**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 UN2001 - ASTR UN2002 | Introduction To Astrophysics, I and INTRO TO ASTROPHYSICS II | 6 |

Students are required to take four additional 3000-level ASTR or PHYS courses, including at least one of ASTR UN3102 or PHYS UN3003, 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: | ||

ASTR UN3101 | Modern Stellar Astrophysics II | 3 |

ASTR UN3103 | GALAXIES | 3 |

ASTR UN3105 | Extrasolar Planets and Astrobiology | 3 |

ASTR UN3601 | 3 | |

ASTR UN3602 | Physical Cosmology and Extragalactic Astronomy | 3 |

ASTR UN3273 | High Energy Astrophysics | 3 |

ASTR UN3646 | Observational Astronomy | 3 |

* | 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 UN1403 Earth, Moon and Planets (Lecture)-ASTR UN1404 STARS, GALAXIES ＆ COSMOLOGY may substitute an additional 3000-level ASTR course for ASTR UN2001 Introduction To Astrophysics, I-ASTR UN2002 INTRO 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 GU4023 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 GU4023 | 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 UN2801 Accelerated Physics I-PHYS UN2802 Accelerated Physics II 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.

## 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 pts of physics at the 3000 level or above can substitute for 3 points of astronomy.

## Astronomy Courses

**ASTR BC1753 LIFE IN THE UNIVERSE.** *3.00 points*.

An introductory course intended primarily for nonscience majors. This interdisciplinary course focuses on the subject of LIfe in the Universe. We will study historical astronomy, gravitation and planetary orbits, the origin of the chemical elements, the discoveries of extrasolar planets, the origin of life on Earth, the evolution and exploration of the Solar Systen, global climate change on Venus, Mars and Earth, and the Search for Extraterrestrial Life (SETI). You cannot receive credit for this course and for ASTR UN1403 or ASTR UN1453. Can be paired with the optional Lab class ASTR UN1903

**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 2021: ASTR BC1754 |
|||||

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

ASTR 1754 | 001/00484 | M W 10:10am - 11:25am 903 Altschul Hall |
David Helfand | 3 | 55 |

**ASTR UN1234 The Universal Timekeeper: Reconstructing History Atom by Atom.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: high school algebra and latent curiosity are assumed.

The goal of the course is to illustrate — and perhaps even inculcate — quantitative and scientific reasoning skills. The subject material employed in this task is the study of atoms and their nuclei which, through a wide variety of physical and chemical techniques, can be used to reconstruct quantitatively the past. Following an introduction to atoms, light, and energy, we will explore topics including the detection of art forgeries, the precise dating of archeological sites, a reconstruction of the development of agriculture and the history of the human diet, the history of past climate (and its implications for the future), the history and age of the Earth, and the history of the Universe. The course has no required text. Readings of relevant articles and use of on-line simulations will be required.

**ASTR UN1403 Earth, Moon and Planets (Lecture).** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: 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. Major planets, the earth-moon system, minor planets, comets. Life in the solar system and beyond. This course is similar to ASTR BC 1753. You cannot enroll in both courses and receive credit for both.

Spring 2021: ASTR UN1403 |
|||||

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

ASTR 1403 | 001/11739 | T Th 1:10pm - 2:25pm Online Only |
James Applegate | 3 | 68/75 |

Fall 2021: ASTR UN1403 |
|||||

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

ASTR 1403 | 001/12831 | T Th 10:10am - 11:25am Room TBA |
David Helfand | 3 | 82/75 |

**ASTR UN1404 STARS, GALAXIES ＆ COSMOLOGY.** *3.00 points*.

CC/GS: Partial Fulfillment of Science Requirement

Distances to, and fundamental properties of, nearby stars; nucleosynthesis and stellar evolution; novae and supernovae; galaxies; the structure of the universe and theories concerning its origin, evolution, and ultimate fate. You can only receive credit for ASTR UN1404 if you have not taken ASTR BC1754, ASTR UN1420 or ASTR UN1836

Fall 2021: ASTR UN1404 |
|||||

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

ASTR 1404 | 001/12832 | T Th 1:10pm - 2:25pm Online Only |
James Applegate | 3.00 | 50/75 |

**ASTR UN1420 Galaxies and Cosmology.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Galaxies contain stars, gas dust, and (usually) super-massive black holes. They are found throughout the Universe, traveling through space and occasionally crashing into each other. This course will look at how these magnificent systems form and evolve, and what they can tell us about the formation and evolution of the Universe itself. You cannot enroll in ASTR UN1420 in addition to ASTR BC1754 or ASTR UN1404 and receive credit for both.

**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 2021: ASTR UN1453 |
|||||

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

ASTR 1453 | 001/11740 | M W 2:40pm - 3:55pm Online Only |
Mary Putman | 3 | 68/75 |

Fall 2021: ASTR UN1453 |
|||||

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

ASTR 1453 | 001/12833 | T Th 1:10pm - 2:25pm Room TBA |
Caleb Scharf | 3 | 75/75 |

**ASTR UN1610 THEOR-UNIVERS:BABYLON-BIG BANG.** *3.00 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). Todays searches for a new grand order in the Universe, which can cope - or maybe not - with these blows to yesterdays comfortable wisdom

**ASTR UN1836 Stars and Atoms.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

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

What is the origin of the chemical elements? This course addresses this question, starting from understanding atoms, and then going on to look at how how atoms make stars and how stars make atoms. The grand finale is a history of the evolution of the chemical elements throughout time, starting from the Big Bang and ending with YOU. You cannot enroll in ASTR UN1836 in addition to ASTR BC1754 or ASTR UN1404 and receive credit for both.

,What is the origin of the chemical elements? This course addresses this question, starting from understanding atoms, and then going on to look at how how atoms make stars and how stars make atoms. The grand finale is a history of the evolution of the chemical elements throughout time, starting from the Big Bang and ending with YOU. You cannot enroll in ASTR W1836 in addition to ASTR BC1754 or ASTR W1404 and receive credit for both.

Spring 2021: ASTR UN1836 |
|||||

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

ASTR 1836 | 001/11741 | M W 1:10pm - 2:25pm Online Only |
Marcel Agueros | 3 | 34/40 |

Fall 2021: ASTR UN1836 |
|||||

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

ASTR 1836 | 001/12834 | M W 1:10pm - 2:25pm Room TBA |
Kathryn Johnston | 3 | 58/75 |

**ASTR UN1903 ASTRONOMY LAB I.** *1.00 point*.

Laboratory for ASTR UN1403. Projects include observations with the departments telescopes, computer simulation, laboratory experiments in spectroscopy, and the analysis of astronomical data. Lab 1 ASTR UN1903 - goes with ASTR BC1753, ASTR UN1403 or ASTR UN1453

Spring 2021: ASTR UN1903 |
|||||

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

ASTR 1903 | 001/12738 | T 6:00pm - 9:00pm Online Only |
David Schiminovich, Yuxi Lu | 1.00 | 9/12 |

ASTR 1903 | 002/12739 | M 6:00pm - 9:00pm Online Only |
David Schiminovich, Christopher Carr | 1.00 | 7/12 |

Fall 2021: ASTR UN1903 |
|||||

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

ASTR 1903 | 001/00150 | M 6:00pm - 9:00pm Room TBA |
Laura Kay | 1.00 | 12/12 |

ASTR 1903 | 002/00151 | T 6:00pm - 9:00pm Room TBA |
Laura Kay | 1.00 | 9/12 |

**ASTR UN1904 ASTRONOMY LAB II.** *1.00 point*.

Laboratory for ASTR UN1404. Projects include use of telescopes, laboratory experiments in the nature of light, spectroscopy, and the analysis of astronomical data. Lab 2 ASTR UN1904 - goes with ASTR BC1754 or ASTR UN1404 (or ASTR UN1836 or ASTR UN1420)

Spring 2021: ASTR UN1904 |
|||||

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

ASTR 1904 | 001/12740 | W 7:00pm - 10:00pm Online Only |
David Schiminovich, Karen Perez | 1.00 | 12/14 |

Fall 2021: ASTR UN1904 |
|||||

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

ASTR 1904 | 001/00146 | W 7:00pm - 10:00pm Room TBA |
Laura Kay | 1.00 | 8/12 |

**ASTR UN2001 Introduction To Astrophysics, I.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: a working knowledge of calculus.

Corequisites: a course in calculus-based general physics.

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, and interacting binary stars.

Fall 2021: ASTR UN2001 |
|||||

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

ASTR 2001 | 001/12835 | M W 1:10pm - 2:25pm Room TBA |
Greg Bryan | 3 | 41/40 |

**ASTR UN2002 INTRO TO ASTROPHYSICS II.** *3.00 points*.

Prerequisites: a working knowledge of calculus.

Corequisites: the second term of a course in calculus-based general physics.

Prerequisites: a working knowledge of calculus. Corequisites: the second term of a course in calculus-based general physics. Continuation of ASTR UN2001; 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, and cosmology

Spring 2021: ASTR UN2002 |
|||||

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

ASTR 2002 | 001/11742 | M W 8:40am - 9:55am Online Only |
Frederik Paerels | 3.00 | 30/45 |

**ASTR UN2900 Frontiers of Astrophysics.** *1 point*.

Several members of the faculty each offer a brief series of talks providing context for a current research topic in the field and then present results of their ongoing research. Opportunities for future student research collaboration are offered. Grading is Pass/Fail.

Fall 2021: ASTR UN2900 |
|||||

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

ASTR 2900 | 001/12836 | F 10:10am - 11:25am Room TBA |
Caleb Scharf | 1 | 35/50 |

**ASTR UN3101 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 UN3102 Planetary Dynamics and Physics of the Solar System.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: one year of calculus-based Physics.

The physics and astrophysics of planets, comets, asteroids, natural and artificial satellites, and pretty much anything in the Solar System - including the Sun. Detailed study of the Earth's atmosphere and oceans: circulations, climate, and weather. Orbital dynamics. The emerging science of extrasolar planets. The origin, evolution, and eventual fate of planets.

**ASTR UN3103 GALAXIES.** *3.00 points*.

Prerequisites: one year of calculus-based general physics.

Prerequisites: one year of calculus-based general physics. Galaxies fill the universe with structure. They are bound objects that harbor stars, gas, dust and dark matter. This course will discuss the content and structure of galaxies. It will start with the Milky Way, a rotating spiral galaxy, with a particular emphasis on the properties of the interstellar medium. Dwarf galaxies, the building blocks of larger galaxies, will subsequently be discussed, followed by spiral, elliptical and irregular galaxies. The formation and evolution of these different galaxy types will be an important focus of the course, as well as the environment in which the galaxies reside. We will intersperse reviews of current papers on galaxies throughout the semester

Spring 2021: ASTR UN3103 |
|||||

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

ASTR 3103 | 001/11743 | T Th 1:10pm - 2:25pm 307 Pupin Laboratories |
David Schiminovich | 3.00 | 21/25 |

**ASTR UN3105 Extrasolar Planets and Astrobiology.** *3 points*.

Prerequisites: One year of calculus-based physics.

The emerging field of extrasolar planets and astrobiology will be covered at a quantitative level, with a major emphasis on astrophysical phenomenae and techniques. The subject will be introduced through an investigation of current planetary formation theories and approaches to planet detection, including what we currently know about extrasolar planets and detailed reference to state-of-the-art studies. An astronomer's view of the origin of life and extreme biology will be developed and applied to questions of cosmo-chemistry, observable life-signatures, habitable zones and other astrophysical constraints on the development of organisms.

Fall 2021: ASTR UN3105 |
|||||

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

ASTR 3105 | 001/12837 | T Th 10:10am - 11:25am Room TBA |
David Kipping | 3 | 20/20 |

**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?

**ASTR UN3273 High Energy Astrophysics.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: one year of calculus-based general physics. No previous,\nastronomy background required.

A survey of the most energetic and explosive objects in the Universe and their radiation. Topics include: techniques of X-ray and gamma-ray astronomy; observations of neutron stars (pulsars) and black holes; accretion disks and relativistic jets; supernovae, supernova remnants, gamma-ray bursts, quasars and active galactic nuclei; clusters of galaxies; cosmic rays and neutrinos.

**ASTR UN3602 Physical Cosmology and Extragalactic Astronomy.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: one year of calculus-based general physics.

The standard hot big bang cosmological model and modern observational results that test it. Topics include the Friedmann equations and the expansion of the universe, dark matter, dark energy, inflation, primordial nucleosynthesis, the cosmic microwave background, the formation of large-scale cosmic structures, and modern cosmological observations.

Fall 2021: ASTR UN3602 |
|||||

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

ASTR 3602 | 001/12838 | M W 10:10am - 11:25am Room TBA |
Zoltan Haiman | 3 | 17/25 |

**ASTR UN3646 Observational Astronomy.** *3 points*.

Prerequisites: one year of general astronomy

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. In research projects, students also work on the analysis of data obtained at National Observatories.

**ASTR UN3985 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 research 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.

**ASTR GU4302 General Relativity, Black Holes, and Cosmology.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: one year of calculus-based general physics.

Einstein's General Theory of Relativity replaced Newtonian gravity with an elegant theory of curved spacetime. Einstein's theory led to unforseen and unnerving predictions of singularities and cosmological instabilities. Nearly a century later, these mathematical oddities have been confirmed astrophysically in the existence of black holes, an expanding universe, and a big bang. The course will cover Einstein's General Theory, beginning with special relativity, with an emphasis on black holes and the big bang.

## Physics Courses

**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 2021: PHYS BC2001 |
|||||

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

PHYS 2001 | 001/00155 | T Th 10:10am - 11:25am Room TBA |
Janna Levin, Stiliana Savin | 4.5 | 27/100 |

**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 2021: PHYS BC2002 |
|||||

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

PHYS 2002 | 001/00525 | T Th 10:10am - 11:25am Room TBA |
Janna Levin | 4.5 | 35 |

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

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

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 2021: PHYS BC3001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3001 | 001/00145 | T Th 10:00am - 11:30am Room TBA |
Timothy Halpin-Healy, Margaret Kaye | 5 | 15/15 |

**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 2021: PHYS BC3006 |
|||||

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

PHYS 3006 | 001/00488 | T Th 10:10am - 11:25am 805 Altschul Hall |
Reshmi Mukherjee | 3 | 8 |

PHYS 3006 | 001/00488 | T Th 8:40am - 9:25am 805 Altschul Hall |
Reshmi Mukherjee | 3 | 8 |

**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 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 2021: PHYS BC3086 |
|||||

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

PHYS 3086 | 001/00489 | |
Reshmi Mukherjee | 3 | 5 |

**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*.

Spring 2021: PHYS BC3088 |
|||||

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

PHYS 3088 | 001/00596 | F 10:30am - 12:00pm Room TBA |
Stiliana Savin | 3 | 5/15 |

Fall 2021: PHYS BC3088 |
|||||

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

PHYS 3088 | 001/00148 | F 10:30am - 12:00pm Room TBA |
Stiliana Savin | 3 | 7/15 |

**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 2021: PHYS BC3900 |
|||||

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

PHYS 3900 | 001/00149 | |
Reshmi Mukherjee | 1-5 | 0 |

**PHYS UN1001 Physics for Poets.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: high school algebra.

This course does not fulfill the physics requirement for admission to medical school. No previous background in physics is expected. An introduction to physics taught through the exploration of the scientific method, and the application of physical principles to a wide range of topics from quantum mechanics to cosmology.

Spring 2021: PHYS UN1001 |
|||||

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

PHYS 1001 | 001/10222 | M W 2:40pm - 3:55pm Online Only |
Szabolcs Marka | 3 | 92/150 |

**PHYS UN1201 General Physics I.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: some basic background in calculus or be concurrently taking MATH UN1101 Calculus I.,The accompanying laboratory is PHYS UN1291-UN1292

The course will use elementary concepts from calculus. The accompanying laboratory is *PHYS UN1291 - UN1292.* Basic introduction to the study of mechanics, fluids, thermodynamics, electricity, magnetism, optics, special relativity, quantum mechanics, atomic physics, and nuclear physics.

Spring 2021: PHYS UN1201 |
|||||

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

PHYS 1201 | 001/10189 | T Th 5:40pm - 6:55pm Online Only |
P. Michael Tuts | 3 | 137/200 |

Fall 2021: PHYS UN1201 |
|||||

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

PHYS 1201 | 001/11931 | M W 10:10am - 11:25am Room TBA |
3 | 160/160 | |

PHYS 1201 | 002/11932 | T Th 5:40pm - 6:55pm Room TBA |
P. Michael Tuts | 3 | 131/160 |

**PHYS UN1202 General Physics II.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: This course will use elementary concepts from calculus. Students should therefore have had some high school calculus, or be concurrently enrolled in MATH UN1101. Taken with accompanying lab PHYS UN1291- PHYS UN1292, the sequence PHYS UN1201- PHYS UN1202 satisfies requirements for medical school.

Electricity, magnetism, optics, and modern physics.

Spring 2021: PHYS UN1202 |
|||||

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

PHYS 1202 | 001/10190 | M W 10:10am - 11:25am Online Only |
Michael Shaevitz | 3 | 146/200 |

PHYS 1202 | 002/12972 | M W 5:40pm - 6:55pm Online Only |
Eric Raymer | 3 | 112/120 |

Summer 2021: PHYS UN1202 |
|||||

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

PHYS 1202 | 002/11140 | M W 6:15pm - 7:30pm Online Only |
Rebecca Grossman | 3 | 49/70 |

**PHYS UN1291 General Physics Laboratory.** *1 point*.

Same course as *PHYS W1291x*, but given off-sequence.

Corequisites: PHYS UN1201

This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Spring 2021: PHYS UN1291 |
|||||

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

PHYS 1291 | 001/10191 | M 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 14/15 |

PHYS 1291 | 002/10192 | M 4:10pm - 7:10pm Online Only |
Giuseppina Cambareri | 1 | 11/15 |

PHYS 1291 | 003/10193 | T 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 14/15 |

PHYS 1291 | 004/10194 | T 7:30pm - 10:30pm Online Only |
Giuseppina Cambareri | 1 | 10/15 |

PHYS 1291 | 005/10195 | W 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 10/15 |

PHYS 1291 | 006/10196 | W 4:10pm - 7:10pm Online Only |
Giuseppina Cambareri | 1 | 10/15 |

PHYS 1291 | 007/10197 | Th 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 11/15 |

PHYS 1291 | 008/10198 | M 7:30pm - 10:30pm Online Only |
Giuseppina Cambareri | 1 | 7/15 |

PHYS 1291 | 010/18017 | F 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

Fall 2021: PHYS UN1291 |
|||||

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

PHYS 1291 | 001/11977 | M 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 002/11978 | M 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 003/11979 | M 4:10pm - 7:10pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 004/11980 | M 4:10pm - 7:10pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 005/11981 | M 7:30pm - 10:30pm Room TBA |
Giuseppina Cambareri | 1 | 9/15 |

PHYS 1291 | 007/11982 | T 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 008/11983 | T 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 009/11984 | T 4:10pm - 7:10pm Room TBA |
Giuseppina Cambareri | 1 | 6/15 |

PHYS 1291 | 010/11985 | T 4:10pm - 7:10pm Room TBA |
Giuseppina Cambareri | 1 | 0/15 |

PHYS 1291 | 011/11986 | T 7:30pm - 10:30pm Room TBA |
Giuseppina Cambareri | 1 | 9/15 |

PHYS 1291 | 013/11988 | W 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 014/11989 | W 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 015/11990 | W 4:10pm - 7:10pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 016/11991 | W 4:10pm - 7:10pm Room TBA |
Giuseppina Cambareri | 1 | 7/15 |

PHYS 1291 | 017/11992 | W 7:30pm - 10:30pm Room TBA |
Giuseppina Cambareri | 1 | 2/15 |

PHYS 1291 | 019/11993 | Th 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 020/11994 | Th 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 021/11995 | Th 4:10pm - 7:10pm Room TBA |
Giuseppina Cambareri | 1 | 11/15 |

PHYS 1291 | 022/11996 | Th 4:10pm - 7:10pm Room TBA |
Giuseppina Cambareri | 1 | 1/15 |

PHYS 1291 | 023/11997 | Th 7:30pm - 10:30pm Room TBA |
Giuseppina Cambareri | 1 | 9/15 |

PHYS 1291 | 025/11998 | F 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1291 | 026/12000 | F 1:00pm - 4:00pm Room TBA |
Giuseppina Cambareri | 1 | 14/15 |

**PHYS UN1292 General Physics Laboratory II.** *1 point*.

Corequisites: PHYS UN1201,PHYS UN1202

This course is the laboratory for the corequisite lecture course (*PHYS UN**1201 - PHYS UN1202*) and can be taken only during the same term as the corresponding lecture.

Spring 2021: PHYS UN1292 |
|||||

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

PHYS 1292 | 001/10199 | M 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1292 | 002/16491 | M 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1292 | 007/10202 | T 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 008/16493 | T 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 009/10203 | T 4:10pm - 7:10pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 010/16494 | T 4:10pm - 7:10pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 011/10204 | T 7:30pm - 10:30pm Online Only |
Giuseppina Cambareri | 1 | 14/15 |

PHYS 1292 | 013/10205 | W 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 14/15 |

PHYS 1292 | 014/16495 | W 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 015/10206 | W 4:10pm - 7:10pm Online Only |
Giuseppina Cambareri | 1 | 15/15 |

PHYS 1292 | 017/10207 | W 7:30pm - 10:30pm Online Only |
Giuseppina Cambareri | 1 | 12/15 |

PHYS 1292 | 018/10208 | Th 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 14/15 |

PHYS 1292 | 019/16497 | Th 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 020/10209 | Th 4:10pm - 7:10pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 022/10210 | Th 7:30pm - 10:30pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 023/10211 | F 1:00pm - 4:00pm Online Only |
Giuseppina Cambareri | 1 | 12/15 |

Summer 2021: PHYS UN1292 |
|||||

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

PHYS 1292 | 001/10291 | M 1:00pm - 4:10pm Online Only |
Giuseppina Cambareri | 1 | 6/15 |

PHYS 1292 | 002/11142 | T 1:00pm - 4:10pm Online Only |
Giuseppina Cambareri | 1 | 14/15 |

PHYS 1292 | 003/11143 | W 1:00pm - 4:10pm Online Only |
Giuseppina Cambareri | 1 | 13/15 |

PHYS 1292 | 004/11144 | Th 1:00pm - 4:10pm Online Only |
Giuseppina Cambareri | 1 | 15/15 |

**PHYS UN1401 Introduction To Mechanics and Thermodynamics.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Corequisites: MATH UN1101

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. Corequisite: MATH UN1101 or the equivalent.

Spring 2021: PHYS UN1401 |
|||||

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

PHYS 1401 | 001/10213 | T Th 10:10am - 11:25am Online Only |
Emlyn Hughes | 3 | 82/200 |

Fall 2021: PHYS UN1401 |
|||||

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

PHYS 1401 | 001/11935 | M W 1:10pm - 2:25pm Room TBA |
Jeremy Dodd | 3 | 29/160 |

PHYS 1401 | 002/11937 | T Th 10:10am - 11:25am Room TBA |
Tanya Zelevinsky | 3 | 11/160 |

**PHYS UN1402 INTRO ELEC/MAGNETSM ＆ OPTCS.** *3.00 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: PHYS UN1401

Corequisites: MATH UN1102

Prerequisites: PHYS W1401. Corequisites: MATH V1102 or the equivalent. Electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves, polarization, geometrical optics, interference, and diffraction

Spring 2021: PHYS UN1402 |
|||||

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

PHYS 1402 | 001/10212 | T Th 10:10am - 11:25am Online Only |
Georgia Karagiorgi | 3.00 | 188/200 |

**PHYS UN2801 Accelerated Physics I.** *4.5 points*.

Prerequisites: Advanced Placement in physics and mathematics, or the equivalent, and the instructor's permission. (A special placement meeting is held during Orientation.)

This accelerated two-semester sequence covers the subject matter of *PHYS UN1601*, *PHYS UN1602* and *PHYS UN2601*, and is intended for those students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, *PHYS UN3081*, in the following year.

Fall 2021: PHYS UN2801 |
|||||

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

PHYS 2801 | 001/11941 | T Th 10:10am - 12:00pm Room TBA |
Norman Christ | 4.5 | 3/100 |

**PHYS UN2802 Accelerated Physics II.** *4.5 points*.

Prerequisites: PHYS UN2801

This accelerated two-semester sequence covers the subject matter of *PHYS UN1601*, *PHYS UN1602* and *PHYS UN2601*, and is intended for those students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, *PHYS UN3081*, in the following year.

Spring 2021: PHYS UN2802 |
|||||

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

PHYS 2802 | 001/10225 | T Th 10:10am - 12:00pm Online Only |
Norman Christ | 4.5 | 32/70 |

**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 2021: PHYS UN3003 |
|||||

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

PHYS 3003 | 001/10226 | M W 10:10am - 11:25am Online Only |
John Parsons | 3 | 48/70 |

**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 2021: PHYS UN3007 |
|||||

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

PHYS 3007 | 001/11942 | M W 11:40am - 12:55pm Room TBA |
Alfred Mueller, Giuseppina Cambareri | 3 | 40/100 |

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

Prerequisites: PHYS UN3008

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 2021: PHYS UN3008 |
|||||

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

PHYS 3008 | 001/10227 | M W 11:40am - 12:55pm 428 Pupin Laboratories |
Alfred Mueller, Giuseppina Cambareri | 3 | 55/70 |

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

Enrollment limited to the capacity of the laboratory.

Prerequisites: PHYS UN3003 or PHYS UN3007 May be taken before or concurrently with this course.

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

Spring 2021: PHYS UN3083 |
|||||

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

PHYS 3083 | 001/10232 | M W 1:10pm - 4:00pm 329 Pupin Laboratories |
John Parsons | 3 | 7/12 |

**PHYS GU4003 Advanced Mechanics.** *3 points*.

Prerequisites: differential and integral calculus, differential equations, and PHYS UN3003 or the equivalent.

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

Spring 2021: PHYS GU4003 |
|||||

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

PHYS 4003 | 001/10235 | M W 4:10pm - 5:25pm Online Only |
James Hill | 3 | 24/45 |

**PHYS GU4021 Quantum Mechanics I.** *3 points*.

Prerequisites: PHYS UN3003 and PHYS UN3007

Formulation of quantum mechanics in terms of state vectors and linear operators. Three dimensional spherically symmetric potentials. The theory of angular momentum and spin. Identical particles and the exclusion principle. Methods of approximation. Multi-electron atoms.

Fall 2021: PHYS GU4021 |
|||||

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

PHYS 4021 | 001/11949 | T Th 11:40am - 12:55pm Room TBA |
William Zajc | 3 | 42/100 |

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

Prerequisites: PHYS GU4021. 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 2021: PHYS GU4022 |
|||||

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

PHYS 4022 | 001/10237 | T Th 11:40am - 12:55pm 329 Pupin Laboratories |
William Zajc | 3 | 28/60 |

**PHYS GU4023 Thermal and Statistical Physics.** *3 points*.

Prerequisites: PHYS GU4021 or the equivalent.

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.

Fall 2021: PHYS GU4023 |
|||||

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

PHYS 4023 | 001/11950 | T Th 1:10pm - 2:25pm Room TBA |
Andrew Millis | 3 | 23/100 |

## Cross-Listed Courses

### Physics

**PHYS UN3002 From Quarks To the Cosmos: Applications of Modern Physics.** *3.5 points*.

**Not offered during 2021-22 academic year.**

Prerequisites: PHYS UN2601 or PHYS UN2802

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.