Advanced Placement for Core Mathematics Classes

The Core Mathematics program at HMC consists of a sequence of eight half-courses (Math 11–14 and 61–64) described below. For an explanation of the half-course model, see the Mathematics Core Curriculum.

A score of 5 on the AP Calculus BC exam is sufficient to place out of Math 11. A score of 5 on the AP Statistics exam is sufficient to place out of Math 62. Placement out of other core math courses is determined either by examination or by a good grade in an sufficiently rigorous college course equivalent. Students wishing to take placement exams should look over the following sample exams (in PDF format) for the Core Mathematics courses. Placement exams will have questions with a comparable balance of topics and range of difficulty.

If you have advanced placement, but don't know what to take, you might consult this schedule of possible paths through the core.

Mathematics 11: Calculus of One Real or Complex Variable

Complex numbers, limits, formal epsilon-delta limit definition, derivatives and differentiation rules; proofs by contradiction and induction; infinite series; integration; applications of the calculus; introduction to calculus of complex-valued functions.

Mathematics 12: Introduction to Linear Algebra and Discrete Dynamical Systems

Mathematics 13: Differential Equations I

Modeling physical systems, first-order ordinary differential equations, existence; uniqueness and long-term behavior of solutions; bifurcations, approximate solutions; second-order ordinary differential equations and their properties, applications; first-order systems of ordinary differential equations.

Mathematics 14: Multivariable Calculus I

Vectors, dot and cross products; vector descriptions of lines and planes; partial derivatives and differentiability; gradients and directional derivatives; chain rule; higher order derivatives and Taylor approximations; double and triple integrals in rectangular and other coordinate systems; line integrals; vector fields, curl, and divergence; introduction to Green's theorem, divergence theorem and Stoke's theorem.

Mathematics 61: Multivariable Calculus II

Review of basic multivariable calculus; optimization and the Second Derivative Test; constrained optimization using Lagrange multipliers; conservative and nonconservative vector fields; Green's theorem; parametrized surfaces and surface integrals; divergence theorem, outline of proof and applications; Stoke's theorem, outline of proof and applications; unification of major vector theorems.

Mathematics 62: Introduction to Probability and Statistics

Sample spaces, events, axioms for probabilities; conditional probabilities and Bayes's theorem; random variables and their distributions, discrete and continuous; expected values, means and variances; covariance and correlation; law of large numbers and central limit theorem; point and interval estimation; hypothesis testing; chi-square goodness of fit; simple linear regression; introduction to analysis of variance; applications to analyzing real data sets.

Mathematics 63: Linear Algebra II

Review of basic linear algebra; vector spaces; row and column spaces of matrices, rank-nullity theorem; orthogonal bases and Gram-Schmidt procedure; orthogonal expansion and Fourier coefficients; linear transformations; change of basis and similarity; eigenvalues, eigenvectors and characteristic polynomials; diagonalization of symmetric matrices; applications of eigenvalues to systems of ordinary differential equations.

Mathematics 64: Differential Equations II

Review of basic ordinary differential equations, especially systems; undriven linear systems; orbital portraits; stability and conservative systems; Lyapunov functions; cycles and long-term behavior of solutions; Sturm-Liouville problems; series solutions near ordinary and regular singular points; Bessel functions; chaos.