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A program of study in General Mathematics is designed to equip you with the skills necessary to be a professional problem-solver, as a mathematician is not defined by his or her knowledge of laws and theorems, but by his or her critical thinking and reasoning skills. As a student of mathematics, your classes will range from courses on mathematical logic and induction to courses on differential equations and analysis. The core Mathematics program is designed to allow you to gain basic training in a variety of mathematical tracks, whereas the advanced electives will provide you with the choice of which higher-level mathematical subfields you wish to progress into further. The complete list of applicable fields for which Mathematics is an integral part is extensive; here we show a few of the more common specializations.

Every course listed in our “Core Program” is required of math majors with the exception of MA111: Introduction to Mathematical Reasoning. This course is recommended before MA231 and MA241 or any of the Advanced Mathematics Electives other than Partial Differential Equations.

In addition to the Core Program, each student should choose seven electives, including at least five from the Advanced Mathematics Electives. At least one must be chosen from Real Analysis II, Complex Analysis, and Probability Theory. At least one must be chosen from Abstract Algebra II and Linear Algebra II. Finally, each student should take two supplementary electives; MA121 cannot be used to satisfy this requirement.  Those choosing to take Elementary Number Theory should treat Abstract Algebra I as a pre- or co-requisite.

For those interested in graduate study in math, we recommend taking as many of the advanced electives as possible, with a focus on real and complex analysis and linear and abstract algebra. For those interested in working in applied mathematics, we recommend Linear Algebra II, Probability Theory, Partial Differential Equations, Numerical Analysis, and Topics in Applied Mathematics. For those interested in statistics, we recommend Real Analysis II, Linear Algebra II, Probability Theory, and Statistics II.

To complete the knowledge equivalent of a mathematics major, you must complete all of the core program except for MA111, which is optional (8 courses) as well as 7 electives of your choosing (7 courses — 5 of which must be “Advanced Mathematics”) for a total of 15 courses.

Interested in the potential to earn college credit for a Mathematics course? Learn more here.


Foundational Material

The courses in this section are not a formal part of the Saylor.org Mathematics Major, which begins with MA101: Single-Variable Calculus I, listed beneath the “Core Program” section below.  These courses are designed to bridge the gap between high school and college-level mathematics.

Core Program

Advanced Mathematics

Elective Courses