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AP PL IE D M AT H E M AT IC S : T H IRD A N D F O U RT H Y EA RS
REQUIRED COURSES
SEMESTER V
SEMESTER VI
SEMESTER VII
APMA E3101 (3)1 Linear algebra (Applied math, I)
APMA E3102 (3)1 Partial differential equations (Applied math, II)
MATH W4061 (3) Modern analysis
APMA E4901 (0) Seminar
ELECTIVES
Course from Group A or Group B2
Course from Group A or Group B2
APMA E4101 (3) Introduction to dynamical systems (Applied math, III)
SEMESTER VIII
APMA E3900 (3)3 Research Courses designated MATH, APMA, or STAT (3)
APMA E4204 (3)1 Complex variables
APMA E4300 (3) Introduction to numerical methods (Computational math, I)
TECH 4
3 points
3 points
3 points
6 points
NONTECH
3 points
3 points
3 points
3 points
15
15
16
15
TOTAL POINTS
APMA E4903 (4) Seminar
MATH V2010 may be substituted for APMA E3101; APMA E4200 or MATH V3028 may be substituted for APMA E3102; MATH V3007 may be substituted for APMA E4204. One course from Group A and one course from Group B required for graduation. Group A: IEOR E3658: Probability; SIEO W4105: Probability; SIEO W3600: Introduction to probability and statistics; SIEO W4150: Introduction to probability and statistics; STAT W3105: Introduction to probability; MATH W4155: Probability theory. Group B: STAT W3107: Statistical inference; STAT W4107: Statistical inference; STAT W4109: Probability and statistical inference; SIEO W 4606: Elementary stochastic processes; IEOR E3106: Introduction to stochastic models; IEOR E4106: Introduction to operations research: stochastic models; IEOR E4703: Monte Carlo simulation; COMS W4771: Machine learning. 3 With an adviser’s permission, an approved technical elective may be substituted. 4 Any course in science or engineering at the 3000 level or above qualifies as a technical elective. 1
2
Technical Electives • Applications of Physics Courses that will give a student a broad background in applications of physics: ELEN E3000x: C ircuits, systems, and electronics (J) MSAE E3103x: Elements of materials science (J) APPH E4010x: Intro to nuclear science PHYS G4018y: Solid-state physics APMA E4101y: Intro to dynamical systems APPH E4110x: Modern optics APPH E4112y: Laser physics APPH E4200x: Physics of fluids APPH E4301y: Intro to plasma physics
• Earth and Atmospheric Sciences The Earth sciences provide a wide range of problems of interest to physicists and mathematicians ranging from the dynamics of the Earth’s climate to earthquake physics to dynamics of Earth’s deep interior. The Lamont-Doherty Earth Observatory, which is part of Columbia University, provides enormous resources for students interested in this area.
ATMOSPHERE, OCEANS, AND CLIMATE APPH E4008y: I ntro to atmospheric science APPH E4200x: Physics of fluids APPH E4210y: Geophysical fluid dynamics EESC W4925x: P rinciples of physical oceanography EESC W4930y: E arth’s oceans and atmosphere SOLID EARTH GEOPHYSICS EESC W4001x: Advanced general geology EESC W4113x: Intro to mineralogy APPH E4200x: Physics of fluids EESC W4701y: Intro to igneous petrology EESC W4941y: Principles of geophysics EESC W4950x: Mathematical methods in the Earth sciences
(See also courses listed under Scientific Computation and Computer Science on page 62.)
• Basic Physics and Astrophysics Fundamental physics and astrophysics can be emphasized. Not only is astrophysics providing a deeper understanding of the universe, but it is also testing the fundamental principles of physics. PHYS W3002y: F rom quarks to the cosmos: applications of modern physics
ASTR C3601x: General relativity, black holes, and cosmology (J) ASTR C3602y: P hysical cosmology (J) ASTR G4001y: Astrophysics, I APMA E4101x: Intro to dynamical systems
• Business and Finance The knowledge of physics and mathematics that is gained in the applied physics and applied mathematics programs is a strong base for a career in business or finance. ECONOMICS ECON W3211x,y: Intermed microeconomics (J) ECON W3213x,y: Intermed macroeconomics(J) INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH IEOR E4003x: Industrial economics IEOR E4201x: The eng of management, I IEOR E4202y: The eng of management, II FINANCE MATH W4071x: Mathematics of finance IEOR E4106y: Intro to operations research: stochastic models (J) SIEO W4150x,y: Probability and statistics (J) ECIE W4280: Corporate finance IEOR E4700x: Intro to financial engineering ENGINEERING 2013– 2014