Astronomy

The Department of Astronomy offers courses on cosmology, the universe, astrophysics, and astronomy.

For questions about specific courses, contact the department:

Departmental Office: 1328 Pupin
212-854-3278
Office Hours: Monday–Friday, 9:00 a.m.–5:00 p.m.

Web: www.astro.columbia.edu/


Directory of Classes

The course information displayed on this page relies on an external system and may be incomplete. Please visit Astronomy on the Directory of Classes for complete course information for:
Fall 2016
Spring 2017

After finding your course in the Directory of Classes, click on the section number to open an expanded view. The "Open To" field will indicate whether the course is open to School of Professional Studies students. If School of Professional Studies is not included in the field, students may still be able to cross-register for the course by obtaining permission after being admitted to an academic program.


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
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1753 001/03007 T Th 2:40pm - 3:55pm
Room TBA
Laura Kay 3 52

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 2017: ASTR BC1754
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1754 001/05649 T Th 2:40pm - 3:55pm
202 Altschul Hall
Laura Kay 3 89/125

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 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 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 C3997 Independent Research. 3 points.

Variety of research projects conducted under the supervision of members of the faculty. Observational, theoretical, and experimental work in galactic and extragalactic astronomy and cosmology. The topic and scope of the work must be arranged with a faculty member in advance: a written paper describing the results of the project will be required at its completion. (A two semester project can be designed so that the grade YC is given after the first term.) Senior majors in Astronomy or Astrophysics wishing to do a Senior Thesis should make arrangements in May of their junior year and sign up for a total of 6 points over their final two semesters. Both a substantial written document and an oral presentation of thesis results will be required.

ASTR C3998 Independent Research. 3 points.

Variety of research projects conducted under the supervision of members of the faculty. Observational, theoretical, and experimental work in galactic and extragalactic astronomy and cosmology. The topic and scope of the work must be arranged with a faculty member in advance: a written paper describing the results of the project will be required at its completion. (A two semester project can be designed so that the grade YC is given after the first term.) Senior majors in Astronomy or Astrophysics wishing to do a Senior Thesis should make arrangements in May of their junior year and sign up for a total of 6 points over their final two semesters. Both a substantial written document and an oral presentation of thesis results will be required.

ASTR G6002 Physics of The Interstellar Medium and Intergalactic Medium. 3 points.

Not offered during 2017-18 academic year.

A survey of diffuse matter in the universe with emphasis on astrophysical processes and their observational consequences. Topics include radiative transfer, dust, ionization, thermal balance, magnetic fields, hydrodynamics, shocks and star formaion in the context of gaseous nebulae and the multi-phase ISM, ICM and IGM.

ASTR G6004 Stellar Structure and Evolution. 3 points.

Topics include the physics of stellar structure, stellar atmospheres, radiation transport, nucleosynthesis, stellar evolution, star formation, pulsation, interacting binary stars, white dwarfs, and neutron stars.

ASTR G6005 Physical Cosmology. 3 points.

Not offered during 2017-18 academic year.

Topics include the extragalactic distance scale, Friedmann models, the microwave background, primordial nucleosynthesis, the formation of bound structures, clusters and superclusters of galaxies, measures of the mean density of the university, dark matter, baryosynthesis, inflation, galaxy formation, the particle physics connection.

ASTR G8001 Observational Astronomy. 3 points.

Not offered during 2017-18 academic year.

Prerequisites: one year of general astronomy.

Detailed introduction to the instrumentation used in astronomy and the methods used to obtain and analyze data. Six main topics are included: the effects of the earth's atmosphere on radiation; astronomical optics and telescopes; detectors; observational methods; data reduction; and statistical methods. All the main observational methods (imaging, photometry, polarimetry, and spectroscopy) are treated.

ASTR GR6001 Radiative Processes. 3 points.

Not offered during 2017-18 academic year.

Prerequisites: 3000-level electromagnetic theory and quantum mechanics.

Radiation mechanisms and interaction of radiation with matter. Applications of classical and semiclassical radiation theory and atomic physics to astrophysical settings. Radiative transfer, polarization, scattering, line radiation, special relativity, bremsstrahlung, synchrotron radiation, inverse compton scattering, ionization losses, shocks and particle acceleration, plasma processes, atomic structure and spectroscopic terms, radiative transitions and oscillator strengths, curve of growth, molecular spectra.

Fall 2017: ASTR GR6001
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 6001 001/72957 M W 10:10am - 11:25am
Room TBA
Jules Halpern 3 1/20

ASTR GR6003 Stellar and Galactic Dynamics. 3 points.

The theory and observations of stellar and galactic dynamics, with emphasis on study of the formation and evolution of galactic structure and the distribution of dark matter.

Spring 2017: ASTR GR6003
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 6003 001/71377 M W 2:40pm - 3:55pm
1332 Pupin Laboratories
Jacqueline van Gorkom, Kathryn Johnston 3 9/20

ASTR GR8003 Astrophysical fluid Dynamics (Lecture). 3 points.

Not offered during 2017-18 academic year.

An introduction to the fundamental concepts of fluid dynamics with focus on standad applications of the theory to a variety of important astrophysical situations and objects. A brief introduction to several key numberical concepts. A brief description of the complications that arise when a fluid is magnetized.

Fall 2017: ASTR GR8003
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 8003 001/18153 T Th 10:10am - 11:25am
Room TBA
Lorenzo Sironi 3 1/20

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 2017: ASTR UN1403
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1403 001/68314 M W 1:10pm - 2:25pm
602 Hamilton Hall
Marcel Agueros 3 54/60
Fall 2017: ASTR UN1403
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1403 001/26019 M W 2:40pm - 3:55pm
Room TBA
James Applegate 3 69/75

ASTR UN1404 Stars, Galaxies and Cosmology (Lecture). 3 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 W1404 if you have not taken ASTR BC1754, ASTR W1420 or ASTR W1836.

Fall 2017: ASTR UN1404
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1404 001/70640 T Th 1:10pm - 2:25pm
Room TBA
Kathryn Johnston 3 57/75

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 2017: ASTR UN1610
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1610 001/11726 T Th 4:10pm - 5:25pm
428 Pupin Laboratories
Joseph Patterson 3 69/90

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 W1836 in addition to ASTR BC1754 or ASTR W1404 and receive credit for both.

Fall 2017: ASTR UN1836
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1836 001/60591 M W 1:10pm - 2:25pm
Room TBA
Marcel Agueros 3 19/50

ASTR UN1903 Astronomy Lab 1. 1 point.

Laboratory for ASTR W1403. Projects include observations with the department's telescopes, computer simulation, laboratory experiments in spectroscopy, and the analysis of astronomical data. Lab 1 ASTR W1903 - goes with ASTR BC1753, ASTR W1403 or ASTR W1453.

Spring 2017: ASTR UN1903
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1903 001/09238 W 7:00pm - 10:00pm
Room TBA
Laura Kay, Steven Mohammed, Zephyr Penoyre 1 7/14
Fall 2017: ASTR UN1903
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1903 001/05225 M 6:00pm - 9:00pm
Room TBA
Laura Kay 1 11/12
ASTR 1903 002/02793 M 7:00pm - 10:00pm
Room TBA
Laura Kay 1 1/12
ASTR 1903 003/01577 T 6:00pm - 9:00pm
Room TBA
Laura Kay 1 5/12
ASTR 1903 004/09273 T 7:00pm - 10:00pm
Room TBA
Laura Kay 1 3/12
ASTR 1903 005/09217 W 7:00pm - 10:00pm
Room TBA
Laura Kay 1 3/12

ASTR UN1904 Astronomy Lab 2. 1 point.

Laboratory for ASTR W1404. Projects include use of telescopes, laboratory experiments in the nature of light, spectroscopy, and the analysis of astronomical data. Lab 2 ASTR W1904 - goes with ASTR BC1754 or ASTR W1404 (or ASTR W1836 or ASTR W1420).

Spring 2017: ASTR UN1904
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1904 001/06986 M 6:00pm - 9:00pm
Room TBA
Laura Kay, Steven Mohammed, Julia Gross 1 13/14
ASTR 1904 002/08347 M 7:00pm - 10:00pm
Room TBA
Laura Kay, Steven Mohammed, Kirsten Blancato 1 8/14
ASTR 1904 003/05781 T 6:00pm - 9:00pm
Room TBA
Laura Kay, Steven Mohammed, Alexander Teachey 1 13/14
ASTR 1904 004/09550 T 7:00pm - 10:00pm
Room TBA
Laura Kay, Steven Mohammed, Daniel DeFelippis 1 7/14
ASTR 1904 005/01805 W 6:00pm - 9:00pm
Room TBA
Laura Kay, Steven Mohammed, Emily Sandford 1 14/14
Fall 2017: ASTR UN1904
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 1904 001/08991 W 6:00pm - 9:00pm
Room TBA
Laura Kay 1 12/14

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 2017: ASTR UN2001
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 2001 001/71032 M W 10:10am - 11:25am
Room TBA
Frederik Paerels 3 25/25

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 2017: ASTR UN2900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 2900 001/74735 F 10:10am - 11:25am
Room TBA
Caleb Scharf 1 14/25

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.

Spring 2017: ASTR UN3105
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 3105 001/80279 M W 1:10pm - 2:25pm
313 Pupin Laboratories
David Kipping 3 20/30

ASTR UN3986 Astrostatistics. 3 points.

Astronomers live in era of “big data”. Whilst astronomers of a century ago collected a handful of photographic plates each night, modern astronomers collect thousands of images encoded by millions of pixels in the same time. Both the volume of data and the ever present desire to dig deeper into data sets has led to a growing interest in the use of statistical methods to interpret observations. This class will provide an introduction to the methods commonly used in understanding astronomical data sets, both in terms of theory and application. It is one six classes the department offers every fourth semester.

Fall 2017: ASTR UN3986
Course Number Section/Call Number Times/Location Instructor Points Enrollment
ASTR 3986 001/15146 M W 2:40pm - 3:55pm
Room TBA
David Kipping 3 7/25

ASTR W1234 The Universal Timekeeper: Reconstructing History Atom by Atom. 3 points.

CC/GS: Partial Fulfillment of Science Requirement
Not offered during 2017-18 academic year.

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 W3105 Extrasolar Planets and Astrobiology (Lecture). 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: one year of calculus based physics.

This class will cover the physics and observations of extrasolar planets at a quantitative level, including: detection methods, theories of planet formation and migration, orbital dynamics, rocky vs. gaseous planets, extrasolar planet atmospheres, and habitability, including possibly observable life signatures and some aspects of astrobiology. We will also cover several recent experimental results.

ASTR W3273 High Energy Astrophysics. 3 points.

CC/GS: Partial Fulfillment of Science Requirement
Not offered during 2017-18 academic year.

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 W3602 Physical Cosmology and Extragalactic Astronomy. 3 points.

CC/GS: Partial Fulfillment of Science Requirement
Not offered during 2017-18 academic year.

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.

ASTR W4260 Modeling the Universe. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: one year of calculus-based general physics.

The goal of this course is to provide a basic hands-on introduction to the practice and theory of scientific computing with applications in astronomy and astrophysics. The course will include an introduction to programming, as well as a sampling of methods and tools from the field of scientific computing. The course will include a hands-on project in which students use numerical methods to solve a research problem. Students who are interested in participating in research projects are strongly encouraged to take the course in their sophomore or junior year.

The University reserves the right to withdraw or modify the courses of instruction or to change the instructors as may become necessary.