Provisional University Bulletin (2024-2025)

• Minor
• Major (BA/BS)
• Master of Science
• Doctor of Philosophy

Undergraduate Major

A typical scenario for a physical explanation of a given situation is this: a small collection of basic physical principles relevant to the situation is used to create a mathematical model of it; computations are carried out using the model, leading to predictions that are checked experimentally; if there is agreement, the physical situation is deemed to have been explained. The objective of the program in physics is to make it possible for students to execute such a scenario for a wide range of physical situations. To that end, students are required to attain a firm grasp of the basic principles of classical physics and familiarity with those of quantum physics, to learn how to decide which principles are relevant to a given situation and how to construct the appropriate mathematical model, to develop the mathematical skills necessary to carry out the computations that generate predictions, and to strengthen the experimental skills used in exploring new phenomena and in carrying out the verification step of the typical scenario.

The ability to execute the typical scenario of physical explanation is useful not only to research physicists, but also to scientists in many other fields, especially interdisciplinary ones, such as biophysics and environmental science; it is also useful to engineers, to members of the medical profession, and to architects. For that reason, the physics program has made special arrangements to integrate a physics major with study preparing for a career in any of the areas mentioned above. Students interested in combining biology and physics should see the interdepartmental program in biological physics elsewhere in this Bulletin.

Graduate Program in Physics

The graduate program in physics is designed to equip students with a broad understanding of major fields of physics and to train them to carry out independent, original research. This objective is to be attained by formal course work and supervised research projects. As the number of students who are accepted is limited, a close contact between students and faculty is maintained, permitting close supervision and guidance of each student.

Advanced degrees will be granted upon evidence of the student's knowledge, understanding, and proficiency in classical and modern physics. The satisfactory completion of advanced courses will constitute partial fulfillment of these requirements. Research upon which theses may be based, with residence at Brandeis, may be carried out in the following areas:

1. Theoretical Physics
   Quantum theory of fields; relativity; supergravity; string theory; condensed matter theory; statistical mechanics; biological physics.
2. Experimental Physics
   High-energy experimental physics; condensed matter physics; astrophysics; and biological physics.

Undergraduate Major

The Brandeis physics major offers students a unique opportunity to prepare for graduate school or employment in a variety of technical fields. Our undergraduate program is strongly based on a first-rate research program by our faculty, which gives students the opportunity to participate in cutting-edge theoretical and experimental research in areas including astrophysics and cosmology, biological physics, condensed matter physics, high-energy particle physics, and gravitational physics, and topics such as string theory, liquid crystals, DNA, polymers, elementary particles, exoplanet physics, and the early universe.

Core Skills

After completing the major, students will:

1. Be able to formulate hypotheses for the physical principles behind observed phenomena. Be able to construct mathematical models embodying these hypotheses, such that the models are consistent with existing data and make testable predictions for further experiments.

2. Be able to evaluate measurement errors in scientific data sets and the effects of these errors on the interpretation of the data; and be able to calculate levels of confidence in conclusions drawn from the data.

3. Be able to explain to a general audience the physical principles that underlie our understanding of nature.

4. Know how to design experiments, computer simulations, and/or theory to test a scientific hypothesis.

5. Have developed their skills in applied mathematics, in laboratory techniques, and in oral and written presentation.

Knowledge

After completing this major, students will have learned at an advanced undergraduate level: Newton’s laws (mechanics), Maxwell's equations (electricity and magnetism), special relativity, statistical mechanics, thermodynamics, quantum mechanics, optics, statistics, and error analysis.

Upon Graduation

While a number of our graduates go on to some of the best graduate programs in physics in the country, many go into high-tech employment in different sectors and other professional studies including medicine and engineering.

Graduate Program in Physics

Master of Science in Physics

Core Skills

After completing their Master's degree, students will:

1. Be able to teach Physics at the high school level,
2. Be able to effectively present, both orally and in writing, their knowledge of physics,
3. Recognize and practice ethical behavior in the sciences, and
4. Be prepared for a career in Physics.

Knowledge

After completing their Master's degree, students will:

1. Have a broad understanding of the major fields of Physics,
2. Have an understanding and proficiency at the graduate level of Quantum Mechanics, Electromagnetism, Statistical Mechanics, and Laboratory Methods.

Social Justice

After completing their Master's degree, students will:

1. Understand the potential impact of scientific discoveries on society, and
2. Understand the responsibilities of conducting publicly funded research.

Graduate Outcomes

After obtaining their Master's degree, our students go on to Ph.D. programs, become teachers in high schools, and are employed in industry and the public sector.

Doctor of Philosophy in Physics

Core Skills

After completing their PhD, students will:

1. Be able to perform independent and original research in their area of specialization,

2. Be able to teach Physics at the college or high school level,

3. Be able to effectively present, both orally and in writing, their research findings,

4. Recognize and practice ethical behavior in the sciences, and

5. Be prepared for a career in Physics.

Knowledge

After completing their PhD, students will:

1. Have a broad understanding of the major fields of Physics,
2. Have an understanding and proficiency at the graduate level of Quantum Mechanics, Electromagnetism, Statistical Mechanics, and Laboratory Methods, and
3. Have an in-depth understanding of the field of Physics relevant to their thesis research.

Social Justice

After completing their PhD, students will:

1. Understand the potential impact of scientific discoveries on society, and
2. Understand the responsibilities of conducting publicly funded research.

Graduate Outcomes

After obtaining their PhDs, our students become postdoctoral fellows at top research labs and universities, become lecturers at universities, and are employed in industry and the public sector.

Because the sequence in which physics courses should be taken is tightly structured, and in most cases requires at least three years to complete, students contemplating a major in physics should consult the physics undergraduate advising coordinator at the first opportunity. For most students, such consultation should take place before enrolling in courses at the beginning of the first year. PHYS 11a or 15a and 19a should normally be part of the first-semester program. Midyear students entering Brandeis in January need to consult the physics undergraduate advising head the summer before they enroll at Brandeis.

The general requirements for admission to the Graduate School, given in an earlier section of this Bulletin, apply to candidates for admission to the graduate area in physics. Admission to advanced courses in physics will be granted following a conference with the student at entrance.

Aram Apyam
Experimental high-energy physics.

Aparna Baskaran, Undergraduate Advising Head and Senior Honors Coordinator
Nonequilibrium statistical mechanics. Biological physics.

Bulbul Chakraborty
Theoretical condensed matter physics.

James Cho
Astrophysical-geophysical fluid dynamics, atmospheric and climate dynamics; extrasolar planets and planetary science.

Guillaume Duclos
Complex fluids and biological physics, active matter and self-organization of living matter, biophysics of multicellular tissues.

Richard Fell
Theoretical quantum electrodynamics.

Seth Fraden
Physics of liquid crystals. Colloids. Macromolecules. Microfluidics.

Michael Hagan
Computation and theory in biological physics.

Matthew Headrick, Graduate Advising Head
String theory, quantum field theory, and geometry.

Jané Kondev
Theoretical condensed matter physics. Biological physics.

Albion Lawrence
Theoretical high-energy physics and cosmology; quantum gravity; physical oceanography; geophysical and astrophysical fluid dynamics.

Peter Mistark
Theoretical condensed matter physics.

Benjamin Rogers
Complex fluids and biological physics, programmable self-assembly of soft materials.

Gabriella Sciolla, Chair
Experimental high-energy physics.

Brian Swingle
Fundamental physics of quantum information, especially in the context of many-body systems and gravity.

Emily Tiberi
Atomic, molecular, and optical (AMO) physics, specifically using ultracold atoms and molecules to probe fundamental physics through precision measurements.

Hannah Yevick
Biological physics, mechanobiology, physics of development

Six semester courses in physics at the level of PHYS 10 or above. Note that PHYS 18a,b and PHYS 19a,b count as one semester courses.

No grade below a C- will be given credit toward the minor and no course taken pass/fail may count toward the minor requirements.

Required of All Majors

Foundational Literacies: As part of completing the Physics major, students must:

• Fulfill the writing intensive requirement by successfully completing one of the following: PHYS 39a or PHYS 99d.

• Fulfill the oral communication requirement by successfully completing one of the following: PHYS 39a or PHYS 99d.

• Fulfill the digital literacy requirement by successfully completing one of the following: PHYS 18a, PHYS 18b, PHYS 19a, or PHYS 19b.

Degree of Bachelor of Arts

The Bachelor of Arts degree is meant for students who are not intending to pursue graduate studies in physics. For example, the student might desire to pursue climate science, science journalism, the history or philosophy of science, patent law, economics, business, pre-medical studies, or K-12 science education. Thus, the BA degree provides a solid grounding in physics, but does not include the breadth of advanced courses in Physics found in the BS requirements. There are 10 total courses required for the major:

1. PHYS 15a,b or PHYS 11a,b
2. PHYS 19a,b or PHYS 18a,b
3. PHYS 20a
4. PHYS 31a
5. PHYS 40a
6. PHYS 39a
7. One semester of mathematics numbered higher than first-year calculus (MATH 10a,b) 
8. One elective physics course
9. No course with a grade of below C- can be used to satisfy the requirements of the major.
10. No course taken pass/fail may count toward the major requirements.

Degree of Bachelor of Science

This degree provides the rigorous training needed for students intending to pursue graduate work in physics or engineering. There are 17 total courses required for the major:

1. PHYS 11a,b or PHYS 15a,b

2. PHYS 19a,b

3. PHYS 20a

4.  PHYS 30a

5. PHYS 31a,b

6. PHYS 40a

7. Two additional semesters of laboratory courses in Physics; ENGR 11a can satisfy one of these semesters.

8. Three additional courses in Physics, two of which must be numbered 20 or above.

9. Either MATH 15a and 20a, or MATH 22a,b.

10. Two additional upper-level courses in the Division of Science excluding Physics courses: Math courses numbered above 22; Computer Science courses numbered above 20; or any other courses approved by the department. Physics courses may not be used to fulfill this requirement, even those that are cross-listed in another department. Courses from other departments that are cross-listed with Physics are eligible. 

11. No course with a grade of below C- can be used to satisfy the requirements of the major.

12. No course taken pass/fail may count toward the major requirements.

There are several natural tracks through the undergraduate physics courses. The first is: Year 1—PHYS 11a,b or 15a,b, PHYS 19a,b, MATH 10a,b or Math 15a and Math20a, or Math 22ab; Year 2—PHYS 20a, PHYS 31a, PHYS 29a, or MATH 15a and 20a, or MATH 22a,b; Year 3—PHYS 30a, 31b, PHYS 39a, PHYS 40a; Year 4—Electives; PHYS 100a is strongly recommended for all majors.

The second, a premedical track, is: Year 1—PHYS 11a,b or 15a,b, PHYS 19a,b, MATH 10a,b; Year 2—PHYS 20a, PHYS 31a, CHEM 11a,b, 18a,b; Year 3—BIOL 22ab, BIOL 18a,b, CHEM 25a,b, 29a; Year 4—PHYS 29a, PHYS 30a, 31b. Note that while the requirements for the BA and BS degrees in physics are not changed for pre-medical students, as many as two suitable upper-level science courses outside of physics may be substituted for physics courses with the permission of the undergraduate advising coordinator. Students should consult the premedical advisors before deciding on a program.

Students are encouraged to construct other tracks that might better suit their needs in consultation with their advisers.

Students considering a career in engineering should consult the description of the Columbia University School of Engineering Combined Degree Program in the special academic opportunities section of this Bulletin.

A student intending to pursue graduate work in physics will normally add to the tracks above courses selected from elective such as PHYS 39a, 100a, 102a, 103a, 104a, 105a, 108b, 110a, and 111a, or graduate courses dealing with previously treated subjects at a more advanced level, such as PHYS 161a,b and 162a,b. Normally only some of the physics elective courses will be offered in a given year; the others will normally be offered in the following year. Undergraduates are not permitted to enroll in physics courses numbered above 160 without the explicit approval of their appropriate major advisers.

A student who has attained a grade of 4 or 5 on the Advanced Placement Examination Physics B may obtain credit for PHYS 10a,b; a student who has attained a grade of 4 or 5 on the Advanced Placement Examination C: Mechanical may obtain credit for PHYS 11a while a grade of 4 or 5 on Advanced Placement Examination Physics C: Electrical may earn credit for PHYS 11b. A student who claims any of these advanced placement credits may not take the same or equivalent courses for credit: PHYS 10a,b, or PHYS 11a,b. If a student wishes to claim AP credit AND take PHYS 15a,b, (recommended for many students with AP credit) then the AP credit earns course credit (towards the 128 total credits degree requirement) but does not count towards the physics major. PHYS 15 earns both course credit and counts toward the physics major.

In order to be a candidate for a degree with distinction in physics, majors must successfully complete and receive a grade of B- or higher in a departmentally approved honors program of either PHYS 99d or two semester courses in physics numbered 161, 162, or 163. Students must have their honors programs approved by the departmental advising coordinator before the beginning of their penultimate semester.

A. Normally, first-year graduate students will elect courses from the 100 series, with at least four courses numbered above 160. The required first-year courses are 

1. PHYS 161a, 
2. PHYS 162a,b
3. PHYS 163a 
4. PHYS 164a

B. A laboratory course, PHYS 169b or QBIO 120b is also required in the first or second year. 

C. To obtain credit toward residence for a graduate course taken at Brandeis, a student must achieve a final grade of B- or better in that course. Students may obtain credit for advanced courses taken at another institution, provided their level corresponds to the level of graduate courses at Brandeis and that an honor grade in those courses was obtained. Please see the GSAS section on transfer credit for more details. To place out of any of the PHYS 161, 162, or 163 sequences, a student must pass an exemption exam before the end of the second week of the course.

Residence Requirement

For those accepted for full-time study, there is a one-year in-person residency requirement. No transfer residence credit will be allowed toward the fulfillment of the Master's requirements. The program may take an additional one or two semesters to complete as an Extended Master's student. Part-time students have an in-person residency requirement that is equivalent to the full-time version of the program.

Course Requirements

1. Eight semester courses in physics (or, with the approval of the Graduate Advising Head, a related subject) numbered above 100.
2. A Master's thesis on an approved topic may be accepted in place of a semester course. Students must electronically deposit their Master’s thesis to ProQuest ETD. For instructions on how to do this, visit the Thesis and Dissertation Guide. The four-credit thesis course PHYS 300a can substitute for one of the eight required physics courses.

Language Requirement

There is no foreign language requirement for advanced degrees in physics.

Qualifying Examination

Satisfactory performance in the qualifying examination is required. The qualifying examination consists of a written and an oral part, and both parts are administered during the first year of the program. The written part of the qualifying examination is the final examinations in PHYS 161a, 162a,b, and 163a; these are also considered as passed if they have been exempted by separate examination, or if credit has been given for equivalent courses taken elsewhere. The student must pass one oral exam on general physics at the college level, consisting of short presentations based on two assigned original papers from the research literature, and questions from members of the examination committee.

Requirements for the Degree of Master of Science in Physics with Specialization in Quantitative Biology

Students wishing to obtain the specialization in Quantitative Biology (QB) must first gain approval of the Physics representative for the QB program (listed online on the Brandeis QB website). This should be done as early as possible in the program. In order to receive the M.S. in Physics with specialization in QB, candidates must complete (a) the requirements for the M.S. described above and (b) the course requirements for the QB specialization described in the QB section of this Bulletin.

Any alteration to the QB course requirements must be approved by both the Physics Program Chair and the QB Program Chair.

All of the requirements for the master's degree as well as the following:

Residence Requirement

The minimum in-person residence requirement is three years. Time spent working at a physics lab outside of Brandeis, such as CERN or a national lab, while carrying out dissertation research is considered in-person residence.

Teaching Requirement

All PhD students are required to participate in undergraduate teaching during the course of their studies. Every graduate teaching assistant (TA) is supervised by a member of the faculty, who serves as a mentor to improve the quality of the TA's teaching.

Please see the GSAS section on Teaching Requirements and the program handbook for more details.

Course Requirements

1. In addition to the general requirements for advanced degree candidates and the requirements for the master’s degree, all PhD students must pass PHYS 161a, 162a,b, and 163a with grades of B or above. 
2. Each student must also take three elective advanced courses in physics or a related subject, including at least one in physics, chosen in consultation with and subject to the approval of the Graduate Advising Head, and passed with a grade of B or above.
3. A total of at least nine semester courses in physics numbered above 160 are required for the doctoral degree.
4. Each summer, full-time PhD students are required to do work related to their research area under the supervision of a faculty member. The work can take the form of dissertation research, or can involve an industrial internship. Students doing dissertation research over the summer should register for CONT 250. Students doing an industrial internship must have the consent of their advisor and should register for PHYS 393g.

Advanced Examinations

Advanced examinations are in topics partitioned in the several areas of research interest of the faculty. Faculty members working in each general area function as a committee for this purpose and provide information about their work through informal discussions and seminars. The advanced examination requirement consists of a written paper and an oral examination. Although no original research by the student is required, it is hoped that a proposal for a possible thesis topic will emerge. It is expected that the candidates will take the advanced examination in the field they wish to pursue for the PhD thesis by the beginning of the fourth term in order to qualify for continued departmental support beyond the second year.

Thesis Research

After passing the advanced examination, the student begins work with an advisor, who guides his or her research program. The advisor should be a member of the Brandeis faculty but in special circumstances may be a scientist associated with another research institution. The student and advisor together choose the dissertation committee, subject to the approval of the Graduate Advising Head.  The student's dissertation advisor will be the chair of the dissertation committee.

Dissertation and Final Oral Examination

The doctoral dissertation must represent research of a standard acceptable to the faculty committee appointed for each PhD candidate. The final oral examination, or defense, is an examination in which the student will be asked questions pertaining to the dissertation research. Students must electronically deposit their dissertation to ProQuest  ETD. For instructions on how to do this, visit the Thesis and Dissertation Guide.

Summer Registration

PhD students in the Physics program are required to be on campus or at a related lab for the full year while engaged in taking classes and/or doing research related to their field of study and will be enrolled in CONT 250b by the Registrar's office. Registration for Graduate Summer Term does not count toward the residency requirement. The summer registration fee will be waived.

Requirements for the Degree of Doctor of Philosophy in Physics with Specialization in Quantitative Biology

Program of Study

Students wishing to obtain the specialization must first gain approval of the Graduate Advising Head for Physics. This should be done as early as possible, ideally during the first year of graduate studies. In order to receive the PhD in physics with additional specialization in quantitative biology, candidates must complete (a) the requirements for the PhD described above and (b) the course requirements for the quantitative biology specialization that are described in the quantitative biology section of this Bulletin.

Any alteration to the quantitative biology course requirements must be approved by the  Graduate Advising Head for Physics and by the quantitative biology program faculty advisory committee.

Every student, whether or not currently in residence, must register at the beginning of each term. All graduate students will be evaluated by the program each spring. At this evaluation the records of all graduate students will be carefully reviewed with reference to the timely completion of coursework and non-course degree requirements, the quality of the work and research in progress and the student’s overall academic performance in the program. 

ENGR 11a Introduction to Design Methodology
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Prerequisite: Instructor permission required.

An introduction to the engineering design process, with a focus on human-centered design. Students work in teams to solve authentic design problems under the theme of “design to repair the world.” Students are guided through a highly scaffolded process in which they form an idea, sketch it, and develop it through multiple iterations leveraging quick feedback loops and the Design Thinking methodology. Students will become fluent in basic additive and subtractive manufacturing, including 3D printing, laser cutting, and CNC machining. Usually offered every year.

ENGR 13a Modeling and Simulation
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Prerequisites: MATH 10a and PHYS 10a or higher, or permission of the instructor. PHYS 11a or 15a is strongly recommended.

Building models of physical systems is a critical aspect of science and engineering. While models are expressed through the languages of math and physics, developing a good mental picture of the system at hand requires drawing on experience. Towards providing students with this experience, this course will build connections between the theoretical, the experimental, and the designed. They will be guided through a structured series of labs on a variety of system classes including nonlinear mechanical systems, infectious disease dynamics, mass transport, and coupled oscillators. In three of the labs, students will not only analyze and model a physical system but also use digital fabrication (3D printing, laser cutting, or CNC milling) to build and test physical versions of their models. This course is intended as a first exposure to modeling. Prior experience in programming is not required. Students will receive Python notebooks for each lab to be used for data analysis, numerically solving dynamical models, fitting models to data, and visualizing results. Practical coding skills, such as debugging, elaborating notebooks and learning to leverage open-source software, will be taught in a lab environment where students and the instructor can readily collaborate and solve challenges. Usually offered every year.

PHYS 10a Introduction to Physical Laws and Phenomena I
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Usually taken with PHYS 18a.

An introduction to Newtonian mechanics, kinetic theory, and thermodynamics. Usually offered every year.

PHYS 10b Introduction to Physical Laws and Phenomena II
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Usually taken with PHYS 18b.

An introduction to electricity and magnetism, optics, special theory of relativity, and the structure of the atom. Usually offered every year.

PHYS 11a Introductory Physics I
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Corequisite: MATH 10a or the equivalent. Usually taken with PHYS 19a.

An introduction to Newtonian mechanics with applications to several topics. Usually offered every year.

PHYS 11b Introductory Physics II
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Corequisite: MATH 10b or the equivalent. Usually taken with PHYS 19b. Prerequisite: PHYS 11a or equivalent.

An introduction to electricity and magnetism and the special theory of relativity. Usually offered every year.

PHYS 12b Algorithmic Art
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Prerequisite: MATH 10a.

Snowflakes, flower petals, the spiral arms of a galaxy, waves and dunes, the stripes on a tiger--all are examples of naturally occurring patterns. While a beautiful pattern appeals to the aesthetic side of our brains, it also begs the question of whether we can recreate such artful designs. Hence, there is a motivation to understand beauty with logic.

Mathematics provides us with tools to characterize patterns, and physics teaches us how to understand the emergence of patterns. This course will help you learn some selected topics in math and physics that you will use to create designs. You will learn to use computer programming to materialize these abstract concepts into powerful visuals. We will start our algorithmic art journey by discussing basics of coding, coordinate geometry, matrix algebra, and using each of these concepts to create something beautiful. Then we will move on to more advanced topics like cluster finding algorithm, differential equations and random walks, and use these sophisticated tools to make art.

This interdisciplinary, interactive course will encourage creativity and teach you many transferrable skills like coding, collaboration, deconstruction of a complex problem into simple parts, communication of ideas by visual means, and teamwork, all of which are useful skills for various types of projects. Towards the end of the semester, you will hear talks from professional artists about their approach to art. As students exploring visual art within the field of science, these talks will enrich our own understanding of beauty and aesthetics and teach you new concepts to apply in your own unique way in the creation of original science-inspired art. Special one-time offering, spring 2024.

PHYS 15a Advanced Introductory Physics I
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Corequisite: MATH 10b or the equivalent. Usually taken with PHYS 19a.

An advanced version of PHYS 11a for students with advanced preparation in physics and mathematics. An introduction to Newtonian mechanics with special applications to several topics. Usually offered every year.

PHYS 15b Advanced Introductory Physics II
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Prerequisite: PHYS 11a or PHYS 15a or the equivalent, and MATH 10b or equivalent, or permission of instructor. Usually taken with PHYS 19b.

An advanced version of PHYS 11b for students with good preparation in physics and mathematics. An introduction to electricity and magnetism and the special theory of relativity for students with advanced preparation. Usually offered every year.

PHYS 18a Introductory Laboratory I
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Corequisite: PHYS 10a. May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10a. Usually offered every year.

PHYS 18b Introductory Laboratory II
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Corequisite: PHYS 10b. May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10b. Usually offered every year.

PHYS 19a Physics Laboratory I
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May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course designed to accompany PHYS 11a and 15a. Introductory statistics and data analysis including use of microcomputers and basic experiments in mechanics. One afternoon or evening of laboratory per week. One one-and-a-half-hour lecture per week. Usually offered every year.

PHYS 19b Physics Laboratory II
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May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course designed to accompany PHYS 11b and 15b. Basic experiments in electricity, magnetism, and optics. Basic electrical measurements. Determination of several fundamental physical constants. One afternoon or evening of laboratory per week. One one-and-a-half-hour lecture per week. Usually offered every year.

PHYS 20a Waves and Oscillations
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Prerequisites: PHYS 11a, PHYS 11b or PHYS 15a, PHYS 15b or permission of the instructor.

A survey of phenomena, ideas, and mathematics underlying modern physics-special relativity, waves and oscillations, and foundations of wave mechanics. Usually offered every year.

PHYS 29a Electronics Laboratory I
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Prerequisites: PHYS 11a, b or PHYS 15a, b; and PHYS 19a, b or permission of instructor. Students without a background in Physics should contact the instructor to discuss course requirements and receive permission to enroll.

Introductory laboratory in electronics. Topics to be covered are time constants, frequency response, rectification, amplification, radio reception, combinatorial logic, digital state machines, and analog-to-digital conversion. The class will solve first and second order differential equations directly and with the help of the complex exponential. Usually offered every spring.

PHYS 30a Electromagnetism
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Prerequisite: PHYS 20a and PHYS 31a, or permission of the instructor.

The fundamentals of electromagnetic theory. Includes electrostatics, magnetostatics, electric and magnetic circuits, and Maxwell's equations. Usually offered every year.

PHYS 31a Quantum Theory I
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Prerequisites: PHYS 20a and either PHYS 11a and b or PHYS 15a and b, or permission of the instructor.

Introduction to quantum mechanics: atomic models, Schrödinger equation, angular momentum, and hydrogen atom. Multielectron atoms and interaction of atoms with the electromagnetic field. Usually offered every year.

PHYS 31b Quantum Theory II
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Prerequisite: PHYS 31a.

A continuation of PHYS 31a. Topics include time-independent and time-dependent perturbation theory, identical particles, with applications to atomic, nuclear and condensed matter physics, scattering theory, and special topics as time allows. Usually offered every year.

PHYS 39a Advanced Physics Laboratory
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Prerequisite: PHYS 20a. This course may be repeated once for credit with permission of the instructor. This course is co-taught with PHYS 169b.

Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three experiments during the term. Usually offered every year.

PHYS 40a Introduction to Thermodynamics and Statistical Mechanics
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Prerequisite: PHYS 20a or permission of the instructor.

Studies the properties of physical systems as predicted by the statistical behavior of their constituent particles. Statistical mechanics provides a molecular-level interpretation of macroscopic thermodynamic quantities such as work, heat, free energy, and entropy. Topics studied will include; the laws of Thermodynamics, semi-classical and quantumstatistical mechanics, ensembles (microcanonical, canonical, and grand canonical), thermodynamic potentials and applications to a number of different systems. Usually offered every year.

PHYS 91g Introduction to Research Practice

Prerequisite: Student must complete online safety training relevant to the research group. Offered exclusively on a credit/no-credit basis. Yields quarter-course credit. May be repeated for credit.

Students engage in Physics research by working in the laboratory of a faculty member for a minimum of 3 hours per week for one semester. Students who have declared a Physics major must receive permission from the Physics Undergraduate Advising Head as well as the faculty sponsor to enroll in PHYS 91g. Usually offered every year.

PHYS 92a Research Internship, Off-Campus

Prerequisite: Permission of the undergraduate advising head.

Same as PHYS 93a but work is performed off-campus. Work done off-campus must be presented in the same forms to the appropriate research group during the semester following completion of the work. Usually offered every year.

PHYS 93a Research Internship

Prerequisite: Permission of the undergraduate advising head required.

The physics research internship provides students with an opportunity to work in a research setting for one semester, on-campus, pursuing a project that has the potential to produce new scientific results. Student and faculty members mutually design a project that supports the research agenda of the group. Students must attend all research group meetings and present their findings in oral and written form at the end of the semester. The project typically includes theoretical, computational, and/or laboratory research, and may involve collaboration with other group members. In some cases, credit toward the physics laboratory requirement may be given. Course requires signature of the instructor, is subject to the availability of undergraduate research positions, and is typically open only to juniors and seniors. Usually offered every year.

PHYS 97a Tutorial in Physics

Tutorial for students studying advanced material not covered in regular courses. Usually offered every year.

PHYS 97b Tutorial in Physics

Tutorial for students studying advanced material not covered in regular courses. Usually offered every year.

PHYS 98a Readings in Physics

Open to exceptional students who wish to study an area of physics not covered in the standard curriculum. Usually offered every year.

PHYS 98b Readings in Physics

Open to exceptional students who wish to study an area of physics not covered in the standard curriculum. Usually offered every year.

PHYS 99d Senior Research

Permission of the undergraduate advising head required.

Original research under the direction of a faculty committee. A written thesis and oral defense are required. The complete set of rules is available from the physics department office. Usually offered every year.

NPHY 115a Dynamical Systems
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Prerequisites: MATH 10a, b or equivalent; MATH 15a and/or some coding experience would be helpful.

An introduction to the theory of nonlinear dynamical systems, including bifurcations, limit cycles, chaos, and coupled oscillators. Covers analytical, computational, and graphical methods of solving sets of nonlinear ordinary differential equations, as well as mathematical modeling of natural phenomena. Examples will be drawn from physics, chemistry, population biology, and neuroscience. Usually offered every third year.

PHYS 100a Classical Mechanics
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Prerequisites: PHYS 20a or permission of the instructor.

The goal of this course is to engage students in an exploration of classical mechanics from a modern perspective. Students are expected to have familiarity with Newtonian Mechanics, and have taken a calculus-based mechanics course. Usually offered every second year.

PHYS 102a General Relativity
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Prerequisites: PHYS 20a or permission of instructor.

An introduction to the basic principles of general relativity. Topics include a review of special relativity, tensor analysis in curved space-times, the principle of equivalence, the Einstein equations, the Schwarzschild solution, and experimental tests of general relativity. Usually offered every second year.

PHYS 104a Condensed Matter Physics
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Prerequisite: Phys 40a or permission of instructor.

Mechanical, thermal, and electronic properties of matter including fluids, solids, liquid crystals, and polymers. Simple models of matter are developed and used to discuss recent experimental findings. Usually offered every second year.

PHYS 105a Biological Physics
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Physical forces in living matter are studied from the perspective offered by statistical mechanics, elasticity theory, and fluid dynamics. Quantitative models for biological structure and function are developed and used to analyze systems such as single molecule experiments, transcriptional regulation networks, the forces arising during DNA packaging in a virus, and mechanisms underlying mammalian pattern formation. Usually offered every second year.

PHYS 107b Particle Physics
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Prerequisite: PHYS 30a or permission of the instructor. Corequisite: PHYS 31a (formerly PHYS 30b) or permission of the instructor.

The phenomenology of elementary particles and the strong, weak, and electromagnetic interactions are studied. Properties of particles, quarks, neutrinos, vector bosons, Higgs particles, supersymmetry, symmetries, and conservation laws are covered. This course is co-taught with the graduate course PHYS 167b, and the workload will be appropriate to each group. Usually offered every second year.

PHYS 108b Astrophysics
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Prerequisites: Physics 20a or permission of instructor.

Application of basic physical principles to the study of stars, galaxies, quasars, and the large-scale structure of the universe. Usually offered every second year.

PHYS 111a Physical Continuum Mechanics
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Prerequisites: PHYS 30a, PHYS 31a, or permission of the instructor.

Studies physics of continuous media, focused on fluid mechanics or the theory of elasticity. Subjects include: basic equations; simple static solutions; small pertubations / wave equations; dislocations in elastic media; instabilities and turbulence in fluids; biophysical and geophysical applications. Usually offered every second year.

PHYS 159b Programming in Physics
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Aimed at students who are looking to learn how to write high quality object-oriented code for physics simulations. In this class, you will learn how to write code that is readable and easily passed to other scientists. How to write tests for your code to be confident in its behavior and how to structure your code so it is easy to add new measurements or simulation features. We will use specific physics applications to demonstrate these concepts; additional applications related to each student’s area of research or interest will be chosen for the final projects. Usually offered every year.

PHYS 161a Electromagnetic Theory I
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Electrostatics, magnetostatics, Maxwell’s equations, electromagnetic waves. Usually offered every year.

PHYS 161b Electromagnetic Theory II
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Radiation. Relativistic dynamics. A selection of other topics such as electromagnetism in matter, optics, and field quantization. Usually offered every second year.

PHYS 162a Quantum Mechanics I
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Lagrangian and Hamiltonian classical mechanics; fundamentals of nonrelativistic quantum theory and its application to simple systems; quantum entanglement and quantum statistical mechanics. Usually offered every year.

PHYS 162b Quantum Mechanics II
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Path integral formulation of quantum mechanics. Quantum treatment of identical particles. Approximate methods: variational, WKB, and perturbation theory. Applications to atoms, molecules, and solids. Usually offered every year.

PHYS 163a Statistical Physics and Thermodynamics
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Prerequisite: PHYS 40a, or graduate level standing.

The thermal properties of matter. Derivation of thermodynamics from statistical physics. Statistical theory of fluctuations. Phases and phase transitions. Usually offered every year.

PHYS 163b Principles of Soft Materials Theory
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Prerequisite: PHYS 163a or the equivalent.

Introduces non equilibrium statistical mechanics and applications of equilibrium and non equilibrium statistical mechanics to understanding emergent phenomena in soft materials such as colloids, polymers and liquid crystals. Usually offered every second year.

PHYS 164a First Year Tutorial I
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Yields half-course credit.

A review of physics from the most elementary topics to those treated in other first-year graduate courses. The environment of an oral qualifying examination is reproduced in the tutorial. Usually offered every year.

PHYS 167b Particle Phenomenology
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The phenomenology of elementary particles and the strong, weak, and electromagnetic interactions. Properties of particles, kinematics of scattering and decay, phase space, quark model, unitary symmetries, and conservation laws. This course is co-taught with PHYS 107b, and the workload will be appropriate to each group. Usually offered every second year.

PHYS 168b Introduction to Astrophysics
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Bremsstrahlung, synchrotron radiation, inverse Compton scattering. Extended and compact radio sources, jets, superluminal motion. Quasars and active galactic nuclei, IR to X-ray continua, spectral line formation. Black holes and accretion disks. Cosmology. Usually offered irregularly as demand requires; consult department.

PHYS 169b Advanced Laboratory
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Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three or four experiments during the term. This course is co-taught with PHYS 39a. Usually offered every year.

PHYS 202a Quantum Field Theory

Prerequisite: PHYS 161a and PHYS 162a, or permission of the instructor.

Methods of statistical and quantum field theory, including path integrals, second quantization, Feynman diagrams, renormalization group, epsilon expansions, effective field theory. Applications ranging from phase transitions and critical phenomena to gauge theories of particle physics. Usually offered every second year.

PHYS 204a Condensed Matter II

Modern techniques such as effective field theory, scaling, and the renormalization group are introduced and used to study solids, magnets, liquid crystals, and macromolecules. Most of the theory is developed on simple models and applied experiments. Usually offered every second year.

PHYS 212a Introduction to Research I

Open to first year graduate students in Physics.

Supervised introductory research, consisting of advanced readings in the primary literature and/or introductory lab work. The student will meet with the instructor weekly to discuss the reading or work, attend group meetings and seminars, and present a short written report and oral presentation at the end of the semester. Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 212b Introduction to Research II

Open to first year graduate students in Physics.

Supervised introductory research, consisting of advanced readings in the primary literature and/or introductory lab work. The student will meet with the instructor weekly to discuss the reading or work; attend group meetings and seminars; and present a short written report and oral presentation at the end of the semester. Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 213a Advanced Examination Tutorial I

Supervised preparation for the advanced examination. Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 213b Advanced Examination Tutorial II

Supervised preparation for the advanced examination. Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 280a Advanced Readings

Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 280b Advanced Readings

Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 300a Master's Thesis

Instructor and DGS permission required.

Students who have selected and received approval from the faculty member supervising the thesis and the Director of Graduate Study, may enroll in this thesis course with their faculty supervisor. The thesis consists of reading some advanced mathematics material in the form of topics books or a series of research articles, writing a thesis on a topic, and presenting the results of your reading and research during an oral presentation at the end of the semester. Usually offered every year.

PHYS 393g Graduate Research Internship

Permission of the graduate program director required. Yields quarter-course credit. May be repeated for credit. For Ph.D. students only.

Offers Ph.D students an opportunity to engage in industrial research in a field which enhances their dissertation research topic in physics by completing a paid or unpaid internship of at least ten weeks duration and forty hours per week, approved and monitored by a faculty member. Usually offered every summer.

PHYS 401a Dissertation Research

Independent research for the PhD. Specific sections for individual faculty members as requested. Usually offered every semester.

PHYS 401b Dissertation Research

Independent research for the PhD. Specific sections for individual faculty members as requested. Usually offered every semester.

PHYS 18a Introductory Laboratory I
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Corequisite: PHYS 10a. May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10a. Usually offered every year.

PHYS 18b Introductory Laboratory II
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Corequisite: PHYS 10b. May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10b. Usually offered every year.

PHYS 19a Physics Laboratory I
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May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course designed to accompany PHYS 11a and 15a. Introductory statistics and data analysis including use of microcomputers and basic experiments in mechanics. One afternoon or evening of laboratory per week. One one-and-a-half-hour lecture per week. Usually offered every year.

PHYS 19b Physics Laboratory II
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May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course designed to accompany PHYS 11b and 15b. Basic experiments in electricity, magnetism, and optics. Basic electrical measurements. Determination of several fundamental physical constants. One afternoon or evening of laboratory per week. One one-and-a-half-hour lecture per week. Usually offered every year.

PHYS 39a Advanced Physics Laboratory
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Prerequisite: PHYS 20a. This course may be repeated once for credit with permission of the instructor. This course is co-taught with PHYS 169b.

Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three experiments during the term. Usually offered every year.

PHYS 99d Senior Research

Permission of the undergraduate advising head required.

Original research under the direction of a faculty committee. A written thesis and oral defense are required. The complete set of rules is available from the physics department office. Usually offered every year.

PHYS 39a Advanced Physics Laboratory
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Prerequisite: PHYS 20a. This course may be repeated once for credit with permission of the instructor. This course is co-taught with PHYS 169b.

Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three experiments during the term. Usually offered every year.

PHYS 99d Senior Research

Permission of the undergraduate advising head required.

Original research under the direction of a faculty committee. A written thesis and oral defense are required. The complete set of rules is available from the physics department office. Usually offered every year.

BCBP 200b Reading in Macromolecular Structure-Function Analysis

Introduces students to chemical and physical approaches to biological problems through critical evaluation of the original literature. Students analyze scientific papers on a wide range of topics in the fields of biochemistry and biophysics. Discussion focuses on understanding of the scientific motivation for and experimental design of the studies. Particular emphasis is placed on making an independent determination of whether the author's conclusions are well justified by the experimental results. Students are also introduced to grant-proposal writing by preparing NIH-format mock proposals for critical discussion and evaluation. Usually offered every year.

ENGR 11a Introduction to Design Methodology
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Prerequisite: Instructor permission required.

An introduction to the engineering design process, with a focus on human-centered design. Students work in teams to solve authentic design problems under the theme of “design to repair the world.” Students are guided through a highly scaffolded process in which they form an idea, sketch it, and develop it through multiple iterations leveraging quick feedback loops and the Design Thinking methodology. Students will become fluent in basic additive and subtractive manufacturing, including 3D printing, laser cutting, and CNC machining. Usually offered every year.

ENVS 110a Data Analysis for Environmental Studies
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People in environmental fields increasingly need career-ready technical skills for managing, analyzing, and representing diverse types of data. The goal of this course is to engage students in authentic work with environmental data through a combination of collaborative, hands-on Python programming and project-based learning. Usually offered every year.

QBIO 110a Numerical Modeling of Biological Systems
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Prerequisite: MATH 10a and b or equivalent.

Modern scientific computation applied to problems in molecular and cell biology. Covers techniques such as numerical integration of differential equations, molecular dynamics and Monte Carlo simulations. Applications range from enzymes and molecular motors to cells. Usually offered every second year.

QBIO 120b Quantitative Biology Instrumentation Laboratory
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Focuses on optical and other instruments commonly used in biomedical laboratories to make quantitative measurements in vivo and in vitro. Students disassemble and reconfigure modular instruments in laboratory exercises that critically evaluate instrument reliability and usability and investigate the origins of noise and systematic error in measurements. Usually offered every year.