Бібліотека курсу

Числа та арифметика

The Integers

Commutative, Associative and Distributive LawsНезабаром
Order of OperationsНезабаром
The Number LineНезабаром
Arithmetic with Negative NumbersНезабаром
Properties of ZeroНезабаром
Absolute ValueНезабаром
Place ValueНезабаром

Fractions

IntroductionНезабаром
Fraction ArithmeticНезабаром
Mixed NumbersНезабаром
Dividing FractionsНезабаром

Decimals

IntroductionНезабаром
Adding and Subtracting DecimalsНезабаром
Ordering DecimalsНезабаром
Multiplying and Dividing DecimalsНезабаром
Converting Decimals and FractionsНезабаром
RoundingНезабаром

Rates, Percentages and Ratios

Ratios and MixturesНезабаром
PercentagesНезабаром
Percentage Increase and DecreaseНезабаром
InterestНезабаром
Ratios and RatesНезабаром

Roots and Exponents

Square and Cube RootsНезабаром
Rational and Irrational NumbersНезабаром
Powers and ExponentsНезабаром
Large and Small NumbersНезабаром
Scientific NotationНезабаром

Рівняння та функції

Introduction to Algebra

IntroductionНезабаром
Constants and VariablesНезабаром
Manipulating ExpressionsНезабаром
ModellingНезабаром

Proportional Relationships

IntroductionНезабаром
Direct and Inverse ProportionНезабаром
Graphing Proportional RelationshipsНезабаром
Constant of ProportionalityНезабаром

Linear Equations

Reasoning with Tape DiagramsНезабаром
Weighing and BalancingНезабаром
Manipulating EquationsНезабаром
Solving Linear EquationsНезабаром
InequalitiesНезабаром

Linear Functions

Input and OutputНезабаром
Graphing FunctionsНезабаром
Slope and InterceptНезабаром
Parallel and Perpendicular LinesНезабаром
Linear FunctionsНезабаром
Piecewise Functions and Systems of EquationsНезабаром

Геометрія

Area and Shapes

IntroductionНезабаром
Parallelograms and TrianglesНезабаром
PolygonsНезабаром
Circles and CircumferencesНезабаром
Area of CirclesНезабаром

Angles and Polygons

AnglesНезабаром
Angles in PolygonsНезабаром
Drawing Triangles
Pythagoras’ TheoremНезабаром
The Coordinate PlaneНезабаром
Transformations and CongruenceНезабаром

3D Solids

IntroductionНезабаром
Nets and Surface AreaНезабаром
Prisms and PyramidsНезабаром
Cylinders and ConesНезабаром
SpheresНезабаром

Units and Measuring

MeasuringНезабаром
Units and ConversionНезабаром
Scale DrawingsНезабаром
Scaling and DimensionsНезабаром
EstimationНезабаром

Імовірність та статистика

Introduction to Probability

IntroductionНезабаром
Computing ProbabilitiesНезабаром
Probability TreesНезабаром
Venn DiagramsНезабаром

Data and Statistics

IntroductionНезабаром
Center and SpreadНезабаром
Visualising DataНезабаром
SamplingНезабаром
Scatter Plots and Linear ModelsНезабаром

Геометрія

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More ConstructionsНезабаром
Angles and ProofsНезабаром
Origami and Paper Folding

Transformations and Symmetry

IntroductionRigid Transformations
CongruenceНезабаром
SymmetrySymmetry Groups and WallpapersSymmetry in PhysicsDilations
SimilarityНезабаром

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and SimilarityНезабаром
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral TrianglesНезабаром
TrigonometrySine and Cosine Rules

Polygons and Polyhedra

PolygonsQuadrilateralsTessellationsPolyhedra
Nets and Cross SectionsНезабаром
Scaling Shapes and SolidsНезабаром
Platonic Solids

Circles and Pi

IntroductionDegrees and RadiansTangents, Chords and Arcs
The Circle TheoremsНезабаром
Cyclic PolygonsНезабаром
Spheres, Cones and CylindersConic Sections

Non-Euclidean Geometry

Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher DimensionsНезабаром

Алгебра

Functions

Relations and FunctionsНезабаром
Graphing and Interpreting FunctionsНезабаром
Linear Functions and EquationsНезабаром
Piecewise FunctionsНезабаром
Absolute Value FunctionsНезабаром
Inverse FunctionsНезабаром
Rates of ChangeНезабаром

Sequences and Patterns

IntroductionArithmetic and Geometric SequencesFigurate Numbers
Sequences as FunctionsНезабаром
Fibonacci NumbersSpecial SequencesPascal’s Triangle
Limits and ConvergenceНезабаром

Quadratic Equations

Introduction
Binomial ExpressionsНезабаром
Solving Quadratic EquationsНезабаром
The Quadratic FormulaНезабаром
Graphing QuadraticsНезабаром
Projectile MotionНезабаром
More ApplicationsНезабаром

Inequalities and Systems of Equations

Systems of Linear EquationsНезабаром
Row Operations and EliminationНезабаром
Linear InequalitiesНезабаром
Systems of InequalitiesНезабаром
Quadratic InequalitiesНезабаром

Exponential Functions

Carbon Dating
Exponential Growth and DecayНезабаром
Comparing ModelsНезабаром
Compound InterestНезабаром
Population DynamicsНезабаром

Імовірність та дискретна математика

Probability

Introduction
Probability Trees and Venn DiagramsНезабаром
Conditional ProbabilityНезабаром
The Monty Hall Problem
The Birthday ProblemНезабаром
True Randomness

Statistics and Data

Casino Mathematics
Data VisualisationНезабаром
Center and Spread of DataНезабаром
Sampling and EstimationНезабаром
Spreadsheets and Frequency TablesНезабаром
Linear ModelsНезабаром

Codes and Ciphers

Introduction
Binary NumbersНезабаром
Error DetectionНезабаром
Secret CodesНезабаром
The EnigmaНезабаром
Public Key CryptographyНезабаром

Game Theory

The Prisoners’ Dilemma
Cards, Coins and DiceНезабаром
The Winning Move
Random WalksНезабаром

Алгебра та аналіз

Polynomials

IntroductionНезабаром
Zeros of PolynomialsНезабаром
Sketching Polynomial FunctionsНезабаром
The Factor and Remainder TheoremsНезабаром
Systems of EquationsНезабаром

Function Transformations

Combining and Composing FunctionsНезабаром
Translating FunctionsНезабаром
Reflecting FunctionsНезабаром
Scaling FunctionsНезабаром
Inverse functionsНезабаром

Rationals and Radicals

Rational and Irrational NumbersНезабаром
Rational Functions and ExpressionsНезабаром
Solving Rational EquationsНезабаром
Exponent LawsНезабаром
Radical FunctionsНезабаром
Solving Radical EquationsНезабаром

Exponentials and Logarithms

Exponential Growth and DecayНезабаром
Exponential FunctionsНезабаром
Introduction to LogarithmsНезабаром
Laws of LogarithmsНезабаром
The Number eНезабаром
Logarithmic FunctionsНезабаром

Sequences and Series

SequencesНезабаром
Series and Sigma NotationНезабаром
Arithmetic and Geometric SeriesНезабаром
The Binomial TheoremНезабаром

Геометрія та лінійна алгебра

Coordinate Geometry

Equations of LinesНезабаром
Parallel and Perpendicular LinesНезабаром
Equations of CirclesНезабаром
Properties of PolygonsНезабаром
TransformationsНезабаром

Trigonometry

The Unit Circle DefinitionНезабаром
Graphs of Trigonometric FunctionsНезабаром
Amplitude, Frequency and TransformationsНезабаром
Pythagorean IdentitiesНезабаром
More Trigonometric IdentitiesНезабаром
Inverse Trigonometric FunctionsНезабаром
Circular MotionНезабаром

Conic Sections and Polar Coordinates

Parametric CurvesНезабаром
Circles and EllipsesНезабаром
ParabolaeНезабаром
HyperbolaeНезабаром
Polar CoordinatesНезабаром

Vectors

IntroductionНезабаром
Vector ArithmeticНезабаром
Scalar Products and Equations of PlanesНезабаром
Cross Products and Equations of LinesНезабаром
Geometry ProblemsНезабаром

Matrices

Matrices as TransformationsНезабаром
Matrix ArithmeticНезабаром
DeterminantsНезабаром
Matrix InversesНезабаром
Cramer’s Rule and Gaussian EliminationНезабаром
Eigenvalues and EigenvectorsНезабаром

Complex Numbers

IntroductionНезабаром
Complex ArithmeticНезабаром
Euler’s IdentityНезабаром
Quadratic, Cubic and Quartic EquationsНезабаром
De Moivre’s Theorem and Roots of UnityНезабаром

Fractals

IntroductionThe Sierpinski TriangleThe Mandelbrot Set
Space Filling CurvesНезабаром

Обчислення

Differentiation

IntroductionНезабаром
Limits and GradientsНезабаром
Differentiation Rules IНезабаром
Differentiation Rules IIНезабаром
Optimisation problemsНезабаром

Integration

IntroductionНезабаром
Integration RulesНезабаром
Definite Integrals and Areas under a CurveНезабаром
Improper IntegralsНезабаром
Solids of RevolutionНезабаром

Numerical Methods

Solving Equations NumericallyНезабаром
The Newton­-Raphson MethodНезабаром
Numerical IntegrationНезабаром
Maclaurin and Taylor seriesНезабаром

Differential Equations

Simple Differential EquationsНезабаром
First Order Separable EquationsНезабаром
Second Order Differential EquationsНезабаром
Homogenous Equations and Particular IntegralsНезабаром
Simple Harmonic MotionНезабаром
Coupled Differential EquationsНезабаром

Chaos Theory

Introduction
Mathematical BilliardНезабаром
The Three Body ProblemНезабаром
Phase Space and Strange AttractorsНезабаром
The Logistic MapНезабаром

Імовірність та статистика

Random Variables

IntroductionНезабаром
Discrete Random VariablesНезабаром
Binomial and Poisson DistributionНезабаром
Continuous Random VariablesНезабаром
The Normal DistributionНезабаром
The Central Limit TheoremНезабаром

Statistics and Hypothesis Tests

Sampling and EstimationНезабаром
Hypothesis Tests and Confidence IntervalsНезабаром
Linear Models and Correlation CoefficientsНезабаром
Contingency tables and Chi Squared TestsНезабаром
Bayesian StatisticsНезабаром

Algorithms

Introduction to ComputingНезабаром
Complexity and O NotationНезабаром
Sorting AlgorithmsНезабаром
Linear Programming and the Simplex AlgorithmНезабаром
Graphs, Trees and NetworksНезабаром

Machine Learning

IntroductionНезабаром
Linear RegressionНезабаром
Support Vector MachinesНезабаром
Neural NetworksНезабаром
Unsupervised LearningНезабаром