### Core Courses

All of these are required by each of the Math, Applied Math, Actuarial Math, Mathematical Biology, and Math-Econ majors (with one exception noted below). For catalog descriptions, prerequisites, and sample syllabi see our undergraduate courses page.

**MATH 0220/30/40, Calculus 1/2/3.**The mathematical study of change. Calculus 1 and 2 focus on introducing, computing, and applying the derivative and the integral of a real-valued function. Calculus 3 extends this to curves and functions of several variables, finishing with Green's and the Stokes and divergence theorems.

(**Note:**certain AP or IB exam scores yield transfer credit for MATH 0220 and/or 0230, see this page.)**MATH 0413, Introduction to Theoretical Mathematics.**Here students learn the language of mathematics and how to make rigorous arguments, while studying the construction and properties of the integers and natural, rational, and real numbers.**MATH 0420, Introduction to the Theory of 1-Variable Calculus.**[not required by the Actuarial Mathematics major] Reconsiders calculus, equipped with tools from MATH 0413. This course focuses on precisely defining continuity, differentiability, and integrability and*proving*results about functions with these properties.**MATH 0500, Professional Development.**A one-credit course focused on introducing students to the spectrum of mathematical careers, university career and scholarly resources, and important mathematical "tools of the trade".**MATH 1180, Linear Algebra.**Along with calculus, a key tool for solving a vast array of real-world and theoretical problems. The subject begins with an algorithm for solving systems of linear equations and moves on to define and study linear transformations.

(**Note**: compared to our linear algebra course for non-majors, MATH 0280, this is more conceptual and covers abstract vector spaces.)**MATH 1270, Ordinary Differential Equations 1.**Builds on calculus, focusing on explicit solutions of equations relating an unknown function and its derivatives. These arise in a wide variety of modeling contexts.

(**Note:**compared to our ODE course for non-majors, MATH 0290, this one more deeply explores solutions of systems using the tools of linear algebra.)

### University Honors Courses

These are faster-paced, deeper versions of our regular courses for talented students who enjoy a challenge. They count toward the degree enhancements offered by the Frederick Honors College (see this page). Each can replace one or more of the core courses above as a prerequisite and toward major requirements.

**MATH 0235**honors replacement for MATH 0220+MATH 0230. Offered every fall semester.**MATH 0450**honors replacement for MATH 0413+MATH 0420. Offered every spring semester.**MATH 1185**honors replacement for MATH 1180. Offered every fall semester.**MATH 1275**honors replacement for MATH 1270. Offered in odd-year spring semesters (eg. Spring '23).