# Major and Minor Requirements

Majors and minors are possible in astronomy, physics, as well as in several interdisciplinary subjects. Special majors in interdisciplinary subjects are arranged in conjunction with the relevant second department at Barnard. A student interested in such possibilities should talk to a faculty member early on in the semester. Some possible majors and minors are:

- Astronomy
- Physics
- Astrophysics
- Biophysics
- Chemical Physics
- Engineering Physics
- Mathematical Physics

## Requirements for the ASTRONOMY Major

- PHY BC 2001: Physics I: Mechanics
- PHY BC 2002: Physics II: Electricity & Magnetism
- PHY BC 3001: Physics III: Waves & Optics

Students may substitute a Columbia College 3-semester calculus-based introductory physics sequence with the lab, as in the physics major. Calculus IV is required as a cognate course, with additional work in mathematics recommended. Also:

- AST UN 2001, 2002: Introduction to Astrophysics I, II

Students who have taken AST UN 1753-4 or UN 1403-4 may substitute an additional 3000-level course for AST UN 2001-2. Finally, students are required to take four 3000-level AST or PHY courses, including at least one of AST 3102 or PHY 3003 Mechanics, and selected so that at least six total points of 3000-level lecture classes are AST courses. Some of the AST courses offered in recent years include:

- AST UN 3101: Modern Stellar Astrophysics
- AST UN 3102: Planetary Dynamics and Physics of the Solar System
- AST UN 3601: General Relativity, Black Holes, and Cosmology
- AST UN 3602: Physical Cosmology and Extragalactic Astronomy
- AST UN 3646: Observational Astronomy

Students planning to study astronomy or astrophysics in graduate school are strongly urged to take PHYS UN 3003, 3007-8, 3006-GU4023, some additional courses in mathematics, and Computer Science (CSC) UN 1003 Programming in C, or UN 1005 Fortran Programming. Note: When any of the required courses is not being given, the department will recommend appropriate substitutions.

## Requirements for the PHYSICS Major

- PHY BC 2001: Physics I: Mechanics
- PHY BC 2002: Physics II: Electricity & Magnetism
- PHY BC 3001: Physics III: Waves & Optics

In lieu of the above, any 3-semester Columbia introductory sequence acceptable for the physics major in Columbia College will do (e.g. PHY C 1601-2, 2601, taken with PHY 1691-3). The accelerated 2-semester Columbia College sequence PHY C 2801-2 is also acceptable. Calculus IV is required as a cognate course, with additional work in mathematics recommended; e.g. Math E 1210x, y: Ordinary Differential Equations, APMA E 3102y: Applied Mathematics II. The calculus sequence should be completed by the end of the sophomore year. At the upper level the following courses are required:

- PHY UN 3003: Mechanics
- PHY UN 3007: Electricity & Magnetism
- PHY UN 3008: Electromagnetism Waves and Optics
- PHY UN 3006: Quantum Physics
- PHY GU 4023: Thermal & Statistical Physics

Also required are 6.0 points total of advanced lab work, preferably PHYS BC 3086 and 3088, taken concurrently with their cognate Columbia lecture courses. Alternately, students may opt for repeated enrollment in PHYS UN 3081, Columbia's 1.5 point EKA laboratory, or Barnard's PHYS BC3082. Finally, the student must take computer Science W 1004 (Java), W 1005 (MATLAB), Engineering E 1006 (Python), or PHY UN 3083 (Electronics Laboratory).

** NOTE:** A Physics major pursuing a Math minor should take electronics lab; otherwise, two distinct COMS courses are necessary.

Students planning to study Physics in graduate school should include several 4000-level electives in their senior year program.

### Requirements for the ASTROPHYSICS Major

Students wishing to major in astrophysics should consult a member of the department.

### Interdisciplinary Major

Special majors in, for example, biophysics, chemical physics, engineering physics, or mathematical physics are all possible and are arranged in conjunction with the relevant second department at Barnard. A student interested in such possibilities should speak to a faculty member early on (i.e., by late fall of her sophomore year) in order to permit the most effective construction of her program of study and the appropriate petition to be made to the Committee on Programs and Academic Standing. The latter is a straightforward procedure associated with the declaration of all special majors at Barnard.

### Requirements for the PHYSICS Minor

Five courses are required for the minor in physics. They are: any three-semester introductory sequence acceptable for the major (see Introductory Sequence page); and two 3-point courses at the 3000-level.

### Requirements for the ASTRONOMY Minor

2 Semesters of Physics with Lab (7-9 pts)

*Students who are majoring in science can omit one semester of 1-1.5 pts of Physics lab.

4 courses in astronomy or astrophysics at the 2000 level or above. (12 pts)

*One of these courses can be replaced by two 1000-level Astronomy courses.

*An additional 3 points of physics at the 3000 level or above can substitute for 3 points of astronomy.