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Numbers and Sets Introduction About Algebra Arithmetic Operations Addition and Subtraction Multiplication and Division Criterions for Divisibility Real Number System Types of Numbers Geometric Interpretation of Real Numbers Irrational Number Properties of Real Numbers Fractions Proportions Property of Equal Proportions Absolute Values Graphical Illustrations Sets and Intervals Sets Subsets Operations with Sets Intervals	Complex Numbers Definition and Properties Basic Definitions Algebraic Operations Complex Conjugation Trigonometrical and Exponential Forms The Complex Plane Complex Numbers in Polar Coordinate System The Euler Formula   Trigonometric Applications   Algebraic Applications Powers of Complex Numbers Complex Roots	Exponentiation Basic Conceptions and Definitions Basic Definitions Exponentiation Rules Radicals Rational Exponents Properties of Expressions Involving Radicals	Algebraic Transformations Algebraic Expressions Basic Definitions Polynomials Algebraic Transformations Outline Factoring Factoring Quadratic Polynomials Factoring Cubic Polynomials Factor Theorems Other Transformations Expanding Completing Perfect Square Rationalizing Denominators

Algebraic Equations and Inequalities Basic Conceptions Properties of Equations and Inequalities Graphical Interpretation of Solutions Linear Equations and Inequalities Linear Equations Linear Inequalities Linear Equations and Inequalities Involving Absolute Values Linear Equations Involving Absolute Value Linear Equations Involving a Few Absolute Values Linear Inequalities Involving Absolute Value Quadratic Equations and Inequalities Quadratic Equations Quadratic Equations and Quadratic Functions Extreme Value of Quadratic Function Quadratic Formula Solving Quadratic Equations by Factoring Quadratic Inequalities	Functions Basic Conceptions Cartesian Coordinate System Domain and Range Inverse Functions Even-Odd Symmetry of Functions Periodicity of Functions Exponential and Logarithmic Functions Exponential Functions Logarithmic Functions   Natural Logarithms	Discrete Algebra Binomial Theorem Sigma-Notations Arithmetic Progressions Geometric Progressions Binomial Theorem Pascal's Triangle Evaluation of Sums of the Form 1k + 2k + ... + nk 1 + 2 + ... + n 1² + 2² + ... + n² 1³ + 2³ + ... + n³ Mathematical Induction Principle Basic Conceptions Constituents of the Induction Principle Model Examples   Example 1   Example 2   Example 3   Example 4   Example 5   Example 6	Basic Formulas Numbers and Fractions Real Numbers Fractions and Proportions Absolute Values Polynomials Quadratic and Cubic Polynomials Binomial Theorem Progressions Arithmetical Progressions Geometrical Progressions Exponential and Logarithmic Functions Exponential Identities Logarithmic Identities Inequalities Hyperbolic Functions	Graphics of Basic Functions Graphics of Power Functions Linear Functions Quadratic Functions Cubic Polynomials Polynomials of Higher Orders Graphics of Exponential and Logarithmic Functions Exponential Functions Logarithmic Functions Exponential and Logarithmic Functions Hyperbolic Functions Hyperbolic Sine Hyperbolic Cosine Hyperbolic Tangent Hyperbolic Cotangent

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