Part I · Chapters 1 to 7
Foundations of Mathematical Judgment
- 015 demonstrations
Algebra
See the Structure Before You Solve
- 024 demonstrations
Geometry
Estimate Shape Before Measuring It
- 034 demonstrations
Trigonometry
Control Angles, Directions, and Oscillations
- 045 demonstrations
Calculus
Turn Local Change into Global Control
- 054 demonstrations
Analysis
Know When Limits and Proofs Are Safe
- 064 demonstrations
Complex Analysis
Turn Analytic Structure into Bounds and Counts
- 075 demonstrations
Linear Algebra
Choose Stable Matrix Methods Before Computing
Part II · Chapters 8 to 11
Discrete Structure and Scale
- 085 demonstrations
Number Theory
Reduce Large Arithmetic to Small Structure
- 094 demonstrations
Combinatorics
Counting Without Exhaustion
- 105 demonstrations
Graph Theory
Structural Tests for Networks
- 115 demonstrations
Asymptotics
Finding What Matters at Scale
Part III · Chapters 12 to 17
Uncertainty, Information, and Value
- 125 demonstrations
Probability
Fast Reasoning Under Uncertainty
- 134 demonstrations
Statistics
From Data to Defensible Decisions
- 145 demonstrations
Stochastic Processes
Rates, Waiting, and Dependence
- 155 demonstrations
Information Theory
Measuring Information and Its Limits
- 165 demonstrations
Measurement and Uncertainty
Building Trustworthy Results
- 175 demonstrations
Financial Mathematics
Comparing Money Across Time
Part IV · Chapters 18 to 21
Modeling, Optimization, and Computation
- 184 demonstrations
Applied Mathematics
Scaling, Regimes, and Model Sanity
- 195 demonstrations
Optimization
Scale, Search, and Certify
- 205 demonstrations
Numerical Methods
Approximation You Can Trust
- 215 demonstrations
Scientific Computing
Precision, Performance, and Reproducibility
Part V · Chapters 22 to 25
Dynamics, Signals, and Feedback
- 225 demonstrations
Ordinary Differential Equations
Choosing and Checking Time Integrators
- 235 demonstrations
Partial Differential Equations
Discretize, Resolve, and Verify
- 244 demonstrations
Signal Processing
Sampling, Resolution, and Spectral Judgment
- 255 demonstrations
Control Theory
Performance, Robustness, and Implementation Reality
Notebooks and skills on GitHub
Every chapter has a Jupyter notebook that reproduces its calculations and figures, and a skill an AI assistant can use to teach the chapter.