# 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

## Requirements for the ASTRONOMY Major

- PHYS BC2001: Mechanics (Lec & Lab)
- PHYS BC2002: Electricity & Magnetism (Lec & Lab)
- PHYS BC3001: Waves & Optics (Lec & Lab)
- ASTR UN2001, 2002: Introduction to Astrophysics I, II

Students are required to take four 3000-level ASTR or PHYS courses, and selected so that at least six total points of 3000-level lecture classes are ASTR courses. Of those four 3000-level course, at least one should be:

- PHYS UN3003: Mechanics

OR

- ASTR UN3102

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
- ASTR C3601: General Relativity, Black Holes, and Cosmology

*

**This is a 9 course minimum for the standard major described above.**

Students planning to study astronomy or astrophysics in graduate school are strongly urged to take PHYS U3003, 3007-8, 3006, GU4023, and some additional courses in Computer Science. We recommend W1004 (Java), Engineering E1006 (Python), COMS BC1016 (Intro to Computational Thinking), EESC BC3050 (Big Data with Python), or ASTR GU4260 (Modeling the Universe).

Note: If the required courses are not offered for some reason, the department will recommend appropriate substitutions.

Students are encouraged to take the calculus I-IV sequence since 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.

**Substitutions:**

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 UN1601-2) combined with BC2009 and BC2019, which are the lab only sections for the Barnard introductory sequence. If you choose to take the 2-semester Columbia sequence, please consult with an advisor in the Barnard Physics and Astronomy department as soon as possible.

Note that PHY UN1201-2 is not acceptable for the major.

If a student opts to take the accelerated 2-semester Columbia College sequence PHY UN2801-2, we strongly encourage that student to seek advice from the Chair of the Barnard Physics and Astronomy Department to determine the remainder of required courses for the major.

Students who have taken two 1000 level courses may substitute an additional 3000-level course for ASTR UN2001-2.

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

## Requirements for the PHYSICS Major

- PHYS BC2001: Mechanics (Lec & Lab)
- PHYS BC2002: Electricity & Magnetism (Lec & Lab)
- PHYS BC3001: Waves & Optics (Lec & Lab)
- PHYS BC3006: Quantum Physics (paired with BC3086 Quantum Physics 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 UN3007 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 are strongly encouraged to include 4000-level electives in their program.

Students are expected to complete 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.

**Substitutions:**

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 UN1601-2) combined with BC2009 and BC2019, which are the lab only sections for the Barnard introductory sequence. If you choose to take the 2-semester Columbia sequence, please consult with an advisor in the Barnard Physics and Astronomy department as soon as possible. Note that PHY UN1201-2 is not acceptable for the major.

If a student opts to take the accelerated 2-semester Columbia College sequence PHY UN2801-2, 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 Degree Audit Change. A student should seek advice from their Physics advisor and/or the Chair of the Barnard Physics Department.

** NOTE:** A Physics major pursuing a Math Sciences 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.

### 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.