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Math, from counting to calculus

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Courses

41 courses

Kindergarten to grade 2

Kindergarten mathKindergarten6 units
  1. Counting and number names
  2. Comparing numbers
  3. Putting together and taking apart
  4. Numbers 11 to 19
  5. Measuring and sorting
  6. Shapes
Grade 1 mathGrade 17 units
  1. Adding and subtracting within 20
  2. The equal sign and missing numbers
  3. Counting to 120
  4. Tens and ones
  5. Measuring length
  6. Time and data
  7. Shapes and equal parts
Grade 2 mathGrade 27 units
  1. Adding, subtracting and word problems
  2. Equal groups
  3. Place value to 1,000
  4. Adding and subtracting big numbers
  5. Measuring length
  6. Time, money and data
  7. Shapes and equal parts

Grades 3 to 5

Grade 3 mathGrade 37 units
  1. Multiplication and division
  2. Problem solving and patterns
  3. Place value and adding big numbers
  4. Fractions as numbers
  5. Time, measurement and data
  6. Area and perimeter
  7. Shapes
Grade 4 mathGrade 47 units
  1. Multiply, divide and solve problems
  2. Place value and multi-digit math
  3. Equivalent fractions and comparing
  4. Adding and multiplying fractions
  5. Decimal fractions
  6. Measurement, data and angles
  7. Lines, angles and shapes
Grade 5 mathGrade 57 units
  1. Expressions and patterns
  2. Place value and decimals
  3. Adding and subtracting fractions
  4. Multiplying and dividing fractions
  5. Measurement, data and volume
  6. The coordinate plane
  7. Classifying shapes

Grades 6 to 8

Grade 6 mathGrade 69 units
  1. Ratios and rates
  2. Dividing fractions
  3. Multi-digit numbers and decimals
  4. Negative numbers and the coordinate plane
  5. Expressions
  6. Equations and inequalities
  7. Two quantities that change together
  8. Area, surface area and volume
  9. Statistics
Grade 7 mathGrade 76 units
  1. Proportional relationships
  2. Operations with negative numbers
  3. Expressions
  4. Equations and inequalities
  5. Geometry
  6. Statistics and probability
Grade 8 mathGrade 810 units
  1. Rational and irrational numbers
  2. Exponents and roots
  3. Transformations, congruence and similarity
  4. Proportional relationships and slope
  5. Linear equations and systems
  6. Functions
  7. Linear functions and models
  8. The Pythagorean theorem
  9. Volume
  10. Patterns in data

High school

Algebra IGrades 8 to 128 units
  1. Relationships between quantities
  2. Linear equations and inequalities
  3. Systems of equations
  4. Graphs of equations and inequalities
  5. Functions
  6. Linear and exponential models
  7. Quadratic expressions and equations
  8. Describing data
GeometryGrades 9 to 127 units
  1. Congruence and proof
  2. Similarity and right triangles
  3. Circles
  4. Geometry with coordinates
  5. Area and volume
  6. Modeling with geometry
  7. Probability
Algebra IIGrades 10 to 1213 units
  1. Polynomials
  2. Rational and radical equations
  3. Complex numbers
  4. Systems of equations
  5. Matrices
  6. Inequalities
  7. Exponential and logarithmic functions
  8. Trigonometric functions
  9. Building and modeling functions
  10. Variation
  11. Conic sections
  12. Modeling with data
  13. Statistics and inference
Integrated Math IGrades 9 to 128 units
  1. Relationships between quantities
  2. Linear equations and inequalities
  3. Linear and exponential relationships
  4. Systems of equations
  5. Functions and their graphs
  6. Describing data
  7. Congruence and constructions
  8. Connecting algebra and geometry
Integrated Math IIGrades 10 to 127 units
  1. Extending the number system
  2. Quadratic functions
  3. Quadratic expressions and equations
  4. Similarity and right triangles
  5. Circles
  6. Volume and cross-sections
  7. Probability
Integrated Math IIIGrades 11 to 126 units
  1. Inferences and conclusions from data
  2. Polynomial, rational and radical relationships
  3. Exponential and logarithmic functions
  4. Trigonometry of general triangles
  5. Trigonometric functions
  6. Mathematical modeling
PrecalculusGrades 10 to 1214 units
  1. Functions: transformations, composition and inverses
  2. Polynomial and rational functions
  3. Exponential and logarithmic functions
  4. Trigonometric functions and the unit circle
  5. Inverse trigonometric functions and equations
  6. Trigonometric identities
  7. Laws of sines and cosines
  8. Vectors
  9. Polar coordinates and complex numbers
  10. Matrices and systems of equations
  11. Conic sections
  12. Parametric equations
  13. Sequences and series
  14. Introduction to limits

AP courses

AP PrecalculusGrades 10 to 124 units
  1. Polynomial and rational functions
  2. Exponential and logarithmic functions
  3. Trigonometric and polar functions
  4. Functions involving parameters, vectors and matrices
AP Calculus ABGrades 11 to 128 units
  1. Limits and continuity
  2. Differentiation: definition and basic rules
  3. Differentiation: composite, implicit and inverse functions
  4. Contextual applications of differentiation
  5. Analytical applications of differentiation
  6. Integration and accumulation of change
  7. Differential equations
  8. Applications of integration
AP Calculus BCGrades 11 to 1210 units
  1. Limits and continuity
  2. Differentiation: definition and basic rules
  3. Differentiation: composite, implicit and inverse functions
  4. Contextual applications of differentiation
  5. Analytical applications of differentiation
  6. Integration and accumulation of change
  7. Differential equations
  8. Applications of integration
  9. Parametric equations, polar coordinates and vector-valued functions
  10. Infinite sequences and series
AP StatisticsGrades 10 to 126 units
  1. Exploring One-Variable Data and Collecting Data
  2. Probability, Random Variables, and Probability Distributions
  3. Inference for Categorical Data: Proportions
  4. Inference for Quantitative Data: Means
  5. Regression Analysis
  6. Beyond the AP exam (optional) (Optional)

College

College AlgebraCollege7 units
  1. Algebraic expressions
  2. Equations and inequalities
  3. Functions and graphs
  4. Polynomial and rational functions
  5. Exponential and logarithmic functions
  6. Systems of equations
  7. Sequences and series
College PrecalculusCollege13 units
  1. Functions
  2. Polynomial and rational functions
  3. Exponential and logarithmic functions
  4. Trigonometric functions
  5. Inverse functions, identities and equations
  6. Laws of sines and cosines
  7. Polar coordinates and complex numbers
  8. Vectors
  9. Matrices and systems
  10. Conic sections
  11. Parametric equations
  12. Sequences and series
  13. Introduction to limits
Calculus ICollege8 units
  1. Limits and continuity
  2. The derivative and its rules
  3. The chain rule and implicit differentiation
  4. Rates of change and linear approximation
  5. Maximum and minimum values, and curve sketching
  6. Integrals and the Fundamental Theorem of Calculus
  7. The substitution rule
  8. Net change and average value
Calculus IICollege7 units
  1. Areas and volumes
  2. Techniques of integration
  3. Further applications of integration
  4. Differential equations
  5. Parametric equations and polar coordinates
  6. Hyperbolic functions and complex exponentials
  7. Sequences and series
Introductory StatisticsCollege9 units
  1. Collecting data
  2. Describing data
  3. Probability
  4. Random variables and distributions
  5. Sampling distributions
  6. Inference for proportions
  7. Inference for means
  8. Chi-square tests
  9. Correlation and regression
Calculus III (Multivariable)College5 units
  1. Vectors and the geometry of space
  2. Vector functions
  3. Partial derivatives
  4. Multiple integrals
  5. Vector calculus
ProbabilityCollege13 units
  1. Sample spaces and the axioms
  2. Counting methods
  3. Conditional probability and Bayes' rule
  4. Independence
  5. Discrete random variables
  6. Expectation and variance
  7. Continuous random variables
  8. Joint distributions
  9. Covariance and correlation
  10. Limit theorems
  11. Moment generating functions
  12. Random vectors and the multivariate normal
  13. Random walks, Poisson processes and Markov chains
Statistical InferenceCollege11 units
  1. Statistics and sampling distributions
  2. Point estimation
  3. Method of moments
  4. Maximum likelihood
  5. Confidence intervals
  6. Hypothesis testing
  7. Power and optimal tests
  8. Likelihood ratio tests
  9. t, chi-square and F tests
  10. Nonparametric methods and the bootstrap
  11. Bayesian inference
Regression AnalysisCollege11 units
  1. Simple linear regression
  2. Inference in simple regression
  3. Residual diagnostics
  4. Multiple regression in matrix form
  5. Interpreting multiple regression
  6. Categorical predictors and interactions
  7. Model selection
  8. Multicollinearity
  9. Transformations and nonlinearity
  10. Logistic regression
  11. Regularization
Introduction to Data ScienceCollege12 units
  1. Data tables and tidy data
  2. Exploratory analysis and visualization
  3. Summary statistics
  4. Data cleaning
  5. Sampling and bias
  6. Simulation and the bootstrap
  7. Hypothesis testing by permutation
  8. Correlation and prediction
  9. Linear regression
  10. Classification
  11. Train/test split and overfitting
  12. Ethics and privacy
Linear Algebra for Data ScienceCollege12 units
  1. Vectors, dot products and norms
  2. Matrices as transformations
  3. Matrix multiplication
  4. Linear systems and elimination
  5. Rank and inverses
  6. Vector spaces and subspaces
  7. Bases and dimension
  8. Orthogonality and projections
  9. Least squares
  10. Eigenvalues and diagonalization
  11. Singular value decomposition
  12. Principal component analysis
Linear AlgebraCollege11 units
  1. Linear systems and row reduction
  2. Span and solution sets
  3. Independence and linear transformations
  4. Matrix algebra
  5. Determinants
  6. Subspaces, bases and dimension
  7. Eigenvalues and eigenvectors
  8. Complex eigenvalues and dynamics
  9. Orthogonality and least squares
  10. Symmetric matrices
  11. Orthogonal matrices and quadratic forms
Vector CalculusCollege8 units
  1. Derivatives as matrices
  2. Extrema and Lagrange multipliers
  3. Coordinates and change of variables
  4. Vector fields and line integrals
  5. Green's theorem, curl and divergence
  6. Surfaces and surface integrals
  7. The theorems of Stokes and Gauss
  8. Vector calculus at work
Differential EquationsCollege8 units
  1. First-order equations
  2. Exact equations and qualitative theory
  3. Hyperbolic functions and complex exponentials
  4. Second-order linear equations
  5. Forced equations
  6. Linear systems and phase portraits
  7. Series solutions
  8. Laplace transforms
Discrete MathematicsCollege8 units
  1. Logic
  2. Methods of proof
  3. Induction and recursion
  4. Sets, functions and relations
  5. Counting
  6. Number theory
  7. Recurrence relations
  8. Graphs and trees
Introduction to ProofsCollege9 units
  1. Logic and quantifiers
  2. Writing proofs
  3. Proof by contradiction
  4. Induction
  5. Sets
  6. Functions
  7. Equivalence relations
  8. Cardinality
  9. Limits with epsilon and delta
Real AnalysisCollege8 units
  1. The real numbers
  2. Sequences
  3. Series
  4. Topology of the real line
  5. Limits and continuity
  6. Differentiation
  7. The Riemann integral
  8. Sequences and series of functions
Abstract AlgebraCollege9 units
  1. Groups
  2. Subgroups and cyclic groups
  3. Permutation groups
  4. Cosets and Lagrange's theorem
  5. Homomorphisms and quotient groups
  6. Direct products and group actions
  7. Rings
  8. Polynomial rings and factorization
  9. Fields
Numerical AnalysisCollege8 units
  1. Floating point and error
  2. Solving nonlinear equations
  3. Interpolation
  4. Numerical differentiation and integration
  5. Solving linear systems
  6. Least squares computation
  7. Computing eigenvalues
  8. Solving differential equations numerically
Mathematical StatisticsCollege9 units
  1. Sampling distributions
  2. Point estimation
  3. Sufficiency and efficiency
  4. Confidence intervals
  5. Hypothesis testing
  6. Linear models
  7. Analysis of variance
  8. Goodness of fit and contingency tables
  9. Nonparametric methods and the bootstrap
Applied StatisticsCollege9 units
  1. Describing data
  2. Probability models for data
  3. Sampling distributions
  4. Confidence intervals
  5. Hypothesis tests
  6. Categorical data
  7. Comparing several groups
  8. Regression and curve fitting
  9. Resampling methods

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