# Physics & Astronomy

504A Altschul Hall

212-854-3628

Department Administrative Assistant: Joanna Chisolm

## Mission

The mission of the Physics and Astronomy Department at Barnard College is to provide students with an understanding of the basic laws of nature, and a foundation in the fundamental concepts of classical and quantum physics, and modern astronomy and astrophysics. Majors are offered in physics, astronomy, or in interdisciplinary fields such as, astrophysics, biophysics, or chemical physics. The goal of the department is to provide students (majors and non-majors) with quality instruction and prepare them for various post-graduate career options, including graduate study in physics and/or astronomy, professional careers in science, technology, education, or applied fields, as well health-related professions. The department strives to be a source of distinguished women scientists. The faculty in the department maintain NSF or NASA-sponsored active research programs that involve undergraduate students. All majors engage in at least one summer of independent research that is often continued during the semester, or the following summer. Students may also carry out their research at other institutions nationally, through NSF-REU (Research Experience for Undergraduates) programs. Students are required to present the results of their research in the annual departmental “Senior Talks,” held in May.

## Student Learning Goals

- Acquire a strong intellectual foundation in physics and/or astronomy.
- Apply scientific thinking to problems in physics and/or astronomy, and translate this to real life problems.
- Use mathematics to describe and manipulate abstract concepts in physics and/or astronomy.
- Perform laboratory experiments to study various physical phenomena, and use statistical approaches to analyze and interpret the data obtained in these experiments.
- Acquire effective oral and written presentation skills to communicate scientific ideas.
- Participate in a research project and stimulate the ability of empirical thought.
- Demonstrate the ability to give a scientific talk on a research topic.

## Student Learning Outcomes

Upon successfully completing the major, students should have the ability to:

- demonstrate a conceptual understanding of the physical laws of nature.
- demonstrate a thorough knowledge of the various subject areas of physics (e.g. classical mechanics, quantum physics, electromagnetism, and thermodynamics) and/or astronomy (e.g. stellar structure and evolution, physics of the solar system, physical cosmology, and observational astronomy).
- apply problem-solving skills beyond graduation in advanced physics and/or astronomy courses in graduate school and independent research projects.
- apply problem-solving and computation skills in future situations in applied or technical jobs, or careers in finance and industry.
- make an effective oral presentation to an audience of peers and faculty on a particular research topic.

From Aristotle's Physics to Newton's Principia, the term "physics," taken literally from the Greek φυσις (= Nature), implied natural science in its very broadest sense. Physicists were, in essence, natural philosophers, seeking knowledge of the observable phenomenal world. Astronomy originally concentrated on the study of natural phenomena in the heavens with the intent to understand the constitution, relative positions, and motions of the celestial bodies in our universe. Though practitioners of these disciplines have become somewhat more specialized in the past century, the spirit that guides them in their research remains the same as it was more than two millennia ago.

In cooperation with the faculty of the University, Barnard offers a thorough pre-professional curriculum in both physics and astronomy. The faculty represents a wide range of expertise, with special strength and distinction in theoretical physics, condensed matter physics, and observational astrophysics.

Separate majors in physics and astronomy are offered. A major in astrophysics is also possible. Furthermore, there are many special interdisciplinary majors possible, such as biophysics, chemical physics, engineering physics, and mathematical physics. There is a physics minor as well. Students should consult members of the department early on in their undergraduate careers in order to plan the most effective course of study. Qualified seniors are invited to participate in the seniors honors program, in which they carry out a year-long research project leading to the thesis.

There are several quite distinct introductory sequences in physics, only one of which may be taken for credit:

- PHYS C1001 Physics for Poets - PHYS C1002 Physics for Poets is a lecture course in physics intended for liberal arts students. A semester of this CU lecture course satisfies the BC Quantitative Reasoning requirement. Note, however, that 1001-2 does not satisfy the premedical nor physics requirement for any major. It should also not be taken to satisfy the BC lab science requirement.
- PHYS V1201 General Physics I - PHYS V1202 General Physics II is satisfactory preparation for medical school and is appropriate for most non-science major premedical students. This course is taught at Columbia in a large lecture hall setting. It is not recommended as a foundation for more advanced work in the field. Taken in conjunction with PHYS UN1291 General Physics Laboratory - PHYS W1292 , this sequence does satisfy the college LAB requirement, but the student population is essentially premed. Note that PHYS V1201 General Physics I / PHYS V1202 General Physics II are required in order to take the lab course.
- PHYS BC2001 Physics I: Mechanics - PHYS BC2002 Physics II: Electricity and Magnetism, PHYS BC3001 Physics III: Classical Waves Optics is Barnard's own three-semester, calculus based introductory sequence in physics. Characterized by modest class sizes, it is designed specifically for Barnard women with a serious interest in any of the natural sciences or mathematics. Moreover, it is especially appropriate for majors in physics, chemistry, or biochemistry, whether premedical or not. Biology majors with some calculus background are also encouraged to take this sequence. Finally, Barnard women contemplating a major in physics or astronomy should take PHYS BC2001 Physics I: Mechanics - PHYS BC2002 Physics II: Electricity and Magnetism in their first year, if possible, or in their second at the latest, to be followed by the third-semester course, Classical Waves and Optics.
- First-year students with exceptional aptitude for physics (as evidenced, for example, by scores of 4 or 5 on the advanced placement C exam) and a good mathematical background may be admitted into the Columbia-taught two-semester sequence PHYS C2801 General Physics - PHYS C2802 General Physics, which replaces all three terms of the sequence for majors. Students considering this sequence are strongly encouraged to consult a Barnard faculty member at the start of the term.

Students unsure about the most appropriate sequence should consult members of the department.

The following courses may be substituted for each other:

PHYS BC2001 Physics I: Mechanics-PHYS BC2002 Physics II: Electricity and Magnetism (sect.1; 4.5pts) = PHYS UN1601 Physics, I: Mechanics and Relativity - PHYS W1602 (3.0pts.) + PHYS BC2001 Physics I: Mechanics - PHYS BC2002 Physics II: Electricity and Magnetism (sect.3; 1.5pts.)

PHYS BC3001 Physics III: Classical Waves Optics (sect.1; 5pts) = PHYS UN2601 Physics, III: Classical and Quantum Waves (3.0pts) + PHYS BC3001 Physics III: Classical Waves Optics(sect.3; 2pts)

ASTR BC1753 Life in the Universe - ASTR BC1754 Stars, Galaxies, and Cosmology = ASTR C1403 Earth, Moon, and Planets (lecture) - ASTR C1404 Stars, Galaxies, and Cosmology

**Chair:** Laura Kay

**Professors:** Timothy Halpin-Healy (Ann Whitney Olin Professor), Reshmi Mukherjee (Helen Goodhart Altschul Professor)

**Associate Professor:** Janna Levin

**Lab Director:** Stiliana Savin

Other officers of the University offering courses listed below:

**Professors:** James Applegate, Norman Christ, Brian Cole, Arlin Crotts, Charles Hailey, Jules Halpern, Tony Heinz, David Helfand, Robert Mawhinney, John Parsons, Frederik Paerels, Joseph Patterson, Michael Shaevitz, Michael Tuts, Jacqueline van Gorkom, William Zajc

**Associate Professors:** Greg Bryan, Zoltan Haiman, Kathryn Johnson, Kristen Menou, David Schiminovich

**Adjunct Professors:** Burton Budick, Morgan May

## Requirements for the Astronomy Major

The courses required for the major in astronomy are as follows:

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

PHYS BC2001 | Physics I: Mechanics ^{*} | 4.5 |

PHYS BC2002 | Physics II: Electricity and Magnetism ^{*} | 4.5 |

PHYS BC3001 | Physics III: Classical Waves & Optics ^{*} | 5 |

Calculus through IV is required, with additional work in mathematics recommended | ||

ASTR C2001 - ASTR C2002 | Introduction to Astrophysics I and Introduction to Astrophysics II ^{**} | 6 |

Students are required to take four additional 3000-level ASTR or PHYS courses, including at least one of ASTR C3102 or PHYS W3003, 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 year include: | ||

Modern Stellar Astrophysics II | ||

Planetary Dynamics | ||

General Relativity, Black Holes, and Cosmology | ||

High Energy Astrophysics | ||

Physical Cosmology and Extragalactic Astronomy | ||

Observational Astronomy |

* | Students may substitute a Columbia College three-semester calculus-based introductory physics sequence with lab taken at Barnard, as in the physics major. |

** | Students who have taken ASTR BC1753 Life in the Universe-ASTR BC1754 Stars, Galaxies, and Cosmology or ASTR C1403 Earth, Moon, and Planets (lecture)-ASTR C1404 Stars, Galaxies, and Cosmology may substitute an additional 3000-level ASTR course for ASTR C2001 Introduction to Astrophysics I-ASTR C2002 Introduction to Astrophysics II. |

Students planning to study astronomy or astrophysics in graduate school are strongly urged to take PHYS BC3006 Quantum Physics, PHYS UN3003 Mechanics, PHYS UN3007 Electricity and Magnetism-PHYS UN3008 Electromagnetic Waves and Optics, PHYS G4023 Thermal and Statistical Physics, some additional courses in mathematics, and Computer Science COMS W1001 Introduction to Information Science or COMS W1004 Introduction to Computer Science and Programming in Java. Note: When any of the required courses is not being given, the department will recommend appropriate substitutions.

## Requirements for the Physics Major

The courses required for the major in physics are:

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

PHYS BC2001 | Physics I: Mechanics ^{*} | 4.5 |

PHYS BC2002 | Physics II: Electricity and Magnetism ^{*} | 4.5 |

PHYS BC3001 | Physics III: Classical Waves & Optics ^{*} | 5 |

Calculus through IV is required, with additional work in mathematics recommended; e.g., MATH E1201x,y, APMA E3102y. The calculus sequence should be completed by the end of the sophomore year. | ||

PHYS UN3003 | Mechanics | 3 |

PHYS BC3006 | Quantum Physics | 3 |

PHYS UN3007 | Electricity and Magnetism | 3 |

PHYS UN3008 | Electromagnetic Waves and Optics | 3 |

PHYS G4023 | Thermal and Statistical Physics | 3 |

PHYS BC3086 - PHYS BC3088 | Quantum Physics Laboratory and Advanced Electromagnetism Laboratory (taken concurrently with their cognate lecture courses) | 6 |

Select one of the following: | 3 | |

COMS W1001 | Introduction to Information Science | 3 |

COMS W1004 | Introduction to Computer Science and Programming in Java | 3 |

PHYS UN3083 | Electronics Laboratory | 3 |

* | In lieu of the above, any three-semester Columbia introductory sequence acceptable for the physics major in Columbia College will do (e.g., PHYS UN1601 Physics, I: Mechanics and Relativity-PHYS UN1602 Physics, II: Thermodynamics, Electricity, and Magnetism, PHYS UN2601 Physics, III: Classical and Quantum Waves, taken with labs at Barnard). The accelerated two-semester Columbia College sequence PHYS C2801 General Physics-PHYS C2802 General Physics is also acceptable. |

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

## Interdisciplinary Major

Special majors in, for example, astrophysics, 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 above) plus two additional 3-point courses at the 3000-level.

## Astronomy Courses

**ASTR BC1753 Life in the Universe.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: recommended preparation: a working knowledge of high school algebra.

Introduction to astronomy intended primarily for nonscience majors. Includes the history of astronomy; the apparent motions of the moon, sun, stars, and planets; gravitation and planetary orbits; the physics of the earth and its atmosphere; and the exploration of the solar system. This course is similar to ASTR W1403. You cannot enroll in both courses and receive credit for both.

Fall 2017: ASTR BC1753 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ASTR 1753 | 001/03007 | T Th 2:40pm - 3:55pm 304 Barnard Hall |
Laura Kay | 3 | 125 |

**ASTR BC1754 Stars, Galaxies, and Cosmology.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: Recommended preparation: A working knowledge of high school algebra.

Corequisites: Suggested parallel laboratory course: ASTR C 1904y.

Examines the properties of stars, star formation, stellar evolution and nucleosynthesis, the Milky Way and other galaxies, and the cosmological origin and evolution of the universe. Students may not receive credit for both ASTR BC 1754 and ASTR C1404.

Spring 2018: ASTR BC1754 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ASTR 1754 | 001/05649 | T Th 2:40pm - 3:55pm 202 Altschul Hall |
3 | 63/120 |

**ASTR C1234 Astronomy-Physics-Geology, The Universal Timekeeper: An Introduction to Scientific Habits of Mind.** *3 points*.

**Not offered during 2017-18 academic year.**

Prerequisites: Prerequisite for ASTR C1235y is ASTR C1234x. Working knowledge of high school algebra.

Introduction to ideas and models of thought in the physical sciences, adopting as its theme the use of the atom as an imperturbable clock. Lectures develop basic physical ideas behind the structure of the atom and its nucleus and then explore such diverse applications as measuring the age of the Shroud of Turin, determining the diets of ancient civilizations, unraveling the evolution of the universe, and charting the history of earth´s climate.

**ASTR C1403 Earth, Moon, and Planets (lecture).** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: Open to any student offering astronomy in partial fulfillment of the science requirement - some sections satisfy QUA requirement. Recommended preparation: A working knowledge of high school algebra.

The overall architecture of the solar system. Motions of the celestial sphere. Time and the calendar. Life in the solar system and beyond. Students may not receive credit for both ASTR BC1753 and ASTR C1403.

**ASTR C1404 Stars, Galaxies, and Cosmology.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: Open to any student offering astronomy in partial fulfillment of the science requirement. Recommended preparation: A working knowledge of high school algebra. Professor Applegate's sections do not qualify for QUA.

Distances to, and fundamental properties of, nearby stars; nucleosynthesis and stellar evolution; novas and supernovas; galaxies; the structure of the universe and theories concerning its origin, evolution, and ultimate fate. Professor Applegate's sections do not qualify for QUA. Students may not receive credit for both ASTR BC1754 and ASTR C1404.

**ASTR C1420 Galaxies and Cosmology.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: Working knowledge of high school algebra.

The content, structure, and possible evolution of galaxies. The '21-centimeter line': the song of interstellar hydrogen. Distribution mass, seen and unseen, in galaxies and clusters of galaxies. Distribution of clusters over the sky. Quasars and the nuclei of galaxies. The origin of the universe, and the present controversy over its eventual fate.

**ASTR UN1610 Theories of the Universe: From Babylon to the Big Bang.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Milestones in the science of cosmology over the past 6000 years. Skylore and observation in ancient cultures. The twin revolutions of the Greeks: Pythagoras and Ptolemy; and Aristotle, Aquinas, and the Great Chain of Being. The "scientific revolution": the impersonal and deterministic world-order of Newton, Laplace, and Kelvin. The erosion of that world-order by mathematics and experiment in the 20th century (relativity, quantum physics, dark matter, and the expanding universe). Today's searches for a new grand order in the Universe, which can cope - or maybe not - with these blows to yesterday's comfortable wisdom.

Spring 2018: ASTR UN1610 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ASTR 1610 | 001/29812 | T Th 4:10pm - 5:25pm Room TBA |
Joseph Patterson | 3 | 90/90 |

**ASTR UN1453 Another Earth.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

This course cannot be taken for credit if BC1753 has been taken.

This course will explore the unique properties of Earth, compared to other planets in the Solar System, and the possibility of Earth-like planets around other stars. The basics of the Solar System, gravity, and light will be covered, as well as the geology and atmospheres of the terrestrial planets. The properties of Earth that allowed life to develop and whether life can develop on other planets will be discussed. Finally, the discovery of planets beyond our Solar System and the likelihood of another Earth will be a key component of the course.

Spring 2018: ASTR UN1453 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ASTR 1453 | 001/76456 | T Th 1:10pm - 2:25pm Room TBA |
David Kipping | 3 | 47/90 |

**ASTR C1836 Stars and Atoms.** *3 points*.

Prerequisites: Recommended preparation: A working knowledge of high school algebra.

Study of the life cycles of stars, from their birth in cold gas clouds to their final throes in supernova explosions. The turn-of-the-century revolution in physics: x-rays, radioactivity, the nuclear atom, and the quantum theory. Energy production by nuclear fission and fusion, and its consequences.

**ASTR C1903 Earth, Moon, and Planets Laboratory.** *1 point*.

Corequisites: ASTR BC1753 or ASTR C1403.

This laboratory is for the lecture courses ASTR BC1753x or ASTR C1403x. The lecture course must be taken concurrently.

**ASTR C1904 Astronomy Lab 2.** *1 point*.

Laboratory for *ASTR C1404*. Projects include use of telescopes, laboratory experiments in the nature of light, spectroscopy, and the analysis of astronomical data.

**ASTR C2001 Introduction to Astrophysics I.** *3 points*.

Prerequisites: A working knowledge of calculus.

Corequisites: A course in calculus-based general physics.

The first term of a two-term, calculus-based introduction to astronomy and astrophysics. Topics include the physics of stellar interiors, stellar atmospheres and spectral classifications, stellar energy generation and nucleosynthesis, supernovae, neutron stars, white dwarfs, interacting binary stars.

**ASTR C2002 Introduction to Astrophysics II.** *3 points*.

Prerequisites: A working knowledge of calculus.

Corequisites: A course in calculus-based general physics.

Continuation of ASTR C2001. These two courses constitute a full year of calculus-based introduction to astrophysics. Topics include the structure of our galaxy, the interstellar medium, star clusters, properties of external galaxies, clusters of galaxies, active galactic nuclei, cosmology.

**ASTR C2900 Frontiers of Astrophysics Research.** *3 points*.

Grading is Pass/Fail.

Several members of the faculty will each offer a brief series of talks providing context for a current research topic in the field and will then present recent results of their ongoing research. Opportunities for future student research collaboration will be offered.

**ASTR C3101 Modern Stellar Astrophysics II.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: one year of calculus-based general physics.

Introductory astronomy is not required, but some exposure to astronomy is preferable. In the first half of the course, we will examine the physics of stellar interiors in detail, leading us to develop models of stellar structure and consider how stars evolve. In the second half of the course, we will discuss special topics, such as pre-main sequence evolution, the late stages of stellar evolution, and supernovae and compact objects.

**ASTR C3102 Planetary Dynamics.** *3 points*.

Planets and planetary dynamics, detecting extrasolar systems, characteristics of extrasolar planets, astrobiology.

**ASTR C3103 The Galaxy and the Interstellar Medium.** *3 points*.

**ASTR UN3106 The Science of Space Exploration.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: one semester course in introductory astronomy or astrophysics (e.g., ASTR UN1403, ASTR UN1404, ASTR UN1420, ASTR UN1836, ASTR UN2001, ASTR UN2002, ASTR BC1753, ASTR BC1754). Ability in mathematics up to and including calculus is strongly urged.

How and why do humans explore space? Why does it require such extraordinary effort? What have we found by exploring our Solar System? We investigate the physics and biological basis of space exploration, and the technologies and science issues that determine what we can accomplish. What has been accomplished in the past, what is being explored now, and what can we expect in the future? How do space scientists explore the Solar System and answer science questions in practice? What do we know about solar systems beyond our own?

Fall 2017: ASTR UN3106 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ASTR 3106 | 001/72193 | T Th 2:40pm - 3:55pm 1332 Pupin Laboratories |
Caleb Scharf | 3 | 18/20 |

**ASTR C3273 High Energy Astrophysics.** *3 points*.

Prerequisites: One year of calculus-based general physics. Physics majors could take this course with no previous astronomy background.

**ASTR C3601 General Relativity, Black Holes, and Cosmology.** *3 points*.

Prerequisites: One year of calculus-based general physics.

Introduction to general relativity, Einstein’s geometrical theory of gravity. Topics include special relativity, tensor calculus, the Einstein field equations, the Friedmann equations and cosmology, black holes, gravitational lenses and mirages, gravitational radiation, and black hole evaporation.

**ASTR C3602 Physical Cosmology and Extragalactic Astronomy.** *3 points*.

**Not offered during 2017-18 academic year.**

Prerequisites: One year of calculus-based general physics.

The standard hot big bang cosmological model and other modern observational results that test it. Topics include the Friedmann equations, the standard model of particle Physics, the age of the universe, primordial nucleosynthesis, the cosmic microwave background, the extragalactic distance scale, and modern observations.

**ASTR C3646 Observational Astronomy.** *3 points*.

Introduction to the basic techniques used in obtaining and analyzing astronomical data. Focus on 'ground-based' methods at optical, infrared, and radio wavelengths. Regular use of the telescope facilities atop the roof of the Pupin Labs and at Harriman Observatory. The radio-astronomy portion consists mostly of computer labs, In research projects, students also work on the analysis of data obtained at National Observatories.

**ASTR C3985 Statistics and the Universe (Seminar).** *3 points*.

Prerequisites: First year calculus required, introductory physics or astronomy

Essential statistical methods will be applied in a series of case studies and reseach projects taken from the latest advances in cosmology, astronomy and physics. Statistics of measurement and detection, fundamentals of hypothesis testing, classifications, data modeling, time-series analysis, correlation and clustering will be explored through hands-on investigation using data from recent experiments and surveys

**ASTR UN3996 Current Research in Astrophysics.** *1 point*.

Prerequisites: two semesters of astronomy classes and two semesters of physics classes.

The goal of this course is to introduce astronomy and astrophysics majors to the methods and topics of current astronomical research. The course will also help with the development of critical thinking skills. Each week, the topic of the course will be centered on the subject of the Astronomy department colloquium; this may include research on planets, stars, galaxies or cosmology. There will be two required meetings per week: the first will be to discuss papers related to the colloquium (time TBD), and the second will be the colloquium itself (at 4:15 pm each Wednesday). Grading is Pass/Fail.

Fall 2017: ASTR UN3996 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ASTR 3996 | 001/76323 | F 10:10am - 11:25am 1402 Pupin Laboratories |
Mary Putman | 1 | 4/20 |

## Physics Courses

**PHYS C1001 Physics for Poets.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).**Not offered during 2017-18 academic year.**

Prerequisites: No previous background in physics is expected; high school algebra is required.

Introduction to physics with emphasis on quantum phenomena, relativity, and models of the atom and its nucleus. Offered in Spring 2011 only.

**PHYS C1002 Physics for Poets.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement, BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).**Not offered during 2017-18 academic year.**

Prerequisites: No previous background in physics is expected; high school algebra is required.

Introduction to physics with emphasis on quantum phenomena, relativity, and models of the atom and its nucleus.

**PHYS V1201 General Physics I.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: This course will use elementary concepts from calculus. Students should therefore have had some high school calculus, or be concurrently enrolled in MATH V1101.

Corequisites: Taken with accompanying lab PHYS V1291-V1292, the sequence PHYS V1201-C1202 satisfies requirements for medical school.

Mechanics, fluids, thermodynamics.

**PHYS V1202 General Physics II.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: This couse will use elementary concepts from calculus. Students should therefore have had some high school calculus, or be cuncurrently enrolled in MATH V1101.

Corequisites: Taken with accompanying lab PHYS V1291-2, the sequence PHYS V1201-2 satisfies requirements for medical school.

Electricity, magnetism, optics, and modern physics.

**PHYS C1291 General Physics I Laboratory.** *1 point*.

Corequisites: Laboratory to accompany PHYS V1201-2, PHYS V1301-2, or PHYS V1001-2.

**PHYS C1292 General Physics II Laboratory.** *1 point*.

Prerequisites: Laboratory to accompany V1201-2, V1301-2, or V1001-2.

**PHYS C1401 Introduction to Mechanics and Thermodynamics.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Corequisites: MATH V1101 or MATH V1105, or the equivalent.

Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, temperature and heat, gas laws, the first and second laws of thermodynamics.

**PHYS C1402 Introduction to Electricity, Magnetism, and Optics.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Lab Required

Prerequisites: PHYS C1401, or the equivalent.

Corequisites: MATH V1102 or V1106, or the equivalent.

Electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves, polarization, geometical optics, interference, and diffraction.

**PHYS V1900 Seminar in Contemporary Physics and Astronomy.** *1 point*.

Prerequisites: (or corequisite) Any 1000-level course in the Physics or Astronomy departments. This course may be repeated for credit only with the instructor's permission.

Lectures on current areas of research with discussions of motivation, techniques, and results, as well as difficulties and unsolved problems. Each student submits a written report on one field of active research.

**PHYS BC2001 Physics I: Mechanics.** *4.5 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Lab Required

Corequisites: Calculus I or the equivalent.

Fundamental laws of mechanics. Kinematics, Newton's laws, work and energy, conservation laws, collisions, rotational motion, oscillations, gravitation.

Fall 2017: PHYS BC2001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 2001 | 001/01611 | T Th 10:10am - 11:25am Ll104 Diana Center |
Reshmi Mukherjee | 4.5 | 48 |

PHYS 2001 | 002/09888 | T Th 10:10am - 11:25am 903 Altschul Hall |
Reshmi Mukherjee | 4.5 | 6 |

PHYS 2001 | 003/01333 | |
Stiliana Savin | 4.5 | 0 |

PHYS 2001 | 004/04444 | T Th 10:10am - 11:25am 530 Altschul Hall |
Stiliana Savin | 4.5 | 40 |

PHYS 2001 | 005/04667 | T Th 10:10am - 11:25am 530 Altschul Hall |
Stiliana Savin | 4.5 | 2 |

**PHYS BC2002 Physics II: Electricity and Magnetism.** *4.5 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Lab Required

Prerequisites: Physics BC2001 or the equivalent.

Corequisites: Calculus II.

Charge, electric field, and potential. Gauss's law. Circuits: capacitors and resistors. Magnetism and electromagnetism. Induction and inductance. Alternating currents. Maxwell's equations.

Spring 2018: PHYS BC2002 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 2002 | 001/07410 | T Th 10:10am - 11:25am 328 Milbank Hall |
Janna Levin | 4.5 | 68 |

PHYS 2002 | 002/08240 | T Th 10:10am - 11:25am 328 Milbank Hall |
Janna Levin | 4.5 | 5 |

PHYS 2002 | 003/01696 | |
Stiliana Savin | 4.5 | 8 |

**PHYS C2801 General Physics.** *4 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Recitation Section Required

Prerequisites: Advanced placement in mathematics or some knowledge of differential and integral calculus and permission of the departmental representative. (A special placement meeting is held during Orientation Week.)

Mechanics, heat, electricity, magnetism, and light.

**PHYS C2802 General Physics.** *4 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Recitation Section Required

Prerequisites: Advanced placement in mathematics or some knowledge of differential and integral calculus and permission of the departmental representative. (A special placement meeting is held during Orientation week.)

Mechanics, heat, electricity, magnetism, and light.

**PHYS BC3001 Physics III: Classical Waves & Optics.** *5 points*.

Prerequisites: Physics BC2002 or the equivalent.

Corequisites: Calculus III.

Nonlinear pendula, transverse vibrations-elastic strings, longitudinal sound waves, seismic waves, electromagnetic oscillations & light, rainbows, haloes, the Green Flash; polarization phenomena - Haidinger's Brush, Brewster's angle, double refraction, optical activity; gravity & capillary waves; interference, diffraction, lenses & mirrors.

Fall 2017: PHYS BC3001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3001 | 001/01361 | T Th 10:00am - 11:30am 510c Altschul Hall |
Timothy Halpin-Healy | 5 | 16 |

PHYS 3001 | 001/01361 | W 4:10pm - 8:00pm 510c Altschul Hall |
Timothy Halpin-Healy | 5 | 16 |

PHYS 3001 | 002/08802 | T Th 10:00am - 11:30am 510c Altschul Hall |
Timothy Halpin-Healy | 5 | 1 |

PHYS 3001 | 003/06186 | W 4:10pm - 8:00pm 510c Altschul Hall |
Timothy Halpin-Healy | 5 | 0 |

**PHYS UN3003 Mechanics.** *3 points*.

Prerequisites: general physics, and differential and integral calculus.

Newtonian mechanics, oscillations and resonance, conservative forces and potential energy, central forces, non-inertial frames of reference, rigid body motion, an introduction to Lagrange's formulation of mechanics, coupled oscillators, and normal modes.

Spring 2018: PHYS UN3003 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3003 | 001/77594 | M W 10:10am - 11:25am Room TBA |
John Parsons | 3 | 48/70 |

**PHYS BC3006 Quantum Physics.** *3 points*.

Prerequisites: BC3001 or C2601 or the equivalent.

Wave-particle duality and the Uncertainty Principle. The Schrodinger equation. Basic principles of the quantum theory. Energy levels in one-dimensional potential wells. The harmonic oscillator, photons, and phonons. Reflection and transmission by one-dimensional potential barriers. Applications to atomic, molecular, and nuclear physics.

Spring 2018: PHYS BC3006 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3006 | 001/07993 | T Th 10:10am - 11:25am 514 Altschul Hall |
Reshmi Mukherjee | 3 | 25 |

**PHYS UN3007 Electricity and Magnetism.** *3 points*.

Prerequisites: general physics, and differential and integral calculus.

Electrostatics and magnetostatics, Laplace's equation and boundary-value problems, multipole expansions, dielectric and magnetic materials, Faraday's law, AC circuits, Maxwell's equations, Lorentz covariance, and special relativity.

Fall 2017: PHYS UN3007 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3007 | 001/71505 | M W 11:40am - 12:55pm 329 Pupin Laboratories |
Abhay Pasupathy | 3 | 57/100 |

**PHYS UN3008 Electromagnetic Waves and Optics.** *3 points*.

Prerequisites: *PHYS W3007*.

Maxwell's equations and electromagnetic potentials, the wave equation, propagation of plane waves, reflection and refraction, geometrical optics, transmission lines, wave guides, resonant cavities, radiation, interference of waves, and diffraction.

Spring 2018: PHYS UN3008 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3008 | 001/22505 | M W 2:40pm - 3:55pm Room TBA |
Yury Levin | 3 | 49/70 |

**PHYS BC3082 Advanced Physics Laboratory.** *1.5 point*.

Barnard College physics laboratory has available a variety of experiments meant to complement 3000-level lecture courses. Each experiment requires substantial preparation, as well as written and oral presentations. Elementary particle experiments: detectors, cosmic ray triggers, muon lifetime.

**PHYS UN3083 Electronics Laboratory.** *3 points*.

Enrollment limited to the capacity of the laboratory.

Prerequisites: *PHYS W3003* or *W3007*. May be taken before or concurrently with this course.

A sequence of experiments in solid-state electronics, with introductory lectures.

Spring 2018: PHYS UN3083 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3083 | 001/24611 | M W 1:10pm - 4:00pm Room TBA |
John Parsons | 3 | 12/12 |

**PHYS BC3086 Quantum Physics Laboratory.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Experiments illustrating phenomenological aspects of the early quantum theory: (i) Hydrogenic Spectra: Balmer Series & Bohr-Sommerfeld Model; (ii) Photoelectric Effect: Millikan's Determination of h/e; (iii) Franck-Hertz Experiment; and (iv) Electron Diffraction Phenomena. Substantial preparation required, including written and oral presentations, as well as an interest in developing the knack and intuition of an experimental physicist. This course is best taken concurrently with PHYS BC3006 *Quantum Physics*.

Spring 2018: PHYS BC3086 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3086 | 001/03377 | F 9:00am - 10:00am 510b Altschul Hall |
Reshmi Mukherjee | 3 | 15 |

**PHYS BC3088 Advanced Electromagnetism Laboratory.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Classical electromagnetic wave phenomena via Maxwell's equations, including: (i) Michaelson and Fabry-Perot Interferometry, as well as a thin-film interference and elementary dispersion theory; (ii) Fraunhofer Diffraction (and a bit of Fresnel); (iii) Wireless Telegraphy I: AM Radio Receivers; and (iv) Wireless Telegraphy II: AM Transmitters. Last two labs pay homage to relevant scientific developments in the period 1875-1925, from the discovery of Hertzian waves to the Golden Age of Radio. Complements PHYS W3008 *Electromagnetic Waves and Optics*.

Fall 2017: PHYS BC3088 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3088 | 001/01858 | F 10:30am - 12:00pm 510b Altschul Hall |
Stiliana Savin | 3 | 8 |

**PHYS BC3900 Supervised Individual Research.** *1-5 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

1-5 points per term.

Prerequisites: Permission of the departmental representative required.

For specially selected students, the opportunity to do a research problem in contemporary physics under the supervision of a faculty member. Each year several juniors are chosen in the spring to carry out such a project beginning in the autumn term. A detailed report on the research is presented by the student when the project is complete.

Fall 2017: PHYS BC3900 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3900 | 001/08319 | |
Reshmi Mukherjee | 1-5 | 0 |

Spring 2018: PHYS BC3900 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

PHYS 3900 | 001/04925 | |
Reshmi Mukherjee | 1-5 | 1 |

**PHYS G4003 Advanced Mechanics.** *3 points*.

Lagrange’s formulation of mechanics, calculus of variations, the Action Principle, Hamilton’s formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics

**PHYS G4021 Quantum Mechanics.** *3 points*.

The formulation of quantum mechanics in terms of state vectors and linear operators, three dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, identical particles

**PHYS GU4022 Quantum Mechanics II.** *3 points*.

Prerequisites:PHYS UN4021.Formulation of quantum mechanics in terms of state vectors and linear operators, three-dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, and identical particles.Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models.

Spring 2018: PHYS GU4022 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 4022 | 001/75555 | T Th 11:40am - 12:55pm Room TBA |
Emlyn Hughes | 3 | 25/60 |

**PHYS G4023 Thermal and Statistical Physics.** *3 points*.

Pre or co-requisite: G4021. Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism

## Cross-Listed Courses

### Physics

**PHYS W3002 From Quarks To the Cosmos: Applications of Modern Physics.** *3.5 points*.

**Not offered during 2017-18 academic year.**

Prerequisites: W2601 or W2802

This course reinforces basic ideas of modern physics through applications to nuclear physics, high energy physics, astrophysics and cosmology. The ongoing Columbia research programs in these fields are used as practical examples. The course is preparatory for advanced work in physics and related fields.