# Ders Kütüphanesi

## Sayılar ve Aritmetik

### 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
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

## Denklemler ve Fonksiyonlar

### 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

## Geometri

### Area and Shapes Introduction
Parallelograms and 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

## Olasılık ve İstatistik

### Introduction to Probability Introduction
Computing Probabilities
Probability Trees
Venn Diagrams

### Combinatorics FactorialsPermutationsCombinations

### Data and Statistics Introduction
Visualising Data
Sampling
Scatter Plots and Linear Models

## Geometri

### Öklid Geometrisi

GirişÖklid’in AksiyomlarıPergel ve çizgilik çizimleri
Daha da fazla inşaat
Açılar ve Kanıtlar
Origami and Kağıt Katlama

### Üçgenler ve Trigonometri

GirişÜçgenlerin Özellikleri
Üçgen Orta Segmentleri
Üçgende EşlikPisagor Teoremi
İkizkenar ve Eşkenar Üçgenler
TrigonometriSinüs ve Kosinüs Kuralları

### Çokgenler ve Çokyüzlü

ÇokgenlerdörtgenlerTessellationsçokyüzlüler
Ağlar ve Kesitler
Prizmalar ve Piramitler
Şekillendirme ve Katılar
Platonik Katılar

### Çemberler ve Pi

GirişDerece ve RadyanTeğetler, Kirişler ve Yaylar
The Circle Theorems
Cyclic Polygons
Küre, Koni ve SilindirKonik Kesitler

### Non-Euclidean Geometry Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher Dimensions

## Cebir

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

### Sequences and Patterns IntroductionArithmetic and Geometric SequencesFigurate Numbers
Sequences as Functions
Limits and Convergence

### İkinci dereceden denklemler

Giriş
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

## Olasılık ve Matematik

### Olasılık

Giriş
Olasılık Ağaçları
Venn Diyagramları
Şartlı olasılık
Monty Hall Problemi
Doğum Günü Sorunu
Esas Rastgelelik

### İstatistikler ve Veriler

Kumarhane Matematiği
Veri Görselleştirme
Veri Merkezi ve Yayılımı
Örnekleme ve Tahmin
Elektronik Tablolar ve Frekans Tabloları
Doğrusal Modeller
Nedensellik - Korelasyon

### 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

## Cebir ve Analiz

### 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 Logic and ParadoxesAxioms and ProofProof by InductionInfinity and Hilbert’s Hotel

## Geometri ve Doğrusal Cebir

### 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

### Fraktallar

GirişSierpinski ÜçgeniMandelbrot Seti
Alan Doldurma Eğrileri

## Calculus

### 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

## Olasılık ve İstatistik

### 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