Kursbibliotek

Siffror och aritmetik

The Integers

Commutative, Associative and Distributive LawsKommer snart
Order of OperationsKommer snart
The Number LineKommer snart
Arithmetic with Negative NumbersKommer snart
Properties of ZeroKommer snart
Absolute ValueKommer snart
Place ValueKommer snart

Fractions

IntroductionKommer snart
Simplifying and Expanding FractionsKommer snart
Adding and Subtracting FractionsKommer snart
Multiplying and Dividing FractionsKommer snart
Mixed NumbersKommer snart

Decimals

IntroductionKommer snart
Adding and Subtracting DecimalsKommer snart
Ordering DecimalsKommer snart
Multiplying DecimalsKommer snart
Dividing DecimalsKommer snart
Converting Decimals and FractionsKommer snart
RoundingKommer snart

Rates, Percentages and Ratios

Ratios and MixturesKommer snart
PercentagesKommer snart
Percentage Increase and DecreaseKommer snart
InterestKommer snart
Ratios and RatesKommer snart

Roots and Exponents

Square and Cube RootsKommer snart
Rational and Irrational NumbersKommer snart
Powers and ExponentsKommer snart
Large and Small NumbersKommer snart
Scientific NotationKommer snart

Ekvationer och funktioner

Introduction to Algebra

IntroductionKommer snart
Constants and VariablesKommer snart
Manipulating ExpressionsKommer snart
ModellingKommer snart

Proportional Relationships

IntroductionKommer snart
Direct and Inverse ProportionKommer snart
Graphing Proportional RelationshipsKommer snart
Constant of ProportionalityKommer snart

Linear Equations

Reasoning with Tape DiagramsKommer snart
Weighing and BalancingKommer snart
Manipulating EquationsKommer snart
Solving Linear EquationsKommer snart
InequalitiesKommer snart

Linear Functions

Input and OutputKommer snart
Graphing FunctionsKommer snart
Slope and InterceptKommer snart
Parallel and Perpendicular LinesKommer snart
Linear FunctionsKommer snart
Piecewise Functions and Systems of EquationsKommer snart

Geometri

Area and Shapes

IntroductionKommer snart
Parallelograms and TrianglesKommer snart
PolygonsKommer snart
Circles and CircumferencesKommer snart
Area of CirclesKommer snart

Angles and Polygons

AnglesKommer snart
Angles in PolygonsKommer snart
Drawing Triangles
Pythagoras’ TheoremKommer snart
The Coordinate PlaneKommer snart
Transformations and CongruenceKommer snart

3D Solids

PolyhedraKommer snart
Nets and Surface AreaKommer snart
Volumes and CuboidsKommer snart
Prisms and PyramidsKommer snart
Cylinders and ConesKommer snart
SpheresKommer snart

Units and Measuring

MeasuringKommer snart
Units and ConversionKommer snart
Scale DrawingsKommer snart
Scaling and DimensionsKommer snart
EstimationKommer snart

sannolikhet och statistik

Introduction to Probability

IntroductionKommer snart
Coins, Cards and DiceKommer snart
Multi-Step ExperimentsKommer snart
Designing SimulationsKommer snart

Data and Statistics

IntroductionKommer snart
Dot Plots and HistogramsKommer snart
Box PlotsKommer snart
Mean, Median and ModeKommer snart
SamplingKommer snart
Comparing PopulationsKommer snart
Scatter Plots and Linear ModelsKommer snart

Geometri

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More ConstructionsKommer snart
Angles and ProofsKommer snart
Origami and Paper Folding

Transformations and Symmetry

IntroductionRigid Transformations
CongruenceKommer snart
SymmetrySymmetry Groups and WallpapersSymmetry in PhysicsDilations
SimilarityKommer snart

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and SimilarityKommer snart
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral TrianglesKommer snart
TrigonometrySine and Cosine Rules

Polygons and Polyhedra

PolygonsQuadrilateralsTessellationsPolyhedra
Nets and Cross SectionsKommer snart
Prisms and PyramidsKommer snart
Scaling Shapes and SolidsKommer snart
Platonic Solids

Circles and Pi

IntroductionDegrees and RadiansTangents, Chords and Arcs
The Circle TheoremsKommer snart
Cyclic PolygonsKommer snart
Spheres, Cones and CylindersConic Sections

Non-Euclidean Geometry

Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher DimensionsKommer snart

Algebra

Functions

Relations and FunctionsKommer snart
Graphing FunctionsKommer snart
Solving Equations GraphicallyKommer snart
Absolute Value FunctionsKommer snart
Inverse FunctionsKommer snart
Rates of ChangeKommer snart

Sekvenser och mönster

IntroduktionAritmetiska och geometriska sekvenserFigurnummer
Sekvenser som funktionerKommer snart
Fibonacci-nummerSpeciella sekvenserPascal's Triangle
Gränser och konvergensKommer snart

Linear Equations and Inequalities

Solving Linear EquationsKommer snart
Graphing Linear FunctionsKommer snart
Systems of Linear EquationsKommer snart
Row Operations and EliminationKommer snart
Linear InequalitiesKommer snart
Inequalities in Two VariablesKommer snart
Systems of InequalitiesKommer snart

Quadratic Equations

Introduction
Binomial ExpressionsKommer snart
Solving Quadratic EquationsKommer snart
The Quadratic FormulaKommer snart
Graphing QuadraticsKommer snart
Projectile MotionKommer snart
More ApplicationsKommer snart

Exponential Functions

Carbon Dating
Exponential Growth and DecayKommer snart
Comparing ModelsKommer snart
Compound InterestKommer snart
Population DynamicsKommer snart

Sannolikhet och diskret matematik

Probability

Introduction
Probability TreesKommer snart
Venn DiagramsKommer snart
Conditional ProbabilityKommer snart
The Monty Hall Problem
The Birthday ProblemKommer snart
True Randomness

Statistics and Data

Casino Mathematics
Data VisualisationKommer snart
Center and Spread of DataKommer snart
Sampling and EstimationKommer snart
Spreadsheets and Frequency TablesKommer snart
Linear ModelsKommer snart
Causation vs CorrelationKommer snart

Codes and Ciphers

IntroductionKommer snart
Binary NumbersKommer snart
Error DetectionKommer snart
Secret CodesKommer snart
The EnigmaKommer snart
Public Key CryptographyKommer snart

Game Theory

The Prisoners’ Dilemma
Cards, Coins and DiceKommer snart
The Winning Move
Random WalksKommer snart

Algebra och analys

Polynomials

IntroductionKommer snart
Zeros of PolynomialsKommer snart
Sketching Polynomial FunctionsKommer snart
The Factor and Remainder TheoremsKommer snart
Systems of EquationsKommer snart

Function Transformations

Combining and Composing FunctionsKommer snart
Translating FunctionsKommer snart
Reflecting FunctionsKommer snart
Scaling FunctionsKommer snart
Inverse functionsKommer snart

Rationals and Radicals

Rational and Irrational NumbersKommer snart
Rational Functions and ExpressionsKommer snart
Solving Rational EquationsKommer snart
Exponent LawsKommer snart
Radical FunctionsKommer snart
Solving Radical EquationsKommer snart

Exponentials and Logarithms

Exponential Growth and DecayKommer snart
Exponential FunctionsKommer snart
Introduction to LogarithmsKommer snart
Laws of LogarithmsKommer snart
The Number eKommer snart
Logarithmic FunctionsKommer snart

Sequences and Series

SequencesKommer snart
Series and Sigma NotationKommer snart
Arithmetic and Geometric SeriesKommer snart
The Binomial TheoremKommer snart

Geometri och linjär algebra

Coordinate Geometry

Equations of LinesKommer snart
Parallel and Perpendicular LinesKommer snart
Equations of CirclesKommer snart
Properties of PolygonsKommer snart
TransformationsKommer snart

Trigonometry

The Unit Circle DefinitionKommer snart
Graphs of Trigonometric FunctionsKommer snart
Amplitude, Frequency and TransformationsKommer snart
Pythagorean IdentitiesKommer snart
More Trigonometric IdentitiesKommer snart
Inverse Trigonometric FunctionsKommer snart
Circular MotionKommer snart

Conic Sections and Polar Coordinates

Parametric CurvesKommer snart
Circles and EllipsesKommer snart
ParabolaeKommer snart
HyperbolaeKommer snart
Polar CoordinatesKommer snart

Vectors

IntroductionKommer snart
Vector ArithmeticKommer snart
Scalar Products and Equations of PlanesKommer snart
Cross Products and Equations of LinesKommer snart
Geometry ProblemsKommer snart

Matrices

Matrices as TransformationsKommer snart
Matrix ArithmeticKommer snart
DeterminantsKommer snart
Matrix InversesKommer snart
Cramer’s Rule and Gaussian EliminationKommer snart
Eigenvalues and EigenvectorsKommer snart

Complex Numbers

IntroductionKommer snart
Complex ArithmeticKommer snart
Modulus and ArgumentKommer snart
Quadratic, Cubic and Quartic EquationsKommer snart
Euler’s Identity and De Moivre’s TheoremKommer snart
Complex Roots of UnityKommer snart

Fraktaler

IntroduktionSierpinski-triangelnMandelbrot-uppsättningen
RymdfyllningskurvorKommer snart

Calculus

Differentiation

IntroductionKommer snart
Limits and GradientsKommer snart
Differentiation Rules IKommer snart
Differentiation Rules IIKommer snart
Optimisation problemsKommer snart

Integration

IntroductionKommer snart
Integration Rules IKommer snart
Integration Rules IIKommer snart
Definite Integrals and Areas under a CurveKommer snart
Numerical IntegrationKommer snart
Improper IntegralsKommer snart
Solids of RevolutionKommer snart

Numerical Methods

Solving Equations NumericallyKommer snart
The Newton­-Raphson MethodKommer snart
Maclaurin and Taylor seriesKommer snart

Differential Equations

Simple Differential EquationsKommer snart
First Order Separable EquationsKommer snart
Second Order Differential EquationsKommer snart
Homogenous Equations and Particular IntegralsKommer snart
Simple Harmonic MotionKommer snart
Coupled Differential EquationsKommer snart

Chaos Theory

Introduction
Mathematical BilliardKommer snart
The Three Body ProblemKommer snart
Phase Space and Strange AttractorsKommer snart
The Logistic MapKommer snart

sannolikhet och statistik

Advanced Probability

IntroductionKommer snart
Discrete Random VariablesKommer snart
The Normal DistributionKommer snart
Binomial and Poisson DistributionKommer snart
Continuous Random VariablesKommer snart
Random WalksKommer snart

Statistics and Hypothesis Tests

Data RepresentationKommer snart
Experiments and SamplingKommer snart
Hypothesis TestsKommer snart
Estimation and Confidence IntervalsKommer snart
The Law of Large Numbers and Central Limit TheoremKommer snart
Chi Squared Tests and Correlation CoefficientsKommer snart
Bayesian StatisticsKommer snart

Algorithms

Introduction to ComputingKommer snart
Complexity and O NotationKommer snart
Sorting AlgorithmsKommer snart
Linear Programming and the Simplex AlgorithmKommer snart
Graphs, Trees and NetworksKommer snart

Machine Learning

IntroductionKommer snart
Linear RegressionKommer snart
Support Vector MachinesKommer snart
Neural NetworksKommer snart
Unsupervised LearningKommer snart
Tensor FlowKommer snart