If you have completed the Math 1a/1b sequence at Harvard or if you have had the equivalent material elsewhere, you may be wondering which course is for you. The mathematics department provides a variety of options which you should consider based on your academic interests and your background. With exceedingly rare exceptions, students in your position are advised to take one (or more) of Math 19a, 19b, 20, 21a, 21b, 23a, 25a, 55a, or 101. (The School of Engineering and Applied Sciences also offers Applied Math 21a,b which covers selected topics from Math 21.) This pamphlet describes the Mathematics Department's offerings and should help you decide which course is for you.

Math 19a and 19b are courses that are designed for students concentrating in the life sciences, chemistry, and the environmental sciences. (These courses are recommended over Math 21a,b by the various life science, environmental science, and chemistry concentrations.) Math 19a is taught in the fall and repeated in the spring; it focuses on differential equations, related techniques and modeling. Math 19b teaches linear algebra, probability and statistics; it is offered only in the spring. Both courses focus on applications and examples from the life sciences. If you passed Mathematics 1b (or have the permission of the instructor), you can take Mathematics 19a,b.

Math 20 is a one-semester course designed for students with an interest in applications to economics and the other social sciences. It provides an alternative to the standard Math 21a,b sequence for those who are not considering further courses in mathematics. Consider taking one of the sequences Math 21a,b or Math 19a,b if you have any thoughts of going further into the subject.

Math 21a,b is the standard second-year calculus and linear algebra sequence. It is normally taken by those students who intend to concentrate in the physical sciences or mathematics and who have had a solid first year calculus course. Math 21 emphasizes computational techniques and applications. It seeks to develop tools and intuition rather than spend time proving the results used. Math 21 is given in semester-long halves which may be taken in either order or concurrently. Math 101 can be taken concurrently with either Math 21a or 21b. The material in Math 21a/b is presented, where feasible, in correlation with Physics 15/16.

Math 21a covers multivariable calculus, while Math 21b is a one-semester introduction to linear algebra and differential equations. First-year students who had an equivalent of Math 21a in high school often take this course in the fall of their freshman year. The students with such background who intend to major in math or theoretical physics should also look into Math 23, Math 25, or Math 55. Those who are considering a concentration in mathematics may want to take Math 101 concurrently with either Math 21a or b.