Architecture of Logic
A Civilization-Length Expedition
The Central Idea
Mathematics was not invented as one giant subject. It emerged because different problems attacked humanity at different moments in history. The school curriculum is a compressed fossil record of human mathematical development.
Farmer Area
Merchant Fractions
Builder Geometry
Astronomer Angles
Civilization Calendars
Banker Interest
Gambler Probability
Physicist Rates of Change
The 28 Mathematical Worlds
Complete Class 6–12 Architecture Matrix
WORLD 01
The Birth of Number
→
3
- Natural & Whole Numbers
- Number Line
- Absolute Value
- Operations
The Arithmetic World
+
×
- Exponents & Powers
- Squares & Cubes
- Roots
- BODMAS / Order
The Void
0
- Invention of Zero
- Negative Numbers
- Integers
- Directional Value
The Fractioned World
- Fractions
- Decimals
- Rational Numbers
- Irrational Numbers
The Prime Architecture
1
2
3
4
5
6
7
8
9
10
- Factors & Multiples
- Prime Numbers
- HCF & LCM
- Fundamental Theorem
The Market
- Ratio & Proportion
- Percentages
- Profit & Loss
- Simple & Compound Interest
Language of the Unknown
x
- Variables & Expressions
- Linear Equations
- Polynomials
- Quadratic Equations
The Collection (Sets)
- Sets & Subsets
- Union & Intersection
- Venn Diagrams
- Cartesian Products
The Function Machine
f(x)
- Relations
- Domain & Range
- Types of Functions
- Inverse & Composition
The Geometric Temple
- Lines & Angles
- Triangles & Circles
- Congruence & Similarity
- Mensuration (Area/Volume)
Astronomer's Triangle
✦
- Trigonometric Ratios
- Identities & Equations
- Heights & Distances
- Inverse Trigonometry
Cartography of Space
- Cartesian Plane
- Distance & Section
- Straight Lines & Slope
- Equation of a Line
The Conic Kingdom
- Circles
- Parabola
- Ellipse
- Hyperbola
The Pattern Engine
- Arithmetic Progression
- Geometric Progression
- Sum to n Terms
- Infinite Series Concepts
Counting Possibilities
- Fundamental Principle
- Factorials
- Permutations
- Combinations
The Binomial Engine
1
1
1
1
2
1
1
3
3
1
- Pascal's Triangle
- Binomial Expansion
- General & Middle Term
- Coefficients
The Horizon (Limits)
- Intuitive Limits
- Left/Right Hand Limits
- Infinite Behavior
- Continuity
The Change Engine
- Derivatives
- Rules & Chain Rule
- Rates of Change
- Maxima & Minima
Accumulation Engine
- Antiderivatives
- Indefinite Integrals
- Definite Integrals
- Area Under Curves
Equations of Motion
- Differential Equations
- Order & Degree
- General Solution
- First-Order Equations
The Vector World
- Magnitude & Direction
- Components
- Dot Product
- Cross Product
The Third Dimension
- 3D Coordinates
- Direction Cosines
- Equations of Lines
- Equations of Planes
Grid of Variables
[
a
b
c
d
e
f
g
h
i
]
- Matrices
- Operations & Transpose
- Determinants
- Inverse & Systems
The Archive of Data
- Mean, Median, Mode
- Variance
- Standard Deviation
- Distributions
Uncertain Universe
- Sample Space & Events
- Classical Probability
- Conditional Probability
- Bayes & Independence
Optimization Chamber
- Constraints
- Feasible Region
- Objective Function
- Graphical Optimization
The Logic Chamber
AND
- Statements & Truth
- Implication & Negation
- Logical Equivalence
- Proof Methods
Computation
- Algorithms
- Binary & Discrete Math
- Mathematical Modeling
- Data Analytics