Most students begin their study of calculus during their first semester at the College. For most, Calculus I (MATH 111) is the right place to start, but for students withor strong calculus backgrounds, a more advanced course may be appropriate.
Once you have a solid foundation in basic Calculus, you move on to Linear Algebra (MATH 211) and Multivariable Calculus (MATH 212 or 213). The Foundations of Mathematics (MATH 214) is a "bridge course" designed to prepare you for the more abstract flavor of upper division courses. The purpose of MATH 214 is to introduce you to the reading and writing of proofs. MATH 214 is a prerequisite for two required courses in the mathematics major (Abstract Algebra, MATH 307 and Elementary Analysis, MATH 311), so should be completed by the end of your second year. MATH 211, 212/213, and/or 214 form the prerequisite for most of the upper division courses.
Upper Division CoursesThe upper division mathematics curriculum at William & Mary attempts to strike a balance between courses that provide a rigorous introduction to the fundamental concepts of modern mathematics and courses that study how mathematics is used to solve interesting problems.
Courses numbered 300 and above are usually courses for juniors and seniors, but you might be ready to begin these courses during your first two years. Indeed, for some students, it would be a mistake to wait. If you are contemplating the teacher certification program in secondary mathematics, you will need to take at least three mathematics courses during one semester of your last two years if you do not take any 300-400 courses during your first two years. For many students, that would be a lot.
Abstract Algebra (MATH 307) and Elementary Analysis (MATH 311) were designed to prepare students to take 400-level courses. As a general rule, students should take MATH 307 and/or MATH 311 before progressing to 400-level courses. Please consult with your mathemathics major advisor to decide which courses will best suit your needs.