Mathematics

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• ☰ 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
  • ☰ 15.1 First-Order Differential Equations
    • ☰ 15.1.1 Separation of variables
  • ☰ 15.2 Second-Order Differential Equations
    • ☰ 15.2.1 Homogeneous equations
• ☰ 16 Number Theory
  • ☰ 16.1 Divisibility and Primes
    • ☰ 16.1.1 Prime factorization
  • ☰ 16.2 Modular Arithmetic
    • ☰ 16.2.1 Congruences
• ☰ 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