A cognate gives you extra flexibility. For each Math program, you are required to take a certain number of math electives. You are allowed the flexibility to substitute at most *one* cognate for a Math elective. All cognates require the approval of the Undergraduate Chair <UGradChair AT math.upenn.edu> and must be part of a well planned selection of electives within the Major.

#### Some Courses Often Approved as COGNATES (Major or Minor)

- Astronomy 011, 012, 111, 410
- Biology 412, 414, 437, 446, 535, 537
- Computer and Information Science 320 The courses CIS 110, 120 and 121 cannot be counted as cognates.
- Economics 104, 212, 242, 245, 222 (old number: Econ 115).
- Finance 205, 206, 235
- Insurance 260
- Mechanical Engineering 210, 211, 221
- Electrical and Systems Engineering 302 (beginning in 2019 this is replaced by 402)
- Philosophy 006, 411, 413 (
*not*Phil 005) - Physics 140, 150, 151, 170, 171
- Statistics 431, 476

#### Some courses often approved as COGNATES for Mathematics Minors

- BEPP 452 (STAT 452), CSE 260, CSE 261, CIS 160.
*Students can count one of these cognate courses towards a Math Minor. Math Majors can count one of the above cognates toward a Math Major, and two if they are double majors.*

#### Courses counting as *inside* the Math. Dept.

The following courses count as being * inside * the Math. Department as far as the Major or Minor is concerned. This means that that counting them toward a Math Minor or Major does not change the number of cognate courses above which can also be counted.

- Statistics 430, 432, 433, 436, 473, 512, and 541 or Systems Engineering ESE 210, 301, ESE 325, or Econ 103, or ENM 375, 503.
Note: Since some courses have similar content, there are restrictions on courses in the following list:

**List A:**Math 430 Stat 430 CIS 261 Econ 103 Systems 301 ENM 375, 503*Math Major or Minor Elective Credit*: At most one of these from List A.*Cognate*: A second course from list A can count as a Cognate -- but not as a Math elective

In applying the above rules, students may substitute Stat 510 for either Math 430 or Stat 430, and Stat 511 for Stat 431. - Computer and Information Science 261, 262, 511.
- Electrical and Systems Engineering 530, 630, 632, 674.
- Engineering Mathematics 251, 321, 375, 503.
- OPIM 930.
- STAT 541

#### Some courses which are *not* approved as COGNATES

for Mathematics Majors or Minors

- OPIM 101 and 102.