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基础

6-8 年级

中级

9-10 年级

高级

11-12 年级

数字和算术

The Integers

Arithmetic

The Number Line

Negative Numbers

Absolute Value

Properties of Zero

Place Value

整除和素数

因子和倍数整除规律素数(又叫质数)素数的分布最小公倍数最大公约数

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

方程和函数

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

几何

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

概率与统计

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

几何

欧几里得几何

引言欧几里得公理直尺与圆规构建

更多的构造

角度与证明

折纸

Untitled Course

介绍刚性转换

一致

对称对称组和墙纸物理对称膨胀

相似

三角形与三角学

引言三角形的性质

中位线与相似性

三角形全等毕达哥拉斯定理

等腰与等边三角形

三角函数正弦与余弦定理

Untitled Course

多边形四边形镶嵌多面体

网格和横截面

棱镜和金字塔

缩放形状和实体

柏拉图多面体

圆与圆周率

引言角度制与弧度制切线、弦和弧

圆的定理

循环多边形

球体、锥体与柱体圆锥曲线

Non-Euclidean Geometry

Spherical Geometry Map Projections Hyperbolic Geometry Metric Spaces Topology

Higher Dimensions

代数

Functions

Relations and Functions

Graphing and Interpreting Functions

Piecewise Functions

Absolute Value Functions

Inverse Functions

Rates of Change

序列和模式

介绍算术序列和几何序列形数

序列作為函數

斐波那契序列特殊序列帕斯卡三角

极限与收敛

Quadratic Equations

Introduction

Binomial Expressions

Solving Quadratic Equations

The Quadratic Formula

Graphing Quadratics

Projectile Motion

More Applications

Inequalities and Systems of Equations

Systems of Linear Equations

Row Operations and Elimination

Linear Inequalities

Systems of Inequalities

Quadratic Inequalities

Exponential Functions

Carbon Dating

Exponential Growth and Decay

Comparing Models

Compound Interest

Population Dynamics

概率论与离散数学

概率

引言

概率树与维恩图

条件概率

蒙提霍尔问题（三门问题）

生日问题

真正的随机性

Statistics and Data

Casino Mathematics

Data Visualisation

Center and Spread of Data

Sampling and Estimation

The Wisdom of Crowds

Spreadsheets and Frequency Tables

Linear Models

Untitled Course

介绍柯尼斯堡的桥梁握手和约会平面图地图着色旅行商问题

调度问题

日常生活中的图表

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

代数与分析

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

几何与线性代数

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

分形

引言谢尔宾斯基三角形曼德布罗特集

空间填充曲线

微积分

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

概率与统计

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

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课程库探索未来的教科书

数字和算术

The Integers

整除和素数

Fractions

Decimals

Rates, Percentages and Ratios

方程和函数

Introduction to Algebra

Linear Equations

Linear Functions

Roots and Exponents

几何

Area and Shapes

Angles and Polygons

3D Solids

Units and Measuring

概率与统计

Introduction to Probability

Combinatorics

Data and Statistics

几何

欧几里得几何

Untitled Course

三角形与三角学

Untitled Course

圆与圆周率

Non-Euclidean Geometry

代数

Functions

序列和模式

Quadratic Equations

Inequalities and Systems of Equations

Exponential Functions

概率论与离散数学

概率

Statistics and Data

Untitled Course

Codes and Ciphers

Game Theory

代数与分析

Polynomials

Function Transformations

Rationals and Radicals

Exponentials and Logarithms

Sequences and Series

Logic, Sets and Proof

几何与线性代数

Coordinate Geometry

Trigonometry

Conic Sections and Polar Coordinates

Vectors

Matrices

Complex Numbers

分形

微积分

Differentiation

Integration

Numerical Methods

Differential Equations

Chaos Theory

概率与统计

Random Variables

Statistics and Hypothesis Tests

Algorithms

Machine Learning

课程库
探索未来的教科书