The Method
REALITY
→
RECOGNITION
→
TOOL
→
SOLUTION
"See the pattern in reality, then summon the mathematics."
The Nine Primitives
COLLECTION
"There are many"
Sets, counting, factorial, combinations. How many electrons? How many isomers?
ARRANGEMENT
"Order matters"
Permutations, matrices, determinants. Stereoisomers, crystal structures.
DIRECTION
"It points"
Vectors, dot product, cross product. Bond angles, dipole moments, orbital orientation.
PROXIMITY
"Near vs far"
Functions, limits, continuity. Potential energy curves, interaction ranges.
SAMENESS
"Unchanged"
Eigenvalues, symmetry, invariants. Molecular orbitals, normal modes, point groups.
CHANGE
"Becoming"
Derivatives, partial derivatives, gradient. Reaction rates, Maxwell relations.
RATE
"How fast"
Differential equations, first-order, second-order. Rate laws, radioactive decay.
ACCUMULATION
"All together"
Integrals, definite integrals, techniques. Work (∫PdV), heat (∫CdT), total yield.
SPREAD
"Distributed"
Probability, distributions, variance. Boltzmann, Maxwell-Boltzmann, quantum averages.
Three Modules
View all lectures →MODULE 1
Structure
"What is a molecule?"
- 01 Orientation — Seeing
- 02 Existence — What Kinds of Numbers?
- 03 Counting Things
- 04 Bonds Point
- 05 Angles & Projections
- 06 Coordinates & Basis
- 07 Grids of Numbers
- 08 Transformations
- 09 Invariance & Symmetry
- 10 Eigenvalues
COLLECTION
ARRANGEMENT
DIRECTION
SAMENESS
MODULE 2
Change
"How do things transform?"
- 11 Functions & Limits
- 12 The Derivative
- 13 Rules of Differentiation
- 14 Extrema & Optimization
- 15 Partial Derivatives
- 16 Taylor Series
- 17 The Integral
- 18 Integration Techniques
- 19 Differential Equations
PROXIMITY
CHANGE
RATE
ACCUMULATION
MODULE 3
Probability
"What happens with many particles?"
SPREAD