Applied Mathematics (BS)

Undergraduate Program in Applied Mathematics

The applied mathematics program is flexible and intensive. A student must take the required courses listed below, or prove equivalent standing, and then may elect the other courses from mathematics, computer science, physics, earth and environmental sciences, biophysics, economics, business and finance, or other application fields.

Each student tailors their own program in close collaboration with an adviser and should confer with their adviser on a regular basis to make sure they are on track for graduation. In particular, all required courses listed in the table must be taken to graduate, however, the specific sequence in which they are taken may depend somewhat on the student’s area of specialization. In general, each student should always check with their adviser. They must also register for the applied mathematics seminar during both the junior and senior years. During the junior year, the student attends the seminar lectures for 0 points; during the senior year, they attend the seminar lectures as well as tutorial problem sessions for 3 or 4 points.

While it is common for students in the program to go on to graduate school, many graduating seniors will find employment directly in industry, government, education, or other fields.

Of the 27 points of elective content in the third and fourth years, at least 15 points of technical courses approved by the adviser must be taken. The remaining points of electives are intended primarily as an opportunity to complete the absolutely mandatory four-year, 27-point nontechnical requirement for the B.S. degree, but if this 27-point nontechnical requirement has been met already, then any type of coursework can satisfy these elective points.

Transfers into the applied mathematics program from other majors require a GPA of 3.0 or above, and the approval of the applied mathematics program chair.

Applied Mathematics Program

An overview of the degree track in PDF format can be found here

First Year
Semester I
MATH UN11011CALCULUS I 
Choose one of the following Physics courses depending on track: 
INTRO TO MECHANICS & THERMO 
PHYSICS I:MECHANICS/RELATIVITY 
ACCELERATED PHYSICS I 
Choose one of the following Chemistry/Biology courses (taken Semester I or II): 
CHEM UN1403 (or higher)
GENERAL CHEMISTRY I-LECTURES 
BIOL UN2001
 
BIOL UN2005 (or higher)
INTRO BIO I: BIOCHEM,GEN,MOLEC 
ENGL CC1010 (taken Semester I or II)UNIVERSITY WRITING 
Complete Required Technical Electives (Student's choice) (taken Semester I, II, III, or IV) 
ENGI E1006 (taken Semester I, II, III, or IV)INTRO TO COMP FOR ENG/APP SCI 
PHED UN1001PHYSICAL EDUCATION ACTIVITIES 
ENGI E1102 (taken Semester I or II)THE ART OF ENGINEERING 
Semester II
MATH UN11021CALCULUS II 
Choose one of the following Physics courses depending on track: 
INTRO ELEC/MAGNETSM & OPTCS 
PHYSICS II: THERMO, ELEC & MAG 
ACCELERATED PHYSICS II 
Choose one of the following Chemistry/Biology courses (taken Semester I or II): 
CHEM UN1403 (or higher)
GENERAL CHEMISTRY I-LECTURES 
BIOL UN2001
 
INTRO BIO I: BIOCHEM,GEN,MOLEC 
ENGL CC1010 (taken Semester I or II)UNIVERSITY WRITING 
Complete Required Technical Electives (Student's choice) (taken Semester I, II, III, or IV) 
ENGI E1006 (taken Semester I, II, III, or IV)INTRO TO COMP FOR ENG/APP SCI 
PHED UN1002PHYSICAL EDUCATION ACTIVITIES 
ENGI E1102 (taken Semester I or II)THE ART OF ENGINEERING 
Second Year
Semester III
APMA E2000
 - APMA E2001 (taken Semester III or IV)1
MULTV. CALC. FOR ENGI & APP SCI 
Choose one of the following Physics courses depending on track: 
INTRO-CLASSCL & QUANTUM WAVES 
PHYSICS III:CLASS/QUANTUM WAVE 
INTERMEDIATE LABORATORY WORK 
Choose one of the following Required Nontechnical Electives: 
EURPN LIT-PHILOS MASTERPIECS I 
CONTEMP WESTERN CIVILIZATION I 
Global Core (3-4)
 
HUMA UN1121 or UN1123MASTERPIECES OF WESTERN ART 
Complete Required Technical Electives (Student's choice) (taken Semester I, II, III, or IV) 
ENGI E1006 (taken Semester I, II, III, or IV)INTRO TO COMP FOR ENG/APP SCI 
Semester IV
APMA E2000
 - APMA E2001 (taken Semester III or IV)1
MULTV. CALC. FOR ENGI & APP SCI 
ODE1,4 
PHYS UN14943INTRO TO EXPERIMENTAL PHYS-LAB 
Choose one of the following Required Nontechnical Electives: 
EURPN LIT-PHILOS MASTRPIECS II 
CONTEMP WESTRN CIVILIZATION II 
Global Core (3-4)
 
ECON UN1105 or UN1155PRINCIPLES OF ECONOMICS 
Complete Required Technical Electives (Student's choice) (taken Semester I, II, III, or IV) 
ENGI E1006 (taken Semester I, II, III, or IV)INTRO TO COMP FOR ENG/APP SCI 
Third Year
Semester V
APMA E31015APPLIED MATH I: LINEAR ALGEBRA 
APMA E42045FUNCTNS OF A COMPLEX VARIABLE 
APMA E4300COMPUT MATH:INTRO-NUMERCL METH 
APMA E4901SEM-PROBLEMS IN APPLIED MATH 
Tech Electives6 
Nontech Electives 
Semester VI
APMA E31025APPLIED MATHEMATICS II: PDE'S 
APMA E4101APPL MATH III:DYNAMICAL SYSTMS 
Course from Group A7 
Tech Electives6 
Nontech Electives 
Fourth Year
Semester VII
MATH GU40615INTRO MODERN ANALYSIS I 
APMA E4903SEM-PROBLEMS IN APPLIED MATH 
Course from Group B7 
Tech Electives6 
Nontech Electives 
Semester VIII
APMA E3900 (With an adviser’s permission, an approved technical elective may be substituted)UNDERGRAD RES IN APPLIED MATH 
Courses designated MATH, APMA, or STAT 
Tech Electives6 
Nontech Electives 
1

Students with advanced standing may start the calculus sequence at a higher level (see Advanced Placement Credit Chart, in which case students are suggested to add linear algebra in the first two years.

2

Transfer students who have not fulfilled the physics requirement prior to enrolling at Columbia may substitute this course with PHYS BC3001 CLASSICAL WAVES - LECTURE LAB.

3

Or a lab course in Astronomy, Astrophysics, Biology, or Chemistry.

4

Applied mathematics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS). Students who take APMA E2101 INTRO TO APPLIED MATHEMATICS prior to declaring their major in applied mathematics may use this course to satisfy their ODE requirement with the permission of the faculty adviser.

5

MATH UN2010 LINEAR ALGEBRA or COMS W3561 may be substituted for APMA E3101 APPLIED MATH I: LINEAR ALGEBRA; MATH UN3028 PARTIAL DIFFERENTIAL EQUATIONS may be substituted for APMA E3102 APPLIED MATHEMATICS II: PDE'S; MATH UN3007 COMPLEX VARIABLES may be substituted for APMA E4204 FUNCTNS OF A COMPLEX VARIABLE; MATH UN2500 ANALYSIS AND OPTIMIZATION may be substituted for MATH GU4061 INTRO MODERN ANALYSIS I.

6

Any course in science, math, or engineering at the 3000 level or above qualifies as a technical elective, except for required or elective courses in the minor in entrepreneurship and innovation which do not count as technical electives unless authorized by an adviser. Elective courses may be chosen from other departments in SEAS and Arts and Sciences, e.g., the Departments of Mechanical Engineering, Electrical Engineering, Mathematics, and Statistics.

7

One course from Group A (Probability) and one course from Group B (Applied Probability/Statistics) required for graduation.

Group A - Probability

IEOR E3658PROBABILITY FOR ENGINEERS3.00
or IEOR E4150 INTRO-PROBABILITY & STATISTICS
STAT GU4203PROBABILITY THEORY3.00
MATH W41553.00

Group B - Applied Probability/Statistics

IEOR E3106STOCHASTIC SYSTEMS AND APPLICATIONS3.00
IEOR E4106STOCHASTIC MODELS3.00
STAT GU4204STATISTICAL INFERENCE3.00
STAT GU4207ELEMENTARY STOCHASTIC PROCESS3.00
COMS W4771MACHINE LEARNING3.00