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Geometria Liczby i algebra Prawdopodobieństwo i zastosowania

Gimnazjum

Euclidean Geometry

Introduction Euclid’s Axioms Ruler and Compass Construction

Even More Constructions

Angles and Proofs

Origami and Paper Folding

Transformations and Symmetry

Introduction Rigid Transformations

Congruence

Symmetry Symmetry Groups and Wallpapers Symmetry in Physics Dilations

Similarity

Triangles and Trigonometry

Introduction Properties of Triangles

Midsegments and Similarity

Triangle Congruence Pythagoras’ Theorem

Isosceles and Equilateral Triangles

Trigonometry Sine and Cosine Rules

Polygons and Polyhedra

Polygons Quadrilaterals Tessellations Polyhedra

Nets and Cross Sections

Platonic Solids

Liceum

Circles and Pi

Introduction Degrees and Radians Tangents, Chords and Arcs

The Circle Theorems

Cyclic Polygons

Spheres, Cones and Cylinders Conic Sections

Non-Euclidean Geometry

Spherical Geometry Map Projections Hyperbolic Geometry Metric Spaces Topology

Higher Dimensions

Fractals

Introduction The Sierpinski Triangle The Mandelbrot Set

Space Filling Curves

Gimnazjum

Divisibility and Primes

Factors and Multiples Divisibility Rules Prime Numbers The Distribution of Primes Lowest Common Multiples Greatest Common Factors

Sequences and Patterns

Introduction Arithmetic and Geometric Sequences Figurate Numbers

Sequences as Functions

Fibonacci Numbers Special Sequences Pascal’s Triangle

Limits and Convergence

Quadratic Equations

Introduction

Binomial Expressions

Solving Quadratic Equations

The Quadratic Formula

Graphing Quadratics

Projectile Motion

More Applications

Liceum

Exponential Functions

Carbon Dating

Exponential Growth and Decay

Comparing Models

Compound Interest

Population Dynamics

Logic, Sets and Proof

Logic and Paradoxes Axioms and Proof Proof by Induction Infinity and Hilbert’s Hotel

Gimnazjum

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

Linear Models

Combinatorics

Factorials Permutations Combinations

Liceum

Graphs and Networks

Introduction The Bridges of Königsberg Handshakes and Dating Planar Graphs Map Colouring The Travelling Salesman Problem

Scheduling Problems

Graphs in Everyday Life

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

Chaos Theory

Introduction

Mathematical Billiard

The Three Body Problem

Phase Space and Strange Attractors

The Logistic Map

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Biblioteka kursówPoznaj Podręcznik Przyszłości

Gimnazjum

Euclidean Geometry

Transformations and Symmetry

Triangles and Trigonometry

Polygons and Polyhedra

Liceum

Circles and Pi

Non-Euclidean Geometry

Fractals

Gimnazjum

Divisibility and Primes

Sequences and Patterns

Quadratic Equations

Liceum

Exponential Functions

Logic, Sets and Proof

Gimnazjum

Probability

Statistics and Data

Combinatorics

Liceum

Graphs and Networks

Codes and Ciphers

Game Theory

Chaos Theory

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