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 UN1101^{1} | CALCULUS 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 UN1001 | PHYSICAL EDUCATION ACTIVITIES | |
ENGI E1102 (taken Semester I or II) | THE ART OF ENGINEERING | |
Semester II | ||
MATH UN1102^{1} | CALCULUS 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 UN1002 | PHYSICAL 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: | ||
PHYS UN1403^{2} | INTRO-CLASSCL ＆ QUANTUM WAVES | |
PHYSICS III:CLASS/QUANTUM WAVE | ||
PHYS UN3081^{3} | 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 UN1123 | MASTERPIECES 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 | |
ODE^{1,4} | ||
PHYS UN1494^{3} | INTRO 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 UN1155 | PRINCIPLES 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 E3101^{5} | APPLIED MATH I: LINEAR ALGEBRA | |
APMA E4204^{5} | FUNCTNS OF A COMPLEX VARIABLE | |
APMA E4300 | COMPUT MATH:INTRO-NUMERCL METH | |
APMA E4901 | SEM-PROBLEMS IN APPLIED MATH | |
Tech Electives^{6} | ||
Nontech Electives | ||
Semester VI | ||
APMA E3102^{5} | APPLIED MATHEMATICS II: PDE'S | |
APMA E4101 | APPL MATH III:DYNAMICAL SYSTMS | |
Course from Group A^{7} | ||
Tech Electives^{6} | ||
Nontech Electives | ||
Fourth Year | ||
Semester VII | ||
MATH GU4061^{5} | INTRO MODERN ANALYSIS I | |
APMA E4903 | SEM-PROBLEMS IN APPLIED MATH | |
Course from Group B^{7} | ||
Tech Electives^{6} | ||
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 Electives^{6} | ||
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
Code | Title | Points |
---|---|---|
IEOR E3658 | PROBABILITY FOR ENGINEERS | 3.00 |
or IEOR E4150 | INTRO-PROBABILITY ＆ STATISTICS | |
STAT GU4203 | PROBABILITY THEORY | 3.00 |
MATH W4155 | 3.00 |
Group B - Applied Probability/Statistics
Code | Title | Points |
---|---|---|
IEOR E3106 | STOCHASTIC SYSTEMS AND APPLICATIONS | 3.00 |
IEOR E4106 | STOCHASTIC MODELS | 3.00 |
STAT GU4204 | STATISTICAL INFERENCE | 3.00 |
STAT GU4207 | ELEMENTARY STOCHASTIC PROCESS | 3.00 |
COMS W4771 | MACHINE LEARNING | 3.00 |