# Undergraduate Programs

The Department of Applied Physics and Applied Mathematics offers three undergraduate programs: applied physics, applied mathematics, and materials science.

The applied physics and applied mathematics programs provide an excellent preparation for graduate study or for careers in which mathematical and technical sophistication are important. Using the large number of electives in these programs, students can tailor their programs to fit their personal and career interests. By focusing their technical electives, students can obtain a strong base of knowledge in a specialized area. In addition to formal minors, some areas of specialization that are available are described in the Specialty Areas section. All technical electives are normally at the 3000 level or above.

See the Materials Science section for more information on the materials science program.

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:

Code | Title | Points |
---|---|---|

ELEN E3000 | ^{x,J} | 3.00 |

MSAE E3010 | FOUNDATIONS OF MATERIALS SCIENCE ^{x} | 3.00 |

APPH E4010 | INTRODUCTN TO NUCLEAR SCIENCE ^{x} | 3.00 |

PHYS GU4018 | SOLID STATE PHYSICS ^{y} | 3.00 |

APMA E4101 | APPL MATH III:DYNAMICAL SYSTMS ^{x} | 3.00 |

APPH E4110 | MODERN OPTICS ^{y} | 3.00 |

APPH E4112 | LASER PHYSICS ^{x} | 3.00 |

APPH E4200 | PHYSICS OF FLUIDS ^{x} | 3.00 |

APPH E4301 | INTRO TO PLASMA PHYSICS ^{y} | 3.00 |

- x
An x following the course number means that the course meets in the fall semester.

- J
The courses that are often taken, or in some cases need to be taken, in the junior year are denoted with a “J.”

- y
A y following the course number means that the course meets in the spring semester.

### Earth and Atmospheric Sciences

The earth sciences provide a wide range of problems of interest to physicists and mathematicians ranging from the dynamics of 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.

Code | Title | Points |
---|---|---|

Atmosphere, Oceans, and Climate | ||

APAM E3109 | 3.00 | |

EESC GU4008 | Introduction to Atmospheric Science | 3.00 |

APPH E4200 | PHYSICS OF FLUIDS | 3.00 |

APPH E4210 | GEOPHYSICAL FLUID DYNAMICS | 3.00 |

EESC GU4925 | INTRO TO PHYSICAL OCEANOGRAPHY | 3.00 |

EESC GU4930 | EARTH'S OCEANS ＆ ATMOSPHERE | 3.00 |

Solid Earth Geophysics | ||

EESC UN3201 | SOLID EARTH DYNAMICS | 3.00 |

EESC GU4085 | GEODYNAMICS | 3.00 |

EESC GU4113 | Mineralogy and Mineral Resources | 4.00 |

EESC GU4300 | THE EARTH'S DEEP INTERIOR | 3.00 |

EESC GU4701 | Introduction to Igneous Petrology | 4.00 |

EESC GU4949 | Introduction to Seismology | 3.00 |

(See also courses listed under Scientific Computation and Computer Science below.)

### 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.

Code | Title | Points |
---|---|---|

PHYS UN3002 | From Quarks To the Cosmos: Applications of Modern Physics ^{y} | 3.50 |

ASTR UN3601 | RELATVITY,BLACK HOLES,COSMOLGY ^{x,J} | 3.00 |

ASTR UN3602 | PHYSICAL COSMOLOGY ^{y,J} | 3.00 |

ASTR GU4001 | ^{y} | 3.00 |

APMA E4101 | APPL MATH III:DYNAMICAL SYSTMS ^{x} | 3.00 |

- y
A y following the course number means that the course meets in the spring semester.

- x
An x following the course number means that the course meets in the fall semester.

- J
The courses that are often taken, or in some cases need to be taken, in the junior year are denoted with a “J.”

### 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.

Code | Title | Points |
---|---|---|

Economics | ||

ECON UN3211 | INTERMEDIATE MICROECONOMICS ^{x,y,J} | 4.00 |

ECON UN3213 | INTERMEDIATE MACROECONOMICS ^{x,y,J} | 4.00 |

Industrial Engineering and Operations Research | ||

IEOR E4003 | CORPORATE FINANCE FOR ENGINEERS ^{x} | 3.00 |

IEOR E4201 | The Engineering of Management, I ^{x} | 3.00 |

IEOR E4202 | The Engineering of Management, II ^{y} | 3.00 |

Finance | ||

MATH GU4071 | Introduction to the Mathematics of Finance ^{x} | 3.00 |

IEOR E4106 | STOCHASTIC MODELS ^{y,J} | 3.00 |

STAT GU4001 | INTRODUCTION TO PROBABILITY AND STATISTICS ^{x,y,J} | 3.00 |

ECON GU4280 | CORPORATE FINANCE ^{x.y} | 3.00 |

IEOR E4700 | INTRO TO FINANCIAL ENGINEERING ^{x} | 3.00 |

- x
An x following the course number means that the course meets in the fall semester.

- y
A y following the course number means that the course meets in the spring semester.

- J
The courses that are often taken, or in some cases need to be taken, in the junior year are denoted with a “J.”

### 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.

Code | Title | Points |
---|---|---|

MATH UN3386 | DIFFERENTIAL GEOMETRY ^{x} | 3.00 |

APMA E4101 | APPL MATH III:DYNAMICAL SYSTMS ^{x} | 3.00 |

APMA E4301 | NUMERICAL METHODS/PDE'S ^{y} | 3.00 |

APMA E4302 | METHODS IN COMPUTATIONAL SCI ^{x} | 3.00 |

PHYS GU4019 | MATHEMATICL METHODS OF PHYSICS ^{y} | 3.00 |

- x
An x following the course number means that the course meets in the fall semester.

- y
A y following the course number means that the course meets in the spring semester.

### 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.

Code | Title | Points |
---|---|---|

MATH UN3386 | DIFFERENTIAL GEOMETRY ^{x} | 3.00 |

APMA E4101 | APPL MATH III:DYNAMICAL SYSTMS ^{x} | 3.00 |

APMA E4150 | APPLIED FUNCTIONAL ANALYSIS ^{x} | 3.00 |

MATH GU4032 | FOURIER ANALYSIS ^{x} | 3.00 |

MATH GU4062 | INTRO MODERN ANALYSIS II ^{y} | 3.00 |

STAT GU4001 | INTRODUCTION TO PROBABILITY AND STATISTICS ^{x,y,J} | 3.00 |

PHYS GU4386 | ^{x} | 3.00 |

PHYS GU4387 | ^{y} | 3.00 |

- x
An x following the course number means that the course meets in the fall semester.

- y
A y following the course number means that the course meets in the spring semester.

- J

### 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.

Code | Title | Points |
---|---|---|

Recommended | ||

BIOL UN2005 | INTRO BIO I: BIOCHEM,GEN,MOLEC ^{x} | 4.00 |

BIOL UN2006 | INTRO BIO II:CELL BIO,DEV/PHYS ^{y} | 4.00 |

APPH E3400 | PHYSICS OF THE HUMAN BODY ^{y} | 3.00 |

APMA E4400 | INTRO TO BIOPHYSICAL MODELING ^{y} | 3.00 |

- x
An x following the course number means that the course meets in the fall semester.

- y
A y following the course number means that the course meets in the spring semester.

#### Other Technical Electives

**(a course in at least two areas recommended):**

Code | Title | Points |
---|---|---|

Biological Materials | ||

BIOL GU4070 | The Biology and Physics of Single Molecules ^{x} | 3.00 |

CHEN E4650 | POLYMER PHYSICS ^{x} | 3.00 |

Biomechanics | ||

BMEN E3320 | FLUID BIOMECHANICS ^{y,J} | 3.00 |

BMEN E4300 | SOLID BIOMECHANICS ^{y,J} | 3.00 |

Genomics and Bioinformatics | ||

BIOL UN3037 | ^{y,J} | 3.00 |

ECBM E3060 | ^{x,J} | 3.00 |

CBMF W4761 | COMPUTATIONAL GENOMICS ^{y} | 3.00 |

Neurobiology | ||

BIOL UN3004 | NEUROBIO I:CELLULAR ＆ MOLECULR ^{x,J} | 4.00 |

BIOL UN3005 | NEUROBIO II: DEVPT ＆ SYSTEMS ^{y,J} | 4.00 |

ELEN E4011 | ^{x} | 3.00 |

- x
An x following the course number means that the course meets in the fall semester.

- y
A y following the course number means that the course meets in the spring semester.

- J

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:

Code | Title | Points |
---|---|---|

MATH UN3020 | NUMBER THEORY AND CRYPTOGRAPHY ^{x,J} | 3.00 |

Select one of the following: | ||

HONORS DATA STRUCTURES ＆ ALGOL ^{x,y,J} | ||

COMS W3139 | ^{y,J} | |

COMS W3157 | ADVANCED PROGRAMMING ^{x,y,J} | 4.00 |

COMS W3203 | DISCRETE MATHEMATICS ^{x,y,J} | 4.00 |

COMS W4203 | Graph Theory ^{y} | 3.00 |

APMA E4300 | COMPUT MATH:INTRO-NUMERCL METH ^{x} | 3.00 |

APMA E4301 | NUMERICAL METHODS/PDE'S ^{y} | 3.00 |

APMA E4302 | METHODS IN COMPUTATIONAL SCI ^{x} | 3.00 |

COMS W4701 | ARTIFICIAL INTELLIGENCE ^{x,y} | 3.00 |

COMS W4771 | MACHINE LEARNING ^{y} | 3.00 |

- x
An x following the course number means that the course meets in the fall semester.

- J
- y
A y following the course number means that the course meets in the spring semester.

### 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:

Code | Title | Points |
---|---|---|

PHYS UN3083 | ELECTRONICS LABORATORY ^{y,J} | 3.00 |

MSAE E3110 | ^{x} | 3.00 |

ELEN E3106 | SOLID STATE DEVICES-MATERIALS ^{x,J} | 3.50 |

MSAE E4100 | CRYSTALLOGRAPHY ^{x} | 3.00 |

PHYS GU4018 | SOLID STATE PHYSICS ^{y} | 3.00 |

MSAE E4206 | ELEC ＆ MAGNETIC PROP OF SOLIDS ^{x} | 3.00 |

- y
A y following the course number means that the course meets in the spring semester.

- J
- x
An x following the course number means that the course meets in the fall semester.