Cursusbibliotheek

Cijfers en rekenen

The Integers

Arithmetic
In opbouw
The Number Line
In opbouw
Negative Numbers
In opbouw
Absolute Value
In opbouw
Properties of Zero
In opbouw
Place Value
In opbouw

Fractions

Introduction
In opbouw
Fraction Arithmetic
In opbouw
Mixed Numbers
In opbouw
Dividing Fractions
In opbouw

Decimals

Introduction
In opbouw
Adding and Subtracting Decimals
In opbouw
Ordering Decimals
In opbouw
Multiplying and Dividing Decimals
In opbouw
Converting Decimals and Fractions
In opbouw
Rounding
In opbouw

Rates, Percentages and Ratios

Ratios and Mixtures
In opbouw
Percentages
In opbouw
Percentage Increase and Decrease
In opbouw
Interest
In opbouw
Ratios and Rates
In opbouw

Vergelijkingen en functies

Introduction to Algebra

Proportional Relationships
In opbouw
Graphs an Variables
In opbouw
Manipulating Expressions
In opbouw
Modelling
In opbouw

Linear Equations

Weighing and Balancing
In opbouw
Tape Diagrams
In opbouw
Solving Linear Equations
In opbouw
Inequalities
In opbouw

Linear Functions

Input, Output and Graphs
In opbouw
Slope and Intercept
In opbouw
Parallel and Perpendicular Lines
In opbouw
Systems of Equations
In opbouw

Roots and Exponents

Square and Cube Roots
In opbouw
Rational and Irrational Numbers
In opbouw
Powers and Exponents
In opbouw
Scientific Notation
In opbouw

Geometrie

Area and Shapes

Introduction
In opbouw
Parallelograms
In opbouw
Triangles
In opbouw
Polygons
In opbouw
Circles and Circumferences
In opbouw
Area of Circles
In opbouw

Angles and Polygons

Angles
In opbouw
Angles in Polygons
In opbouw
Drawing Triangles
Pythagoras’ Theorem
In opbouw
The Coordinate Plane
In opbouw
Transformations and Congruence
In opbouw

3D Solids

Introduction
In opbouw
Nets and Surface Area
In opbouw
Prisms and Pyramids
In opbouw
Cylinders and Cones
In opbouw
Spheres
In opbouw

Units and Measuring

Measuring
In opbouw
Units and Conversion
In opbouw
Scale Drawings
In opbouw
Scaling and Dimensions
In opbouw
Estimation
In opbouw

Waarschijnlijkheid en statistieken

Introduction to Probability

Introduction
In opbouw
Computing Probabilities
In opbouw
Probability Trees
In opbouw
Venn Diagrams
In opbouw

Data and Statistics

Introduction
In opbouw
Center and Spread
In opbouw
Visualising Data
In opbouw
Sampling
In opbouw
Scatter Plots and Linear Models
In opbouw

Geometrie

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More Constructions
In opbouw
Angles and Proofs
In opbouw
Origami and Paper Folding

Transformations and Symmetry

IntroductionRigid Transformations
Congruence
In opbouw
SymmetrySymmetry Groups and WallpapersSymmetry in PhysicsDilations
Similarity
In opbouw

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and Similarity
In opbouw
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral Triangles
In opbouw
TrigonometrySine and Cosine Rules

Polygons and Polyhedra

PolygonsQuadrilateralsTessellationsPolyhedra
Nets and Cross Sections
In opbouw
Scaling Shapes and Solids
In opbouw
Platonic Solids

Circles and Pi

IntroductionDegrees and RadiansTangents, Chords and Arcs
The Circle Theorems
In opbouw
Cyclic Polygons
In opbouw
Spheres, Cones and CylindersConic Sections

Algebra

Functions

Relations and Functions
In opbouw
Graphing and Interpreting Functions
In opbouw
Piecewise Functions
In opbouw
Absolute Value Functions
In opbouw
Inverse Functions
In opbouw
Rates of Change
In opbouw

Sequences and Patterns

IntroductionArithmetic and Geometric SequencesFigurate Numbers
Sequences as Functions
In opbouw
Fibonacci NumbersSpecial SequencesPascal’s Triangle
Limits and Convergence
In opbouw

Quadratic Equations

Introduction
Binomial Expressions
In opbouw
Solving Quadratic Equations
In opbouw
The Quadratic Formula
In opbouw
Graphing Quadratics
In opbouw
Projectile Motion
In opbouw
More Applications
In opbouw

Inequalities and Systems of Equations

Systems of Linear Equations
In opbouw
Row Operations and Elimination
In opbouw
Linear Inequalities
In opbouw
Systems of Inequalities
In opbouw
Quadratic Inequalities
In opbouw

Exponential Functions

Carbon Dating
Exponential Growth and Decay
In opbouw
Comparing Models
In opbouw
Compound Interest
In opbouw
Population Dynamics
In opbouw

Waarschijnlijkheid en discrete wiskunde

Probability

Introduction
Probability Trees and Venn Diagrams
In opbouw
Conditional Probability
In opbouw
The Monty Hall Problem
The Birthday Problem
In opbouw
True Randomness

Statistics and Data

Casino Mathematics
Data Visualisation
In opbouw
Center and Spread of Data
In opbouw
Sampling and Estimation
In opbouw
The Wisdom of Crowds
In opbouw
Spreadsheets and Frequency Tables
In opbouw
Linear Models
In opbouw

Codes and Ciphers

Introduction
Binary Numbers
In opbouw
Error Detection
In opbouw
Secret Codes
In opbouw
The Enigma
In opbouw
Public Key Cryptography
In opbouw

Game Theory

The Prisoners’ Dilemma
Cards, Coins and Dice
In opbouw
The Winning Move
Random Walks
In opbouw

Algebra en analyse

Polynomials

Introduction
In opbouw
Zeros of Polynomials
In opbouw
Sketching Polynomial Functions
In opbouw
The Factor and Remainder Theorems
In opbouw
Systems of Equations
In opbouw

Function Transformations

Combining and Composing Functions
In opbouw
Translating Functions
In opbouw
Reflecting Functions
In opbouw
Scaling Functions
In opbouw
Inverse functions
In opbouw

Rationals and Radicals

Rational and Irrational Numbers
In opbouw
Rational Functions and Expressions
In opbouw
Solving Rational Equations
In opbouw
Exponent Laws
In opbouw
Radical Functions
In opbouw
Solving Radical Equations
In opbouw

Exponentials and Logarithms

Exponential Growth and Decay
In opbouw
Exponential Functions
In opbouw
Introduction to Logarithms
In opbouw
Laws of Logarithms
In opbouw
The Number e
In opbouw
Logarithmic Functions
In opbouw

Sequences and Series

Sequences
In opbouw
Series and Sigma Notation
In opbouw
Arithmetic and Geometric Series
In opbouw
The Binomial Theorem
In opbouw

Logic, Sets and Proof

Logic and Paradoxes
In opbouw
Axioms and Proof
In opbouw
Proof by Induction
In opbouw
Infinity and Hilbert’s Hotel
In opbouw

Meetkunde en lineaire algebra

Coordinate Geometry

Equations of Lines
In opbouw
Parallel and Perpendicular Lines
In opbouw
Equations of Circles
In opbouw
Properties of Polygons
In opbouw
Transformations
In opbouw

Trigonometry

The Unit Circle Definition
In opbouw
Graphs of Trigonometric Functions
In opbouw
Amplitude, Frequency and Transformations
In opbouw
Pythagorean Identities
In opbouw
More Trigonometric Identities
In opbouw
Inverse Trigonometric Functions
In opbouw
Circular Motion
In opbouw

Conic Sections and Polar Coordinates

Parametric Curves
In opbouw
Circles and Ellipses
In opbouw
Parabolae
In opbouw
Hyperbolae
In opbouw
Polar Coordinates
In opbouw

Vectors

Introduction
In opbouw
Vector Arithmetic
In opbouw
Scalar Products and Equations of Planes
In opbouw
Cross Products and Equations of Lines
In opbouw
Geometry Problems
In opbouw

Matrices

Transformations
In opbouw
Matrix Arithmetic
In opbouw
Determinants
In opbouw
Matrix Inverses
In opbouw
Cramer’s Rule and Gaussian Elimination
In opbouw
Eigenvalues and Eigenvectors
In opbouw

Complex Numbers

Introduction
In opbouw
Complex Arithmetic
In opbouw
Euler’s Formula
In opbouw
Solving Polynomials
In opbouw
De Moivre’s Theorem and Roots of Unity
In opbouw

Fractals

IntroductionThe Sierpinski TriangleThe Mandelbrot Set
Space Filling Curves
In opbouw

Calculus

Differentiation

Introduction
In opbouw
Limits and Gradients
In opbouw
Differentiation Rules I
In opbouw
Differentiation Rules II
In opbouw
Optimisation problems
In opbouw

Integration

Introduction
In opbouw
Integration Rules
In opbouw
Definite Integrals and Areas under a Curve
In opbouw
Improper Integrals
In opbouw
Solids of Revolution
In opbouw

Numerical Methods

Solving Equations Numerically
In opbouw
The Newton-Raphson Method
In opbouw
Numerical Integration
In opbouw
Maclaurin and Taylor series
In opbouw

Differential Equations

Simple Differential Equations
In opbouw
First Order Separable Equations
In opbouw
Second Order Differential Equations
In opbouw
Homogenous Equations and Particular Integrals
In opbouw
Simple Harmonic Motion
In opbouw
Coupled Differential Equations
In opbouw

Chaos Theory

Introduction
Mathematical Billiard
In opbouw
The Three Body Problem
In opbouw
Phase Space and Strange Attractors
In opbouw
The Logistic Map
In opbouw

Waarschijnlijkheid en statistieken

Random Variables

Introduction
In opbouw
Discrete Random Variables
In opbouw
Binomial and Poisson Distribution
In opbouw
Continuous Random Variables
In opbouw
The Normal Distribution
In opbouw
The Central Limit Theorem
In opbouw

Statistics and Hypothesis Tests

Sampling and Estimation
In opbouw
Hypothesis Tests and Confidence Intervals
In opbouw
Linear Models and Correlation Coefficients
In opbouw
Contingency tables and Chi Squared Tests
In opbouw
Bayesian Statistics
In opbouw

Algorithms

Introduction to Computing
In opbouw
Complexity and O Notation
In opbouw
Sorting Algorithms
In opbouw
Linear Programming and the Simplex Algorithm
In opbouw
Graphs, Trees and Networks
In opbouw

Machine Learning

Introduction
In opbouw
Linear Regression
In opbouw
Support Vector Machines
In opbouw
Neural Networks
In opbouw
Unsupervised Learning
In opbouw