

- Conjugation of verbs OFFRIR (to give), RECEVOIR (to receive), and RENDRE (to give back, return).

- Conjugation of verbs of the 3rd group, ending in -IR, -OIR, and -RE.

- The adverb.

- The proposition.

- The conjunction & interjection.

- The structure of a phrase in French.

2. Practicum:

- Translation of texts from English to French and vice-versa.

- Practical conversation in French.

I use an easy approach to learning mathematics, stressing practical solutions of problems and simple theory.

I use this technique to make the student understand the basic mathematics principles, theorems and axioms, and learn to solve problems. I will tutor, solve problems and go over the class homework assignments with the student. The subjects I will tutor in geometry will include:

- Vertical, supplementary & complimentary angles.

- Congruent & isosceles triangles.

- Parallel lines.

- Sum of angles of a triangle.

- Exterior angles of a triangle.

- Similar triangles.

- Proportions in a right triangle.

Level II:

- Quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid.

- Special right triangles (30, 45 and 60 degrees).

- Circle: tangents to a circle, angles and arcs in a circle, angles made by chords and tangents to a circle, chord and diameter in a circle (inscribed right angle).

- Area: rectangles, squares, parallelograms, triangles, trapezoids, circles.

I am qualified to tutor Pre-calculus. I have taught mathematics for over 30 years at several colleges in New York City, including New York City College of Technology (formerly New York City Technical College) and Medgar Evers College, of the City University of New York, St. Francis College and College of New Rochelle. In addition, I have a 7-year experience as an independent contractor, tutoring math and ELA on individual one-on-one basis at students’ homes throughout New York City five boroughs. I currently teach mathematics at Boricua College, in New York City. My teaching and tutoring methods involve an easy approach to learning remedial and advanced mathematics, stressing on practical solutions of problems in algebra, geometry, trigonometry, analytic geometry, infinitesimal calculus, and mathematics for the GED. My educational background is a B.S. in math & civil engineering from Brooklyn Polytech, an M.S. in civil engineering from Polytechnic Institute of New York University, and a PhD in political science from Richardson University. I also have a Teachers’ License from the University of the State of New York, Education Department, Albany, N.Y.

I will tutor, solve problems and go over the class homework assignments on the following topics:

1. The Real Number System:

- The real numbers.

- Sets, Intervals, and inequalities.

- Absolute value.

- The coordinate plane.

2. Functions and their graphs:

- The function concept.

- Real functions.

- Graphs of functions.

- Construction of functions from other functions.

- Inverse of a function.

- Periodic functions.

- Odd & even functions; zeros of functions.

3. Algebraic functions.

- Polynomials and polynomial functions.

- Linear functions and their graphs.

- Quadratic functions.

- Graphs of quadratic functions.

- Polynomials of higher degree.

- Zeros of a polynomial function.

- Graphing polynomial functions.

- Rational expressions and partial fractions.

- Rational functions and their graphs.

- Irrational algebraic functions.

4. Exponential & logarithmic functions:

- Exponents.

- Exponential functions.

- Law of exponential growth.

- Logarithmic functions.

- Exponential & logarithmic equations.

5. The circular functions:

- The Sine & Cosine functions.

- Other circular functions.

- Fundamental identities.

- The Cosine sum-difference identities

- Sum-difference identities for Sine and Tangent.

- Multiple-value identities.

- Trigonometric equations.

- Graphs of Sine and Cosine functions.

- Graphs of other circular functions.

- The inverse circular functions and their graphs.

6. The trigonometric functions and applications:

- Angle and angle measure.

- Trigonometric functions of angles.

- Trigonometric ratios and right-angle trigonometry.

- Oblique triangles: the Law of Sines & Cosines

7. Coordinate geometry in the plane:

- The straight line.

- The circle.

- The parabola.

- The ellipse.

- The hyperbola.

- Transformation of coordinates.

- Equations in polar coordinates.

- Polar equations.

8. Systems of equations and inequalities:

- Systems of linear equations.

- Systems of equations in three variables

- Matrices and solutions of systems.

- Determinants and Cramer’s rule.

- Systems of inequalities

- Linear programming.

9. Complex numbers:

- Complex numbers and their operations.

- Geometric representation of complex numbers.

- Demoivre’s Theorem: powers and roots.

10. Sequences and series:

- Sequences and series.

- Arithmetic sequences and series.

- Geometric sequences and series.

- Mathematical induction.

- The Binomial Theorem.

I am qualified to tutor SAT Math. I have taught mathematics for over 30 years at several colleges in New York City, including New York City College of Technology (formerly New York City Technical College) and Medgar Evers College, of the City University of New York, St. Francis College and College of New Rochelle. In addition, I have a 7-year experience as an independent contractor, tutoring math and ELA on individual one-on-one basis at students’ homes throughout New York City five boroughs. I currently teach mathematics at Boricua College, in New York City. My teaching and tutoring methods involve an easy approach to learning remedial and advanced mathematics, stressing on practical solutions of problems in algebra, geometry, trigonometry, analytic geometry, infinitesimal calculus, and mathematics for the GED. My educational background is a B.S. in math & civil engineering from Brooklyn Polytech, an M.S. in civil engineering from Polytechnic Institute of New York University, and a PhD in political science from Richardson University. I also have a Teachers’ License from the University of the State of New York, Education Department, Albany, N.Y.

I will tutor, solve problems and go over the class homework assignments on the following topics:

- Numbers and operations.

- Algebra and functions.

- Geometry and measurement.

- Data analysis, statistics, and probability

I am qualified to tutor Spanish. I am a native Spanish-speaker (Spain), a writer, public speaker and Spanish language consultant. I have taught Spanish (2001-2004) for the Department of Human Resources, Fairfax County, Springfield, Virginia. I have been a translator and interpreter (Spanish/English/Spanish, and English/French/English for books, newsletters and political and religious institutions in the United States, Europe and Africa, including the World Council of Churches, Catholic Relief Services and the White House. I have written three books in Spanish and translated them into English and French. Since 2005, I have been an independent contractor, tutoring students on individual one-on-one basis at their homes throughout New York City five boroughs. My teaching and tutoring methods involve an easy approach to learning Spanish, stressing on grammar, reading, writing, translation and practical conversation. My educational background is a B.S. in math & civil engineering from Brooklyn Polytech, an M.S. in civil engineering from Polytechnic Institute of New York University, and a PhD in political science from Richardson University. I also have a Teachers’ License from the University of the State of New York, Education Department, Albany, N.Y.

I will tutor and go over the class homework assignments on the following topics:

1. The Castilian or Spanish alphabet:

- 28 letters , a-z, (including ch, ll, ñ, rr).

2. Castilian and Latin American accents. Pronunciation of the c, ll, rr and the z in Spain and in Spanish speaking America.

3. Spanish grammar:

- Orthography rules:

- Writing names with the letter b.

- Writing names with the letter v.

- Writing names with g and before e or i.

- Writing names with j and before e or i.

- Writing names with the letter h.

- Orthographic use of letter k.

- Writing m.

- Writing r.

- Writing x instead of s.

4. Punctuation:

Prosodic & orthographical accent.

5. Article:

- Noun.

- Genre.

6. Number:

- Formation of plurals.

- Plurals of common names.

- Plurals of proper names.

- Plurals of abstract names.

- Plurals of foreign words or names.

7. Derivations.

8. Adjectives:

- Qualifying adjectives: feminine, plural.

- Level of signification of adjectives: positive, comparative, superlative.

- Agreement of adjectives with several nouns.

- Numeral adjective.

9. Pronoun:

- Adjectives & demonstrative prono0uns.

- Adjectives and possessives pronouns.

- Personal pronouns.

- Relative pronouns.

- Interrogative pronouns.

- Exclamatory pronouns.

- Indefinite pronouns.

10. Adverb.

11. Preposition.

12. Conjunction.

13. Conjunction.

14. Verbs:

- types.

- Accidents of verbs.

- Conjugation of verbs.

- Verbs ending in -LLIR, -ÑER, ÑIR.

- Verbs ending in -CAR, -GAR, -GUAR, -ZAR.

- Verbs ending in -CER, -CIR, -GER, -GIR, -GUIR, -QUIR.

15. Auxiliary verbs HABER ( to have) and SER (to be).

16. Model regular verbs: AMAR (to love), TEMER (to fear) and PARTIR (to break).

17. Conjugation of auxiliary (HABER and SER), regular (AMAR, TEMER and PARTIR) and some

irregular verbs (Examples: andar, mantener, poner, decir, etc.).

18. Practicum:

- Translation of text from Spanish to English and vice-versa.

- Reading & Writing essays in Spanish.

- Conversation in Spanish as it is spoken in Spain.

Presently, I teach mathematics at Boricua College. I teach algebra, trigonometry, matrices and determinants, among other subjects.

My teaching and tutoring techniques involve an easy approach to learning remedial and advanced mathematics, stressing on practical solutions of problems and simple theory so that the student will have a good comprehension of the subject, and he/she is able to solve the assigned problems and do well in school.

Utilizing the same methods I have used with success in more than three decades, I will tutor, solve problems and go over the class homework assignments with the student.

The subjects in trigonometry I will tutor include:

- Angle measurement: degree and radians.

- Trigonometric ratios.

- Special angles.

- Co-terminal angles.

- Quadrants.

- Graphs of trigonometric functions.

- Fundamental relations.

- Reciprocal.

- Trigonometric identities.

- Trigonometric equations.

- Addition formulas.

- Double angle.

- Half angle.

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