The following courses are lectures unless otherwise indicated.

The Universe: Its Nature and History
V85.0007 Offered every year. 4 points.
Qualitative introduction to our understanding of the nature and evolution of the universe. Topics include the creation of the cosmos; its explosive evolution, present structure, and ultimate fate; the nature of stars and galaxies; the structure and evolution of our Milky Way; the birth, life, and eventual death of the solar system; our place and role in the universe; and the relationship of modern astronomical ideas to other cultural disciplines.

Origins of Astronomy
V85.0008 Identical to V65.0008. Not open to students who completed V55.0206. Offered every other year. 4 points.
Introduction to the historical development of astronomy, from earliest times through the Copernican revolution. Traces the changes in our perception of the heavens and the influences that led to those changes, from astrology to the discoveries of Galileo and the physics of Newton. Includes descriptive astronomy of the solar system and a trip to the Hayden Planetarium.

Sound and Music
V85.0010 Assumes high school-level mathematics background. Offered every year. 4 points.
Explores the production of musical sound and how it is perceived by us, dealing mainly with the physical basis of sound. Covers sound waves, resonance, how musical instruments produce sound, the concepts of scales and harmony, physical acoustics, physiological factors of perception, acoustics of auditoria, and sound recording and reproduction. Develops the necessary physics for the course, as needed.

General Physics I
V85.0011 Prerequisite: V63.0121 or permission of the instructor. With V85.0012, forms a two-semester sequence that must be taken in order. Lecture and laboratory-recitation. Not open to students who have completed V85.0091 with a grade of C- or better. Offered in the fall. 5 points.
Begins a two-semester introduction to physics intended primarily for preprofessional students and for those majoring in a science other than physics, although well-prepared students may wish to take the physics majors sequence V85.0091, V85.0093, V85.0094, V85.0095, and V85.0096 instead. Topics include kinematics and dynamics of particles; momentum, work, and energy; gravitation; circular, angular, and harmonic motion; mechanical and thermal properties of solids, liquids, and gases; heat and thermodynamics.

General Physics II
V85.0012 Prerequisite: V85.0011 with a grade of C- or better, or permission of the department. Lecture and laboratory-recitation. Offered in the spring. 5 points.
Continuation of V85.0011. Topics include electric charge, field, and potential; magnetic forces and fields; resistive, capacitive, and inductive circuits; electromagnetic induction; wave motion; electromagnetic waves; geometrical optics; interference, diffraction, and polarization of light; relativity; atomic and nuclear structure; elementary particle physics.

Observational Astronomy
V85.0013 Prerequisite: V55.0202 or above, V85.0007 or above, or permission of the instructor for nonscience majors and minors; no prerequisite for science majors and minors or those automatically satisfying Natural Science I requirements. Lecture and laboratory session. Offered every year. 4 points.
Introduction to the theory and practice of technical amateur astronomy. The approach is hands-on, with weekly evening laboratory/observing sessions. Topics include astronomical coordinate systems, optics, how to use a telescope, and the phenomena that can be seen in the urban night sky. Observing sessions involve the use of eight-inch telescopes.

20th-Century Concepts of Space, Time, and Matter
V85.0020 Assumes high-school-level geometry and intermediate algebra background. Not open to students who have completed V55.0204. Offered every year. 4 points.
The 20th century has been witness to two major revolutions in man's concepts of space, time, and matter. Einstein's special and general theories of relativity: implications of the special theory, for our understanding of the unity of space and time, and the general theory, for our understanding of the nature of gravity. Quantum mechanics: a new picture of the basic structure and interactions of atoms, molecules, and nuclei. Topics include the uncertainty principle, wave-particle duality, and the continuing search for the fundamental constituents of matter.

Engineering Physics I
V85.0081 Corequisite: V63.0122. Lecture and recitation. Offered in the spring. 3 points.
This course and the following two courses provide an introductory course in physics useful for engineering students. The following topics are covered: straight line motion, velocity, speed, acceleration; vectors; motion in two and three dimensions; force and motion: Newton's laws, friction, circular motion; kinetic energy and work; potential energy and conservation of energy; systems of particles; center of mass, conservation laws; elastic and inelastic collisions; rotation, torque, angular momentum; rolling, torque, and angular momentum; oscillations, harmonic motion, pendulum, damped and forced oscillations; transverse and longitudinal waves, interference, sound.

Engineering Physics II
V85.0082 Prerequisite: V85.0081. Lecture and recitation. Offered in the fall. 3 points.
The following topics are covered: electric charge and Coulomb's law; electric fields, Gauss's law; electric potential; capacitance; current and resistance; circuits; magnetic fields; magnetic fields due to currents, Ampere's law; induction and inductance, Faraday's and Lenz's law; magnetism of matter, Maxwell's equations; electromag-netic oscillations and alternating current; electromagnetic waves.

Engineering Physics III
V85.0083 Prerequisite: V85.0082. Lectures, recitations, and laboratories. Offered in the spring. 4 points.
The following topics are covered: images, mirrors, and lenses; interference; diffraction; relativity; photons and the photoelectric effect; matter waves; atoms; electricity in solids, semiconductors; nuclear physics, radioactivity, alpha and beta decays; fission and fusion.

Physics I
V85.0091 Corequisite: V63.0121 or V63.0221. Lecture and recitation. Offered in the fall. 3 points.
With V85.0093 and V85.0095, forms a three-semester sequence that must be taken in order, starting in the fall semester. Begins a three-semester introduction to physics intended for physics majors and other interested science and mathematics majors. Topics include kinematics and dynamics of particles; energy and momentum; rotational kinematics and dynamics; harmonic oscillators; gravitational fields and potentials; special relativity.

Physics II
V85.0093 Prerequisite: V85.0091 with a grade of C or better, or permission of the department. Corequisite: V63.0122, except for students who have completed V63.0222. Physics majors must also register for V85.0094. Lecture and recitation. Offered in the spring. 3 points.
Continuation of V85.0091. Topics include electrostatics; dielectrics; currents and circuits; the magnetic field and magnetic materials; induction; AC circuits; Maxwell's equations.

Physics II Laboratory
V85.0094 Corequisite: V85.0093. Laboratory. Offered in the spring. 2 points.
Experiments are based on subjects covered in V85.0091 and V85.0093.

Physics III
V85.0095 Prerequisite: V85.0093 with a grade of C or better, or permission of the department. Lecture and recitation. Corequisite: V63.0123 or V63.0222. Offered in the fall. 3 points.
Physics majors must also register for V85.0096. Continuation of V85.0093. Topics include wave motion; Fourier series; sound; the reflection, refraction, interference, and diffraction of light; polarization; thermodynamics; kinetic theory and statistical physics.

Physics III Laboratory
V85.0096 Prerequisite: V85.0094 with a grade of C or better, or permission of the department. Corequisite: V85.0095. Laboratory. Offered in the fall. 2 points.
Continuation of V85.0094. Experiments are based on subjects covered in V85.0093 and V85.0095.

Modern Physics I, II
V85.0103,0104 Prerequisites: V85.0095 or V85.0012, and V63.0123 or V63.0222. Lecture and laboratory. Offered every year (Modern Physics I, spring; Modern Physics II, fall). 5 points per term.
Introduction to modern physics for students who have had at least one year of college physics and three semesters of calculus or intensive calculus. Topics include special relativity, introductory quantum mechanics, hydrogen atom, atomic and molecular structure, nuclear physics, elementary particle physics, solid-state physics, and chemical physics. Provides applications to current technology and scientific research.

Classical and Quantum Waves
V85.0105 Prerequisites V85.0095. Offered in the spring. 3 points.
Introduction to the physics of classical and quantum waves for students who have had at least one year of college physics and three semesters of calculus or intensive calculus. Topics include linear and non-linear oscillators, resonance, coupled oscillators, normal modes, mechanical waves, light, matter waves, Fourier analysis, Fourier optics (diffraction), and an introduction to numerical (computer) methods for solving differential equations.

Mathematical Physics
V85.0106 Prerequisites: V85.0095 and either V63.0123 or V63.0222. Lecture and recitation. Offered in the spring. 3 points.
Mathematical preparation for the junior and senior courses in physics. Vector analysis, Fourier series and integrals, ordinary differential equations, matrices, partial differential equations, and boundary-value problems.

Classical and Quantum Waves Laboratory
V85.0107 Corequisite: V85.0105. Offered in the spring. 2 points.
The course introduces students to experiments pertaining to the subjects of the associated lecture course and to experimental methods used in contemporary physics research.

Electronics for Scientists
V85.0110 Identical to V23.0110, V25.0671. Prerequisite: V85.0012, V85.0093, or permission of the instructor. Lecture and laboratory. Offered in the fall. 5 points.
Introduction to basic analog and digital electronics used in modern experiments and computers. For students of all science disciplines. Basic concepts and devices presented in lecture are studied in the laboratory. Covers filters, power supplies, transistors, operational amplifiers, digital logic gates, and both combinatorial and sequential digital circuits. Students learn the functions of modern electronic instrumentation and measurement.

Experimental Physics
V85.0112 Prerequisites: V85.0096 and V85.0103. Laboratory. Offered in the spring. 3 points.
Introduces the experiments and techniques of modern physics. Following a number of introductory experiments, students have at their option a variety of open-ended experiments they can pursue, including the use of microcomputers for data analysis. Experimental areas include Mossbauer effect, cosmic rays, magnetic resonance, and relativistic mass.

Dynamics
V85.0120 Prerequisites: V85.0095 and V85.0106. Offered in the fall. 3 points.
Intermediate-level course on the principles and applications of dynamics. Emphasis on the formulation of problems and their numerical solution. Topics include conservation laws, central force motion, Lagrange's and Hamilton's equations, normal modes and small oscillations, and accelerated reference frames.

Quantum Mechanics I, II
V85.0123,0124 Prerequisites: V85.0104, V85.0120, and V85.0132. Offered every year (Quantum Mechanics I, fall; Quantum Mechanics II, spring). 3 points per term.
Designed to deepen the insights into quantum mechanics introduced in V85.0103,0104 and to provide an introduction to the more formal mathematical structure of quantum mechanics. The Schrödinger and Heisenberg description of quantal systems; perturbation theory; spin and statistics; coupling of angular momenta; scattering theory; and applications to atomic, molecular, nuclear, and elementary particle physics.

Electricity and Magnetism I, II
V85.0131,0132 Prerequisites: V85.0095 and V85.0106. Offered every year (Electricity and Magnetism I, fall; Electricity and Magnetism II, spring). 3 points per term.
Introduction to Maxwell's equations with applications to physical problems. Topics include electrostatics, magnetostatics, the solution of the Laplace and Poisson equations, dielectrics and magnetic materials, electromagnetic waves and radiation, Fresnel equations, transmission lines, wave guides, and special relativity.

Optics
V85.0133 Prerequisites: V85.0095 and V85.0106 or permission of the department. Offered every other year. 3 points.
Introduction to physical and geometrical optics. Wave phenomena including diffraction, interference, first- and higher-order coherence. Holography, phase contrast and atomic force microscopy, and limits of resolution are some of the subjects included. Atomic energy levels and radiative transitions, detectors from photon counting to bolometers in the infrared.

Condensed Matter Physics
V85.0135 Prerequisite: V85.0103. Corequisite: V85.0104. Offered every other year. 3 points.
Designed as an introduction to condensed matter physics for students with knowledge of elementary quantum mechanics. Topics include crystal structure, lattice vibrations, and the energy band theory of metals and semiconductors. Covers the electronic, magnetic, and optical properties of solids. In addition, the course may include some modern research topics such as the physics of nano-structures, soft condensed matter physics, and superconductivity.

Readings in Particle Physics
V85.0136 Prerequisite: V85.0103. Corequisite: V85.0104. Offered every other year. 3 points.
Particle physics is the study of the very fundamental constituents of matter and of the forces between them. By its nature it is microscopic, but it also connects with astrophysics and cosmology on the largest scales. This course introduces the most important advances in elementary particle physics. It centers on journal articles in which these advances were first published, with overview lectures, original reading, discussion, and student presentations. Topics include the discovery of elementary particles in cosmic rays, antimatter, symmetries found in nature, and the invention of the Quark model of elementary particles and its experimental verification.

Thermal and Statistical Physics
V85.0140 Prerequisites: V85.0103 and V85.0106. Offered in the spring. 3 points.
Topics include relation of entropy to probability and energy to temperature; the laws of thermodynamics; Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics; equations of state for simple gases and chemical and magnetic systems; and elementary theory of phase transitions.

Astrophysics
V85.0150 Prerequisite: V85.0012, V85.0095, or permission of the instructor. Offered every other year. 4 points.
Introduction to modern astrophysical problems with an emphasis on the physical concepts involved: radio, optical, and X-ray astronomy; stellar structure and evolution; white dwarfs, pulsars, and black holes; and galaxies, quasars, and cosmology.

Physics of Biology
V85.0160 Prerequisites: Physics I-III. Offered every other year. 3 points.
Using basic physical concepts such as energy, entropy and force, explores biology from a different perspective. Presents a survey of basic biological processes at all levels of organization (molecular, cellular, organismal, and population) in the light of simple ideas from physics. To illustrate this approach, examines a few contemporary research topics, including self-assembly, molecular motors, low Reynolds fluid dynamics, optical imaging, and single-molecule manipulation. Attempts to construct links between fundamental concepts of biology and physics and to expose enormous open questions in the life sciences from the point of view of a physicist. Geared toward students with a background in mathematics and the physical sciences.

General Relativity
V85.0170 Prerequisites: V85.0120 or permission by instructor. Offered in the spring. 3 points.
This course provides an introduction to general relativity, stressing physical phenomena and their connection to experiments and observations. Topics include: special relativity, gravity as geometry, black holes, gravitational waves, cosmology, Einstein equations.

Computational Physics
V85.0210 Prerequisites: V85.0103 and V85.0106 or equivalent, or permission of the instructor, and knowledge of a scientific programming language (such as FORTRAN, Pascal, or C). Offered every other year. 4 points.
Introduction to computational physics, with an emphasis on fields of current research interest where numerical techniques provide unique physical insight. Topics are chosen from various branches of physics, including numerical solution of ordinary and partial differential equations, eigenvalue problems, Monte Carlo methods in statistical mechanics, field theory, dynamical systems, and chaos. 

Special Topics in Physics
V85.0800 Prerequisites vary with the topic. Offered in the fall. 3 points.
Covers advanced topics or recent developments in physics. Detailed course descriptions are made available when topics are announced.

Independent Study
V85.0997 (fall), V85.0998 (spring) Prerequisite: permission of the director of undergraduate studies. 2 to 4 points per term.