# 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
- Mathematical Physics

## Requirements for the ASTRONOMY Major

- PHYS BC2001: Physics I: Mechanics (Lec & Lab)
- PHYS BC2002: Physics II: Electricity & Magnetism (Lec & Lab)
- PHYS BC3001: Physics III: Waves & Optics (Lec & Lab)

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:

- ASTR UN2001, 2002: Introduction to Astrophysics I, II

Students who have taken ASTR UN1753-4 or UN1403-4 may substitute an additional 3000-level course for ASTR UN2001-2. Finally, students are required to take four 3000-level ASTR or PHYS courses, including at least one of AST UN3102 or PHYS UN3003 Mechanics, and selected so that at least six total points of 3000-level lecture classes are ASTR courses. Some of the ASTR courses offered in recent years include:

- ASTR UN3101: Modern Stellar Astrophysics
- ASTR UN3103: GALAXIES
- ASTR UN3105: Extrasolar Planets and Astrobiology
- ASTR UN3602: Physical Cosmology and Extragalactic Astronomy
- ASTR UN3273: High Energy Astrophysics
- ASTR UN3646: Observational Astronomy

Students planning to study astronomy or astrophysics in graduate school are strongly urged to take PHYS UN3003, 3007-8, 3006-GU4023, some additional courses in mathematics, and Computer Science COMS UN1003 Programming in C, or UN1005 Fortran Programming. Note: When any of the required courses is not being given, the department will recommend appropriate substitutions.

## Requirements for the PHYSICS Major

- PHYS BC2001: Physics I: Mechanics (Lec & Lab)
- PHYS BC2002: Physics II: Electricity & Magnetism (Lec & Lab)
- PHYS BC3001: Physics III: Waves & Optics (Lec & Lab)
- PHYS BC3006: Quantum Physics (Lec & Lab)

- PHYS UN3003: Mechanics
- PHYS UN3007: Electricity & Magnetism
- PHYS UN3008: Electromagnetism Waves and Optics
- PHYS GU4023: Thermal & Statistical Physics

Also required are 6.0 points total of advanced lab work, preferably:

- PHYS BC3086: Quantum Physics Laboratory
- PHYS BC3088: Advanced Electromagnetism Laboratory

best taken concurrently with their cognate lecture courses, which are BC3006 and PHYS W3008 respectively. Alternatively, in lieu of PHYS BC3088, students may opt for Electronics Lab PHYS UN3083 or a 3pt combination of PHYS UN3081 and PHYS BC3082.

- Computer Science

The student must take a Computer Science class. We recommend W1004 (Java), W1005 (MATLAB), Engineering E1006 (Python), or PHYS UN3083 (Electronics Laboratory). Other options include COMS BC1016 (Intro to Computational Thinking), EESC BC3050 (Big Data with Python), ASTR GU4260 (Modeling the Universe).

**This is an 11 course minimum for the standard major described above.**

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

We recommend completing the calculus I-IV sequence by the end of the second year, as Calculus courses will be pre-requisites to many of the upper-level classes. Other Calculus options include Honors Math A-B, Accelerated Multivariable Calculus, and Multivariable Calculus for Engineering and Applied Science. Additional work in mathematics is recommended; e.g. Math UN1210: Linear Algebra, APMA E3102: Applied Mathematics II.

While we recommend students take the Barnard sequence, in lieu of the two introductory courses BC2001 & 2002, a 2-semester Columbia introductory sequence acceptable for the physics major in Columbia College can be substituted (e.g. PHY UN 1601-2) combined with BC2009 and BC2019, which are the lab only sections for the Barnard introductory sequence. If you choose to take the Columbia sequence, please consult with an advisor in the Barnard Physics and Astronomy department as soon as possible.

If a student opts to take the accelerated 2-semester Columbia College sequence PHY UN 2801-2, we strongly encourage that student to seek advice from the Chair of the Barnard Physics Department to determine the remainder of required courses for the major.

Any other substitutions to the major may require a petition. A student should seek advice from their advisor and/or the Chair of the Barnard Physics Department.

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

### 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; 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.