The Mathematics Department teaches two subjects at the 200 level: multivariable calculus and linear algebra. If you are at present finishing Calculus II, we strongly encourage you to consider taking one or both of these classes even if they are not required by your major. The major requirements set a basic minimum, but more mathematics is often helpful, especially if you are thinking of going to graduate school in science, engineering, medicine or a mathematically based social science such as economics. The use of mathematics is increasing in all these disciplines, and now is your chance to extend your knowledge of it.
First year calculus develops the basics of one variable calculus -- but almost no real-life situation depends on only one variable. For example, one needs at least three dimensions (or variables) to describe most situations in physics, while the movement of something like the stock market depends on many variables. CALCULUS III studies calculus in spaces of two and three dimensions. It develops concepts that are fundamental to understanding movement in three dimensions, three dimensional geometry, electricity, the motion of fluids, probability, volume, as well as how to maximize quantities (such as profit) that depend on many variables. There are two versions of Calculus III. The first (MAT 203 and AMS 261) continues the spirit of the applications-based first year courses, while the second (MAT 205) is recommended for students who would like to understand the underlying mathematical concepts more deeply. Either version is acceptable for the mathematics major, though some other departments require one version rather than another. After Calculus III, possibilities open up: Calculus III is sufficient prerequisite for classes such as the new MAT 364 (Geometry and Topology), MAT 331 (Problem Solving with Computers), and MAT 316 (Invitation to Modern Mathematics).
LINEAR ALGEBRA is an essential tool in many areas of mathematics, both theoretical and applied. Again one is studying situations that depend on many variables, but now one considers only the simplest functions (the linear ones) thus avoiding calculus. The importance of linear algebra is that the resulting equations are easy to solve. The solutions may be described in terms of certain fundamental algebraic ideas (bases and eigenvalues, for example), that are then used to help understand more complicated phenomena such as the resonance of vibrating systems or fluctuations in populations. The two sophomore linear algebra courses AMS 210 and MAT 211 are somewhat different: the AMS course is more applied while the MAT version spends more time discussing the foundations of the subject. Besides being required for the major, MAT 211 is a prerequisite for many 300 level MAT classes, and its approach is very useful preparation for 300 level MAT classes. We strongly encourage MAT majors to take it early on. It can be taken in the first year together with Calculus II and is very helpful background for MAT 205. It is a corequisite for the new course MAT 318 (Classical Algebra), and together with Calculus III forms the prerequisite for courses such as MAT 311 (Number Theory), MAT 312 (Applied Algebra) and MAT 313 (Abstract Algebra).
The PROBLEM SEMINAR (MAT 250, 1 credit) is a new course
that is intended for students who are interested in developing their mathematical
intuition and ability to express mathematical ideas, while having some
fun solving problems. It can be taken repeatedly for credit. Students will
have the opportunity to sign up for the Putnam exam, a competitive national
mathematics exam for undergraduates which is held each December.
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