# 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

Contact: info@mindrocket.info