**1. Two semesters of calculus are required.** MATH UN1102 Calculus II followed by MATH UN1201 Caluclus III. We also encourage you to take MATH UN1202 Calculus IV if you are able to do so since it is a prerequisite to many upper-level mathematics courses. Also acceptable is a more fast-paced sequence for advanced students -- UN1207-8 Honors Calculus A and B.

**2. Two semesters of statistics and econometrics are required.** Students should take Intro to Probability and Statistics, STAT GU4001. Students with little or no statistics preparation are advised (not required) to take a Calculus-based statistics course such as STAT UN1201 prior to STAT GU4001. Ambitious students can take STAT GU4203 Probability Theory **plus **STAT GU4204 Statistical Inference as a substitute for STAT GU4001. In addition, majors may consult the department chair about other possible substitutes.

Most students take Econometrics (ECON BC3018) but Introduction to Econometrics (ECON UN3412 at Columbia) is also acceptable.

**3. In addition to the courses listed above, majors must take 4 more mathematics courses.** You should take Linear Algebra (MATH UN2010) as soon as you can after the calculus sequence followed by Analysis and Optimization (MATH UN2500). Note that Introduction to Modern analysis (MATH GU4061) is an acceptable subsitute for MATH UN2500 though it does have a higher prerequisite level.

For the two remaining mathematics elective courses above the 2000 level, you should consider Ordinary Differential Equations, (either MATH E1210 which emphasizes practical applications, or MATH UN3027), Dynamical Systems (MATH UN3030), and Introduction to Modern Analysis (MATH GU4061). Many other mathematics elective course are also available and you should pick these in consultation with your major advisors.

**Substitutes and Overlaps:**

MATH E1210 and MATH UN3027, both titled Ordinary Differential Equations, are considered equivalents. Both can NOT be taken for credit.

MATH UN2500 Analysis & Optimization and MATH GU4061 Intro to Modern Analysis, while having some overlap, are enough different that both CAN be taken for credit.