Specialty Areas in APAM
Both applied physics and applied mathematics students can focus their technical electives and develop a strong base of knowledge in a specialty area. There is no requirement to focus electives, so students may take as many or as few of the recommended courses in a specialty area as is appropriate to their schedules and interests. Some specialties are given below, but this is not an exclusive list and others can be worked out in coordination with the student’s adviser. The courses that are often taken, or in some cases need to be taken, in the junior year are denoted with a “J.”
Technical Electives
• Applications of Physics
Courses that will give a student a broad background in applications of physics:
ELEN E3000x: Circuits, systems, and electronics (J)
MSAE E3103x: Elements of material science (J)
APPH E4010x: Intro to nuclear science
PHYS GU4018y: 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
APAM E3109: Climate physics
EESC GU4008: Intro to atmospheric science
APPH E4200: Physics of fluids
APPH E4210: Geophysical fluid dynamics
EESC GU4925: Principles of physical oceanography
EESC GU4930: Earth’s oceans and atmosphere
SOLID EARTH GEOPHYSICS
EESC UN3201: Solid earth dynamics
EESC GU4085: Geodynamics
EESC GU4113: Intro to mineralogy
EESC E4300: Earth's deeper interior
EESC GU4701: Intro to igneous petrology
EESC GU4949: Introduction to seismology
See also courses listed under Scientific Computation and Computer Science.
• 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 UN3002y: From quarks to the cosmos: applications of modern physics
ASTR UN3601x: General relativity, black holes, and cosmology (J)
ASTR UN3602y: Physical cosmology (J)
ASTR GU4001y: 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 UN3211x,y: Intermed microeconomics (J)
ECON UN3213x,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 GU4071x: Mathematics of finance
IEOR E4106y: Intro to operations research: stochastic models (J)
STAT GU4001x,y: Probability and statistics (J)
ECIE GU4280: Corporate finance
IEOR E4700x: Intro to financial engineering
• Mathematics Applicable to Physics
Applied physics students can specialize in the mathematics that is applicable to physics. This specialization is particularly useful for students interested in theoretical physics.
MATH UN3386x: Differential geometry
APMA E4101x: Intro to dynamical systems
APMA E4301x: Numerical methods for partial differential equations
APMA E4302x: Parallel scientific computing
PHYS GU4019y: Mathematical methods of physics
• Fundamental Mathematics in Applied Mathematics
This specialization is intended for students who desire a more solid foundation in the mathematical methods and underlying theory. For example, this specialization could be followed by students with an interest in graduate work in applied mathematics.
MATH UN3386x: Differential geometry
APMA E4101x: Intro to dynamical systems
APMA E4150x: Applied functional analysis
MATH GU4032x: Fourier analysis
MATH GU4062y: Mathematical analysis, II
STAT GU4001x,y: Intro to probability and statistics (J)
PHYS GU4386x-W4387y: Geometrical concepts in physics
• Quantitative Biology
Traditionally biology was considered a descriptive science in contrast to the quantitative sciences that are based on mathematics, such as physics. This view no longer coincides with reality. Researchers from biology as well as from the physical sciences, applied mathematics, and computer science are rapidly building a quantitative base of biological knowledge. Students can acquire a strong base of knowledge in quantitative biology, both biophysics and computational biology, while completing the applied physics or applied mathematics programs.
RECOMMENDED:
BIOL UN2005x-UN2006y: Intro biology, I and II
APPH E3400y: Physics of the human body
APMA E4400y: Intro to biophysical modeling
OTHER TECHNICAL ELECTIVES (A COURSE IN AT LEAST TWO AREAS RECOMMENDED):
BIOLOGICAL MATERIALS
BIOL GU4070x: The biology and physics of single molecules
CHEN E4650x: Biopolymers
BIOMECHANICS
BMEN E3320y: Fluid biomechanics (J)
BMEN E4300y: Solid biomechanics (J)
GENOMICS AND BIOINFORMATICS
BIOL UN3037y: Whole genome bioinformatics (J)
ECBM E3060x: Introduction to genomic information science and technology (J)
CBMF W4761y: Computational genomics
NEUROBIOLOGY
BIOL UN3004x: Neurobiology, I (J)
BIOL UN3005y: Neurobiology, II (J)
ELEN E4011x: Computational neuroscience
The second term of biology will be considered a technical elective if a student has credits from at least two other of the recommended courses in quantitative biology at the 3000-level or above.
• Scientific Computation and Computer Science
Advanced computation has become a core tool in science, engineering, and mathematics and provides challenges for both physicists and mathematicians. Courses that build on both practical and theoretical aspects of computing and computation include:
MATH UN3020x: Number theory and cryptography (J)
COMS W3137x,y: Data structures and algorithms (or COMS W3139y: Honors data structures and algorithms) (J)
COMS W3157x,y: Advanced programming (J)
COMS W3203x,y: Discrete mathematics: intro to combinatorics and graph theory (J)
COMS W4203y: Graph theory
APMA E4300x: Intro to numerical methods
APMA E4301y: Numerical methods for partial differential equations
APMA E4302x: Methods in computational scienceg
COMS W4701x,y: Artificial intelligence
COMS W4771y: Machine learning
• Solid-State Physics
Much of modern technology is based on solid-state physics, the study of solids and liquids. Courses that will build a strong base for a career in this area are:
PHYS UN3083y: Electronics laboratory (J)
MSAE E3110x: Introduction to materials science, I
ELEN E3106x: Solid-state devices and materials (J)
MSAE E4100x: Crystallography
PHYS GU4018y: Solid-state physics
MSAE E4206x: Electronic and magnetic properties of solids
Undergraduate Program in Materials Science and Engineering
For more information click here.