KursbibliotekUtforska framtidens lärobok

Siffror och aritmetik

The Integers

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

Fractions

Introduction
Fraction Arithmetic
Mixed Numbers
Dividing Fractions

Decimals

Introduction
Ordering Decimals
Multiplying and Dividing Decimals
Converting Decimals and Fractions
Rounding

Rates, Percentages and Ratios

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

Ekvationer och funktioner

Introduction to Algebra

Proportional Relationships
Graphs an Variables
Manipulating Expressions
Modelling

Linear Equations

Weighing and Balancing
Tape Diagrams
Solving Linear Equations
Inequalities

Linear Functions

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

Roots and Exponents

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

Geometri

Area and Shapes

Introduction
Parallelograms
Triangles
Polygons
Circles and Circumferences
Area of Circles

Angles and Polygons

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

3D Solids

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

Units and Measuring

Measuring
Units and Conversion
Scale Drawings
Scaling and Dimensions
Estimation

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Introduction to Probability

Introduction
Computing Probabilities
Probability Trees
Venn Diagrams

Combinatorics

FactorialsPermutationsCombinations

Data and Statistics

Introduction
Visualising Data
Sampling
Scatter Plots and Linear Models

Geometri

Euclidean Geometry

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

Transformationer och symmetri

IntroduktionStela transformationer
Kongruens
SymmetriSymmetri grupper och bakgrundsbilderSymmetri i fysikutvidgningar
Likhet

Triangles and Trigonometry

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

Polygoner och polyhedra

Nät och tvärsnitt
Prismor och pyramider
Skalningsformer och fasta ämnen
Platoniska fasta partiklar

Cirklar och Pi

The Circle Theorems
Cykliska polygoner
Sfärer, kottar och cylindrarKoniska sektioner

Non-Euclidean Geometry

Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher Dimensions

Algebra

Functions

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

Sekvenser och mönster

IntroduktionAritmetiska och geometriska sekvenserFigurnummer
Sekvenser som funktioner
Fibonacci-nummerSpeciella sekvenserPascal&#39;s Triangle
Gränser och konvergens

Introduction
Binomial Expressions
Projectile Motion
More Applications

Inequalities and Systems of Equations

Systems of Linear Equations
Row Operations and Elimination
Linear Inequalities
Systems of Inequalities

Exponential Functions

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

Sannolikhet och diskret matematik

Probability

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

Statistics and Data

Casino Mathematics
Data Visualisation
Sampling and Estimation
The Wisdom of Crowds
Linear Models

Codes and Ciphers

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

Game Theory

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

Algebra och analys

Polynomials

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

Function Transformations

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

Rational and Irrational Numbers
Rational Functions and Expressions
Solving Rational Equations
Exponent Laws

Exponentials and Logarithms

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

Sequences and Series

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

Logic, Sets and Proof

Axioms and Proof
Proof by Induction
Infinity and Hilbert’s Hotel

Geometri och linjär algebra

Coordinate Geometry

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

Trigonometry

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

Conic Sections and Polar Coordinates

Parametric Curves
Circles and Ellipses
Parabolae
Hyperbolae
Polar Coordinates

Vectors

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

Matrices

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

Complex Numbers

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

Fraktaler

IntroduktionSierpinski-triangelnMandelbrot-uppsättningen
Rymdfyllningskurvor

Calculus

Differentiation

Introduction
Differentiation Rules I
Differentiation Rules II
Optimisation problems

Integration

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

Numerical Methods

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

Differential Equations

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

Chaos Theory

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

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Random Variables

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

Statistics and Hypothesis Tests

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

Algorithms

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

Machine Learning

Introduction
Linear Regression
Support Vector Machines
Neural Networks
Unsupervised Learning