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Entdecken Sie das Lehrbuch der Zukunft

Grundlagen

6. – 8. Klasse

Erweitert

9. – 10. Klasse

Fortgeschritten

Oberstufe

Zahlen und Arithmetik

The Integers

Arithmetic

The Number Line

Negative Numbers

Absolute Value

Properties of Zero

Place Value

Teilbarkeit und Primzahlen

Teiler und Vielfache Teilbarkeitsregeln Primzahlen Die Verteilung der Primzahlen Kleinstes gemeinsames Vielfaches Größter gemeinsamer Teiler

Fractions

Introduction

Fraction Arithmetic

Mixed Numbers

Dividing Fractions

Decimals

Introduction

Adding and Subtracting Decimals

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

Gleichungen und Funktionen

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

Geometrie

Area and Shapes

Introduction

Parallelograms

Triangles

Polygons

Circles and Circumferences

Area of Circles

Winkel und Vielecke

Winkel

Winkel in Vielecken

Dreiecke zeichnen

Der Satz des Pythagoras

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

Wahrscheinlichkeit und Statistik

Introduction to Probability

Introduction

Computing Probabilities

Probability Trees

Venn Diagrams

Combinatorics

Factorials Permutations Combinations

Data and Statistics

Introduction

Center and Spread

Visualising Data

Sampling

Scatter Plots and Linear Models

Geometrie

Euklidische Geometrie

Einführung Euklids Axiome Konstruktion mit Zirkel und Lineal

Noch mehr Konstruktionen

Winkel und Beweise

Origami und Papierfalten

Abbildungen und Symmetrie

Einführung Kongruenzabbildungen

Kongruenz

Symmetrie Symmetriegruppen und Muster Symmetrie in der Physik Streckung

Ähnlichkeit

Dreiecke und Trigonometrie

Einführung Eigenschaften von Dreiecken

Mittelparallelen und Ähnlichkeit

Kongruenzsätze Der Satz des Pythagoras

Gleichschenklige und gleichseitige Dreiecke

Trigonometrie Sinus- und Kosinussätze

Vielecke und Polyeder

Vielecke (Polygone)Vierecke Parkettierung (Tessellation)Polyeder

Netze und Querschnitte

Prismen und Pyramiden

Platonische Körper

Kreise und Pi

Einführung Grad und Radiant Tangenten, Sehnen und Kreisbögen

Die Kreissätze

Regelmäßige Vielecke

Kugeln, Kegel und Zylinder Kegelschnitte

Non-Euclidean Geometry

Spherical Geometry Map Projections Hyperbolic Geometry Metric Spaces Topology

Higher Dimensions

Algebra

Functions

Relations and Functions

Graphing and Interpreting Functions

Piecewise Functions

Absolute Value Functions

Inverse Functions

Rates of Change

Sequences and Patterns

Introduction Arithmetic and Geometric Sequences Figurate Numbers

Sequences as Functions

Fibonacci Numbers Special Sequences Pascal’s Triangle

Limits and Convergence

Quadratische Gleichungen

Einführung

Binomische Formeln

Quadratische Gleichungen Lösen

Die Quadratische Formel

Quadratische Funktionen

Projektilbewegung

Noch Mehr Anwendungen

Inequalities and Systems of Equations

Systems of Linear Equations

Row Operations and Elimination

Linear Inequalities

Systems of Inequalities

Quadratic Inequalities

Exponentialfunktionen

Kohlenstoff-Datierung

Exponentielles Wachstum und Zerfall

Comparing Models

Zinseszins

Population Dynamics

Wahrscheinlichkeit und diskrete Mathematik

Wahrscheinlichkeit

Einführung

Probability Trees

Venn-Diagramme

Conditional Probability

Das Ziegenproblem

Das Geburtstagsproblem

Echte Zufälligkeit

Statistik und Daten

Casino-Mathematik

Data Visualisation

Center and Spread of Data

Sampling and Estimation

Spreadsheets and Frequency Tables

Linear Models

Causation vs Correlation

Graphen und Netzwerke

Einführung Die Brücken von Königsberg Händeschütteln und Dating Planare Graphen Karten färben Problem des Handlungsreisenden

Terminplanungs-Probleme

Graphen im Alltag

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 und Analysis

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

Rationals and Radicals

Rational and Irrational Numbers

Rational Functions and Expressions

Solving Rational Equations

Exponent Laws

Radical Functions

Solving Radical Equations

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

Logic and Paradoxes

Axioms and Proof

Proof by Induction

Infinity and Hilbert’s Hotel

Geometrie und Lineare 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

Fraktale

Einführung Das Sierpinski-Dreieck Die Mandelbrot-Menge

Raumfüllungskurven

Infinitesimalrechnung

Differentiation

Introduction

Limits and Gradients

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

Wahrscheinlichkeit und Statistik

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

Sprache ändern

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Alle KurseEntdecken Sie das Lehrbuch der Zukunft

Zahlen und Arithmetik

The Integers

Teilbarkeit und Primzahlen

Fractions

Decimals

Rates, Percentages and Ratios

Gleichungen und Funktionen

Introduction to Algebra

Linear Equations

Linear Functions

Roots and Exponents

Geometrie

Area and Shapes

Winkel und Vielecke

3D Solids

Units and Measuring

Wahrscheinlichkeit und Statistik

Introduction to Probability

Combinatorics

Data and Statistics

Geometrie

Euklidische Geometrie

Abbildungen und Symmetrie

Dreiecke und Trigonometrie

Vielecke und Polyeder

Kreise und Pi

Non-Euclidean Geometry

Algebra

Functions

Sequences and Patterns

Quadratische Gleichungen

Inequalities and Systems of Equations

Exponentialfunktionen

Wahrscheinlichkeit und diskrete Mathematik

Wahrscheinlichkeit

Statistik und Daten

Graphen und Netzwerke

Codes and Ciphers

Game Theory

Algebra und Analysis

Polynomials

Function Transformations

Rationals and Radicals

Exponentials and Logarithms

Sequences and Series

Logic, Sets and Proof

Geometrie und Lineare Algebra

Coordinate Geometry

Trigonometry

Conic Sections and Polar Coordinates

Vectors

Matrices

Complex Numbers

Fraktale

Infinitesimalrechnung

Differentiation

Integration

Numerical Methods

Differential Equations

Chaos Theory

Wahrscheinlichkeit und Statistik

Random Variables

Statistics and Hypothesis Tests

Algorithms

Machine Learning

Alle Kurse
Entdecken Sie das Lehrbuch der Zukunft