Prior to Moderation, a student has usually completed Physics 141 and 142, Introduction to Physics I and II; Mathematics 141 and 142, Calculus I and II; and Physics 241, Modern Physics.

Before Moderation

Prior to Moderation, a student has usually completed Physics 141 and 142, Introduction to Physics I and II; Mathematics 141 and 142, Calculus I and II; and Physics 241, Modern Physics.

To enter into the Upper College and moderate in physics, a student writes two short papers, one describing the work they have done in the Lower College and the other describing their plans for the Upper College and beyond. The student then meets with a Moderation Board of three faculty (two from the Physics Program) for an in-depth discussion of the work the student has done so and to develop the student’s best curriculum for work in the Upper College. Students are expected to follow the standard divisional procedure for Moderation and to fulfill the college-wide distribution and First-Year Seminar requirements.

Before Graduation

In addition to the courses required for Moderation, physics majors must complete Physics 221 and 222, Mathematical Methods of Physics I and II; Physics 303, Mechanics; Physics 312, Electricity and Magnetism; Physics 314, Thermal Physics; Physics 321, Quantum Mechanics; and the Senior Project.

Coursework

Most students take the core course sequence listed below, but a particular curriculum is fashioned to reflect each student’s interests and level of preparation. Beyond the core courses, each student chooses a number of Physics and divisional electives according to their focus of study. Visit the Bard College course list to view Physics courses offered for the upcoming semester.

Introductory Course Requirements

Introductory Course Requirements

The introductory courses for the major consist of a three-semester physics sequence, Physics 141, Physics 142, and Physics 241; and a four-semester mathematics sequence Math 141, Math 142, Physics 221, and Physics 222.

Physics 141 and Physics 142 (Introduction to Physics I and II) are offered as a one-year sequence, and most Physics majors would take both in the first year of classes. Students with advanced preparation might skip one or both of these courses. If a student does not start in the introductory sequence until the sophomore year, completing a physics major is still possible in four years at Bard, but the number of possible upper college physics classes one could take would be limited. Physics 241 (Modern Physics) is offered every fall and is typically taken sophmore year, although students with advanced preparation may take this course in their first year.

Advanced Course Requirements

Advanced Course Requirements

Three of the required advanced-level physics courses—Physics 303 (Mechanics), Physics 312 (Electricity and Magnetism), and Physics 314 (Thermal Physics)—are offered on a one-and-a-half year cycle. Most physics majors will take at least one of these courses before Moderation. The final required advanced-level physics course, Physics 321 (Quantum Mechanics), is offered every spring. Students interested in experimental work generally take Physics 210 (Introduction to Electronics).

Mathematics Course Requirements

Mathematics Course Requirements

The mathematics sequence consists of two calculus courses, Math 141 and Math 142 (Calculus I and II), followed by two courses on mathematical methods for physicists, Physics 221 and Physics 222 (Mathematical Methods I and II), which contain topics in linear algebra, differential equations, vector calculus, probability, and statistics. Students may place out of one or both of the calculus courses depending on their previous preparation and the results of their math placement diagnostic.

Senior Project

Senior Project

All physics majors must complete a Senior Project. This is generally an experimental or theoretical study on a topic of the student's choice. By working closely with the faculty adviser, the student chooses a Senior Project topic based on their interests and background.

Sample Four-Year Schedule

Sample Four-Year Schedule

Fall Semester

Spring Semester

First Year

Intro Physics I (141)

Calculus I (Math 141)

Intro Physics II (142)

Calculus II (Math 142)

Sophomore Year

Modern Physics (241)

Math Methods I (221)

Mechanics (303)

Math Methods II (222)

Junior Year

Electricity & Magnetism (312)

Electronics (210)

Thermal Physics (314)

Quantum Mechanics (322)

Senior Year

Advanced Courses, Tutorials, Senior Project

Advanced Courses, Tutorials, Senior Project

Divisional course in robotics. Photo by Pete Mauney ’93 MFA ’00

Tutorials and Electives

In addition to the required courses, recent advanced courses and tutorials have included General Relativity, Condensed Matter Physics, Nuclear and Particle Physics, and Scientific Programming. Students are encouraged to take intermediate and advanced courses throughout the division, depending on their interests and their post-Bard plans. In consultation with the student’s adviser and Moderation board, courses in Mathematics, Computer Science, or Chemistry might be recommended for Physics students.

Course Descriptions

Introductory Courses

Introductory Courses

Introduction to Physics I Physics 141 A calculus-based survey of physics. The first semester covers topics in mechanics, heat and thermodynamics, and wave motion. The course stresses ideas—the unifying principles and characteristic models of physics. Labs develop the critical ability to elicit understanding of the physical world. Corequisite: Mathematics 141.

Introduction to Physics II Physics 142 This is the second part of a calculus-based survey course, continuing with electricity and magnetism, light, and basic atomic and modern physics. Prerequisites: Physics 141 and Mathematics 141.

Intermediate Courses

Intermediate Courses

Introduction to Electronics Physics 210 This course is a survey of analog electronics, beginning with Kirchhoff’s laws, voltage dividers, and filters, and proceeding to power supplies, amplifiers, oscillators, operational amplifiers, timers, and integrated circuits (ICs). Semiconductor diodes, bipolar and field-effect transistors, and ICs are employed. The semester ends with a brief introduction to digital electronics. Boolean algebra and some basic digital electronic functions are explored, along with construction of a pared down bus-architecture prototype. The course consists of equal parts lecture and lab. Corequisites: at least one physics course and one mathematics course numbered above 140.

Mathematical Methods of Physics I Physics 221 This course presents mathematical methods that are useful in the physical sciences. While some proofs and demonstrations are given, the emphasis is on the applications. Topics include: complex functions, vector spaces, matrices, coordinate transformations, power series, probability and statistics, and multi-variable differentiation and integration. Prerequisites: Mathematics 141–142, or equivalent, and strong preparation in physics comparable to Physics 141.

Mathematical Methods of Physics II Physics 222 This is the second part of a two-part course series that introduces mathematical topics and techniques that are commonly encountered in the physical sciences, including complex numbers and analytic functions, Fourier series and orthogonal functions, standard types of partial differential equations, and special functions. Prerequisites: Mathematics 141–142, or equivalent, and strong preparation in physics comparable to Physics 141–142. Recommended: Physics 221, Mathematical Methods of Physics I.

Computational Physics Physics 225 This course is designed to teach computational techniques that can be used to solve problems in the sciences, generally in physics and engineering. Students will spend most of their time programming specific physical problems as well as learning the theory behind the phenomena being modeled. No prior experience with computer programming is required. Students will be exposed to the Python programming language and its visual capabilities through VPython, as well as Structured Query Language (SQL) and MATLAB. Topics will include Newtonian Mechanics, Thermodynamics, Quantum Mechanics and Astronomy. As part of this course, students are required to complete an individual class project. Prerequisites: Physics 141 and Mathematics 141, or equivalent experience.

The Atmosphere and Ocean in Motion Physics 234 A great deal of what climate change would look like depends on fluid motions: Would Europe wither in deep chill? That depends in part on the response of the Gulf Stream system to greenhouse forcing. Would Middle Eastern wars rage on for another century, taking on the new guise of water wars? That depends on the response of the North Atlantic to thickening atmosphere and the Jet Stream’s response to the North Atlantic. Would polar bears go extinct? That depends in part on circulation changes in the Arctic Ocean. It’s all, or mostly, in the motion. This is a semi-technical course designed to help interested students acquire the tools needed and used to answer the questions like those above. A thorough technical treatment is deliberately sacrificed for a more intuitive and heuristic understanding. Prerequisites: Physics 141 or its equivalent, and a willingness to learn some new self-contained math.

Modern Physics Physics 241 An extension of introductory physics concentrating on developments in physics that stem from the theory of relativity, quantum mechanics, and statistical mechanics. A major focus will be understanding classical and quantum waves, but there will also be overviews of particle physics, nuclear physics, optical and molecular physics, condensed matter physics, astronomy, and cosmology. Prerequisites: Physics 141–142 and Mathematics 141–142.

Astrophysics Physics 250 This course is an introduction to modern astrophysics from the solar system to the basic ideas of cosmology. Starting from methods of measuring astronomical distances and the laws of planetary motion, we study the cosmos using classical mechanics, special relativity and basic quantum mechanics. Topics may include: solar system, the interior of the sun, star classification, the life cycle of stars, black holes, galaxies, dark matter, search for alien life, and cosmology including the Big Bang theory and dark energy. Prerequisites: Physics 241

Advanced Courses

Advanced Courses

Mechanics Physics 303 This course in particle kinematics and dynamics in one, two, and three dimensions covers conservation laws, coordinate transformations, and problem-solving techniques in differential equations, vector calculus, and linear algebra. Lagrangian and Hamiltonian formulations are also studied. Prerequisites: Physics 141–142 and Mathematics 141–142.

Electricity and Magnetism Physics 312 This course considers electrostatics, conductors, and dielectrics; Laplace’s equation and characteristic fields; magnetostatics, magnetodynamics, and the magnetic properties of matter; flow of charge and circuit theory; and Maxwell’s equations and the energy/momentum transfer of electromagnetic radiation. Prerequisites: Physics 141–142 and Mathematics 211.

Thermal Physics Physics 314 This course studies the thermal behavior of physical systems, employing thermodynamics, kinetic theory, and statistical mechanics. Thermodynamical topics include equations of state, energy and entropy, and the first and second laws of thermodynamics. Both classical and quantum statistical mechanics are covered, including distribution functions, partition functions, and the quantum statistics of Fermi-Dirac and Bose-Einstein systems. Applications include atoms, molecules, gases, liquids, solids, and phase transitions. Prerequisites: Physics 141–142, Mathematics 141–142.

Quantum Mechanics Physics 321 Quantum mechanics is our most successful scientific theory: spectacularly tested, technologically paramount, conceptually revolutionary. This course will provide a comprehensive introduction to this remarkable theory. We will begin by establishing the structure of quantum mechanics in the context of its simplest case, the so-called qubit. Simultaneously, we will refresh the mathematical apparatus required to formulate quantum mechanics. To explore some of quantum mechanic’s most interesting phenomena, including contextuality, entanglement, and nonlocality, we will next study systems of qubits. After an interlude on the interpretation of quantum mechanics, we will consider a variety of applications of quantum mechanics: 1-dimensional systems, including the harmonic oscillator, 3-dimensional systems, including the hydrogen atom, and quantum statistical mechanics, including that of identical particles as well as scattering and perturbation theory. We will conclude by learning the path integral formulation of quantum mechanics. Time permitting, we will touch on such topics as decoherence and quantum computation. Prerequisite: Physics 241, Mathematics 213.

General Relativity Physics 327 This course provides an introduction to Einstein’s theory of gravity. Beginning with a discussion of special relativity, this course teaches the mathematics of differential geometry in order to describe the formulation of gravity as the curvature of space and time. Experimental verifications of the theory, such as the variability of the rate of the flow of time with height and the bending of starlight will be discussed. Applications covered in the course might include calibration of the Global Positioning System (GPS), black holes, cosmology, or gravitational waves. Prerequisites: One of Physics 241, Physics 303, Mathematics 241; or permission of course instructor.

Condensed Matter Physics Physics 418 This course is an introduction to the foundations of solid state physics: quantum mechanical models of electronic transport, crystal structure, band structure, semiconductors and semiconductor devices, phonons, quasiparticles, magnetism, and superconductivity; along with overviews of more advanced and contemporary topics such as density functional theory, quantum Hall effects, mesoscopic transport, and Dirac fermions. Corequisites: Physics 314, 321.

General Science Courses

General Science Courses

Acoustics Physics 116 This laboratory course provides an introduction to the phenomena of acoustics, particularly aspects that are important in the production and perception of music. The physics of sound is covered in depth, and characteristics of acoustic and electronic instruments are discussed. Mathematical and laboratory techniques are introduced as needed. No specific science or mathematics background beyond algebra is assumed.

Light and Color Physics 118 An introduction to light, optical phenomena, and related devices, including some historical perspective; classical and modern models of light; light and color in nature and vision; the geometrical optics of lenses, mirrors, and related devices; the physical optics of interference and diffraction; spectroscopy and polarization; color science, lasers, and holography. Without assuming prior knowledge of physics or higher mathematics, the class develops models and explores them in weekly labs. Prerequisites: high school algebra and trigonometry (certified at registration).

Global Energy Physics 120 A laboratory-based physics class designed to introduce non-science majors to the different types of energy (mechanical, thermal, electromagnetic, chemical, nuclear); the methods by which modern societies produce, transmit, and convert between these types; how different demand sectors (electricity, heating, transportation) shape our energy production infrastructure; the promises of future energy technology and the insurmountable physical constraints on them; and the environmental and economic costs associated with different types of energy production. The bulk of the course will be an examination of each of the major contemporary means of energy production (fossil fuels, nuclear, hydropower) and the emerging alternative means (wind, solar,biofuels). The course will seek to emphasize some of the subtleties behind energy production usually glossed over in popular discussion, and will rely heavily on developing students’ abilities to perform “back-of-the-envelope” calculations to estimate quantities of interest on a global scale.

Paint and Examination of Paintings Science 123 This course is about the composition of pigments, dyes and paints, the chemistry underlying selected techniques (e.g. ,Attic vase and fresco painting), and scientific methods for examining paintings, with an emphasis on case studies. As light and atoms and molecules are central to paints and techniques for examining paintings, the course begins with these foundational topics. Laboratory work includes synthesis and analysis of pigments and dyes, preparation of binders and paints, and fresco painting. Students preregistered for the course undertake to review selected topics from high school chemistry and take an online quiz before the start of the semester to assess their understanding.

Climate Change Physics 124 This lab course explores the physical principles underlying climate and anthropogenic climate change. We will start with a survey of the most compelling lines of evidence for climate change, how they are obtained/derived and some of their limitations. We will then discuss in some depth idealized one-dimensional planetary radiative and thermal balance, first in the absence of an atmosphere, and then in the presence of a radiatively active one, with variable number of layers. In this context, it will become interesting to explore atmospheric opacity with respect to various radiative types, and what natural and anthropogenic effects affect this opacity. A related topic will be natural feedbacks, such as water vapor and could feedbacks. We will next place current (modern) observations of climate change in the broader context of past climates, emphasizing the last couple millennia, hundreds of millennia, and finally the ten million–year scale geological record. We will conclude the course with some discussion about the objective of a successful policy mitigation efforts, and their implementation obstacles. While not technical per se, participation in this course does require the ability to solve a couple of linear algebraic equations (like solving x + 4 = 2y and 2x – 3y = 6 for x and y) and to perform some very basic manipulation of data and plot the results (using, e.g., Microsoft’s Excel).

Photographic Processes Science 125 Topics covered in this course range from the chemistry of silver and non-silver photographic processes to the physics of CCD cameras. Laboratory work emphasizes the chemical transformations involved in making gum dichromate prints, cyanotypes, blueprints, salted paper prints and black-and-white silver emulsion prints. Registered students undertake to review elementary topics from high school chemistry and take an online quiz before the start of the semester to assess their understanding of these topics.

Astronomy Physics 126 Have you ever looked up at the night sky and wondered what you are seeing? Astronomy is one of the oldest of the natural sciences, dating back to prehistoric times. It studies planets, stars, galaxies, and the universe as a whole from its earliest time to the present day. This course is an introduction to astronomy including laboratory work where we will perform and interpret observations. Topics include: the solar system, telescopes, history of astronomy, the sun, galaxies, and cosmology. Prerequisite: passing score on Part I of the Mathematics Diagnostic.

Learning About Learning: A Quantitative Study of the Evolution of the Self Science 127 What is learning? How can we learn more quickly? What happens in our brains when we learn? This course will tackle an experimental investigation of what influences the depth and quality of our learning. We will take a synthetic look at the psychology, philosophy, and cognitive science of learning, reading books such as Tim Ferriss’ Four Hour Chef and Daniel Kahneman’s Thinking, Fast and Slow. A major focus of the course will be student-generated, quantitative experiments designed to test ideas about learning. A succinct motto that will inform our approach is “It costs very little to find out,” that is, we will aim to test ideas by trying them. This course will challenge you to take a more active role in choosing how you go about learning. No mathematics background will be assumed for the course.

Chernobyl: Man-Made Disaster Ideas 130 Cross-listed: Human Rights; Political Studies; Science We will employ the Chernobyl disaster as a case study of the environmental and human consequences of technology. In April 1986, the nuclear power plant in Chernobyl, Ukraine suffered a major technical problem leading to a meltdown in the reactor core. The radiation release and ensuing clean-up operation required the Soviet authorities to evacuate a large local region, affecting millions of people and leaving a region which is mostly uninhabited to this day. Chernobyl remains the worst civilian nuclear accident in history and its aftermath offers scientific, social, and political insights. This “big ideas” course will take an interdisciplinary approach to the meaning of Chernobyl: it will explore the issue of nuclear power, the social and technological aspects of the plant’s construction and operation, what led to the accident, the authorities’ response to it, and the environmental and social impacts on the region since that time. Laboratory sessions will focus on the physics of nuclear power and radiation, the biological effect of radiation, and the environmental impact of the Chernobyl accident. Parallel consideration will be given to its implications for Soviet governance, nuclear energy and proliferation, and the social impacts of Chernobyl and human-created nuclear and non-nuclear disasters. Examining this event in readings, lectures, and laboratory investigations will foster a deeper appreciation of the complex and interconnected contexts in which such disasters must be studied in order to be understood. The course will feature guest lectures in science, politics, human rights and literature, speaking on issues arising from the accident.

Milk and Its Contents Science 133 What is milk made of, and why, and how is it transformed into foods such as yogurt and cheese? The answers to these questions, which lie in the chemical composition of milk, are the subject of this course. The effect of milk on humans, the effect of milk production on animals and the environment, and the politics and marketing of milk and dairy foods are among the topics that will arise naturally. However, the focal points of this course are the chemical analysis of milk and the chemistry underlying its transformations into other foods. Three visits to dairy farms and a milk-processing plant will be scheduled on Fridays (probably). Students registering for this class commit to reviewing elementary topics from high school chemistry and taking an online quiz before the start of the semester.

Starlight Science 143 One of our species’ most amazing achievements is that we have a pretty good idea of what stars are made of, despite our confinement to Earth. Not even a space probe has gone anywhere near any star besides the Sun. Our understanding of the composition of stars comes from close examination of starlight (by a process resembling Isaac Newton’s decomposition of sunlight into its colors) and our modern understanding of atoms and molecules. This course is about the analysis of starlight: what it tells us about the composition of stars, their temperatures and their motions. We start with inquiring into the nature of light and the structure of atoms and molecules and their energy levels. This understanding will be applied to light coming from stars and other astronomical objects. Laboratory experiments involve the use of spectrophotometers to study light emitted, absorbed and reflected by atoms and molecules. Although the course is intensive, no mathematics beyond algebra is required.

Cosmology Science 162 A descriptive review of the astrophysical theories of the origin and development of the early universe. The Big Bang theory is examined in detail, with attendant evidence and theories of particles, fields, energy and entropy, and space-time geometry. Current models of supernovas, quasars, black and white holes, dark matter, quantum foam, and recent alternative models of supersymmetry and superstrings are reviewed. Historical notions of time, space, matter, and cause frame the discussions. This course can be taken for distribution credit in science, but does not meet the Q requirement or provide laboratory experience.

Science History and Philosophy Courses

Science History and Philosophy Courses

Schrödinger’s Cat and All of That Science History and Philosophy 111 While quantum physics is a successful physical theory, it includes many philosophical ideas and experimental results that seem to defy common sense. Is the electron a particle or a wave? Does God roll dice? Is Schrödinger’s cat dead or alive before we look in the box? This seminar examines aspects of subatomic phenomena that scientists and others find puzzling. There are no specific math or science prerequisites, but comfort with basic algebra is assumed.

Physical Science before Newton Science History and Philosophy 222 An introduction to the history and philosophy of science. T. S. Kuhn’s model of historical progress is used to examine selected parts of discourses involving pre-Socratic philosophy, mythology, Copernican astronomy, Galileo’s trial, and Newton’s philosophy. A critique of method introduces modern historiographic and philosophic controversies. Designed as a core course for studies in history, philosophy, and sociology of science; no prior mathematical or technical expertise is presumed at this level. Readings include excerpts from the Enuma Elish, the Milesians, Pythagoras, Heraclitus, Plato, Aristotle, Ptolemy, Copernicus, Kepler, Galileo, and Newton. Students also read secondary commentary by Nahm, Butterfield, Kuhn, Munitz, and others.

Physical Science after Newton Science History and Philosophy 223 A survey of major agendas of physical science since 1750. Characteristic episodes include Lavoisier and the theory of elements; Maxwell and the mathematization of physics; arguments about light from Newton, Young, Michelson, and Einstein; 20th-century atomic theory; and the emergence of “big science.”

Einstein Science History and Philosophy 225 This course examines Einstein’s life and work, the impact of his work on worldviews, and some of the many controversies involved therein. It makes use of biographical and popular descriptions of the relativity theories, atomic theories, and optical theories and assesses the advantages of methods of positivism and realism in philosophy and of internalism and externalism in the history of science. Readings include some primary sources, as well as Clark, Holton, Pais, Miller, Reichenbach, and Zukav.

Science and Pseudoscience Science History and Philosophy 227 The search for a demarcation between “science” and “pseudoscience” has generated many productive developments in the academic philosophy of science. These two areas are also significant in “civilian” culture as considerable damage, both civic and psychological, has surrounded adherence to alleged pseudosciences in both the recent and distant past. This course examines a number of well-studied 20th-century incidences of pseudoscience in physical science, including Blondlot’s N-rays, Barkla’s J-rays, Langmuir’s criteria, Ehrenhaft’s electrons, polywater, cold fusion, the fifth force, and other minimally controversial situations, as well as a few cases not yet clearly decided. No background in science or mathematics is required. Readings include selections from works by Gardner, Gratzer, Holton, Popper, and others, as well as journals of history and philosophy of science.

Philosophy of Science Science History and Philosophy 304 A historical reconstruction of recent developments in epistemology, focusing on the emergence of realism and antipositivism in the 1980s. Readings include Ayer, Feyerabend, Foucault, Hempel, Lakatos, Laudan, MacIntyre, Popper, and Stegmuller. Prerequisites: Science History and Philosophy 222 and 223, at least one course each in Kant and modern philosophy, and permission of the instructor.

Discover Physics at Bard

Hal Haggard, Director Physics Program Bard College | PO Box 5000 Annandale-on-Hudson, NY 12504 [email protected] | 845-758-7216