# Библиотека курсаИзучите учебник будущего

## Числа и Арифметика

### 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
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

## Уравнения и функции

### 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

## Геометрия

### 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

## Вероятность и статистика

### Introduction to Probability

Introduction
Computing Probabilities
Probability Trees
Venn Diagrams

### Combinatorics

FactorialsPermutationsCombinations

### Data and Statistics

Introduction
Visualising Data
Sampling
Scatter Plots and Linear Models

## Геометрия

### Евклидова геометрия

ВведениеАксиомы ЕвклидаПостроение с линейкой и циркулем
Еще больше конструкций
Углы и доказательства
Складывание оригами

### Преобразования и симметрия

ВведениеИзометрические преобразования
Конгруэнтность
СимметрияГруппы симметрии и орнаментаСимметрия в физикеГомотетия
Подобие

### Треугольники и тригонометрия

ВведениеСвойства треугольников
Средняя линия и подобие
Конгруэнтность треугольникаТеорема Пифагора
Равнобедренные и равносторонние треугольники
ТригонометрияТеоремы синусов и косинусов

### Многоугольники и многогранники

ПолигоныЧетырехугольникиЗамощениеМногогранники
Развёртки и сечения
Призмы и пирамиды
Масштабирование форм и тел
Платоновы тела

### Круги и Пи

ВведениеГрадусы и радианыКасательные, хорды и дуги
Теоремы об окружностях
Циклические многоугольники
Сферы, конусы и цилиндрыКонические сечения

### Non-Euclidean Geometry

Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher Dimensions

## Алгебра

### Functions

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

### Последовательности и паттерны

ВведениеАрифметические и геометрические прогрессииФигурные числа
Последовательности как функции
Числа ФибоначчиОсобые последовательностиТреугольник Паскаля
Пределы и сходимости

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

## Вероятность и дискретная математика

### 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
Center and Spread of Data
Sampling and Estimation
The Wisdom of Crowds
Spreadsheets and Frequency Tables
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

## Алгебра и анализ

### 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

### 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

## Геометрия и линейная алгебра

### 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

### Фракталы

ВведениеТреугольник СерпинскогоМножество Мандельброта
Кривые заполнения пространства

## Вычисления

### 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

## Вероятность и статистика

### 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