# Placement for Core Mathematics Classes

At Harvey Mudd College, all students take at least three
semesters of mathematics, regardless of their major. These three
semesters are known as the *common core mathematics
courses*.

A year of calculus at the high-school level is an entrance requirement for HMC, so familiarity with limits, differentiation and integration is assumed in all mathematics courses.

## Placement Into Math 30B or Math 30G

Incoming students will be placed in either Math 30B or Math 30G based on their score on a placement examination that is administered during orientation. Students who qualify to take Math 35B may choose to take Math 35G instead.

### What is the difference between Math 30B and Math 30G?

Math 30G | Math 30B |
---|---|

Every HMC student is entitled to take Math 30G. | Students must place into Math 30B by examination only. |

Assumes some foundation in single-variable calculus. | Requires a strong foundation in single-variable calculus. |

Focuses on deepening and strengthening single-variable calculus foundations while introducing multivariable calculus and linear algebra. | Assumes a more thorough background than Math 30G, allowing for a deeper study of selected topics in calculus. |

In sum, taking Math 30G over Math 30B or vice versa will not affect your eligibility for course placement beyond the first semester. Both courses will prepare you equally well for the rest of the math core. Based on our past experience, we expect about 70% of students to take Math 30G, about 25% to take Math 30B, and about 5% to place out of both.

## Placing Out of Other Math Courses and Other Questions

Placing out of any math course requires a meeting with the department's placement director or taking a suitable placement examination.

For other questions, contact the department's placement
director, Professor Talithia Williams, at `placement@math.hmc.edu`

.

## Core Mathematics Course Descriptions

The following lists summarize the course descriptions and prerequisites for the mathematics core classes for different classes.

### Current Core Classes

#### Mathematics 30G: Calculus

A comprehensive view of the theory and techniques of differential and integral calculus of a single variable; infinite series, including Taylor series and convergence tests. Focus on mathematical reasoning, rigor and proof, including continuity, limits, induction. Introduction to multivariable calculus, including partial derivatives, double and triple integrals.

**Prerequisites:** One year of calculus at the high-school level.

#### Mathematics 30B: Calculus

A comprehensive view of the theory and techniques of differential and integral calculus of a single variable; infinite series, including Taylor series and convergence tests. Focus on mathematical reasoning, rigor and proof, including continuity, limits, induction. Introduction to multivariable calculus, including partial derivatives, double and triple integrals. Placement into Math 30B is by exam and assumes a more thorough background than Math 30G; it allows for a deeper study of selected topics in calculus.

**Prerequisites:** Mastery of single-variable calculus—entry by department placement only.

#### Mathematics 35: Probability and Statistics

Sample spaces, events, axioms for probabilities; conditional probabilities and Bayes' 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; simple linear regression; applications to analyzing real data sets.

**Prerequisites:** Math 30B or Math 30G.

#### Mathematics 40: Introduction to Linear Algebra

Theory and applications of linearity, including vectors, matrices, systems of linear equations, dot and cross products, determinants, linear transformations in Euclidean space, linear independence, bases, eigenvalues, eigenvectors, and diagonalization.

**Prerequisites:** Math 30 or one year of calculus at the high-school level.

#### Mathematics 45: Introduction to Differential Equations

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.

**Prerequisites:** Math 30B or Math 30G.

#### Mathematics 60: Multivariable Calculus

Linear approximations, the gradient, directional derivatives and the Jacobian; optimization and the second derivative test; higher-order derivatives and Taylor approximations; line integrals; vector fields, curl, and divergence; Green's theorem, divergence theorem and Stokes' theorem, outline of proof and applications.

**Prerequisites:** (Math 30B or Math 30G) and Math 40.

#### Mathematics 65: Differential Equations and Linear Algebra II

General vector spaces and linear transformations; change of basis and similarity. Applications to linear systems of ordinary differential equations, matrix exponential; nonlinear systems of differential equations; equilibrium points and their stability.

**Prerequisites:** Math 40 and Math 45, or permission of instructor.