library-tree.json

[{"subfields":[{"subfields":["Fields","Polynomials"],"name":"Fields and polynomials"},{"subfields":["Group axioms","Subgroups","Cyclic groups","Permutation Groups","Product of groups","Cosets, Lagrange theorem and Normality","Quotient groups","Homomorphisms","Group actions"],"name":"Groups"},{"subfields":["Ring axioms","Units and zero divisors","Ideals and Homomorphisms","Quotient Rings and Polynomial Rings"],"name":"Rings"}],"name":"Abstract Algebra"},{"subfields":[{"subfields":["Linear Expressions","Working with linear expressions","Linear functions","Formulas for Linear Functions","Geometric Properties of Linear Functions","Equations for lines","Solving linear equations","Rate of Change","Fitting Linear Functions to Data","Linear Modeling","Functions and Function Notation","Review Exercises"],"name":"Linear functions, expressions, and equations"},{"subfields":["Completing the Square","Factoring Quadratics","Quadratic Functions","Quadratic expressions"],"name":"Quadratic Functions"},{"subfields":["Algebraic Expressions","Algebraic Fractions","Coordinate Geometry","Equations","Equivalent Equations","Equivalent Expressions","Expanding and Factoring","Exponents and Radicals","Fractional Expressions","Inequalities","Problem Solving with Equations","Reordering and Regrouping","The Distributive Law"],"name":"Basic Algebra"},{"subfields":["Exponential Functions","Four Ways to Represent a Function","Inverse Functions and Logarithms","Mathematical Models: A Catalog of Essential Functions","New Functions from Old Functions"],"name":"Functions and Models"},{"subfields":["Algebra, Mathematical Models, and Problem Solving","Algebraic Expressions and Real Numbers","Graphing Equations","Operations with Real Numbers and Simplifying Algebraic Expressions","Properties of Integral Exponents","Scientific Notation"],"name":"Algebra, Mathematical Models and Problem Solving"},{"subfields":["Functions and Linear Functions","Introduction to Functions","The Algebra of Functions"],"name":"Functions and linear functions"},{"subfields":["Compound Inequalities","Equations and Inequalities Involving Absolute Value","Solving Linear Inequalities"],"name":"Inequalities and problem solving"},{"subfields":["A General Factoring Strategy","Factoring Polynomials by Grouping","Factoring Special Forms","Factoring Trinomials","Introduction to Polynomials and Polynomial Functions","Multiplication of Polynomials","Polynomial Equations and Their Applications"],"name":"Polynomials, polynomial functions, and factoring"},{"subfields":["Rational Expressions and Functions: Adding and Subtracting","Rational Expressions and Functions: Multipying and Dividing"],"name":"Rational expressions, functions and equations"},{"subfields":["Combinations Of Functions","Composition Of Functions","Inverse Functions","Review Exercises And Problems"],"name":"Compositions, inverses, and combinations of functions"},{"subfields":["Circles","Ellipses","Hyperbolas","Parabolas","Shifted conics","Misc."],"name":"Conic sections"},{"subfields":["Graphs of Equations","The Coordinate Plane"],"name":"Coordinates and Graphs"},{"subfields":["Counting Principles","Permutations and Combinations","Probability"],"name":"Counting and Probability"},{"subfields":["Absolute Value","Algebraic and Graphical Solutions of Equations","Complex Numbers","Linear Inequalities","Modeling with Equations","Nonlinear Equations","Nonlinear Inequalities","Other Equations","Quadratic Equations"],"name":"Equations and Inequalities"},{"subfields":["Exponential Functions","Modeling with Exponential Functions","Working with the Base","Working with the Exponent","Comparing Exponential and Linear Functions","Continuous Growth and the Number e","Graphs of  Exponential Functions","Introduction to the Family of Exponential Functions","Review Exercises and Problems"],"name":"Exponential Functions"},{"subfields":["Exponential Functions","Working with the Exponent"],"name":"Exponential Functions, Expressions, and Equations"},{"subfields":["Applications of Exponential and Logarithmic Functions","Exponential Functions","Exponential and Logarithmic Equations","Exponential and Logarithmic Functions","Laws of Logarithms","Logarithmic Functions","The Natural Exponential Function"],"name":"Exponential and Logarithmic Functions"},{"subfields":["Applied Functions: Variation","Average Rate of Change: Increasing and Decreasing Functions","Combining Functions","Composing Functions","Composite and Inverse Functions","Concavity","Domain and Range","Evaluation and Solving","Even and Odd","Expanding and Simplifying Functions","Exponential","Extreme Values of Functions","Graphing Calculator","Graphs of Equations","Graphs of Functions","Input and Output","Inverse Functions","Logarithmic","Modeling with Functions","One-to-one Functions and Their Inverses","Piecewise Defined Functions","Polynomial","Quadratic Functions","Review Exercises and Problems","Transformations of Functions","What is a Function?"],"name":"Functions"},{"subfields":["Constraint Optimization","Simplex Method","Misc."],"name":"Linear Programming"},{"subfields":["Logarithmic Scales","Logarithms and Exponential Models","Logarithms and Their Properties","Review Exercises and Problems","The Logarithmic Functions","Misc."],"name":"Logarithmic functions"},{"subfields":["Solving Equations"],"name":"Logarithms"},{"subfields":["Inverse Functions"],"name":"More on Functions"},{"subfields":["Complex Roots/Fundamental Theorem of Algebra","Dividing Polynomials","Polynomial Functions","Polynomial Functions and Their Roots","Polynomial Functions and their Graphs","Power Functions","Rational Functions","Real Zeros of Polynomials","Evaluating polynomials","Comparing Power, Exponential, And Log Functions","Fitting Exponentials And Polynomials To Data","The Short-Run Behavior Of Polynomials","The Short-Run Behavior Of Rational Functions","Review Exercises And Problems","Misc."],"name":"Polynomial and rational functions"},{"subfields":["Power Equations","Power Expressions","Power Functions"],"name":"Power Functions"},{"subfields":["Arithmetic Sequences","Geometric Sequences","Recursive Functions","Sequences and Series Notation","The Binomial Theorem"],"name":"Sequences and Series"},{"subfields":["Determinants and Cramer's Rule","Inverses of Matrices and Matrix Equations","Pairs of Lines","Partial Fractions","Systems of Equations","Systems of Inequalities","The Algebra of Determinants","The Algebra of Matrices"],"name":"Systems of Equations and Inequalities"},{"subfields":["Horizontal Stretches and Compressions","Inverse Trigonometric Functions","Reflections and Symmetry","Review Exercises and Problems","The Family of Quadratic Functions","Vertical Stretches and Compressions","Vertical and Horizontal Shifts","Vertical and Horizontal Stretches and Compressions","Misc."],"name":"Transformations of functions and their graphs"}],"name":"Algebra"},{"subfields":[{"subfields":["Arc Length and Speed","Calculus of Vector-Valued Functions","Curvature","Motion in Three-Space","Planetary Motion According to Kepler and Newton","Vector-Valued Functions"],"name":"Calculus of Vector-Valued Functions"},{"subfields":["Differentiability, Linear Approximation, and Tangent Planes","Functions of Two or More Variables","Lagrange Multipliers: Optimizing with a Constraint","Limits and Continuity in Several Variables","Optimization in Several Variables","Partial Derivatives","The Chain Rule","The Gradient and Directional Derivatives"],"name":"Differentiation"},{"subfields":["Divergence Theorem","Greens Theorem","Stokes Theorem"],"name":"Fundamental Theorems"},{"subfields":["Conservative Vector Fields","Line Integrals","Parametrized Surfaces and Surface Integrals","Surface Integrals of Vector Fields","Vector Fields"],"name":"Line and Surface Integrals"},{"subfields":["Applications of Double Integrals","Applications of Multiple Integrals","Center of Mass","Change of Variable, Cylindrical and Spherical Coordinates","Change of Variables","Change of Variables in Multiple Integrals","Double Integrals in Polar Coordinates","Double Integrals over General Regions","Double Integrals over More General Regions","Double Integrals over Rectangles","Integration in Polar, Cylindrical, and Spherical Coordinates","Integration in Several Variables","Iterated Integrals","Surface Area","Triple Integrals","Triple Integrals in Cylindrical and Spherical Coordinates","Triple Integrals in Polar Coordinates","Volume and Cavalieri's Principle","Volumes"],"name":"Multiple Integrals"},{"subfields":["Directional Derivatives","Directional Derivatives and the Gradient Vector","Extreme Values","Functions of Several Variables","Graphs and Level Surfaces","Lagrange Multipliers","Limits","Limits and Continuity","Maximum and Minimum Values","Partial Derivatives","Tangent Planes","The Chain Rule","Misc."],"name":"Partial Derivatives"},{"subfields":["Curl and Divergence","Green's Theorem","Line Integrals","Parameterized Surfaces and Their Areas","Parametric Surfaces and Their Areas","Stokes Theorem","Surface Integrals","The Divergence Theorem","The Fundamental Theorem for Line Integrals","Vector Fields"],"name":"Vector Calculus"},{"subfields":["Graphs"],"name":"Vector Fields"},{"subfields":["Arc Length and Curvature","Derivatives and Integrals of Vector Functions","Motion in Space: Velocity and Acceleration","Vector Function and Space Curves","Vector Functions and Space Curves"],"name":"Vector Functions"},{"subfields":["A Survey of Quadratic Surfaces","Cylindrical and Spherical Coordinates","Dot Product and the Angle Between Two Vectors","Planes in Three-Space","The Cross Product"],"name":"Vector Geometry"},{"subfields":["Cross Product","Cylindrical and Spherical Coordinates","Equations of Lines and Planes","The Cross Product","The Dot Product","Three-Dimensional Coordinate Systems","Vectors"],"name":"Vectors and the Geometry of Space"}],"name":"Calculus - multivariable"},{"subfields":[{"subfields":["Motivational applications (estimation)","Finding limits using graphs","Rules of limits - basic","Evaluating limits - factoring","Evaluating limits - rationalizing","Evaluating limits - rational expressions","Evaluating limits - trigonometric","Squeeze theorem","One-sided limits - concept of","Continuity - concept of","Continuity - classifying discontinuities","Continuity - intermediate value theorem","Infinite limits and vertical asymptotes","Limits at infinity, horizontal and oblique asymptotes","Estimating limits numerically","Applications - instantaneous rate of change","Applications - tangent lines and slopes","Applications - finding all asymptotes","Applications - other","Definitions and existence (conceptual)"],"name":"Limits and Continuity"},{"subfields":["Definition of the derivative","Conceptual understanding of derivatives","Derivatives of polynomials and power functions","Product rule (without trigonometric functions)","Product rule (with trigonometric functions)","Quotient rule (without trigonometric functions)","Quotient rule (with trigonometric functions)","Derivatives of trigonometric functions","Derivatives of exponential functions","Derivatives of logarithmic functions","Derivatives of inverse functions","Derivatives of inverse trigonometric functions","Hyperbolic functions","Derivatives of hyperbolic functions","Chain rule (without trigonometric functions)","Chain rule (with trigonometric functions)","Higher-order derivatives","Derivatives involving multiple rules (no product, quotient, or chain rule)","Derivatives involving multiple rules (no chain rule)","Derivatives involving multiple rules (all rules)","Logarithmic differentiation","Implicit differentiation"],"name":"Differentiation"},{"subfields":["Mean value theorem","Rates of change - general","Rates of change - business and economics","Rates of change - engineering and physics","Rates of change - natural and social sciences","Increasing/decreasing functions and local extrema","Concavity and points of inflection","Global extrema","Summary of curve sketching","Optimization - general","Optimization - business and economics","Optimization - engineering and physics","Optimization - natural and social sciences","Linear approximation and differentials","Related rates","Indeterminate forms and L'Hopital's rule","Newton's method","Elasticity of demand"],"name":"Applications of Differentiation"},{"subfields":["Antiderivatives","Area and Distance","Indefinite Integrals","Net and Total Change","Substitution","Tables of Integrals","The Definite Integral","The Fundamental Theorem of Calculus"],"name":"Integrals"},{"subfields":["Approximating Integrals","Improper Integrals","Integrals of Hyperbolic and Inverse Hyperbolic Functions","Integration by Partial Fractions","Integration by Parts","Strategy for Integration","Trigonometric Integrals","Trigonometric Substitution"],"name":"Techniques of Integration"},{"subfields":["Applications to Economics","Applications to Physics and Engineering","Arc Length","Area of a Surface of Revolution","Areas Between Curves","Average Value of a Function","Distribution Functions","Probability, Mean and Median","Solids of Revolution","Volumes","Volumes by Cylindrical Shells","Work"],"name":"Applications of Integration"},{"subfields":["Absolute Convergence and the Ratio and Root Tests","Alternating Series","Applications of Taylor Polynomials","Convergence of Series with positive terms","Fourier Series","Geometric Series","Infinite Sequences and Series","Power Series","Representations of Functions as Power Series","Sequences","Series","Strategy for Testing Series","Taylor and Maclaurin series","The Binomial Series","The Comparison Tests","The Integral Test and Estimates of Sums"],"name":"Infinite Sequences and Series"},{"subfields":["Curves Defined by Parametric Equations","Polar Coordinates","Arc Length and Speed","Arc Length and Surface Area","Area and arc length in polar coordinates","Tangents and Areas"],"name":"Parametric Equations and Polar Coordinates"}],"name":"Calculus - single variable"},{"subfields":[{"subfields":["Polynomials and Rational Functions"],"name":"Elementary functions"},{"subfields":["Regions and domains","Functions","Limits","Harmonic functions","Analyticity","Series","Derivatives","Cauchy's theorem","Entire functions","Applications"],"name":"Analytic functions"}],"name":"Complex analysis"},{"subfields":[{"subfields":["Shift cipher"],"name":"Classic ciphers"}],"name":"Cryptography"},{"subfields":[{"subfields":["Autonomous Differential Equations","Classification of Differential Equations","Definitions and Terminology","Direction Fields and Euler's Method","Exponential Growth and Decay","Fundamental Theorem of Ordinary Differential Equations","Graphical and Numerical Methods","Higher Order Differential Equations","Integrals as Solutions","Introduction to Differential Equations","Linear Equations","Modeling with Differential Equations","Models involving y' = k(y - b)","Parametric Equations","Solving Differential Equations","Systems of Differential Equations","The Logistic Equation","Vectors in Three Dimensions","Verifying Solutions"],"name":"Introduction"},{"subfields":["Exact equations","Existence and Uniqueness","Integrals as Solutions","Introduction to Differential Equations","Linear ODEs and the Integrating Factor","Linear equations","Phase portraits","Separable equations"],"name":"First order"},{"subfields":["Higher Order Linear","Second Order Linear","Second Order Linear Nonhomogeneous"],"name":"Higher Order Differential Equations"},{"subfields":["Convolution","Delta Function","Laplace Transforms","Partial Fractions","Periodic Functions","Misc."],"name":"Laplace Transforms"},{"subfields":["Linear Systems","Nonhomogeneous linear systems"],"name":"Linear systems"},{"subfields":["Applications of Second-Order Differential Equations","Nonhomogeneous Linear Equations","Second-Order Differential Equations","Second-Order Linear Equations"],"name":"Second order"},{"subfields":["Introduction to Systems"],"name":"Systems of Differential Equations"}],"name":"Differential equations"},{"subfields":[{"subfields":["Algorithms","Bin Packing","Scheduling"],"name":"Algorithms"},{"subfields":["Counting"],"name":"Combinatorics"},{"subfields":["Misc."],"name":"Graph Theory"},{"subfields":["First Order Logic","Quantifiers","Reasoning","Misc."],"name":"Logic"},{"subfields":["Recurrence Relations"],"name":"Number Theory"},{"subfields":["Basic Operations","The Inclusion Exclusion Principle"],"name":"Set Theory"}],"name":"Discrete Mathematics"},{"subfields":[{"subfields":["Analysis Techniques","Basic Analysis Using Kirchhoff's Laws","Impedance and Admittance","Sinusoids"],"name":"AC Steady-State Analysis"},{"subfields":["Introduction","Maximum Power Transfer","Superposition","Thevenin's and Norton's Theorems","Misc."],"name":"Additional Analysis Techniques"},{"subfields":["Units and Scales"],"name":"Basic Components and Electric Circuits"},{"subfields":["Circuit Elements","System of Units"],"name":"Basic Concepts"},{"subfields":["Capacitor and Inductor Combinations","Capacitors","Inductors"],"name":"Capacitance and Inductance"},{"subfields":["Mutual Inductance","The Ideal Transformer"],"name":"Magnetically Coupled Networks"},{"subfields":["Loop Analysis","Nodal Analysis"],"name":"Nodal and Loop Analysis Techniques"},{"subfields":["Fundamental Op-Amp Circuits"],"name":"Operational Amplifiers"},{"subfields":["Source/Load Connections"],"name":"Polyphase Circuits"},{"subfields":["Circuits with Dependent Sources","Circuits with Series-Parallel Resistor Combinations","Kirchhoff's Law","Ohm's Law","Series and Parallel Resistor Combinations","Single-Loop Circuits","Single-Node-Pair Circuits","Wye-Delta Transformations"],"name":"Resistive Circuits"},{"subfields":["Average Power","Complex Power","Effective or rms Values","Maximum Average Power Transfer","The Power Factor"],"name":"Steady-State Power Analysis"},{"subfields":["The Single-Loop Circuit"],"name":"Voltage and Current Laws"}],"name":"Electric Circuits"},{"subfields":[{"subfields":["Simple"],"name":"Word Problems"}],"name":"Elementary School"},{"subfields":[{"subfields":["Annuities","Geometric Sums","Loans","Perpetuities","Sinking Funds","Varying Payments","Misc."],"name":"Annuities"},{"subfields":["Bonds","Book Value","Other Bonds","Yield Rates","Misc."],"name":"Bonds"},{"subfields":["Dollar Weighted Rate of Return","Time Weighted Rate of Return","Unknown Time and Logarithms"],"name":"Equations of Value"},{"subfields":["Algebra Prerequisites","Compound Interest","Effective and Nominal Rates of Interest","Present and Future Value","Simple Interest","Time Value of Money","Misc."],"name":"Introduction to Interest"},{"subfields":["Binomial Trees","Hedging Strategies","Introduction to Options"],"name":"Options"},{"subfields":["Contingent Payments","Expected Values","Introduction to Probability"],"name":"Probability and Contingent Payments"}],"name":"Financial Mathematics"},{"subfields":[{"subfields":["Systems with 2 variables","Systems with 3 variables","Systems with 4 or more variables","Matrix-vector forms","Vector equations","Augmented matrices","Applications"],"name":"Systems of linear equations"},{"subfields":["Matrix algebra","Row operations","Echelon form","Rank","Transpose and trace","Inverses","Elementary matrices","Complex entries","Quadratic forms"],"name":"Matrices"},{"subfields":["Diagonalization","LU factorization","QR factorization","Singular value decomposition"],"name":"Matrix factorizations"},{"subfields":["Vectors","Linear combinations","Span","Linear independence","Subspaces","Basis and dimension","Row, column, and null spaces","Coordinate vectors and change of basis"],"name":"Euclidean spaces"},{"subfields":["Linear combinations","Span","Linear independence","Subspaces","Basis and dimension","Coordinate vectors and change of basis"],"name":"Abstract vector spaces"},{"subfields":["Computing eigenvalues and eigenvectors","Properties","Complex eigenvalues and eigenvectors","Quadratic forms","Applications"],"name":"Eigenvalues and eigenvectors"},{"subfields":["Computing dot products","Computing inner products","Orthogonal and orthonormal sets","Projection and distance","Gram-Schmidt process","Orthogonal matrices","Orthogonal subspaces","Applications"],"name":"Inner products"},{"subfields":["Properties","Evaluating linear transformations","Associated matrices","One-to-one and onto","Kernel and image","Inverses"],"name":"Linear transformations"},{"subfields":["Computing determinants","Properties","Applications"],"name":"Determinants"}],"name":"Linear algebra"},{"subfields":[{"subfields":["Misc."],"name":"Addition and subtraction"},{"subfields":["Absolute Value","Adding Integers","Algebraic Expressions","Evaluating Expressions","Inductive Reasoning","Integer Mult and Division","Order Of Operations","Patterns","Subtracting Integers","The Coordinate Plane"],"name":"Algebraic expressions and integers"},{"subfields":["Misc."],"name":"Arithmetic word problems"},{"subfields":["Misc."],"name":"Binomial data from graph"},{"subfields":["Misc."],"name":"Binomial difference of squares"},{"subfields":["Intro To Metric System","Mean Median Mode","Rounding and Estimating Products Quotients","Rounding and Estimating Sums Differences","Solving Equations Add Subtract Decimals","Solving Equations Mult Divide Decimals","Using Formulas"],"name":"Decimals and Equations"},{"subfields":["Misc."],"name":"Distance angle"},{"subfields":["Misc."],"name":"Distributive Law"},{"subfields":["Misc."],"name":"Evaluation by substitution"},{"subfields":["Misc."],"name":"Exponents"},{"subfields":["Misc."],"name":"Factoring"},{"subfields":["Divisibility and Factors","Exponents","Prime Factors","Rational Numbers","Reduced Fractions"],"name":"Factors, Fractions, and Exponents"},{"subfields":["Misc."],"name":"Fractions"},{"subfields":["Misc."],"name":"Functions"},{"subfields":["Misc."],"name":"GCF-LCM"},{"subfields":["Misc."],"name":"Geometry_Figures"},{"subfields":["2006"],"name":"Grade 3"},{"subfields":["Misc."],"name":"Graphs"},{"subfields":["Misc."],"name":"Greatest Common Factor"},{"subfields":["Misc."],"name":"Inequalities"},{"subfields":["Misc."],"name":"Interpret_Verbal_Description"},{"subfields":["Misc."],"name":"Introduction to WeBWorK"},{"subfields":["Misc."],"name":"Irrationals_Numbers"},{"subfields":["Misc."],"name":"Miscellaneous_Contest_Problems"},{"subfields":["Misc."],"name":"Multiplication_Division"},{"subfields":["Misc."],"name":"Next_Term_in_a_Sequence"},{"subfields":["Misc."],"name":"Number_Theory"},{"subfields":["Adding Fractions","Fractions and Decimals","Multiplying Fractions","Ordering Fractions","Solving Equations Add Subtract Fractions","Solving Equations Multiplying Fractions"],"name":"Operations with Fractions"},{"subfields":["Misc."],"name":"Order_of_Operations"},{"subfields":["Misc."],"name":"Percent"},{"subfields":["Misc."],"name":"Polynomials"},{"subfields":["Misc."],"name":"Probability"},{"subfields":["Misc."],"name":"Ratios"},{"subfields":["Probability","Proportions","Ratios and Rates","Similar Figures"],"name":"Ratios, Proportions, and Percents"},{"subfields":["Misc."],"name":"ScientificNotation"},{"subfields":["Misc."],"name":"Scientific_Notation"},{"subfields":["Misc."],"name":"September review"},{"subfields":["Misc."],"name":"Simplify_Expressions"},{"subfields":["Misc."],"name":"Solve_Equation"},{"subfields":["Misc."],"name":"Solve_Equations"},{"subfields":["Inequalities and their graphs","Multiplication Properties","Properties of Numbers","Simplifying Variable Expressions","Solving Equalities Addition Subtraction","Solving Equalities Mult Division","Solving Expressions Add Subtract","Solving Inequalities Addition Subtraction","Solving Inequalities Multiplication Division"],"name":"Solving One-Step Equations and Inequalities"},{"subfields":["Misc."],"name":"Square_Root"},{"subfields":["Misc."],"name":"Statistics"},{"subfields":["Misc."],"name":"Summation_of_Finite_Sequences"},{"subfields":["Too much information"],"name":"Word problems"}],"name":"Middle school"},{"subfields":[{"subfields":["2008","2009"],"name":"Grade 11"},{"subfields":["2006","2008","2009"],"name":"Grade 3"},{"subfields":["2008","2009"],"name":"Grade 4"},{"subfields":["2005","2006","2007","2008","2009"],"name":"Grade 5"},{"subfields":["2005","2006","2007","2008","2009"],"name":"Grade 6"},{"subfields":["2005","2006","2007","2008","2009"],"name":"Grade 7"},{"subfields":["2005","2006","2007","2008","2009"],"name":"Grade 8"}],"name":"NECAP"},{"subfields":[{"subfields":["Definitions","Division algorithm","Prime factorization","GCDs and LCMs"],"name":"Divisibility"},{"subfields":["Modular arithmetic","Linear congruences","Fast powering","Chinese remainder theorem","Multiplicative orders","Fermat's little theorem"],"name":"Congruences"},{"subfields":["Pythagorean triples","Fermat's last theorem"],"name":"Diophantine equations"}],"name":"Number theory"},{"subfields":[{"subfields":["Arithmetic","Other bases"],"name":"Integers"},{"subfields":[],"name":"Rational numbers"},{"subfields":["Properties","Rounding","Misc."],"name":"Real numbers"},{"subfields":["Arithmetic","Polar form","Properties"],"name":"Complex numbers"}],"name":"Numbers"},{"subfields":[{"subfields":["Misc."],"name":"Newtonian Mechanics"}],"name":"Physics"},{"subfields":[{"subfields":["Conditional Probability","Events/Probability Calculation","Mutual Exclusivity"],"name":"Discrete Probability"},{"subfields":["Binomial Distribution","Exponential Distribution","Normal Distribution","Other Distributions","Poisson Distribution","Uniform Distribution"],"name":"Distributions"},{"subfields":["Conditional Probability","Expected Value","Joint Distributions","Random Variables","The Central Limit Theorem"],"name":"Theory"}],"name":"Probability"},{"subfields":[{"subfields":["Limit points"],"name":"Limits and accumulation points"}],"name":"Real analysis"},{"subfields":[{"subfields":["Subset","Specifying sets","Union and intersection","Set difference","Complement","Product","Power set"],"name":"Basic properties and operations"},{"subfields":["General relations","Equivalence relations"],"name":"Relations"},{"subfields":["Definition of function","Injective, surjective, bijective"],"name":"Functions"}],"name":"Set theory"},{"subfields":[{"subfields":["One Sample - Mean"],"name":"Confidence Intervals"},{"subfields":["Misc."],"name":"Continuous Probability Distributions"},{"subfields":["The Chi-Squared Probability Distribution","The F-Distribution","The Normal Probability Distribution","The Uniform Probability Distribution"],"name":"Continuous Random Variables and Their Probability Distributions"},{"subfields":["Linear regression"],"name":"Correlation/Regression"},{"subfields":["Chebyshevs Theorem","Frequency Tables","Mode","Quartiles","Sample Mean"],"name":"Descriptive Statistics"},{"subfields":["Normal Distribution"],"name":"Distributions"},{"subfields":["Confidence Intervals","Correlation and Regression","Evaluating the Goodness of a Point Estimator","Large-Sample Confidence Intervals","Selecting Sample Size","Small-Sample Confidence Intervals for u and u1-u2"],"name":"Estimation"},{"subfields":["Sampling"],"name":"Experiment Design"},{"subfields":["ANOVA/Analysis of Variance","Analysis of Variance","Common Large-Sample Tests","Common Small-Sample Tests","Comparing Multiple Samples","Contingency Tables","Correct Test Determination","Elements of a Statistical Test","Goodness of Fit/Chi-Squared","Inference Samples","Multinomial Contingency","One Population - Means","One Sample - Means, Sigma known","One Sample - Means, Sigma not known","P-Value Calculation","Significance Levels","Type I/Type II Errors","Misc."],"name":"Hypothesis Testing"},{"subfields":["Misc."],"name":"Inference About a Population"},{"subfields":["Misc."],"name":"Multiple regression"},{"subfields":["Analysis of Variance"],"name":"Multivariate Techniques"},{"subfields":["Chapter 1: Picturing Distributions with Graphs","Chapter 2: Describing Distributions with Numbers","Chapter 3: The Normal Distributions","Chapter 4: Scatterplots and Correlation","Chapter 5: Regression"],"name":"Part 1: Exploring Data"},{"subfields":["Chapter 10: Introducing Probability","Chapter 11: Sampling Distributions","Chapter 14: Introduction to Inference","Chapter 15: Thinking About Inference","Chapter 9: Producing Data: Experiments"],"name":"Part II From Exploration to Inference"},{"subfields":["Chapter 8: Producing Data: Sampling"],"name":"Part II: From Exploring to Inference"},{"subfields":["Chapter 17: Inference About a Population Mean","Chapter 18: Two-Sample Problems","Chapter 19: Inference About a Population Proportion","Chapter 20: Comparing Two Proportions"],"name":"Part III: Inference About Variables"},{"subfields":["Chapter 22: Two Categorical Variables: The Chi-Square Test","Chapter 24: One-Way Analysis of Variance: Comparing Several Means"],"name":"Part IV: Inference About Relationships"},{"subfields":["Misc."],"name":"Probability"},{"subfields":["Misc."],"name":"Random Variables"},{"subfields":["Central Limit Theorem","Chebyshev's theorem","Sample Mean"],"name":"Sampling Distributions and the Central Limit Theorem"},{"subfields":["Regression Equation"],"name":"Simple Linear Regression"},{"subfields":["Characterizing a Set of Measurements: Graphical Methods","Characterizing a Set of Measurements: Numerical Methods","Introduction","Supplementary Exercises","Misc."],"name":"What is Statistics?"}],"name":"Statistics"},{"subfields":[{"subfields":["Addition and Subtraction Formulas","Double and Half Angle Formulas","Double- and Half-Angle/Product-Sum Formulas","Inverse Trigonometric Functions","Proving Identities","Trigonometric Equations","Trigonometric Functions of Angles","Trigonometric Identities"],"name":"Analytic Trigonometry"},{"subfields":["Arc Length and Area","Reference Angles and Radian Measure","Misc."],"name":"Circular Definition for Trig functions"},{"subfields":["Applications to Right Triangles","Definition using Triangles","Right Triangles"],"name":"Right Triangle Trigonometry"},{"subfields":["Solving Equations"],"name":"Trigonometric Equations"},{"subfields":["Angle Measure","The Law of Cosines","The Law of Sines","Trigonometric Functions of Angles","Trigonometry of Right Triangles"],"name":"Trigonometric Functions of Angles"},{"subfields":["Hyperbolic Functions","The Unit Circle","Trigonometric Functions of Real Numbers","Trigonometric Graphs","Misc."],"name":"Trigonometric Functions of Real Numbers"},{"subfields":["Graphs Of The Sine And Cosine","Introduction to Periodic Functions","Inverse Trigonometric Functions","Other Trigonometric Functions","Radians","Review Exercises and Problems","Sinusoidal Functions","The Sine And Cosine Functions","Misc."],"name":"Trigonometric functions"},{"subfields":["Sum and Difference Formulas for Sine and Cosine","Trigonometric Identities"],"name":"Trigonometry"}],"name":"Trigonometry"},{"subfields":[{"subfields":["Answers","Grading","Graphs","JavaScript","Problem","Questionnaire","tex"],"name":"Demos"},{"subfields":["AIM Tutorial: New Problems","AIM Tutorial: Old Problems","ASU","CSLB","Fort Lewis Tutorial 2011","MAA Tutorial","Rochester","Surveys","WeBWorK Tutorial"],"name":"WeBWorK Tutorial"},{"subfields":["Calculus entrance","Derivative","Integral","Calculus II entrance"],"name":"Calculus gateway"}],"name":"WeBWorK"}]