Information Relevant to Advising Students about the Mathematics
Core and Preparing for the Mathematics Major

(Information taken from the web sites: www.math.hmc.edu/intermath/ and www.math.hmc.edu/placement/what-to-take.html)

Department of Mathematics
Mathematics Core Curriculum

At Harvey Mudd College, all students take at least four semesters of mathematics, regardless of their major. These four semesters are known as the common core mathematics courses. The four semesters are divided into eight half-courses:

• Math 11. Basic calculus of one real and one complex variable.
• Math 12. Introduction to discrete dynamical systems and linear algebra.
• Math 13. Introduction to differential equations.
• Math 14. Basic multivariable calculus.
• Math 61. More sophisticated multivariable calculus.
• Math 62. Introduction to probability and statistics.
• Math 63. More sophisticated linear algebra.
• Math 64. More sophisticated differential equations.

For more detailed course descriptions and placement information, see the placement examination webpage. Math 11-14 are normally taken in the first year, and Math 61-64 in the second year. There are several reasons motivating this structure, including:

1. To return to key subject matter and applications several times at increasingly more sophisticated levels.
2. To introduce important mathematical concepts from discrete mathematics, linear algebra, and differential equations into the first year.
3. To provide a calculus based introduction to probability and statistics for all second year students.
4. To integrate topics and examples with other 1st and 2nd year courses, especially physics, chemistry, and systems engineering.
5. To make it easier for students with a strong introduction to certain mathematical ideas to be placed more accurately in modules that fit their preparation.

The accelerated calculus course (Math 11) introduces calculus in the context of both real and complex variables, and students are given an early exposure to some basic residue calculations. To compensate for the diminished review of single variable calculus, we have implemented web-based calculus tutorials which are available to students during the summer before they enroll and which are completed early in the first semester.

Other material in the core includes an introduction to discrete dynamics (in Math 12) as a way of motivating iterated maps and linear algebra, and a half-course introduction to probability and statistics (Math 62), which has proven very useful to students in their laboratory courses.

The multivariable curriculum is split into two half-semesters (Math 14 and 61) with topics timed so that the vector theorems are coincident with material covered in Physics 51 (Electricity and Magnetism) which most students are taking at the same time. Having some linear algebra (Math 12) before multivariable calculus is helpful to reinforce the importance of determinants, and complex calculus ideas in Math 11 are reinforced by parametrized curves and Green's theorem in multivariable calculus. Semesters of linear algebra and differential equations are now split into half-courses in the first and second years (Math 12/63 and Math 13/64), and the timing of these courses is such that students with advanced placement out of other core math courses could take these courses sequentially if their schedule permits.

Students interested in advanced placement should first check out the sample placement exams on the Mathematics Department website. Those with advanced placement can see suggested paths through core math.

Harvey Mudd College
Department of Mathematics
Paths through Core Math

This page has suggestions for how to plan your schedule of core math courses. Elsewhere, you can also see a general description of the four-semester core mathematics sequence for all Harvey Mudd students, and obtain more information on advanced placement in mathematics.

The core math courses are usually offered in the following schedule (but consult the latest course catalog to double-check.) Bear in mind that the prerequisite for Math 12, 13, and 14 is Math 11; also, Math 61 has prerequisite Math 14, Math 62 has prerequisite Math 11, Math 63 has prerequisite Math 12, and Math 64 has prerequisites Math 13 and 63.

Since not every course is offered every half-semester, the following suggestions can be used as a guide for some very common placement scenarios:

Less common placement scenarios include:

Other paths can be worked out in consultation with a mathematics professor.