Computation
Algorithms, Data, Modeling & Synthetic Execution
The Human Problem
Until now, mathematics was primarily learning to describe, reason about, and solve structures. Now we ask: What happens when we turn mathematical reasoning into a procedure that a machine can execute? A formula alone is not enough to find the shortest path through a million cities or analyze a billion data points. We need a procedure.
The 99 Computational Cells
The Bridge to Computer Science & AI
Computational Foundations
- What is Computation?
- Computable Problem
- Algorithm vs Formula
- Input / Output
- Finiteness & Precision
- Algorithmic Thinking
- Pseudocode & Flowcharts
- Decision / Control
Algorithmic Structures
- Loops & Iteration
- Recursion (Fibonacci Algorithm)
- Searching (Linear, Binary)
- Sorting (Families, Divide & Conquer)
- Greedy Methods
- Dynamic Programming
Correctness & Complexity
- Algorithm Correctness
- Loop Invariants
- Complexity Analysis
- Big-O Notation (O(1), O(n), O(n²))
- Exponential Time
Binary & Digital Math
- Binary Numbers & Base 2
- Decimal ↔ Binary Conversion
- Bits, Bytes & Arithmetic
- Hexadecimal — Preview
- Integer & Floating Point Rep.
- Rounding Error & Stability
Discrete Mathematics
- Discrete Structures
- Graph Theory & Applications
- Paths & Shortest Path
- Trees
- Boolean Logic & Logic Gates
- Data Structures — Preview
Mathematical Modeling
- Modeling Pipeline & Assumptions
- Variables / Parameters
- Dimensional Analysis
- Proportional, Linear, Exponential
- Logarithmic, Power-Law, Polynomial
- Simulation
Probabilistic Computation
- Monte Carlo — Preview
- Sampling
- Probability Simulation
- Numerical Probability
Data Analytics
- Data Pipeline & Cleaning
- Descriptive & Diagnostic
- Predictive & Prescriptive
- Correlation & Regression — Preview
- Overfitting & Train/Test
- Interpolation / Extrapolation
- Visualization & High-Dimensional Data
Mathematical Connections
- Comp + Sequences / Logic
- Comp + Probability / Calculus
- Comp + Matrices / Vectors
- Comp + Optimization
The Computational Universe
- Computability & Complexity Theory
- P vs NP / Numerical Analysis
- Scientific Computing
- Math → Algorithm → Computation
- Data → Model → Decision
Exit Portal
We have given machines the ability to execute mathematical structures at enormous scale. The next natural door is not simply another chapter of school mathematics. We have reached the point where the Universe branches into the mathematical machinery underlying AI, advanced science and higher mathematics.