Biblioteca del curs

Nombres i Aritmètica

The Integers

Commutative, Associative and Distributive LawsPròximament
Order of OperationsPròximament
The Number LinePròximament
Arithmetic with Negative NumbersPròximament
Properties of ZeroPròximament
Absolute ValuePròximament
Place ValuePròximament

Fractions

IntroductionPròximament
Fraction ArithmeticPròximament
Mixed NumbersPròximament
Dividing FractionsPròximament

Decimals

IntroductionPròximament
Adding and Subtracting DecimalsPròximament
Ordering DecimalsPròximament
Multiplying and Dividing DecimalsPròximament
Converting Decimals and FractionsPròximament
RoundingPròximament

Rates, Percentages and Ratios

Ratios and MixturesPròximament
PercentagesPròximament
Percentage Increase and DecreasePròximament
InterestPròximament
Ratios and RatesPròximament

Roots and Exponents

Square and Cube RootsPròximament
Rational and Irrational NumbersPròximament
Powers and ExponentsPròximament
Large and Small NumbersPròximament
Scientific NotationPròximament

Equacions i funcions

Introduction to Algebra

IntroductionPròximament
Constants and VariablesPròximament
Manipulating ExpressionsPròximament
ModellingPròximament

Proportional Relationships

IntroductionPròximament
Direct and Inverse ProportionPròximament
Graphing Proportional RelationshipsPròximament
Constant of ProportionalityPròximament

Linear Equations

Reasoning with Tape DiagramsPròximament
Weighing and BalancingPròximament
Manipulating EquationsPròximament
Solving Linear EquationsPròximament
InequalitiesPròximament

Linear Functions

Input and OutputPròximament
Graphing FunctionsPròximament
Slope and InterceptPròximament
Parallel and Perpendicular LinesPròximament
Linear FunctionsPròximament
Piecewise Functions and Systems of EquationsPròximament

Geometria

Area and Shapes

IntroductionPròximament
Parallelograms and TrianglesPròximament
PolygonsPròximament
Circles and CircumferencesPròximament
Area of CirclesPròximament

Angles and Polygons

AnglesPròximament
Angles in PolygonsPròximament
Drawing Triangles
Pythagoras’ TheoremPròximament
The Coordinate PlanePròximament
Transformations and CongruencePròximament

3D Solids

IntroductionPròximament
Nets and Surface AreaPròximament
Prisms and PyramidsPròximament
Cylinders and ConesPròximament
SpheresPròximament

Units and Measuring

MeasuringPròximament
Units and ConversionPròximament
Scale DrawingsPròximament
Scaling and DimensionsPròximament
EstimationPròximament

Probabilitat i estadístiques

Introduction to Probability

IntroductionPròximament
Computing ProbabilitiesPròximament
Probability TreesPròximament
Venn DiagramsPròximament

Data and Statistics

IntroductionPròximament
Center and SpreadPròximament
Visualising DataPròximament
SamplingPròximament
Scatter Plots and Linear ModelsPròximament

Geometria

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More ConstructionsPròximament
Angles and ProofsPròximament
Origami and Paper Folding

Transformations and Symmetry

IntroductionRigid Transformations
CongruencePròximament
SymmetrySymmetry Groups and WallpapersSymmetry in PhysicsDilations
SimilarityPròximament

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and SimilarityPròximament
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral TrianglesPròximament
TrigonometrySine and Cosine Rules

Polygons and Polyhedra

PolygonsQuadrilateralsTessellationsPolyhedra
Nets and Cross SectionsPròximament
Scaling Shapes and SolidsPròximament
Platonic Solids

Cercles i Pi

IntroduccióGraus i RadiansTangents, Acords i Arcs
Els teoremes del cerclePròximament
Polígons cíclicsPròximament
Esferes, cons i cilindresSeccions còniques

Non-Euclidean Geometry

Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher DimensionsPròximament

Àlgebra

Functions

Relations and FunctionsPròximament
Graphing and Interpreting FunctionsPròximament
Linear Functions and EquationsPròximament
Piecewise FunctionsPròximament
Absolute Value FunctionsPròximament
Inverse FunctionsPròximament
Rates of ChangePròximament

Seqüències i patrons

IntroduccióAritmètica i seqüències geomètriquesNombres figurats
Seqüències com a funcionsPròximament
Nombres de FibonacciSeqüències especialsTriangle de Pascal
Límits i ConvergènciaPròximament

Quadratic Equations

Introduction
Binomial ExpressionsPròximament
Solving Quadratic EquationsPròximament
The Quadratic FormulaPròximament
Graphing QuadraticsPròximament
Projectile MotionPròximament
More ApplicationsPròximament

Inequalities and Systems of Equations

Systems of Linear EquationsPròximament
Row Operations and EliminationPròximament
Linear InequalitiesPròximament
Systems of InequalitiesPròximament
Quadratic InequalitiesPròximament

Exponential Functions

Carbon Dating
Exponential Growth and DecayPròximament
Comparing ModelsPròximament
Compound InterestPròximament
Population DynamicsPròximament

Probabilitat i Matemàtiques Discretes

Probability

Introduction
Probability Trees and Venn DiagramsPròximament
Conditional ProbabilityPròximament
The Monty Hall Problem
The Birthday ProblemPròximament
True Randomness

Statistics and Data

Casino Mathematics
Data VisualisationPròximament
Center and Spread of DataPròximament
Sampling and EstimationPròximament
Spreadsheets and Frequency TablesPròximament
Linear ModelsPròximament

Codes and Ciphers

Introduction
Binary NumbersPròximament
Error DetectionPròximament
Secret CodesPròximament
The EnigmaPròximament
Public Key CryptographyPròximament

Game Theory

The Prisoners’ Dilemma
Cards, Coins and DicePròximament
The Winning Move
Random WalksPròximament

Àlgebra i Anàlisi

Polynomials

IntroductionPròximament
Zeros of PolynomialsPròximament
Sketching Polynomial FunctionsPròximament
The Factor and Remainder TheoremsPròximament
Systems of EquationsPròximament

Function Transformations

Combining and Composing FunctionsPròximament
Translating FunctionsPròximament
Reflecting FunctionsPròximament
Scaling FunctionsPròximament
Inverse functionsPròximament

Rationals and Radicals

Rational and Irrational NumbersPròximament
Rational Functions and ExpressionsPròximament
Solving Rational EquationsPròximament
Exponent LawsPròximament
Radical FunctionsPròximament
Solving Radical EquationsPròximament

Exponentials and Logarithms

Exponential Growth and DecayPròximament
Exponential FunctionsPròximament
Introduction to LogarithmsPròximament
Laws of LogarithmsPròximament
The Number ePròximament
Logarithmic FunctionsPròximament

Sequences and Series

SequencesPròximament
Series and Sigma NotationPròximament
Arithmetic and Geometric SeriesPròximament
The Binomial TheoremPròximament

Geometria i Àlgebra Lineal

Coordinate Geometry

Equations of LinesPròximament
Parallel and Perpendicular LinesPròximament
Equations of CirclesPròximament
Properties of PolygonsPròximament
TransformationsPròximament

Trigonometry

The Unit Circle DefinitionPròximament
Graphs of Trigonometric FunctionsPròximament
Amplitude, Frequency and TransformationsPròximament
Pythagorean IdentitiesPròximament
More Trigonometric IdentitiesPròximament
Inverse Trigonometric FunctionsPròximament
Circular MotionPròximament

Conic Sections and Polar Coordinates

Parametric CurvesPròximament
Circles and EllipsesPròximament
ParabolaePròximament
HyperbolaePròximament
Polar CoordinatesPròximament

Vectors

IntroductionPròximament
Vector ArithmeticPròximament
Scalar Products and Equations of PlanesPròximament
Cross Products and Equations of LinesPròximament
Geometry ProblemsPròximament

Matrices

Matrices as TransformationsPròximament
Matrix ArithmeticPròximament
DeterminantsPròximament
Matrix InversesPròximament
Cramer’s Rule and Gaussian EliminationPròximament
Eigenvalues and EigenvectorsPròximament

Complex Numbers

IntroductionPròximament
Complex ArithmeticPròximament
Quadratic, Cubic and Quartic EquationsPròximament
Euler’s IdentityPròximament
De Moivre’s Theorem and Roots of UnityPròximament

Fractals

IntroduccióEl Triangle de SierpinskiEl Conjunt Mandelbrot
Curves d’ompliment d’espaiPròximament

Càlcul

Differentiation

IntroductionPròximament
Limits and GradientsPròximament
Differentiation Rules IPròximament
Differentiation Rules IIPròximament
Optimisation problemsPròximament

Integration

IntroductionPròximament
Integration RulesPròximament
Definite Integrals and Areas under a CurvePròximament
Improper IntegralsPròximament
Solids of RevolutionPròximament

Numerical Methods

Solving Equations NumericallyPròximament
The Newton­-Raphson MethodPròximament
Numerical IntegrationPròximament
Maclaurin and Taylor seriesPròximament

Differential Equations

Simple Differential EquationsPròximament
First Order Separable EquationsPròximament
Second Order Differential EquationsPròximament
Homogenous Equations and Particular IntegralsPròximament
Simple Harmonic MotionPròximament
Coupled Differential EquationsPròximament

Chaos Theory

Introduction
Mathematical BilliardPròximament
The Three Body ProblemPròximament
Phase Space and Strange AttractorsPròximament
The Logistic MapPròximament

Probabilitat i estadístiques

Random Variables

IntroductionPròximament
Discrete Random VariablesPròximament
Binomial and Poisson DistributionPròximament
Continuous Random VariablesPròximament
The Normal DistributionPròximament
The Central Limit TheoremPròximament

Statistics and Hypothesis Tests

Sampling and EstimationPròximament
Hypothesis Tests and Confidence IntervalsPròximament
Linear Models and Correlation CoefficientsPròximament
Contingency tables and Chi Squared TestsPròximament
Bayesian StatisticsPròximament

Algorithms

Introduction to ComputingPròximament
Complexity and O NotationPròximament
Sorting AlgorithmsPròximament
Linear Programming and the Simplex AlgorithmPròximament
Graphs, Trees and NetworksPròximament

Machine Learning

IntroductionPròximament
Linear RegressionPròximament
Support Vector MachinesPròximament
Neural NetworksPròximament
Unsupervised LearningPròximament