Like programming, mathematics has a culture -- Polynomials -- On pace and patience -- Sets -- Variable names, overloading, and your brain -- Graphs -- The many subcultures of mathematics -- Calculus with one variable -- On types and tail cells -- Linear algebra -- Live and learn linear algebra (again) -- Eigenvectors and eigenvalues -- Rigor and formality -- Multivariable calculus and optimization -- The argument for big-O notation -- Groups -- A new interface.