# Math Requirements

**MATHEMATICS**

- Students in all majors, joint majors, and the concentration in economics must take two semesters of calculus,
**MATH V1101**Calculus I, and**MATH V1201**, Calculus III. Alternatively, students may take the Honors math sequence,**MATH V1207**and**MATH V1208**.

- Students do
__not__have to take**MATH V1102**Calculus II to complete their economics requirements, except for students who are majoring in econ-math or econ-statistics.

- Students must complete
**Calculus I**before taking**ECON W3213 Intermediate Macroeconomics**and must complete**Calculus III**before taking**ECON W3211 Intermediate Microeconomics.**Alternatively, if you are taking the honors sequence in math, you may register for both Intermediate Macro and intermediate Micro after completing**MATH V1207 Honors****Math**.

- More information about placement in the calculus sequence can be found on the Department of Mathematics website.

- Students who initially skip
**MATH V1102**Calculus II may still take Calculus II after they have completed MATH V1201 Calculus III.

The math requirement is designed to better fit the needs of the economics students at Columbia. Undergraduate economics education relies heavily on the differential calculus of functions of one and several variables. Few, if any, economics courses will use integral calculus and those that do will make use of only the most basic of integrals. Calculus I is an introduction to the differential and integral calculus of functions of one variable. Calculus III extends the differential calculus to of functions of several variables. Hence, these are the two classes that teach the calculus used in the economics courses. Calculus II focuses on advanced integration techniques of functions of one variable. These techniques are used very rarely in undergraduate economics courses, so Calculus II is not required for the economics major.

The differential calculus is the study of the slope (or derivative) of a function or the rate of change of a function. The rate of change of a function (called a derivative) is an extremely useful concept in economics. For example, a cost function tells us the total cost associated with each quantity level of production of a firm. The rate of change of the cost function is called the marginal cost of the firm and it tells us how much it will cost the firm to produce one additional unit. Similarly, the revenue function of a firm tells us the total revenue generated by the sales of each quantity level and the rate of change of the revenue function, the marginal revenue, tells us how much additional revenue is generated by an additional sale. If the cost of producing one additional unit is less than the additional revenues generated by that unit, then the firm can earn more profits by producing and selling that extra unit. In other words, if the rate of change of the cost function is less than the rate of change of the revenue function, then a profit-seeking firm should produce and sell more units of the good.

The cost function is an example of a function of a single variable (the variable is the quantity produced). The study of the calculus of a single variable will teach you how to solve a wide range of economics problems, such as whether or not the firm can earn additional profits by producing and selling an additional unit. Calculus I will teach you how to solve these problems.

Economic problems often involve functions of several variables. For example, living in New York City, I can choose from a wide variety of entertainments, such as movies, concerts, plays, etc., but I don't have an infinite amount of money to spend on my entertainment (nor an infinite amount of time to enjoy all of these activities). Indeed, I must decide how to allocate my budget among these many variable choices where I must think about giving up one good (e.g., a concert) in order to get more of another (e.g., a play). In order to choose the best allocation of my budget for me, I must solve a problem of several, variables. Fortunately, we can extend the results from the calculus of one variable to that of several variables to solve these more complicated economics problems. Calculus III will teach you how to solve these types of problems.

The integral calculus begins with the study of the area under a curve. It is used sparingly (if at all) in undergraduate economics courses but extensively in engineering, physics, and statistics. The derivative of a function is in general quite straightforward to calculate, but the integral is not. In fact, the knowledge of a wide range of techniques is needed calculate many integrals. Calculus IIA teaches these many tricks of integration. Since none of these tricks are ever used in an undergraduate course, this class is not required as part of the economics major.

**STATISTICS**

Students in all majors, joint majors, and concentrations must take **STAT W1211 **Introduction to Statistics B (or a higher-level statistics course such as SIEO W4150; STAT W3105 and W3107).

The department considers the statistics and econometrics courses as a year-long sequence in statistical methods. The design of STAT W1211 was done in consultation with the econometrics professors in the economics department. The material covered in STAT W1211 was chosen in order to ease the transition from statistics to the econometrics course offered in the department.** The department also strongly recommends to all students that they take the two courses W1211 and W3412 in consecutive semesters.**

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