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### 1. Arithmetic and Elementary Algebra

• 1.1. Real Numbers
• 1.1.1. Integer Numbers
• 1.1.2. Real, Rational, and Irrational Numbers
• 1.2. Equalities and Inequalities. Arithmetic Operations. Absolute Value
• 1.2.1. Equalities and Inequalities
• 1.2.2. Addition and Multiplication of Numbers
• 1.2.3. Ratios and Proportions
• 1.2.4. Percentage
• 1.2.5. Absolute Value of a Number (Modulus of a Number)
• 1.3. Powers and Logarithms
• 1.3.1. Powers and Roots
• 1.3.2. Logarithms
• 1.4. Binomial Theorem and Related Formulas
• 1.4.1. Factorials. Binomial Coefficients. Binomial Theorem
• 1.4.2. Related Formulas
• 1.5. Arithmetic and Geometric Progressions. Finite Sums and Products
• 1.5.1. Arithmetic and Geometric Progressions
• 1.5.2. Finite Series and Products
• 1.6. Mean Values and Inequalities of General Form
• 1.6.1. Arithmetic Mean, Geometric Mean, and Other Mean Values. Inequalities for Mean Values
• 1.6.2. Inequalities of General Form
• 1.7. Some Mathematical Methods