MAT175 Math Economics/Life Sciences

Schedule: MW at 8:30 AM, at 11 AM or at 1:30 PM, Friday precepts; Fall and Spring. Optional review sessions are helpful, but they are scheduled only after classes begin. 

Brief Course Description: Generalizes MAT103 (Calculus I) to higher dimensions as preparation for further work in economics and the sciences, and thus has substantial overlap with MAT201.  Topics include review of definite integrals in a single variable with a view to applications like population growth, average values and cumulative change. Brief treatment of double and triple integrals. Main focus is vectors, lines, planes, curves and surfaces in 3-space, functions of more than one variable, partial derivatives, the gradient, directional derivatives, optimization of functions of two or more variables with constraints, emphasizing the method of Lagrange multipliers. Includes a very brief introduction to linear algebra (matrices, solving systems by row reduction, 2x2 and 3x3 determinants and Cramer’s Rule, as time permits). Although examples from economics or biology may appear, the main focus is on the underlying mathematics.

Why take this course? It provides a more accessible treatment of some topics in multivariable mathematics selected for their importance in economics and the life sciences, allowing students to bypass MAT104 and still learn the basics of using derivatives and integrals in a multivariable setting.

Prerequisites:  MAT103 or equivalent. More than that, this course requires expert familiarity (without a calculator) in working with the standard library of functions: polynomials, rational and root functions, logarithms and exponentials, trigonometric functions and their inverses. This includes solving equations with these functions, computing their derivatives and sketching their graphs.

Who takes this course? Most students in this course are first- or second-year students planning to major in economics or one of the natural sciences other than physics. Some pre-med students take this class to fulfill the calculus requirement, and it may also be useful for quantitatively inclined students interested in public policy or politics. Students interested in math-track economics and finance or engineering or physics should take 201 instead. Be aware that some programs will not accept 175 in place of 201. Please check with the departments that interest you before you take this class. Because of the overlap in topics, only one of 175, 201 and 203 can be counted toward graduation. There is, however, very little overlap between this course and 104, and students who took 104 for credit can and do opt for 175 instead of 201. 

Talk to your advisers and listen to what they say at least as seriously as you listen to your friends.  Advice from other students does not always take into account the differences in background and learning styles that may be relevant to your decisions.

FAQ: 

• Your math placement says 104/175. What does that even mean? If you need to take 201-202 for your program (required for BSE), then you will need 104. If you want to do finance or math-track economics, then 104 is the right choice. 175 is a less intensive version of multivariable calculus. Along with 103 it minimally satisfies the prerequisites for the economics major but it is not at all optimal for finance. 

• Your math placement says 103, but your friends tell you that 103 is harder than 175 and you don’t really want to take two math courses if you can avoid it. Math is really not your thing. You will not be able to do well in 175 unless you really have a good working knowledge of derivatives and all the topics you learned back in precalculus in high school. Try the Sample Problems for 103 to see if you really have enough background. If you can solve most of those problems, go ahead and sign up for 175, but take your experience in the first two weeks seriously. Seek help early! Be honest with yourself as you get more information throughout the drop/add period. MAT175 is at least as hard as 103, and you will pay a high price in stress and in GPA if you are not adequately prepared.

• You don't have any standardized test scores but you took calculus in high school. Try the sample problems for the calculus courses you consider. If the problems look mostly familiar and you can actually solve at least half of them, then it makes sense to try the next course up in the sequence and drop back if necessary during the drop/add period

• What kind of calculator do you need for calculus at Princeton? The math department courses do not use calculators. If you normally rely on your calculator to translate a function or equation into a graph, to solve equations, or to find values of trigonometric functions at the standard angles, then 175 will be very challenging. Consider 103 instead.

• Are you serious about no calculators? Why? Calculators can be useful, but these courses want to teach students how to think independently in a quantitative setting and calculators can function as substitute for thinking at the beginning. Students need to learn the basic vocabulary and grammar of mathematics so that they can recognize patterns and common features by working through simple well-chosen examples. For instance, a program like 'Google translate' can be helpful to a person with basic knowledge of a language to decipher a complicated sentence or even to write a correct one, but without a good foundation to refine and direct its application, the results of blindly applying this useful technological tool can be wildly off the mark.