Mathematics Courses

We develop Mathematics courses tailored to specific requirements of various secondary College Preparatory schools, such as charter and private schools

Algebra:

Expressions and Equations
Graphs and Lines
Linear and Quadratic Functions
Exponents and Radicals
Polynomials
Complex Numbers
Rational Function
Exponential and Logarithmic Functions
Systems of Equations and Inequalities
Sequences and Series
Introduction to Trigonometry
Trigonometric Functions
Unit Circle
Analytic Trigonometry
Application of Trigonometric Functions
Polar Coordinates
Sequences and Binomial Theorem
Counting and Probability
Analytic Geometry
Introduction to Calculus

Logic:

Informal Fallacies and Definitions
Categorical Propositions
Categorical Syllogisms
Statements, Negations, and Quantified Statements
Compound Statements and Connectives
Conditional statements, bi-conditional statements, tautalogies
Converse, inverse, and contrapositive
Truth Tables for Negation, Conjunction, Disjunction
Truth Tables for the Conditional and the Biconditional
Equivalence of Statements
Argument Forms
Arguments and Truth Tables

Sets:

Basic Set Concepts
Subsets, Power Set, Cartesian Product
Quantifiers
Venn Diagrams and Set Operations
Set Equivalence

Geometry:

Cartesian coordinates
Graphs and Equations
Perpendicular and Parallel Lines
Tangents and Normal Linse
Angles, Triangles, Quadrilaterals
Circle, Parabola, Ellipse, Hyperbola
Loci

Matrices and Vectors:

Linear Algebra
Matrices and Systems of Equations
Systems of Linear Equations
Matrix Arithmetic
Matrix Algebra
Determinants
Basic Vector operations
Vector Spaces
Linear Independence
Basis and Dimension
Row Space and Column Space
Linear Transformations
Matrix Representations of Linear Transformations
The Scalar Product in Rn
Orthogonal Subspaces
Inner Product Spaces
Eigenvalues and Eigenvectors

Probability and Statistics:

Conditional Probability
Independent Events
Bayes’s Theorem
Random Variables of the Discrete Type
Mathematical Expectation
Mean, Variance, and Standard Deviation
Bernoulli Trials and the Binomial Distribution
Poisson Distribution
Continuous-Type Data
Exploratory Data Analysis
Random Variables of the Continuous Type
Uniform and Exponential Distributions
Gamma and Chi-Square Distributions
Normal Distribution
Distributions of Two Random Variables
Correlation Coefficient
Conditional Distributions
Distributions of Functions of Random Variables
Functions of One Random Variable
Transformations of Two Random Variables
Central Limit Theorem
Approximations for Discrete Distributions
Point Estimation
Confidence Intervals for Means
Confidence Intervals for Difference of Two Means
Confidence Intervals for Variances
Confidence Intervals for Proportions
Sample Size
Tests of Statistical Hypotheses
Tests about Proportions
Tests about One Mean
Tests of the Equality of Two Means
Tests for Variances
One-Factor Analysis of Variance
Two-Factor Analysis of Variance
Tests Concerning Regression and Correlation

Business Calculus:

Limits and the Derivatives
Infinite Limits and Limits at Infinity
Continuity
Derivative
Basic Differentiation Properties
Differentials
Marginal Analysis in Business and Economics
The Constant e and Continuous Compound Interest
Derivatives of Exponential and Logarithmic Functions
Derivatives of Products and Quotients
The Chain Rule
Implicit Differentiation
Related Rates
Elasticity of Demand
First Derivative Test
Second Derivative Test
L’Hôpital’s Rule
Curve Sketching Techniques
Maxima and Minima
Optimization
Antiderivatives and Indefinite Integrals
Integration by Substitution
Differential Equations; Growth and Decay
Definite Integral
Fundamental Theorem of Calculus
Area Between Curves
Applications in Business and Economics



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