
B.S. in Applied Physics, Applied Mathematics, or Materials Science

Undergraduate Double Major in Applied Physics and Applied Mathematics

Combined Plan Progam
 Undergraduate Minor in Applied Physics, Applied Mathematics, or Materials Science
B.S. in AP, AM, or MSE

Applied Physics Undergraduate Program

Applied Mathematics Undergraduate Program

Materials Science Undergraduate Program
Undergraduate Double Major in Applied Physics and Applied Mathematics
Students satisfy all requirements for both majors, except for the seminar requirements. They are required to take both senior seminars, APMA E4903 and APPH E4903 (taking one in the junior year and one in the senior year, due to timing conflicts), but not the junior seminars, APMA E4901 and APPH E4901. A single course may be used to fulfill a requirement in both majors. Students must maintain a GPA at or above 3.75, and must graduate with at least 143 points, 15 above the regular 128point requirement. These extra 15 points should be technical electives appropriate for one or both majors.
To apply, a student first obtains the approval of both the general undergraduate AP advisor and the general undergraduate AM advisor, and then the approval of the Dean.
Combined Plan Progam
Columbia Engineering maintains cooperative program relationships with institutions nationwide and with other Columbia University undergraduate divisions. These programs allow students to complete the equivalent of the First Year–Sophomore Program and transfer directly to a field of specialization in the School, beginning their study at the School as juniorlevel students.
The Combined Plan (32) Program within Columbia University
Students who follow this program apply through their own school at Columbia College, Barnard College, or the School of General Studies for admission. Under this plan, the preengineering student studies in the appropriate college for three years, then attends Columbia Engineering for two years and is awarded the Bachelor of Arts degree and the Bachelor of Science degree in engineering upon completion of the fifth year. This fiveyear program is optional at Columbia, but the School recommends it to all students who wish greater enrichment in the liberal arts and pure sciences.
For more information, please see: Combined Plan Program
Undergraduate Minor in Applied Physics, Applied Mathematics, or Materials Science
SEAS Bulletin: Undergraduate Minors
Minor in Applied Physics
Prospective students should consult the first and secondyear requirements for applied physics majors to ensure that prerequisites for the applied physics minor are satisfied in the first two years.
Course work counting toward the applied physics minor may not include advanced placement credits.

APPH E4901: Seminar: problems in applied physics 1.0 points

APPH E3200: Mechanics 3.0 points

APPH E3100: Introduction to quantum mechanics 3.0 points

APPH E3300: Applied electromagnetism 3.0 points

MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics 3.0 points

Two of the following courses:

APPH E4010: Introduction to nuclear science 3.0 points

APPH E4100: Quantum physics of matter 3.0 points

APPH E4110: Modern optics 3.0

APPH E4112: Laser physics 3.0 points

APPH E4300: Applied electrodynamics 3.0 points

APPH E4301: Introduction to plasma physics 3.0 points
Minor in Applied Mathematics
Prospective students should consult the first and secondyear requirements for applied mathematics majors to ensure that prerequisites for the applied mathematics minor are satisfied in the first two years.
Course work counting toward the applied mathematics minor may not include advanced placement credits. Any substitutions for the courses listed below require the approval of the applied mathematics program adviser.

APMA E3101: Linear algebra 3.0 points or
MATH V2010: Linear algebra 3.0 points

APMA E3102: Partial differential equations 3.0 points or
MATH V3028: Partial differential equations 3.0 points

 5. Three of the following courses:

APMA E4300: Introduction to numerical methods 3.0 points

APMA E4204: Functions of a complex variable 3.0 points

APMA E4101: Introduction to: dynamical systems 3.0 points

MATH V2500: Analysis and optimization 3.0 points

SIEO W4105: Introduction to probablity and statistics 3.0 points

STAT W4107: Statistical inference 3.0 points
 or any other course designated APMA, MATH, STAT, IEOR, or COMS that is approved by the applied mathematics program adviser.
Minor in Materials Science

MSAE E3103: Elements of materials science 3.0 points
  3. Two of the following courses:

MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics 3.0 points or

MSAE E3141: Metals and semiconductors 3.0 points
 MSAE E3142: Ceramics and polymers 3.0 points

MSAE E4206: Electronic and magnetic properties of solids 3.0 points

MSAE E4100: Crystallography 3.0 points
 MSAE E4101: Structural analysis of materials 3.0 points
4. – 6. Three of the following courses
(other materialsrelated courses may be acceptable):

APPH E4100: Quantum physics of matter 3.0 points

CHEE E4050: Industrial and environmental electrochemistry 3.0 points

CHEE E4252: Introduction to surface and colloid chemistry 3.0 points

CHEE E4530: Corrosion of metals 3.0 points

CHEE E4620: Introduction to polymer science 3.0 points

CHEN E4630: Polymer laboratory 3.0 points

CHEM C3443: Organic chemistry 3.5 points

EAEE E4900: Applied transport and chemical rate phenomena 3.0 points

ELEN E3106: Solidstate devices and materials 3.5 points

ELEN E4411: Fundamentals of photonics 3.0 points

ELEN E4301: Introduction to semiconductor devices 3.0 points

ELEN E4944: Principles of device microfabrication 3.0 points

ENME E4113: Advanced mechanics of solids 3.0 points

ENME E4114: Mechanics of fracture and fatigue 3.0 points

MECE E4608: Manufacturing processes 3.0 points

MECE E4701: Introductory biomechanics 3.0 points