Biblioteca de curs

Fundaţii

Clasele 6–8

Intermediar

Clasele 9-10

Avansat

Clasele 11–12

Numere și Aritmetică

The Integers

Arithmetic

The Number Line

Negative Numbers

Absolute Value

Properties of Zero

Place Value

Divizibilitate și Numere Prime

Factori și Multipli Criterii de Divizibilitate Numere Prime Distribuția Numerelor Prime Cel Mai Mic Multiplu Comun Cel Mai Mare Divizor Comun

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

Ecuații și funcții

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

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

Probabilități și Statistici

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

Geometria Euclidiană

Introducere Axiomele lui Euclid Construcții cu rigla și compasul

Și mai multe construcții

Unghiuri și Demonstrații

Origami și Plierea Hârtiei

Transformări și Simetrie

Introducere Transformări Rigide

Congruența

Simetria Grupuri de Simetrie și Tapete Simetria în Fizică Omotetii

Asemănare

Triunghiuri și Trigonometrie

Introducere Proprietățile triunghiurilor

Linii mijlocii și Asemănare

Congruența triunghiurilor Teorema lui Pitagora

Triunghiuri Isoscele și Echilaterale

Trigonometrie Teorema Sinusurilor și Teorema Cosinusului

Poligoane și Poliedre

Poligoane Patrulatere Mozaicări Poliedre

Plase și Secțiuni Transversale

Prisme și Piramide

Scalarea Formelor și a Solidelor

Corpurile lui Platon

Cercuri și Pi

Introducere Grade și Radiani Tangente, Corzi și Arce

Teorema Cercului

Poligoane ciclice

Sfere, Conuri și Cilindri Secțiuni conice

Non-Euclidean Geometry

Spherical Geometry Map Projections Hyperbolic Geometry Metric Spaces Topology

Higher Dimensions

Algebră

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

Ecuații de gradul al doilea

Introducere

Expresii binomiale

Rezolvarea ecuațiilor de gradul al doilea

Soluțiile ecuației de gradul al doilea

Graficul funcțiilor de gradul al doilea

Mișcarea proiectilelor

Mai multe aplicații

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

Probabilități și Matematică Discretă

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

Grafice și rețele

Introducere Podurile din Königsberg Strângeri de mână și întâlniri Graficele planare Harta de colorat Problema vânzătorului călător

Programarea problemelor

Grafice în viața de zi cu zi

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

Algebră și analiză

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 și Algebră liniară

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

fractalii

Introducere Triunghiul Sierpinski Setul Mandelbrot

Curbe de umplere spațială

Analiză

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

Probabilități și Statistici

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

Schimbă limba

Conectați-vă la Mathigon

Biblioteca de curs

Numere și Aritmetică

The Integers

Divizibilitate și Numere Prime

Fractions

Decimals

Rates, Percentages and Ratios

Ecuații și funcții

Introduction to Algebra

Linear Equations

Linear Functions

Roots and Exponents

Geometrie

Area and Shapes

Angles and Polygons

3D Solids

Units and Measuring

Probabilități și Statistici

Introduction to Probability

Combinatorics

Data and Statistics

Geometrie

Geometria Euclidiană

Transformări și Simetrie

Triunghiuri și Trigonometrie

Poligoane și Poliedre

Cercuri și Pi

Non-Euclidean Geometry

Algebră

Functions

Sequences and Patterns

Ecuații de gradul al doilea

Inequalities and Systems of Equations

Exponential Functions

Probabilități și Matematică Discretă

Probability

Statistics and Data

Grafice și rețele

Codes and Ciphers

Game Theory

Algebră și analiză

Polynomials

Function Transformations

Rationals and Radicals

Exponentials and Logarithms

Sequences and Series

Logic, Sets and Proof

Geometrie și Algebră liniară

Coordinate Geometry

Trigonometry

Conic Sections and Polar Coordinates

Vectors

Matrices

Complex Numbers

fractalii

Analiză

Differentiation

Integration

Numerical Methods

Differential Equations

Chaos Theory

Probabilități și Statistici

Random Variables

Statistics and Hypothesis Tests

Algorithms

Machine Learning