课程库

数字和算术

The Integers

Commutative, Associative and Distributive Laws快来了
Order of Operations快来了
The Number Line快来了
Arithmetic with Negative Numbers快来了
Properties of Zero快来了
Absolute Value快来了
Place Value快来了

Fractions

Introduction快来了
Simplifying and Expanding Fractions快来了
Adding and Subtracting Fractions快来了
Multiplying and Dividing Fractions快来了
Mixed Numbers快来了

Decimals

Introduction快来了
Adding and Subtracting Decimals快来了
Ordering Decimals快来了
Multiplying Decimals快来了
Dividing Decimals快来了
Converting Decimals and Fractions快来了
Rounding快来了

Rates, Percentages and Ratios

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

Roots and Exponents

Square and Cube Roots快来了
Rational and Irrational Numbers快来了
Powers and Exponents快来了
Large and Small Numbers快来了
Scientific Notation快来了

方程和函数

Introduction to Algebra

Introduction快来了
Constants and Variables快来了
Manipulating Expressions快来了
Modelling快来了

Proportional Relationships

Introduction快来了
Direct and Inverse Proportion快来了
Graphing Proportional Relationships快来了
Constant of Proportionality快来了

Linear Equations

Reasoning with Tape Diagrams快来了
Weighing and Balancing快来了
Manipulating Equations快来了
Solving Linear Equations快来了
Inequalities快来了

Linear Functions

Input and Output快来了
Graphing Functions快来了
Slope and Intercept快来了
Parallel and Perpendicular Lines快来了
Linear Functions快来了
Piecewise Functions and Systems of Equations快来了

几何

Area and Shapes

Introduction快来了
Parallelograms and Triangles快来了
Polygons快来了
Circles and Circumferences快来了
Area of Circles快来了

Angles and Polygons

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

3D Solids

Polyhedra快来了
Nets and Surface Area快来了
Volumes and Cuboids快来了
Prisms and Pyramids快来了
Cylinders and Cones快来了
Spheres快来了

Units and Measuring

Measuring快来了
Units and Conversion快来了
Scale Drawings快来了
Scaling and Dimensions快来了
Estimation快来了

概率统计

Introduction to Probability

Introduction快来了
Coins, Cards and Dice快来了
Multi-Step Experiments快来了
Designing Simulations快来了

Data and Statistics

Introduction快来了
Dot Plots and Histograms快来了
Box Plots快来了
Mean, Median and Mode快来了
Sampling快来了
Comparing Populations快来了
Scatter Plots and Linear Models快来了

几何

Euclidean Geometry

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

Transformations and Symmetry

IntroductionRigid Transformations
Congruence快来了
SymmetrySymmetry Groups and WallpapersSymmetry in PhysicsDilations
Similarity快来了

Triangles and Trigonometry

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

Polygons and Polyhedra

PolygonsQuadrilateralsTessellationsPolyhedra
Nets and Cross Sections快来了
Prisms and Pyramids快来了
Scaling Shapes and Solids快来了
Platonic Solids

圆与圆周率

引言角度制与弧度制切线、弦和弧
圆的定理快来了
循环多边形快来了
球体、锥体与柱体圆锥曲线

代数

Functions

Relations and Functions快来了
Graphing Functions快来了
Solving Equations Graphically快来了
Absolute Value Functions快来了
Inverse Functions快来了
Rates of Change快来了

序列和模式

介绍算术序列和几何序列形数
序列作為函數快来了
斐波那契序列特殊序列帕斯卡三角
极限与收敛快来了

Linear Equations and Inequalities

Solving Linear Equations快来了
Graphing Linear Functions快来了
Systems of Linear Equations快来了
Row Operations and Elimination快来了
Linear Inequalities快来了
Inequalities in Two Variables快来了
Systems of Inequalities快来了

Quadratic Equations

Introduction
Binomial Expressions快来了
Solving Quadratic Equations快来了
The Quadratic Formula快来了
Graphing Quadratics快来了
Projectile Motion快来了
More Applications快来了

Exponential Functions

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

概率论与离散数学

Probability

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

Statistics and Data

Casino Mathematics
Data Visualisation快来了
Center and Spread of Data快来了
Sampling and Estimation快来了
Spreadsheets and Frequency Tables快来了
Linear Models快来了
Causation vs Correlation快来了

Codes and Ciphers

Introduction快来了
Binary Codes快来了
Error Detection快来了
Secret Codes快来了
The Enigma快来了
Public Key Cryptography快来了

Game Theory

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

代数与分析

Polynomials

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

Function Transformations

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

Rationals and Radicals

Rational and Irrational Numbers快来了
Rational Functions and Expressions快来了
Solving Rational Equations快来了
Exponent Laws快来了
Radical Functions快来了
Solving Radical Equations快来了

Exponentials and Logarithms

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

Sequences and Series

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

几何与线性代数

Coordinate Geometry

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

Trigonometry

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

Conic Sections and Polar Coordinates

Parametric Curves快来了
Circles and Ellipses快来了
Parabolae快来了
Hyperbolae快来了
Polar Coordinates快来了

Vectors

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

Matrices

Matrices as Transformations快来了
Matrix Arithmetic快来了
Determinants快来了
Matrix Inverses快来了
Cramer’s Rule and Gaussian Elimination快来了
Eigenvalues and Eigenvectors快来了

Complex Numbers

Introduction快来了
Complex Arithmetic快来了
Modulus and Argument快来了
Quadratic, Cubic and Quartic Equations快来了
Euler’s Identity and De Moivre’s Theorem快来了
Complex Roots of Unity快来了

分形

简介塞尔平斯基三角曼德布罗特集
空间填充曲线快来了

结石

Differentiation

Introduction快来了
Limits and Gradients快来了
Differentiation Rules I快来了
Differentiation Rules II快来了
Optimisation problems快来了

Integration

Introduction快来了
Integration Rules I快来了
Integration Rules II快来了
Definite Integrals and Areas under a Curve快来了
Numerical Integration快来了
Improper Integrals快来了
Solids of Revolution快来了

Numerical Methods

Solving Equations Numerically快来了
The Newton­-Raphson Method快来了
Maclaurin and Taylor series快来了

Differential Equations

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

Chaos Theory

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

概率统计

Advanced Probability

Introduction快来了
Discrete Random Variables快来了
The Normal Distribution快来了
Binomial and Poisson Distribution快来了
Continuous Random Variables快来了
Random Walks快来了

Statistics and Hypothesis Tests

Data Representation快来了
Experiments and Sampling快来了
Hypothesis Tests快来了
Estimation and Confidence Intervals快来了
The Law of Large Numbers and Central Limit Theorem快来了
Chi Squared Tests and Correlation Coefficients快来了
Bayesian Statistics快来了

Algorithms

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

Machine Learning

Introduction快来了
Linear Regression快来了
Support Vector Machines快来了
Neural Networks快来了
Unsupervised Learning快来了
Tensor Flow快来了