Mathematics

☰ 1. Foundations of Mathematics

☰ 1.1. What Is Mathematics
- ☰ 1.1.1. Purpose of mathematics
- ☰ 1.1.2. Branches of mathematics
- ☰ 1.1.3. Mathematics in daily life
☰ 1.2. Mathematical Language
- ☰ 1.2.1. Symbols and notation
- ☰ 1.2.2. Variables and constants
- ☰ 1.2.3. Mathematical statements
☰ 1.3. Sets and Logic
- ☰ 1.3.1. Sets and elements
- ☰ 1.3.2. Set notation
- ☰ 1.3.3. Venn diagrams
- ☰ 1.3.4. Logical operators
☰ 1.4. Numbers and Number Systems
- ☰ 1.4.1. Natural numbers
- ☰ 1.4.2. Integers
- ☰ 1.4.3. Rational numbers
- ☰ 1.4.4. Irrational numbers
- ☰ 1.4.5. Real numbers

☰ 2. Arithmetic

☰ 2.1. Basic Operations
- ☰ 2.1.1. Addition
- ☰ 2.1.2. Subtraction
- ☰ 2.1.3. Multiplication
- ☰ 2.1.4. Division
☰ 2.2. Fractions
- ☰ 2.2.1. Proper and improper fractions
- ☰ 2.2.2. Mixed numbers
- ☰ 2.2.3. Operations with fractions
☰ 2.3. Decimals and Percentages
- ☰ 2.3.1. Decimal notation
- ☰ 2.3.2. Fraction–decimal conversion
- ☰ 2.3.3. Percent calculations
☰ 2.4. Powers and Roots
- ☰ 2.4.1. Exponents
- ☰ 2.4.2. Square roots
- ☰ 2.4.3. Laws of exponents
☰ 2.5. Ratios and Proportions
- ☰ 2.5.1. Ratios
- ☰ 2.5.2. Proportions
- ☰ 2.5.3. Direct variation
- ☰ 2.5.4. Inverse variation

☰ 3. Pre-Algebra

☰ 3.1. Variables and Expressions
- ☰ 3.1.1. Algebraic expressions
- ☰ 3.1.2. Evaluating expressions
☰ 3.2. Linear Equations
- ☰ 3.2.1. One-variable equations
- ☰ 3.2.2. Word problems
☰ 3.3. Inequalities
- ☰ 3.3.1. Solving inequalities
- ☰ 3.3.2. Graphing inequalities
☰ 3.4. Coordinate Plane
- ☰ 3.4.1. Cartesian coordinates
- ☰ 3.4.2. Plotting points
☰ 3.5. Introduction to Functions
- ☰ 3.5.1. Input–output concept
- ☰ 3.5.2. Function notation

☰ 4. Algebra I

☰ 4.1. Linear Functions
- ☰ 4.1.1. Slope
- ☰ 4.1.2. Intercept form
- ☰ 4.1.3. Graphing lines
☰ 4.2. Systems of Linear Equations
- ☰ 4.2.1. Graphical method
- ☰ 4.2.2. Substitution
- ☰ 4.2.3. Elimination
- ☰ 4.2.4. Gaussian elimination
☰ 4.3. Polynomials
- ☰ 4.3.1. Polynomial terms
- ☰ 4.3.2. Polynomial operations
☰ 4.4. Factoring
- ☰ 4.4.1. Common factors
- ☰ 4.4.2. Quadratic factoring
- ☰ 4.4.3. Special products
☰ 4.5. Quadratic Equations
- ☰ 4.5.1. Factoring method
- ☰ 4.5.2. Completing the square
- ☰ 4.5.3. Quadratic formula

☰ 5. Algebra II

☰ 5.1. Polynomial Functions
- ☰ 5.1.1. Degree and behavior
- ☰ 5.1.2. Zeros of functions
☰ 5.2. Rational Functions
- ☰ 5.2.1. Domain
- ☰ 5.2.2. Asymptotes
☰ 5.3. Exponential Functions
- ☰ 5.3.1. Growth
- ☰ 5.3.2. Decay
- ☰ 5.3.3. Applications
  - ☰ 5.3.3.1. Physical models
  - ☰ 5.3.3.2. Population models
  - ☰ 5.3.3.3. Cryptography
☰ 5.4. Logarithms
- ☰ 5.4.1. Logarithmic laws
- ☰ 5.4.2. Solving equations
☰ 5.5. Complex Numbers
- ☰ 5.5.1. Imaginary unit
- ☰ 5.5.2. Operations with complex numbers

☰ 6. Geometry

☰ 6.1. Points, Lines, and Angles
- ☰ 6.1.1. Angle types
- ☰ 6.1.2. Parallel and perpendicular lines
☰ 6.2. Triangles
- ☰ 6.2.1. Classification
- ☰ 6.2.2. Pythagorean theorem
- ☰ 6.2.3. Congruence
☰ 6.3. Polygons
- ☰ 6.3.1. Quadrilaterals
- ☰ 6.3.2. Regular polygons
☰ 6.4. Circles
- ☰ 6.4.1. Radius and diameter
- ☰ 6.4.2. Arcs and sectors
☰ 6.5. Area and Volume
- ☰ 6.5.1. Area formulas
- ☰ 6.5.2. Volume of solids

☰ 7. Trigonometry

☰ 7.1. Angles and Radians
- ☰ 7.1.1. Degrees
- ☰ 7.1.2. Radians
☰ 7.2. Trigonometric Ratios
- ☰ 7.2.1. Sine
- ☰ 7.2.2. Cosine
- ☰ 7.2.3. Tangent
☰ 7.3. Unit Circle
- ☰ 7.3.1. Exact values
☰ 7.4. Trigonometric Functions
- ☰ 7.4.1. Graphs
- ☰ 7.4.2. Periodicity
☰ 7.5. Trigonometric Identities
- ☰ 7.5.1. Pythagorean identities
- ☰ 7.5.2. Sum and difference formulas

☰ 8. Analytic Geometry

☰ 8.1. Conic Sections
- ☰ 8.1.1. Parabolas
- ☰ 8.1.2. Ellipses
- ☰ 8.1.3. Hyperbolas
☰ 8.2. Parametric Equations
- ☰ 8.2.1. Parametric curves
☰ 8.3. Polar Coordinates
- ☰ 8.3.1. Polar graphing
☰ 8.4. Vectors in the Plane
- ☰ 8.4.1. Vector addition
- ☰ 8.4.2. Dot product

☰ 9. Precalculus

☰ 9.1. Function Analysis
- ☰ 9.1.1. Domain and range
- ☰ 9.1.2. Monotonicity
☰ 9.2. Composite and Inverse Functions
- ☰ 9.2.1. Function composition
- ☰ 9.2.2. Inverse functions
☰ 9.3. Limits
- ☰ 9.3.1. Intuitive idea
- ☰ 9.3.2. One-sided limits

☰ 10. Calculus – Differential Calculus

☰ 10.1. Limits and Continuity
- ☰ 10.1.1. Formal limits
- ☰ 10.1.2. Continuity
☰ 10.2. Derivatives
- ☰ 10.2.1. Definition
- ☰ 10.2.2. Differentiation rules
☰ 10.3. Applications of Derivatives
- ☰ 10.3.1. Optimization
- ☰ 10.3.2. Related rates
- ☰ 10.3.3. Curve sketching

☰ 11. Calculus – Integral Calculus

☰ 11.1. Indefinite Integrals
- ☰ 11.1.1. Antiderivatives
☰ 11.2. Definite Integrals
- ☰ 11.2.1. Riemann sums
- ☰ 11.2.2. Fundamental theorem of calculus
☰ 11.3. Applications of Integrals
- ☰ 11.3.1. Area
- ☰ 11.3.2. Volume

☰ 12. Linear Algebra

☰ 12.1. Vectors and Matrices
- ☰ 12.1.1. Vector operations
- ☰ 12.1.2. Matrix operations
☰ 12.2. Determinants
- ☰ 12.2.1. Properties of determinants
☰ 12.3. Eigenvalues and Eigenvectors
- ☰ 12.3.1. Diagonalization

☰ 13. Probability and Statistics

☰ 13.1. Probability Basics
- ☰ 13.1.1. Sample spaces
- ☰ 13.1.2. Events
☰ 13.2. Random Variables
- ☰ 13.2.1. Discrete variables
- ☰ 13.2.2. Continuous variables
☰ 13.3. Probability Distributions
- ☰ 13.3.1. Binomial distribution
- ☰ 13.3.2. Normal distribution
☰ 13.4. Descriptive Statistics
- ☰ 13.4.1. Mean
- ☰ 13.4.2. Variance
- ☰ 13.4.3. Standard deviation
☰ 13.5. Inferential Statistics
- ☰ 13.5.1. Confidence intervals
- ☰ 13.5.2. Hypothesis testing

☰ 14. Discrete Mathematics

☰ 14.1. Logic and Proof
- ☰ 14.1.1. Propositions
- ☰ 14.1.2. Logical equivalence
☰ 14.2. Combinatorics
- ☰ 14.2.1. Permutations
- ☰ 14.2.2. Combinations
☰ 14.3. Graph Theory
- ☰ 14.3.1. Trees

☰ 15. Differential Equations

☰ 16. Number Theory

☰ 17. Mathematical Proofs

☰ 17.1. Proof Techniques
- ☰ 17.1.1. Direct proof
- ☰ 17.1.2. Proof by contradiction
- ☰ 17.1.3. Mathematical induction
☰ 17.2. Writing Proofs
- ☰ 17.2.1. Structure
- ☰ 17.2.2. Clarity