We assume that by now you've completed, or are in the process of completing, one of the single-variable calculus sequences (2250–2260 or 2310H). Next, students normally take the following classes. The multivariable calculus and differential equations classes are still rather computational in nature. The 3000-level courses are "bridge" courses designed to help you make the transition to the 4000-level courses that are more conceptual and require understanding and writing proofs. We recommend that you take a MATH 3200 as early as possible to experience this different "flavor" of mathematics.

MATH 3200: Introduction to Higher Mathematics—the course designed to help you master basic techniques in reading and writing mathematics; topics include aspects of logic, sets, functions and relations.

MATH 2270 or 2500: Multivariable Calculus—vectors and differential and integral calculus of several variables, culminating in the higher-dimensional version(s) of the Fundamental Theorem of Calculus. MATH 2270 is a 4-hour version of the course, including further physical applications. MATH 2270 is strongly preferred for students contemplating majoring in mathematics.
MATH 2700: Differential Equations—an introductory course in ordinary differential equations, with emphasis on first- and second-order equations and their applications. 

one of the following:

MATH 3000: Introduction to Linear Algebra—a study of linear equations, matrices, linear transformations, eigenvalues and eigenvectors, and applications, including proofs.

MATH 3300: Applied Linear Algebra—similar material to MATH 3000, but from an applied and computational viewpoint, with less emphasis on proofs.  Students pursuing the standard mathematics major should take MATH 3000 instead of this course.

one of the following:

MATH 3100: Sequences and Series—a careful treatment of limits, sequences, series, power series, and applications, including proofs.

MATH 3100H: Sequences and Series (Honors)—Honors equivalent of MATH 3100, which does not have MATH 3200 as a prerequisite but is taught at a somewhat higher level.

N.B. Each of these courses has a prerequisite of MATH 2260 or MATH 2310H. MATH 3200 is a prerequisite for both MATH 3000 and MATH 3100. 

As an alternative to MATH 2270/2500 and MATH 3000/3300, we offer the two-semester sequence MATH 3500(H)–3510(H) (Multivariable Mathematics I and II) starting in the fall semester. This class is at a somewhat higher level, with greater emphasis on concepts and proofs, and highlights the deep connections between linear algebra and multivariable calculus. These courses carry Honors credit, so it's ideal for the students who've completed MATH 2310H who wish to continue their Honors study of mathematics. But it's also recommended for the students completing MATH 2260—or for freshmen with a 5 on the Calculus BC Advanced Placement test—who are ready for a more rigorous and conceptual treatment of the material. (To help with this transition, some students choose to take MATH 3200 concurrently with MATH 3500(H).) As a bit of incentive for you to take this more challenging route, both these classes will count towards the major.