curriculum.yaml

# ==============================================================================
# Mathigon Curriculum Outline
# (c) Mathigon
# ==============================================================================



# ------------------------------------------------------------------------------
# Foundations

integers:
  title: The Integers
  color: 22ab24
  sections:
    # TODO Update Sections
    - title: Commutative, Associative and Distributive Laws
    - title: Order of Operations
    - title: The Number Line
    - title: Arithmetic with Negative Numbers
    - title: Properties of Zero
    - title: Absolute Value
    - title: Place Value

divisibility:
  title: Divisibility and Primes
  description: Prime numbers represent both the most basic properties and the most complex unsolved problems. Here you can learn about the building blocks of mathematics.
  color: 1fab40

fractions:
  title: Fractions
  color: 1dab5b
  sections:
    # TODO Update Sections
    - title: Introduction
    - title: Simplifying and Expanding Fractions
    - title: Adding and Subtracting Fractions
    - title: Multiplying and Dividing Fractions
    - title: Mixed Numbers

decimals:
  title: Decimals
  color: 1aaa77
  sections:
    # TODO Update Sections
    - title: Introduction
    - title: Adding and Subtracting Decimals
    - title: Ordering Decimals
    - title: Multiplying Decimals
    - title: Dividing Decimals
    - title: Converting Decimals and Fractions
    - title: Rounding

percentages:
  title: Rates, Percentages and Ratios
  color: 18a38a
  sections:
    # TODO Update Sections
    - title: Ratios and Mixtures
    - title: Percentages
    - title: Percentage Increase and Decrease
    - title: Interest
    - title: Ratios and Rates

exponents:
  title: Roots and Exponents
  color: 15a1ab
  sections:
    # TODO Update Sections
    - title: Square and Cube Roots
    - title: Rational and Irrational Numbers
    - title: Powers and Exponents
    - title: Large and Small Numbers
    - title: Scientific Notation

shapes:
  title: Area and Shapes
  color: 0f82f2
  sections:
    - title: Introduction
    - title: Parallelograms and Triangles
    - title: Polygons
    - title: Circles and Circumferences
    - title: Area of Circles

polygons:
  title: Angles and Polygons
  color: 2c63e8

solids:
  title: 3D Solids
  color: 4a40de
  sections:
    - title: Polyhedra
    - title: Nets and Surface Area
    - title: Volumes and Cuboids
    - title: Prisms and Pyramids
    - title: Cylinders and Cones
    - title: Spheres

measuring:
  title: Units and Measuring
  color: 6f27cc
  sections:
    # TODO Update Sections
    - title: Measuring
    - title: Units and Conversion
    - title: Scale Drawings
    - title: Scaling and Dimensions
    - title: Estimation

algebra:
  title: Introduction to Algebra
  color: fd8c00
  sections:
    # TODO Update Sections
    - title: Introduction
    - title: Constants and Variables
    - title: Manipulating Expressions
    - title: Modelling

proportional:
  title: Proportional Relationships
  color: f76f0a
  sections:
    # TODO Update Sections
    - title: Introduction
    - title: Direct and Inverse Proportion
    - title: Graphing Proportional Relationships
    - title: Constant of Proportionality

linear-equations:
  title: Linear Equations
  color: f15315
  sections:
    - title: Reasoning with Tape Diagrams
    - title: Weighing and Balancing
    - title: Manipulating Equations
    - title: Solving Linear Equations
    - title: Inequalities

linear-functions:
  title: Linear Functions
  color: ea3620

basic-probability:
  title: Basic Probability
  color: cd0e66
  sections:
    - title: Introduction
    - title: Coins, Cards and Dice
    - title: Multi-Step Experiments
    - title: Designing Simulations

combinatorics:
  title: Combinatorics
  color: af1589
  sections:
    - title: Factorials
      preview: /world/Combinatorics
    - title: Permutations
      preview: /world/Combinatorics#permutations
    - title: Combinations
      preview: /world/Combinatorics#combinations
    - title: Winning the Lottery
      preview: /world/Combinatorics#lottery

data:
  title: Data and Statistics
  color: 901cac
  sections:
    - title: Introduction
    - title: Dot Plots and Histograms
    - title: Box Plots
    - title: Mean, Median and Mode
    - title: Sampling
    - title: Comparing Populations
    - title: Scatter Plots and Linear Models


# ------------------------------------------------------------------------------
# Intermediate

euclidean-geometry:
  title: Euclidean Geometry
  description: Geometry is one of the oldest parts of mathematics – and one of the most useful. Its logical, systematic approach has been copied in many other areas.
  color: 0f82f2
  next: transformations

transformations:
  title: Transformations and Symmetry
  description: Symmetry can be seen everywhere in nature – but it also underlies completely invisible laws of nature. Mathematics can explain why that is the case.
  color: 216fec
  next: triangles

triangles:
  title: Triangles and Trigonometry
  description: "Triangles are some of the most important shapes in geometry: they have countless interesting properties and appear everywhere in engineering and technology."
  color: 325ce6
  next: polyhedra

polyhedra:
  title: Polygons and Polyhedra
  description: Geometric shapes are everywhere around us. In this course you will learn about angels, polygons, tessellations, polyhedra and nets.
  color: "4346e0"
  next: circles

circles:
  title: Circles and Pi
  trailer: tBJUNvCBkLo
  color: 5934d9
  next: graph-theory

non-euclidean-geometry:
  title: Non-Euclidean Geometry
  color: 6f27cc
  sections:
    - title: Spherical Geometry
      preview: /world/Dimensions_and_Distortions#spherical
    - title: Map Projections
      preview: /world/Dimensions_and_Distortions#projections
    - title: Hyperbolic Geometry
      preview: /world/Dimensions_and_Distortions#hyperbolic
    - title: Metric Spaces
      preview: /world/Dimensions_and_Distortions#metric
    - title: Topology
      preview: /world/Dimensions_and_Distortions#topology
    - title: Higher Dimensions

functions:
  title: Functions
  color: fd8c00
  sections:
    - title: Relations and Functions
    - title: Graphing Functions
    - title: Solving Equations Graphically
    - title: Domain and Range
    - title: Absolute Value Functions
    - title: Inverse Functions
    - title: Rates of Change

sequences:
  title: Sequences and Patterns
  description: Learn about some of the most fascinating patterns in mathematics, from triangle numbers to the Fibonacci sequence and Pascal’s triangle.
  trailer: u2vwpDVj5rU
  color: f97607
  next: quadratics

equations:
  title: Linear Equations and Inequalities
  color: f46110
  sections:
    - title: Solving Linear Equations
    - title: Graphing Linear Functions
    - title: Systems of Linear Equations
    - title: Row Operations and Elimination
    - title: Linear Inequalities
    - title: Inequalities in Two Variables
    - title: Systems of Inequalities

quadratics:
  title: Quadratic Equations
  color: ef4b18
  next: graph-theory

exponentials:
  title: Exponential Functions
  color: ea3620

probability:
  title: Probability
  description: "Cards, dice, roulette and game shows: probability is one of the most fun areas of mathematics, full of surprises and real life applications."
  color: cd0e66
  next: statistics

statistics:
  title: Statistics
  color: bb127b
  next: graph-theory

graph-theory:
  title: Graphs and Networks
  description: "Discover the mathematical principles that connect our world: from shaking hands to travel and navigation, colouring maps and social networks."
  color: aa1690
  next: probability

codes:
  title: Codes and Ciphers
  color: 971aa6

game-theory:
  title: Game Theory
  color: 8220b9


# ------------------------------------------------------------------------------
# Advanced

polynomials:
  title: Polynomials
  color: fd8c00
  sections:
    - title: Introduction
    - title: Zeros of Polynomials
    - title: Sketching Polynomial Functions
    - title: The Factor and Remainder Theorems
    - title: Systems of Equations

function-transforms:
  title: Function Transformations
  color: fa7b06
  sections:
    - title: Combining and Composing Functions
    - title: Translating Functions
    - title: Reflecting Functions
    - title: Scaling Functions
    - title: Inverse functions

rationals:
  title: Rationals and Radicals
  color: f66a0c
  sections:
    - title: Rational and Irrational Numbers
    - title: Rational Functions and Expressions
    - title: Solving Rational Equations
    - title: Exponent Laws
    - title: Radical Functions
    - title: Solving Radical Equations

logarithms:
  title: Exponentials and Logarithms
  color: f25813
  sections:
    - title: Exponential Growth and Decay
    - title: Exponential Functions
    - title: Introduction to Logarithms
    - title: Laws of Logarithms
    - title: The Number e
    - title: Logarithmic Functions

series:
  title: Sequences and Series
  color: ee4719
  sections:
    - title: Sequences
    - title: Series and Sigma Notation
    - title: Arithmetic and Geometric Series
    - title: The Binomial Theorem

logic:
  title: Logic, Sets and Proof
  color: ea3620
  sections:
    - title: Logic and Paradoxes
      preview: /world/Logic_and_Paradoxes
    - title: Sets, Axioms and Proof
      preview: /world/Axioms_and_Proof
    - title: Proof by Contradiction
      preview: /world/Axioms_and_Proof#contradiction
    - title: Proof by Induction
      preview: /world/Axioms_and_Proof#induction
    - title: Infinity and Hilbert’s Hotel
      preview: /world/Infinity

coordinate-geometry:
  title: Coordinate Geometry
  color: 0f82f2
  sections:
    - title: Equations of Lines
    - title: Parallel and Perpendicular Lines
    - title: Equations of Circles
    - title: Properties of Polygons
    - title: Transformations

trigonometry:
  title: Trigonometry
  color: 216fec
  sections:
    - title: The Unit Circle Definition
    - title: Graphs of Trigonometric Functions
    - title: Amplitude, Frequency and Transformations
    - title: Pythagorean Identities
    - title: More Trigonometric Identities
    - title: Inverse Trigonometric Functions
    - title: Circular Motion

conics:
  title: Conic Sections and Polar Coordinates
  color: 325ce6
  sections:
    - title: Parametric Curves
    - title: Circles and Ellipses
    - title: Parabolae
    - title: Hyperbolae
    - title: Polar Coordinates

vectors:
  title: Vectors
  color: "4346e0"

matrices:
  title: Matrices
  color: 5934d9
  sections:
    - title: Matrices as Transformations
    - title: Matrix Arithmetic
    - title: Determinants
    - title: Matrix Inverses
    - title: Cramer’s Rule and Gaussian Elimination
    - title: Eigenvalues and Eigenvectors

complex:
  title: Complex Numbers
  color: 6f27cc

fractals:
  title: Fractals
  trailer: ohygDnKg5mg
  color: 8220b9

differentiation:
  title: Differentiation
  color: 22ab24
  sections:
    - title: Introduction
    - title: Limits and Gradients
    - title: Differentiation Rules I
    - title: Differentiation Rules II
    - title: Optimisation problems

integration:
  title: Integration
  color: 1fab40
  sections:
    - title: Introduction
    - title: Integration Rules I
    - title: Integration Rules II
    - title: Definite Integrals and Areas under a Curve
    - title: Numerical Integration
    - title: Improper Integrals
    - title: Solids of Revolution

numerical:
  title: Numerical Methods
  color: 1dab5b
  sections:
    - title: Solving Equations Numerically
    - title: The Newton­-Raphson Method
    - title: Maclaurin and Taylor series

diff-equations:
  title: Differential Equations
  color: 1aaa77
  sections:
    - title: Simple Differential Equations
    - title: First Order Separable Equations
    - title: Second Order Differential Equations
    - title: Homogenous Equations and Particular Integrals
    - title: Simple Harmonic Motion
    - title: Coupled Differential Equations

chaos:
  title: Chaos Theory
  color: 18a38a

adv-probability:
  title: Advanced Probability
  color: cd0e66
  sections:
    - title: Introduction
    - title: Discrete Random Variables
    - title: The Normal Distribution
    - title: Binomial and Poisson Distribution
    - title: Continuous Random Variables
    - title: Random Walks

adv-statistics:
  title: Statistics and Hypothesis Tests
  color: bb127b
  sections:
    - title: Data Representation
    - title: Experiments and Sampling
    - title: Hypothesis Tests
    - title: Estimation and Confidence Intervals
    - title: The Law of Large Numbers and Central Limit Theorem
    - title: Chi Squared Tests and Correlation Coefficients
    - title: Bayesian Statistics

algorithms:
  title: Algorithms
  color: aa1690
  sections:
    - title: Introduction to Computing
    - title: Complexity and O Notation
    - title: Sorting Algorithms
    - title: Linear Programming and the Simplex Algorithm
    - title: Graphs, Trees and Networks

machine-learning-1:
  title: Machine Learning
  color: 971aa6
  sections:
    - title: Introduction
    - title: Linear Regression
    - title: Support Vector Machines
    - title: Neural Networks
    - title: Unsupervised Learning
    - title: Tensor Flow


# ------------------------------------------------------------------------------
# External

exploding-dots:
  title: Exploding Dots
  description: A mathematical story developed for Global Math Week – learn about place value, infinity and p-adic numbers.
  color: 6f27cc
  hideTitle: true