Библиотека курса

Числа и Арифметика

The Integers

Commutative, Associative and Distributive LawsСкоро
Order of OperationsСкоро
The Number LineСкоро
Arithmetic with Negative NumbersСкоро
Properties of ZeroСкоро
Absolute ValueСкоро
Place ValueСкоро

Fractions

IntroductionСкоро
Fraction ArithmeticСкоро
Mixed NumbersСкоро
Dividing FractionsСкоро

Decimals

IntroductionСкоро
Adding and Subtracting DecimalsСкоро
Ordering DecimalsСкоро
Multiplying and Dividing DecimalsСкоро
Converting Decimals and FractionsСкоро
RoundingСкоро

Rates, Percentages and Ratios

Ratios and MixturesСкоро
PercentagesСкоро
Percentage Increase and DecreaseСкоро
InterestСкоро
Ratios and RatesСкоро

Roots and Exponents

Square and Cube RootsСкоро
Rational and Irrational NumbersСкоро
Powers and ExponentsСкоро
Large and Small NumbersСкоро
Scientific NotationСкоро

Уравнения и функции

Introduction to Algebra

IntroductionСкоро
Constants and VariablesСкоро
Manipulating ExpressionsСкоро
ModellingСкоро

Proportional Relationships

IntroductionСкоро
Direct and Inverse ProportionСкоро
Graphing Proportional RelationshipsСкоро
Constant of ProportionalityСкоро

Linear Equations

Reasoning with Tape DiagramsСкоро
Weighing and BalancingСкоро
Manipulating EquationsСкоро
Solving Linear EquationsСкоро
InequalitiesСкоро

Linear Functions

Input and OutputСкоро
Graphing FunctionsСкоро
Slope and InterceptСкоро
Parallel and Perpendicular LinesСкоро
Linear FunctionsСкоро
Piecewise Functions and Systems of EquationsСкоро

Геометрия

Area and Shapes

IntroductionСкоро
Parallelograms and TrianglesСкоро
PolygonsСкоро
Circles and CircumferencesСкоро
Area of CirclesСкоро

Angles and Polygons

AnglesСкоро
Angles in PolygonsСкоро
Drawing Triangles
Pythagoras’ TheoremСкоро
The Coordinate PlaneСкоро
Transformations and CongruenceСкоро

3D Solids

IntroductionСкоро
Nets and Surface AreaСкоро
Prisms and PyramidsСкоро
Cylinders and ConesСкоро
SpheresСкоро

Units and Measuring

MeasuringСкоро
Units and ConversionСкоро
Scale DrawingsСкоро
Scaling and DimensionsСкоро
EstimationСкоро

Вероятность и статистика

Introduction to Probability

IntroductionСкоро
Computing ProbabilitiesСкоро
Probability TreesСкоро
Venn DiagramsСкоро

Data and Statistics

IntroductionСкоро
Center and SpreadСкоро
Visualising DataСкоро
SamplingСкоро
Scatter Plots and Linear ModelsСкоро

Геометрия

Евклидова геометрия

ВведениеАксиомы ЕвклидаПостроение с линейкой и циркулем
Еще больше конструкцийСкоро
Углы и доказательстваСкоро
Складывание оригами

Треугольники и тригонометрия

ВведениеСвойства треугольников
Средняя линия и подобиеСкоро
Конгруэнтность треугольникаТеорема Пифагора
Равнобедренные и равносторонние треугольникиСкоро
ТригонометрияТеоремы синусов и косинусов

Многоугольники и многогранники

ПолигоныЧетырехугольникиЗамощениеМногогранники
Развёртки и сеченияСкоро
Призмы и пирамидыСкоро
Масштабирование форм и телСкоро
Платоновы тела

Круги и Пи

ВведениеГрадусы и радианыКасательные, хорды и дуги
Теоремы об окружностяхСкоро
Циклические многоугольникиСкоро
Сферы, конусы и цилиндрыКонические сечения

Non-Euclidean Geometry

Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher DimensionsСкоро

Алгебра

Functions

Relations and FunctionsСкоро
Graphing and Interpreting FunctionsСкоро
Linear Functions and EquationsСкоро
Piecewise FunctionsСкоро
Absolute Value FunctionsСкоро
Inverse FunctionsСкоро
Rates of ChangeСкоро

Последовательности и паттерны

ВведениеАрифметические и геометрические последовательностиФигурные числа
Последовательности как функцииСкоро
Числа ФибоначчиОсобые последовательностиТреугольник Паскаля
Пределы и сходимостиСкоро

Quadratic Equations

Introduction
Binomial ExpressionsСкоро
Solving Quadratic EquationsСкоро
The Quadratic FormulaСкоро
Graphing QuadraticsСкоро
Projectile MotionСкоро
More ApplicationsСкоро

Inequalities and Systems of Equations

Systems of Linear EquationsСкоро
Row Operations and EliminationСкоро
Linear InequalitiesСкоро
Systems of InequalitiesСкоро
Quadratic InequalitiesСкоро

Exponential Functions

Carbon Dating
Exponential Growth and DecayСкоро
Comparing ModelsСкоро
Compound InterestСкоро
Population DynamicsСкоро

Вероятность и дискретная математика

Probability

Introduction
Probability Trees and Venn DiagramsСкоро
Conditional ProbabilityСкоро
The Monty Hall Problem
The Birthday ProblemСкоро
True Randomness

Statistics and Data

Casino Mathematics
Data VisualisationСкоро
Center and Spread of DataСкоро
Sampling and EstimationСкоро
Spreadsheets and Frequency TablesСкоро
Linear ModelsСкоро

Codes and Ciphers

Introduction
Binary NumbersСкоро
Error DetectionСкоро
Secret CodesСкоро
The EnigmaСкоро
Public Key CryptographyСкоро

Game Theory

The Prisoners’ Dilemma
Cards, Coins and DiceСкоро
The Winning Move
Random WalksСкоро

Алгебра и анализ

Polynomials

IntroductionСкоро
Zeros of PolynomialsСкоро
Sketching Polynomial FunctionsСкоро
The Factor and Remainder TheoremsСкоро
Systems of EquationsСкоро

Function Transformations

Combining and Composing FunctionsСкоро
Translating FunctionsСкоро
Reflecting FunctionsСкоро
Scaling FunctionsСкоро
Inverse functionsСкоро

Rationals and Radicals

Rational and Irrational NumbersСкоро
Rational Functions and ExpressionsСкоро
Solving Rational EquationsСкоро
Exponent LawsСкоро
Radical FunctionsСкоро
Solving Radical EquationsСкоро

Exponentials and Logarithms

Exponential Growth and DecayСкоро
Exponential FunctionsСкоро
Introduction to LogarithmsСкоро
Laws of LogarithmsСкоро
The Number eСкоро
Logarithmic FunctionsСкоро

Sequences and Series

SequencesСкоро
Series and Sigma NotationСкоро
Arithmetic and Geometric SeriesСкоро
The Binomial TheoremСкоро

Геометрия и линейная алгебра

Coordinate Geometry

Equations of LinesСкоро
Parallel and Perpendicular LinesСкоро
Equations of CirclesСкоро
Properties of PolygonsСкоро
TransformationsСкоро

Trigonometry

The Unit Circle DefinitionСкоро
Graphs of Trigonometric FunctionsСкоро
Amplitude, Frequency and TransformationsСкоро
Pythagorean IdentitiesСкоро
More Trigonometric IdentitiesСкоро
Inverse Trigonometric FunctionsСкоро
Circular MotionСкоро

Conic Sections and Polar Coordinates

Parametric CurvesСкоро
Circles and EllipsesСкоро
ParabolaeСкоро
HyperbolaeСкоро
Polar CoordinatesСкоро

Vectors

IntroductionСкоро
Vector ArithmeticСкоро
Scalar Products and Equations of PlanesСкоро
Cross Products and Equations of LinesСкоро
Geometry ProblemsСкоро

Matrices

Matrices as TransformationsСкоро
Matrix ArithmeticСкоро
DeterminantsСкоро
Matrix InversesСкоро
Cramer’s Rule and Gaussian EliminationСкоро
Eigenvalues and EigenvectorsСкоро

Complex Numbers

IntroductionСкоро
Complex ArithmeticСкоро
Quadratic, Cubic and Quartic EquationsСкоро
Euler’s IdentityСкоро
De Moivre’s Theorem and Roots of UnityСкоро

Фракталы

ВведениеСерпинский треугольникМножество Мандельброта
Кривые заполнения пространстваСкоро

Вычисления

Differentiation

IntroductionСкоро
Limits and GradientsСкоро
Differentiation Rules IСкоро
Differentiation Rules IIСкоро
Optimisation problemsСкоро

Integration

IntroductionСкоро
Integration RulesСкоро
Definite Integrals and Areas under a CurveСкоро
Improper IntegralsСкоро
Solids of RevolutionСкоро

Numerical Methods

Solving Equations NumericallyСкоро
The Newton­-Raphson MethodСкоро
Numerical IntegrationСкоро
Maclaurin and Taylor seriesСкоро

Differential Equations

Simple Differential EquationsСкоро
First Order Separable EquationsСкоро
Second Order Differential EquationsСкоро
Homogenous Equations and Particular IntegralsСкоро
Simple Harmonic MotionСкоро
Coupled Differential EquationsСкоро

Chaos Theory

Introduction
Mathematical BilliardСкоро
The Three Body ProblemСкоро
Phase Space and Strange AttractorsСкоро
The Logistic MapСкоро

Вероятность и статистика

Random Variables

IntroductionСкоро
Discrete Random VariablesСкоро
Binomial and Poisson DistributionСкоро
Continuous Random VariablesСкоро
The Normal DistributionСкоро
The Central Limit TheoremСкоро

Statistics and Hypothesis Tests

Sampling and EstimationСкоро
Hypothesis Tests and Confidence IntervalsСкоро
Linear Models and Correlation CoefficientsСкоро
Contingency tables and Chi Squared TestsСкоро
Bayesian StatisticsСкоро

Algorithms

Introduction to ComputingСкоро
Complexity and O NotationСкоро
Sorting AlgorithmsСкоро
Linear Programming and the Simplex AlgorithmСкоро
Graphs, Trees and NetworksСкоро

Machine Learning

IntroductionСкоро
Linear RegressionСкоро
Support Vector MachinesСкоро
Neural NetworksСкоро
Unsupervised LearningСкоро