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.
Note that as the college transitions to a revamped core, the Class of 2013 has some special circumstances affecting placement that do not apply to later classes.
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 25B may choose to take Math 25G 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 Dagan Karp, at placement@math.hmc.edu.
Special Placement Information for the Class of 2013
The Class of 2013 was the first class to be affected by the college's revamping of the core, which involved some transitional courses and some remaining special exceptions. The following information only applies to students expecting to graduate in 2013.
You may receive credit for Math 62 if you received a 5 on the AP Statistics BC examination.
No credit will be given for a score of 5 (or below) on the AP Calculus BC examination.
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: 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.
Core Classes for the Class of 2014
Mathematics 25G: Calculus and Linear Algebra
Theory and techniques of differential and integral calculus of a single real or complex variable; infinite series, including Taylor series and convergence tests. Theory and applications of vectors and matrices, including systems of linear equations; linear transformations in Euclidean space; determinants, eigenvalues, eigenvectors, and diagonalization. An introduction to multivariable calculus, including partial derivatives, double and triple integrals.
Prerequisites: One year of calculus at the high-school level.
Mathematics 25B: Calculus and Linear Algebra
Theory and techniques of differential and integral calculus of a single real or complex variable; infinite series, including Taylor series and convergence tests. Theory and applications of vectors and matrices, including systems of linear equations; linear transformations in Euclidean space; determinants, eigenvalues, eigenvectors, and diagonalization. An introduction to multivariable calculus, including partial derivatives, double and triple integrals. The topics covered in 25B are the same as those covered in 25G, but 25B digs deeper into the theory and applications of the materials.
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 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.
Core Classes for the Class of 2013
Mathematics 11: Calculus
Limits, derivatives and differentiation rules; partial derivatives; gradients and directional derivatives; introduction to calculus of complex-valued functions; infinite series, Taylor series, convergence tests; fundamental theorem of calculus; techniques of integration; double and triple integrals.
Prerequisites: One year of calculus at the high-school level.
Mathematics 12: Introduction to Linear Algebra
Complex numbers; proofs by contradiction and induction; matrix representation of systems of equations, matrices, operations, determinants, row and column spaces; vectors, dot and cross products; vector descriptions of lines and planes; linear independence and dependence, bases; eigenvalues and eigenvectors; examples of discrete dynamical systems.
Prerequisites: One year of calculus at the high-school level.
Mathematics 13: 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 11 or Math 11M, or equivalent.
Mathematics 14: Multivariable Calculus I
Review of basic multivariable calculus; 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 11 or Math 11M, or equivalent.
Mathematics 62: Introduction to 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 12.
Mathematics 64A: Differential Equations/Linear Algebra II
General vector spaces and linear transformations; change of basis and similarity; generalized eigenvectors; Jordan canonical forms. Applications to linear systems of ordinary differential equations, matrix exponential; Nonlinear systems of differential equations; equilibrium points and their stability.
Prerequisites: Math 12 and Math 13, or permission of instructor.
Core Classes for the Classes of 2012 and Earlier
Mathematics 11: Calculus
Limits, derivatives and differentiation rules; partial derivatives; gradients and directional derivatives; introduction to calculus of complex-valued functions; infinite series, Taylor series, convergence tests; fundamental theorem of calculus; techniques of integration; double and triple integrals.
Prerequisites: One year of calculus at the high-school level.
Mathematics 12: Introduction to Linear Algebra
Complex numbers; proofs by contradiction and induction; matrix representation of systems of equations, matrices, operations, determinants, row and column spaces; vectors, dot and cross products; vector descriptions of lines and planes; linear independence and dependence, bases; eigenvalues and eigenvectors; examples of discrete dynamical systems.
Prerequisites: One year of calculus at the high-school level.
Mathematics 13: 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 11 or Math 11M, or equivalent.
Mathematics 14: Multivariable Calculus I
Review of basic multivariable calculus; 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 11 or Math 11M, or equivalent.
Mathematics 61: Multivariable Calculus II
Constrained optimization using Lagrange multipliers; conservative and nonconservative vector fields; Green's theorem; parameterized surfaces and surface integrals; divergence theorem, outline of proof and applications; Stokes' theorem, outline of proof and applications, unification of major vector theorems.
Prerequisites: Math 14.
Mathematics 62: Introduction to 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 12.
Mathematics 63: Linear Algebra II
General vector spaces and linear transformations; rank-nullity theorem; orthogonal expansion and Fourier coefficients; change of basis and similarity; generalized eigenvalues and eigenvectors; diagonalization of symmetric matrices; applications of eigenvalues to systems of ordinary differential equations; LU, QR, and singular value decomposition theorems; Jordan canonical forms.
Prerequisites: Math 12.
Mathematics 64: Differential Equations II
Linear systems of homogeneous ordinary differential equations, matrix exponential and non-homogeneous linear systems; non-linear systems; equilibrium points and their stability; phase portraits.
Prerequisites: Math 12 and Math 13.
