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

☰ 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