Knjižnica tečajeva
Istražite udžbenik budućnosti

Brojevi i aritmetika

The Integers

Arithmetic
U izradi
The Number Line
U izradi
Negative Numbers
U izradi
Absolute Value
U izradi
Properties of Zero
U izradi
Place Value
U izradi

Fractions

Introduction
U izradi
Fraction Arithmetic
U izradi
Mixed Numbers
U izradi
Dividing Fractions
U izradi

Decimals

Introduction
U izradi
Adding and Subtracting Decimals
U izradi
Ordering Decimals
U izradi
Multiplying and Dividing Decimals
U izradi
Converting Decimals and Fractions
U izradi
Rounding
U izradi

Rates, Percentages and Ratios

Ratios and Mixtures
U izradi
Percentages
U izradi
Percentage Increase and Decrease
U izradi
Interest
U izradi
Ratios and Rates
U izradi

Jednadžbe i funkcije

Introduction to Algebra

Proportional Relationships
U izradi
Graphs an Variables
U izradi
Manipulating Expressions
U izradi
Modelling
U izradi

Linear Equations

Weighing and Balancing
U izradi
Tape Diagrams
U izradi
Solving Linear Equations
U izradi
Inequalities
U izradi

Linear Functions

Input, Output and Graphs
U izradi
Slope and Intercept
U izradi
Parallel and Perpendicular Lines
U izradi
Systems of Equations
U izradi

Roots and Exponents

Square and Cube Roots
U izradi
Rational and Irrational Numbers
U izradi
Powers and Exponents
U izradi
Scientific Notation
U izradi

Geometrija

Area and Shapes

Introduction
U izradi
Parallelograms
U izradi
Triangles
U izradi
Polygons
U izradi
Circles and Circumferences
U izradi
Area of Circles
U izradi

Angles and Polygons

Angles
U izradi
Angles in Polygons
U izradi
Drawing Triangles
Pythagoras’ Theorem
U izradi
The Coordinate Plane
U izradi
Transformations and Congruence
U izradi

3D Solids

Introduction
U izradi
Nets and Surface Area
U izradi
Prisms and Pyramids
U izradi
Cylinders and Cones
U izradi
Spheres
U izradi

Units and Measuring

Measuring
U izradi
Units and Conversion
U izradi
Scale Drawings
U izradi
Scaling and Dimensions
U izradi
Estimation
U izradi

Vjerojatnost i statistika

Introduction to Probability

Introduction
U izradi
Computing Probabilities
U izradi
Probability Trees
U izradi
Venn Diagrams
U izradi

Data and Statistics

Introduction
U izradi
Center and Spread
U izradi
Visualising Data
U izradi
Sampling
U izradi
Scatter Plots and Linear Models
U izradi

Geometrija

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More Constructions
U izradi
Angles and Proofs
U izradi
Origami and Paper Folding

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and Similarity
U izradi
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral Triangles
U izradi
TrigonometrySine and Cosine Rules

Poligoni i poliedri

poligoničetverokutatessellationspoliedra
Mreže i presjeci
U izradi
Prizme i piramide
U izradi
Oblici skaliranja i kruta tijela
U izradi
Platonske čvrste tvari

Algebra

Functions

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

Nizovi i obrasci

UvodAritmetički i geometrijski nizFigurativni brojevi
Niz kao funkcija
U izradi
Fibonaccijevi brojeviPosebni nizoviPascalov trokut
Limesi i konvergencija
U izradi

Quadratic Equations

Introduction
Binomial Expressions
U izradi
Solving Quadratic Equations
U izradi
The Quadratic Formula
U izradi
Graphing Quadratics
U izradi
Projectile Motion
U izradi
More Applications
U izradi

Inequalities and Systems of Equations

Systems of Linear Equations
U izradi
Row Operations and Elimination
U izradi
Linear Inequalities
U izradi
Systems of Inequalities
U izradi
Quadratic Inequalities
U izradi

Exponential Functions

Carbon Dating
Exponential Growth and Decay
U izradi
Comparing Models
U izradi
Compound Interest
U izradi
Population Dynamics
U izradi

Vjerojatnost i diskretna matematika

Probability

Introduction
Probability Trees and Venn Diagrams
U izradi
Conditional Probability
U izradi
The Monty Hall Problem
The Birthday Problem
U izradi
True Randomness

Statistics and Data

Casino Mathematics
Data Visualisation
U izradi
Center and Spread of Data
U izradi
Sampling and Estimation
U izradi
The Wisdom of Crowds
U izradi
Spreadsheets and Frequency Tables
U izradi
Linear Models
U izradi

Codes and Ciphers

Introduction
Binary Numbers
U izradi
Error Detection
U izradi
Secret Codes
U izradi
The Enigma
U izradi
Public Key Cryptography
U izradi

Game Theory

The Prisoners’ Dilemma
Cards, Coins and Dice
U izradi
The Winning Move
Random Walks
U izradi

Algebra i analiza

Polynomials

Introduction
U izradi
Zeros of Polynomials
U izradi
Sketching Polynomial Functions
U izradi
The Factor and Remainder Theorems
U izradi
Systems of Equations
U izradi

Function Transformations

Combining and Composing Functions
U izradi
Translating Functions
U izradi
Reflecting Functions
U izradi
Scaling Functions
U izradi
Inverse functions
U izradi

Rationals and Radicals

Rational and Irrational Numbers
U izradi
Rational Functions and Expressions
U izradi
Solving Rational Equations
U izradi
Exponent Laws
U izradi
Radical Functions
U izradi
Solving Radical Equations
U izradi

Exponentials and Logarithms

Exponential Growth and Decay
U izradi
Exponential Functions
U izradi
Introduction to Logarithms
U izradi
Laws of Logarithms
U izradi
The Number e
U izradi
Logarithmic Functions
U izradi

Sequences and Series

Sequences
U izradi
Series and Sigma Notation
U izradi
Arithmetic and Geometric Series
U izradi
The Binomial Theorem
U izradi

Logic, Sets and Proof

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

Geometrija i linearna algebra

Coordinate Geometry

Equations of Lines
U izradi
Parallel and Perpendicular Lines
U izradi
Equations of Circles
U izradi
Properties of Polygons
U izradi
Transformations
U izradi

Trigonometry

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

Conic Sections and Polar Coordinates

Parametric Curves
U izradi
Circles and Ellipses
U izradi
Parabolae
U izradi
Hyperbolae
U izradi
Polar Coordinates
U izradi

Vectors

Introduction
U izradi
Vector Arithmetic
U izradi
Scalar Products and Equations of Planes
U izradi
Cross Products and Equations of Lines
U izradi
Geometry Problems
U izradi

Matrices

Transformations
U izradi
Matrix Arithmetic
U izradi
Determinants
U izradi
Matrix Inverses
U izradi
Cramer’s Rule and Gaussian Elimination
U izradi
Eigenvalues and Eigenvectors
U izradi

Complex Numbers

Introduction
U izradi
Complex Arithmetic
U izradi
Euler’s Formula
U izradi
Solving Polynomials
U izradi
De Moivre’s Theorem and Roots of Unity
U izradi

Fraktali

UvodSierpinski trokutMandelbrotov set
Krivulje za ispunjavanje prostora
U izradi

Infinitezimalni račun

Differentiation

Introduction
U izradi
Limits and Gradients
U izradi
Differentiation Rules I
U izradi
Differentiation Rules II
U izradi
Optimisation problems
U izradi

Integration

Introduction
U izradi
Integration Rules
U izradi
Definite Integrals and Areas under a Curve
U izradi
Improper Integrals
U izradi
Solids of Revolution
U izradi

Numerical Methods

Solving Equations Numerically
U izradi
The Newton-Raphson Method
U izradi
Numerical Integration
U izradi
Maclaurin and Taylor series
U izradi

Differential Equations

Simple Differential Equations
U izradi
First Order Separable Equations
U izradi
Second Order Differential Equations
U izradi
Homogenous Equations and Particular Integrals
U izradi
Simple Harmonic Motion
U izradi
Coupled Differential Equations
U izradi

Chaos Theory

Introduction
Mathematical Billiard
U izradi
The Three Body Problem
U izradi
Phase Space and Strange Attractors
U izradi
The Logistic Map
U izradi

Vjerojatnost i statistika

Random Variables

Introduction
U izradi
Discrete Random Variables
U izradi
Binomial and Poisson Distribution
U izradi
Continuous Random Variables
U izradi
The Normal Distribution
U izradi
The Central Limit Theorem
U izradi

Statistics and Hypothesis Tests

Sampling and Estimation
U izradi
Hypothesis Tests and Confidence Intervals
U izradi
Linear Models and Correlation Coefficients
U izradi
Contingency tables and Chi Squared Tests
U izradi
Bayesian Statistics
U izradi

Algorithms

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

Machine Learning

Introduction
U izradi
Linear Regression
U izradi
Support Vector Machines
U izradi
Neural Networks
U izradi
Unsupervised Learning
U izradi