All Lectures

Lecture 1 Live

Orientation: Learning to See

Introduction to the course philosophy and approach.

philosophy primitives

Lecture 2 Live

What Kinds of Numbers?

EXISTENCE

Number systems and their roles in chemistry.

integers rationals reals

Lecture 3 Live

Counting Things

COLLECTION

Sets, factorials, and counting in chemistry.

sets factorial combinations

Lecture 4 Live

Bonds Point (Vectors)

DIRECTION

Introduction to vectors through molecular geometry.

vectors magnitude unit vectors

Lecture 5 Live

Angles and Projections

DIRECTION

The dot product reveals angles between vectors. Understanding bond angles, orthogonality, and projection.

dot product bond angles projection

Lecture 6 Live

Coordinates and Basis

DIRECTION

Same vector, different numbers. Basis vectors, change of basis, and the meaning of MO coefficients.

basis coordinates Gram-Schmidt

Lecture 7 Live

Grids of Numbers

ARRANGEMENT

Matrices as organized collections. Operations, multiplication, and the Hückel matrix.

matrices multiplication Hückel

Lecture 8 Live

Transformations

ARRANGEMENT

What matrices do to space. Determinants, kernel, image, and molecular symmetry operations.

transformations determinant symmetry

Lecture 9 Live

What Doesn't Change? (Invariance)

SAMENESS

Invariants and conserved quantities — what remains unchanged under transformation.

similarity trace determinant

Lecture 10 Live

What Survives? (Eigenvalues)

SAMENESS

Eigenvalues and eigenvectors — the directions that transformation preserves.

eigenvalues eigenvectors Hückel MO

Lecture 11 Live

As X Approaches... (Functions & Limits)

PROXIMITY

Functions and limits — the mathematics of nearness and approach.

functions limits continuity

Lecture 12 Live

Instantaneous Rate (The Derivative)

CHANGE

The derivative — capturing "how fast, right now?" Reaction rates, force from potential.

derivative tangent rate

Lecture 13 Live

Rules of Change (Differentiation)

CHANGE

Differentiation rules — building complex derivatives from simple pieces.

power rule product rule chain rule

Lecture 14 Live

Finding Extrema (Optimization)

CHANGE

First and second derivative tests. Lennard-Jones minimum, Maxwell-Boltzmann peak.

critical points optimization concavity

Lecture 15 Live

Partial Derivatives

CHANGE

Functions of several variables. Gradients, Hessians, and potential energy surfaces.

partials gradient Hessian

Lecture 16 Live

Approximations and Constraints

CHANGE

Taylor series for local behavior. Lagrange multipliers for constrained optimization.

Taylor series Lagrange constraints

Lecture 17 Live

Adding It All Up (Integrals)

ACCUMULATION

The integral — from rates back to amounts. Riemann sums, FTC, chemistry applications.

integrals FTC work Gaussian

Lecture 18 Live

Integration Techniques

ACCUMULATION

Integration by parts, partial fractions, trig substitution, and more.

by parts partial fractions trig sub

Lecture 19 Live

Differential Equations

DYNAMICS

From rates to trajectories. Separable, linear, second-order ODEs with chemistry applications.

kinetics oscillators quantum Euler

Lecture 20 Live

Probability Basics

SPREAD

The mathematics of uncertainty. Sample spaces, axioms, Bayes' theorem, independence.

Bayes independence branching

Lecture 21 Live

Distributions

SPREAD

Boltzmann, Gaussian, Maxwell-Boltzmann — how probability spreads across states.

Boltzmann Gaussian speeds

Lecture 22 Live

Expectation, Variance, and Error

SPREAD

The gap between calculation and observation. Error propagation and uncertainty.

variance propagation Monte Carlo

Lecture 23 Live

Dimensional Analysis

SPREAD

Units as a reasoning tool — checking, deriving, and transforming.

dimensions scaling linearization

Lecture 24 Live

Synthesis

SYNTHESIS

The complete map — seeing the whole.

nine primitives tool reference course map