Rockefeller Building

http://www.phys.cwru.edu/

Phone: 216.368.4000; Fax: 216.368.4671

Kathleen Kash, Department Chair

http://www.phys.cwru.edu/

Phone: 216.368.4000; Fax: 216.368.4671

Kathleen Kash, Department Chair

The Department of Physics offers programs leading to the following undergraduate degrees: Bachelor of Arts, Bachelor of Science in physics, Bachelor of Science in mathematics and physics, and Bachelor of Science in engineering with an engineering physics major. Associated with the Bachelor of Science in physics degree are optional concentrations in mathematical physics and in biophysics. The department also offers the graduate degrees Master of Science and Doctor of Philosophy, as well as a unique master’s degree in entrepreneurship.

All of these programs involve the study of the basic laws of nature and the properties of energy and matter in their various forms. The curriculum reflects the varied interests of the faculty and will prepare students for a wide range of future activities. At the undergraduate level, open electives and engineering physics concentration area courses tailor the programs to the student’s interests and career plans. Employment opportunities at the bachelor’s level include research, development, and technical assistance (engineering, computer programming, management) in industrial, government, and university settings.

A similar flexibility exists in the first few years of graduate study. The research leading to the PhD degree normally centers on a specific area of physics. However, even at this stage, the broad background and training characteristic of a physics degree are emphasized.

Kathleen Kash, PhD

(Massachusetts Institute of Technology)*Professor and Chair*

Experimental condensed matter and mesoscopic physics; synthesis of novel semiconductors

Daniel S. Akerib, PhD

(Princeton University)*Professor*

Experimental astrophysics

Jesse Berezovsky, PhD

(University of California, Santa Barbara)*Assistant Professor*

Imaging coherent transport in mesoscopic graphene; optical readout of single spin dynamics in a quantum dot; spin dynamics in layered core/shell nanocrystal quantum dots; measurements of nuclear and electron spin at a ferromagnetic/semiconductor interface; spatio-temporal imaging and simulation of magnetization dynamics in ferromagnetic structures

Robert W. Brown, PhD

(Massachusetts Institute of Technology)*Distinguished University Professor and Institute Professor*

Medical imaging; industrial physics; particle physics theory; cosmology

Gary S. Chottiner, PhD

(University of Maryland)*Professor and Director of Undergraduate Studies*

Experimental physics of surfaces and thin films

Corbin E. Covault, PhD

(Harvard University)*Professor*

Experimental high-energy astrophysics

Claudia de Rham, PhD

(University of Cambridge)*Assistant Professor*

Massive gravity and degravitation; Supersymmetric Large Extra Dimensions (SLED); physics of codimension-2 objects; cosmological perturbations

Diana I. Driscoll, PhD

(Case Western Reserve University)*Instructor*

Introductory physics

Xuan Gao, PhD

(Columbia University)*Associate Professor*

Experimental condensed matter physics; nanomaterials; electron transport in nanostructures; correlated electrons in low dimensions

Kenneth L. Kowalski, PhD

(Brown University)*Professor*

Theoretical and experimental particle physics

Walter R. Lambrecht, PhD

(University of Ghent)*Professor*

Theoretical condensed matter physics; electronic structure-based physics of materials

Michael A. Martens, PhD

(Case Western Reserve University)*Associate Professor*

Medical imaging physics, high energy particle physics, accelerator physics

Harsh Mathur, PhD

(Yale University)*Associate Professor*

Condensed matter theory, particle-astrophysics theory

Rolfe G. Petschek, PhD

(Harvard University)*Professor*

Theoretical condensed matter; optical materials

Charles Rosenblatt, PhD

(Harvard University)*Professor and Ohio Eminent Scholar in Condensed Matter Physics*

Experimental condensed matter; liquid crystals and complex fluids

John E. Ruhl, PhD

(Princeton University)*Professor*

Experimental astrophysics and cosmology

Jie Shan, PhD

(Columbia University)*Associate Professor*

Experimental condensed matter physics; electronic and optoeletronic properties and dynamics of nanoscale materials

Thomas A. Shutt, PhD

(University of California, Berkeley)*Agnar Pytte Professor*

Experimental astrophysics

Kenneth D. Singer, PhD

(University of Pennsylvania)*Ambrose Swasey Professor of Physics; Director, Engineering Physics*

Experimental condensed matter physics; nonlinear optics

Glenn D. Starkman, PhD

(Stanford University)*Professor; Director, Center for Education and Research in Cosmology and Astrophysics (CERCA)*

Theoretical cosmology, particle physics, astrophysics

Giuseppe Strangi, PhD

(University of Calabria, Italy)*Professor and The Ohio Research Scholar in Surfaces of Advanced Materials*

Opto-Plasmonics of Soft Composite Metamaterials; Liquid Crystal Photonics

Cyrus C. Taylor, PhD

(Massachusetts Institute of Technology)*Albert A. Michelson Professor in Physics; Dean, College of Arts and Sciences*

Theoretical and experimental particle physics; physics entrepreneurship

Philip L. Taylor, PhD

(University of Cambridge)*Distinguished University Professor and Perkins Professor of Physics*

Theory of solids, polymers and other materials

Andrew J. Tolley, PhD

(University of Cambridge)*Assistant Professor*

Early universe cosmology; dark energy; gravity; extra dimensions; branes

J. Iwan Alexander, PhD

(Washington State University)*Professor, Department of Mechanical and Aerospace Engineering, Case School of Engineering*

Fluid dynamics, energy research

Roger H. French, PhD

(Massachusetts Institute of Technology)*F. Alex Nason Professor, Department of Materials Science and Engineering, Case School of Engineering*

Optical materials and technologies; experimental VIS/UV/VUV optical properties and long range interactions

Mark A. Griswold, PhD

(University of Wuerzburg)*Associate Professor, Department of Radiology, School of Medicine*

Medical imaging, MRI

Eckhard Jankowsky, PhD

(Dresden Institute of Technology)*Associate Professor, Department of Biochemistry, School of Medicine*

Proteins and enzymes; structural biology; regulation of gene expression

R. Earle Luck, PhD

(University of Texas at Austin)*Worcester R. and Cornelia B. Warner Professor of Astronomy*

Stellar and galactic chemical evolution; stellar spectrophotometry

J. Christopher Mihos, PhD

(University of Michigan)*Worcester R. and Cornelia B. Warner Professor, Department of Astronomy*

Galaxy formation and evolution; galaxy interactions; clusters of galaxies; observational and computational astrophysics

Heather Morrison, PhD

(Australian National University)*Professor, Department of Astronomy*

Galactic structure; stellar populations; dark matter

Idit Zehavi, PhD

(Hebrew University of Jerusalem)*Assistant Professor, Department of Astronomy*

Astrophysics

Edward M. Caner, MS

(Case Western Reserve University)*Full-time Lecturer; Director, Science and Technology Entrepreneurship Program*

Science entrepreneurship

James H. Andrews, PhD

(Case Western Reserve University)*Adjunct Professor; Professor of Physics, Youngstown State University*

Optical materials

Pierre Carlès, PhD, Habilitation

(National Polytechnic Institute, Toulouse)*Adjunct Associate Professor; Associate Professor, Université Pierre et Marie Curie, Paris*

Fluid mechanics; critical behavior; stability

Craig J. Copi, PhD

(University of Chicago)*Adjunct Instructor; Senior Research Associate*

Theoretical cosmology; particle physics; astrophysics

Michael R. Dragowsky, PhD

(Oregon State University)*Adjunct Associate Professor*

Nuclear and particle astrophysics experiment

Jeffrey S. Dyck, PhD

(Case Western Reserve University)*Adjunct Associate Professor; Associate Professor, John Carroll University*

Experimental condensed matter physics

Karsten Eggert, PhD

(RWTH Aachen University)*Adjunct Professor*

Experimental particle physics; cosmic ray physics; diffractive physics; TOTEM experiment at CERN

Hiroyuki Fujita, PhD

(Case Western Reserve University)*Adjunct Professor; President and CEO, Quality Electrodynamics and eQED*

Hardware technology in imaging and renewable energies

Evalyn Gates, PhD

(Case Western Reserve University)*Adjunct Professor; Executive Director and CEO, Cleveland Museum of Natural History*

Cosmology and particle astrophysics

John T. Giblin, Jr., PhD

(Yale University)*Adjunct Assistant Professor*

Theoretical cosmology; high energy physics and particle physics; high performance computing and gravitational waves

E. Mark Haacke, PhD

(University of Toronto)*Adjunct Professor; Professor, Wayne State University*

Physics of imaging; experimental biophysics

Daeseung Kang, PhD

(Case Western Reserve University)*Adjunct Associate Professor*

Experimental condensed matter; liquid crystal

Peter J. Kernan, PhD

(Ohio State University)*Adjunct Instructor; Senior Research Associate*

Cosmology; Astrophysics

Gerald T. Mearini, PhD

(Case Western Reserve University)*Adjunct Associate Professor; Genvac Aerospace Corporation*

Timothy Peshek, PhD

(Case Western Reserve University)*Adjunct Assistant Professor*

Experimental semiconductor physics

Andrey Petukhov, PhD

(St. Petersburg State Technical University)*Adjunct Associate Professor; Associate Professor of Physics, South Dakota School of Mines and Technology*

Irina Shiyanovskaya, PhD

(Institute of Physics, National Academy of Science of Ukraine)*Adjunct Associate Professor; Kent Displays, Inc.*

Shmaryu Shvartsman, PhD

(Tomsk State University)*Adjunct Professor; Principal Scientist, ViewRay Inc.*

General physics research and development

Mano Singham, PhD

(University of Pittsburgh)*Adjunct Associate Professor; Director, University Center for Innovation in Teaching and Education (UCITE)*

Particle physics; physics teaching

Michael Thompson, PhD

(Case Western Reserve University)*Adjunct Assistant Professor; Director of Research, Development, and Advanced Applications, AllTech Medical Systems America *

MRI signal acquisition

Mesfin Tsige, PhD

(Case Western Reserve University)*Adjunct Associate Professor*

Theory of solids; polymers and other materials

Jesse M. Kinder, PhD

(University of Pennsylvannia)*Visiting Assistant Professor*

Theoretical solid state physics; nanotechnology; strongly correlated systems; modeling and method development

Ina Martin

(Colorado State University)*MORE Center Director of Operations*

Thermal management materials; photovoltaic materials

BA in Physics | BS in Physics | BSE in Engineering Physics | BS Math and Physics | Minor

Course requirements and typical schedules for the majors are summarized in the Plan of Study Grids (click the button above).

The BA physics major includes a large number of elective courses, making it easy for the student to pursue other interests or complete a second major while earning a degree in physics.

The Physics Department offers a special option for undergraduate students who wish to pursue a Physics major and a career in teaching. The Adolescent to Young Adult (AYA) Teacher Education Program in Physical Sciences prepares CWRU students to receive an Ohio Teaching License for grades 7-12. Students declare a second major in Education - which involves 34 hours in Education and practicum requirements - and complete a planned sequence of Physics courses within the context of the B.A. Physics major. The program is designed to offer several unique features not found in other programs and to place students in mentored teaching situations throughout their teacher preparation career. This small, rigorous program is designed to capitalize on the strengths of CWRU's Physics Department, its Teacher Education Program, and the relationships the University has built with area schools. (For details on education course work, see the program description for Teacher Licensure elsewhere in this bulletin.)

The BS degree has two alternatives to the standard program: a mathematical physics concentration and a biophysics concentration.

The BSE degree in engineering physics supplies an excellent background for graduate studies in physics, but is also designed for students who value an engineering credential and who are considering a career in engineering, either through employment following the BSE or through engineering graduate studies. This degree is awarded by the Case School of Engineering and includes the Engineering Core Curriculum. The technical electives in this program are concentrated in any of sixteen specific engineering areas.

The BS in mathematics and physics is a single degree for students interested in advanced mathematics and theoretical physics and their relationships. This degree is distinct from the mathematical physics concentration in the BS in physics degree. The program is jointly administered by the Departments of Physics and Mathematics, and students may be advised by faculty members from either department.

All BS, BA, and BSE candidates complete a year-long senior project in which they work one-on-one with a faculty researcher, write a senior thesis, and present their work in public.

Course requirements for the minor in physics are as follows:

PHYS 121 | General Physics I - Mechanics | 4 |

or PHYS 116 | Introductory Physics II | |

or PHYS 123 | Physics and Frontiers I - Mechanics | |

PHYS 122 | General Physics II - Electricity and Magnetism | 4 |

or PHYS 116 | Introductory Physics II | |

or PHYS 124 | Physics and Frontiers II - Electricity and Magnetism | |

PHYS 221 | Introduction to Modern Physics | 3 |

Two of the following courses: | 6 | |

Advanced Laboratory Physics I | ||

Classical Mechanics | ||

Thermodynamics and Statistical Mechanics | ||

Introduction to Solid State Physics | ||

Introduction to Nuclear and Particle Physics | ||

Electricity and Magnetism I | ||

Physical Optics | ||

Laser Physics | ||

Cosmology and the Structure of the Universe | ||

or PHYS 336 | Modern Cosmology | |

Introduction to Quantum Mechanics I | ||

Introduction to Quantum Mechanics II | ||

Total Units | 17 |

* | The Case School of Engineering has a policy stating that “no more than two courses taken for the minor may be used simultaneously to satisfy the requirements of the student’s major field, including departmental requirements, technical electives and the Engineering Core.” Thus, engineering students may have to choose between using physics courses as technical electives or counting them as part of a minor in physics. |

The Department of Physics offers programs of study and research leading to both the Master of Science and the Doctor of Philosophy degrees. Graduate assistantships are available for the full-time support of qualified students. All MS programs in physics, with or without a thesis, normally can be completed in less than two years. The requirements for the PhD degree in physics include a flexible program of courses that typically is completed within three years, and a concurrent program of directed research with less course work and more research in each succeeding year.

In addition to a traditional physics program, the department has created a Physics Entrepreneurship master’s degree program, which is part of the university’s larger Science and Technology Entrepreneurship Program. This two-year program is designed to empower physicists as entrepreneurs. It enables students and graduates to build on their physics skills to start new high-tech businesses or to launch new product lines in existing companies. The program provides top-level academic instruction and real-world entrepreneurial experience while connecting students with the business executives and leaders, experts, and venture capitalists who are crucial to success in start-up and growing ventures.

For the PhD degree, the student is required to pass a general qualifying examination in physics, which is normally taken after the first year of study, and a topical oral examination within one year of joining a research group. The student must then prepare a dissertation based on the results of independent research. There is no foreign language requirement. Research pursuant to any of the graduate degree programs in physics may be carried out in five areas:

*Condensed Matter Physics*. An extensive experimental and theoretical program in the electronic properties of solids; quantum liquids; mesoscopic physics; localization and quantum Hall effect; the physics of polymers, liquid crystals, and complex fluids; thin films; fluids dynamics; materials synthesis; the physics of surfaces and interfaces; electronic structure of materials and their defects; vibrational properties of solids (phonons); magnetism and magnetic materials; nano- and organic electronics.

*Particle/Astrophysics and Cosmology*. The experimental efforts in this area include the study of the nature of dark matter in the universe, observations of high-energy gamma rays and cosmic rays, and measurements of the cosmic microwave background. Theoretical studies include the cosmic microwave background, gravitational lensing, dark matter, dark energy, structure formation, neutrino astrophysics, topological defects, phase transitions, inflation, non-gaussianities, gravitational waves, black holes, extra dimensions, modified gravity, and tests of General Relativity.

The Center for Education and Research in Cosmology and Astrophysics (CERCA) comprises groups from the Departments of Physics and Astronomy and the Cleveland Museum of Natural History. The center organizes international conferences, hosts visitors and lectures, and supports students and faculty in their research. As it grows, it will provide postdoctoral research positions and will also prepare public programs on cosmology and astrophysics.

*Elementary Particle Physics*. Theoretical studies in the strong, weak, and electromagnetic interactions of the elementary particles, and in all areas of particle theory, gravitation, and cosmology.

*Optics and Optical Materials*. Both experimental and theoretical programs in nonlinear optics, integrated optics, ultrafast optics, and the optical properties of fluids, liquid crystals, polymers, and crystals, including semiconductors, semiconductor mesoscopic systems, photonic crystals, and nanoscopic systems.

*Imaging Physics, Biophysics, and Inverse Problems*. An experimental and theoretical program in aspects of non-invasive imaging, including magnetic resonance imaging and ultrasound; medical diagnostic techniques to measure iron in the liver; and industrial and medical applications in electromagnetic field modeling.

The Bachelor of Arts degree with a physics major requires completion of the Arts and Sciences General Education Requirements (GER) and 120 total credits, of which 59 are specified by the physics department as shown below. Courses specified for this major satisfy the 6-credit Arts and Sciences GER in Sciences and Mathematics.

One of the following: | 4 | |

Introductory Physics I | ||

General Physics I - Mechanics | ||

Physics and Frontiers I - Mechanics | ||

One of the following: | 4 | |

Introductory Physics II | ||

General Physics II - Electricity and Magnetism | ||

Physics and Frontiers II - Electricity and Magnetism | ||

All of the following: | ||

PHYS 221 | Introduction to Modern Physics | 3 |

PHYS 250 | Computational Methods in Physics | 3 |

PHYS 301 | Advanced Laboratory Physics I | 3 |

PHYS 303 | Advanced Laboratory Physics Seminar ^{1} | 1 |

PHYS 313 | Thermodynamics and Statistical Mechanics | 3 |

PHYS 331 | Introduction to Quantum Mechanics I | 3 |

PHYS 351 | Senior Physics Project (PHYS 351 is taken twice for 2 credit hours each) ^{1} | 4 |

PHYS 352 | Senior Physics Project Seminar (PHYS 352 is taken twice for 1 credit hour each) ^{1} | 2 |

Two of the following: | 6 | |

Classical Mechanics | ||

Electricity and Magnetism I | ||

Introduction to Solid State Physics | ||

Introduction to Nuclear and Particle Physics | ||

Physical Optics | ||

Laser Physics | ||

Cosmology and the Structure of the Universe ^{2} | ||

Modern Cosmology ^{2} | ||

General Relativity | ||

All of the following: | ||

Intro Science 1 ^{3} | 3 | |

Intro Science 2 ^{3} | 3 | |

ENGR 131 | Elementary Computer Programming ^{4} | 3 |

MATH 121 | Calculus for Science and Engineering I | 4 |

One of the following: | 4 | |

Calculus for Science and Engineering II | ||

Calculus II | ||

Math and Calculus Applications for Life, Managerial, and Social Sci II | ||

MATH 223 | Calculus for Science and Engineering III | 3 |

or MATH 227 | Calculus III | |

MATH 224 | Elementary Differential Equations | 3 |

PHED Physical Education (2 semesters) | 0 | |

SAGES First and University Seminars | 10 | |

Breadth Requirements ^{5} | 12 | |

Open electives ^{6} | 39 | |

Total Units | 120 |

^{1} | PHYS 303 Advanced Laboratory Physics Seminar + PHYS 352 Senior Physics Project Seminar satisfy the SAGES departmental seminar requirement. PHYS 351 Senior Physics Project is an approved SAGES capstone course. |

^{2} | Students may choose only one of these two courses to satisfy the requirements of the BA degree. |

^{3} | A two-course science sequence chosen from CHEM 105 Principles of Chemistry I and CHEM 106 Principles of Chemistry II; CHEM 111 Principles of Chemistry for Engineers and ENGR 145 Chemistry of Materials; BIOL 214 Genes, Evolution and Ecology and BIOL 215 Cells and Proteins; or another two-course sequence totaling 6 or more credits in a quantitative science (other than physics), with written approval of the physics undergraduate curriculum committee. |

^{4} | Or other approved computational course. |

^{5} | The breadth requirements include 6 hours of Social Sciences and 6 hours of Arts and Humanities. This may increase by 3 credits if the required Global and Cultural Diversity course is not also one of the breadth requirement courses. Courses required for the BA in Physics satisfy the 6-credit GER for Natural Sciences and Mathematics as well as the Quantitative Reasoning course requirement. |

^{6} | The BA degree requires a minimum of 30 semester hours at the 300-400 level, of which only 22 are specified as PHYS courses. |

First Year | Units | |
---|---|---|

Fall | Spring | |

Introductory Physics I (PHYS 115) or General Physics I - Mechanics (PHYS 121) or Physics and Frontiers I - Mechanics (PHYS 123) | 4 | |

Calculus for Science and Engineering I (MATH 121) | 4 | |

Intro Science Elective I | 3 | |

SAGES First Seminar | 4 | |

Physics Today and Tomorrow (PHYS 166) | 1 | |

PHED Physical Education Activities | 0 | |

Introductory Physics II (PHYS 116) or General Physics II - Electricity and Magnetism (PHYS 122) or Physics and Frontiers II - Electricity and Magnetism (PHYS 124) | 4 | |

Calculus for Science and Engineering II (MATH 122) | 4 | |

Intro Science Elective II | 3 | |

University Seminar | 3 | |

Elementary Computer Programming (ENGR 131) | 3 | |

PHED Physical Education Activities | 0 | |

Year Total: | 16 | 17 |

Second Year | Units | |

Fall | Spring | |

Introduction to Modern Physics (PHYS 221) | 3 | |

Calculus for Science and Engineering III (MATH 223) | 3 | |

University Seminar | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Computational Methods in Physics (PHYS 250) | 3 | |

Physics Elective | 3 | |

Elementary Differential Equations (MATH 224) | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Year Total: | 15 | 15 |

Third Year | Units | |

Fall | Spring | |

Advanced Laboratory Physics I (PHYS 301) | 3 | |

Advanced Laboratory Physics Seminar (PHYS 303) | 1 | |

Thermodynamics and Statistical Mechanics (PHYS 313) | 3 | |

Introduction to Quantum Mechanics I (PHYS 331) | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 2 | |

Physics Elective | 3 | |

Global and Cultural Diversity Elective | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Open Elective | 3 | |

Year Total: | 15 | 15 |

Fourth Year | Units | |

Fall | Spring | |

Senior Physics Project (PHYS 351) | 2 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Open Elective | 3 | |

Open Elective | 3 | |

Open Elective | 3 | |

Open Elective | 3 | |

Senior Physics Project (PHYS 351) | 2 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Open Elective | 3 | |

Open Elective | 3 | |

Open Elective | 3 | |

Year Total: | 15 | 12 |

Total Units in Sequence: | 120 |

The Bachelor of Science in physics requires completion of the courses listed in the table below as well as the Arts and Sciences General Education Requirements, for a total of 127 credits. Many courses may be taken at times other than those shown in the "Typical Schedule" tables below.

PHYS 121 | General Physics I - Mechanics | 4 |

or PHYS 123 | Physics and Frontiers I - Mechanics | |

PHYS 122 | General Physics II - Electricity and Magnetism | 4 |

or PHYS 124 | Physics and Frontiers II - Electricity and Magnetism | |

PHYS 221 | Introduction to Modern Physics | 3 |

PHYS 203 | Analog and Digital Electronics | 4 |

PHYS 204 | Advanced Instrumentation Laboratory | 4 |

PHYS 250 | Computational Methods in Physics | 3 |

PHYS 310 | Classical Mechanics | 3 |

PHYS 301 | Advanced Laboratory Physics I | 3 |

PHYS 303 | Advanced Laboratory Physics Seminar ^{1} | 1 |

PHYS 313 | Thermodynamics and Statistical Mechanics | 3 |

PHYS 331 | Introduction to Quantum Mechanics I | 3 |

PHYS 332 | Introduction to Quantum Mechanics II | 3 |

PHYS 302 | Advanced Laboratory Physics II | 4 |

PHYS 324 | Electricity and Magnetism I | 3 |

PHYS 325 | Electricity and Magnetism II | 3 |

PHYS 351 | Senior Physics Project (PHYS 351 is taken twice for 2 credit hours each) ^{1} | 4 |

PHYS 352 | Senior Physics Project Seminar (PHYS 352 is taken twice for 1 credit hour each) ^{1} | 2 |

Choose one of the following: | 3 | |

Introduction to Solid State Physics | ||

Physical Optics | ||

Laser Physics | ||

Choose one of the following: | 3 | |

Introduction to Nuclear and Particle Physics | ||

Cosmology and the Structure of the Universe | ||

Modern Cosmology | ||

General Relativity | ||

CHEM 105 | Principles of Chemistry I | 3-4 |

or CHEM 111 | Principles of Chemistry for Engineers | |

CHEM 106 | Principles of Chemistry II | 3-4 |

or ENGR 145 | Chemistry of Materials | |

ENGR 131 | Elementary Computer Programming ^{2} | 3 |

MATH 121 | Calculus for Science and Engineering I | 4 |

MATH 122 | Calculus for Science and Engineering II | 4 |

or MATH 124 | Calculus II | |

MATH 223 | Calculus for Science and Engineering III | 3 |

or MATH 227 | Calculus III | |

MATH 224 | Elementary Differential Equations | 3 |

PHED Physical Education (2 semesters) | 0 | |

SAGES First and University Seminars | 10 | |

Breadth Requirements ^{3} | 12 | |

Open Electives ^{4} | 22 | |

Total Units | 127-129 |

^{1} | PHYS 303 Advanced Laboratory Physics Seminar + PHYS 352 Senior Physics Project Seminar satisfy the SAGES departmental seminar requirement. PHYS 351 Senior Physics Project is an approved SAGES capstone course. |

^{2} | Or other approved computational course. |

^{3} | The breadth requirements include 6 hours of Social Sciences and 6 hours of Arts and Humanities. This may increase by 3 credits if the required Global and Cultural Diversity course is not also one of the breadth requirement courses. Courses required for the BS in physics satisfy the 6-credit GER for Natural Sciences and Mathematics as well as the Quantitative Reasoning course requirement. |

^{4} | The number of open electives may vary, depending on how many credits a student needs to reach the required total of 127. |

First Year | Units | |
---|---|---|

Fall | Spring | |

General Physics I - Mechanics (PHYS 121) or Physics and Frontiers I - Mechanics (PHYS 123) | 4 | |

Calculus for Science and Engineering I (MATH 121) | 4 | |

Principles of Chemistry I (CHEM 105) or Principles of Chemistry for Engineers (CHEM 111) | 3-4 | |

SAGES First Seminar | 4 | |

Physics Today and Tomorrow (PHYS 166) | 1 | |

PHED Physical Education Activities | 0 | |

General Physics II - Electricity and Magnetism (PHYS 122) or Physics and Frontiers II - Electricity and Magnetism (PHYS 124) | 4 | |

Calculus for Science and Engineering II (MATH 122) | 4 | |

Principles of Chemistry II (CHEM 106) or Chemistry of Materials (ENGR 145) | 3-4 | |

Elementary Computer Programming (ENGR 131) | 3 | |

University Seminar | 3 | |

PHED Physical Education Activities | 0 | |

Year Total: | 16-17 | 17-18 |

Second Year | Units | |

Fall | Spring | |

Analog and Digital Electronics (PHYS 203) | 4 | |

Introduction to Modern Physics (PHYS 221) | 3 | |

Calculus for Science and Engineering III (MATH 223) | 3 | |

University Seminar | 3 | |

Humanities/Social Science Elective | 3 | |

Advanced Instrumentation Laboratory (PHYS 204) | 4 | |

Computational Methods in Physics (PHYS 250) | 3 | |

Classical Mechanics (PHYS 310) | 3 | |

Elementary Differential Equations (MATH 224) | 3 | |

Humanities/Social Science Elective | 3 | |

Year Total: | 16 | 16 |

Third Year | Units | |

Fall | Spring | |

Advanced Laboratory Physics I (PHYS 301) | 3 | |

Advanced Laboratory Physics Seminar (PHYS 303) | 1 | |

Thermodynamics and Statistical Mechanics (PHYS 313) | 3 | |

Introduction to Quantum Mechanics I (PHYS 331) | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Advanced Laboratory Physics II (PHYS 302) | 4 | |

Electricity and Magnetism I (PHYS 324) | 3 | |

Introduction to Quantum Mechanics II (PHYS 332) | 3 | |

Global and Cultural Diversity Elective | 3 | |

Open Elective | 3 | |

Year Total: | 16 | 16 |

Fourth Year | Units | |

Fall | Spring | |

Electricity and Magnetism II (PHYS 325) | 3 | |

Senior Physics Project (PHYS 351) | 2 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Condensed Matter Physics Elective | 3 | |

Open Elective | 3 | |

Open Elective | 3 | |

Senior Physics Project (PHYS 351) | 2 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Particle/Astrophysics Elective | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Open Elective | 3 | |

Year Total: | 15 | 15 |

Total Units in Sequence: | 127-129 |

Students who are interested in theoretical physics and who have a strong background in mathematics may consider this concentration. The program is based on the BS in physics, but with certain substitutions in the course requirements. Several of the laboratory courses are replaced by advanced mathematics courses, and some of the undergraduate physics courses are replaced by graduate courses.

This program is not the same as the BS program in mathematics and physics, which provides a coherent and parallel education in both mathematics and physics.

The following table shows the requirements for the Bachelor of Science in physics with mathematical physics concentration.

PHYS 121 | General Physics I - Mechanics | 4 |

or PHYS 123 | Physics and Frontiers I - Mechanics | |

PHYS 122 | General Physics II - Electricity and Magnetism | 4 |

or PHYS 124 | Physics and Frontiers II - Electricity and Magnetism | |

PHYS 221 | Introduction to Modern Physics | 3 |

PHYS 203 | Analog and Digital Electronics (or M-Group 1²) | 4 |

PHYS 250 | Computational Methods in Physics | 3 |

PHYS 310 | Classical Mechanics | 3 |

PHYS 301 | Advanced Laboratory Physics I | 3 |

PHYS 303 | Advanced Laboratory Physics Seminar ^{3} | 1 |

PHYS 349 | Methods of Mathematical Physics I | 3 |

PHYS 313 | Thermodynamics and Statistical Mechanics | 3 |

PHYS 481 | Quantum Mechanics I | 3 |

Choose PHYS 423 or both PHYS 324 & PHYS 325 | 3 | |

Classical Electromagnetism | ||

Electricity and Magnetism I | ||

Electricity and Magnetism II | ||

PHYS 482 | Quantum Mechanics II | 3 |

PHYS 350 | Methods of Mathematical Physics II | 3 |

M-Group 1, 2 & 3 ^{1} | 9 | |

PHYS 351 | Senior Physics Project (PHYS 351 is taken twice for 2 credit hours each) ^{2} | 4 |

PHYS 352 | Senior Physics Project Seminar (PHYS 352 is taken twice for 1 credit hour each) ^{2} | 2 |

Choose one of the following: | 3 | |

Introduction to Solid State Physics | ||

Physical Optics | ||

Laser Physics | ||

Choose one of the following: | 3 | |

Introduction to Nuclear and Particle Physics | ||

Cosmology and the Structure of the Universe | ||

Modern Cosmology | ||

General Relativity | ||

CHEM 105 | Principles of Chemistry I | 3-4 |

or CHEM 111 | Principles of Chemistry for Engineers | |

CHEM 106 | Principles of Chemistry II | 3-4 |

or ENGR 145 | Chemistry of Materials | |

ENGR 131 | Elementary Computer Programming ^{3} | 3 |

MATH 121 | Calculus for Science and Engineering I | 4 |

MATH 122 | Calculus for Science and Engineering II | 4 |

or MATH 124 | Calculus II | |

MATH 223 | Calculus for Science and Engineering III | 3 |

or MATH 227 | Calculus III | |

MATH 224 | Elementary Differential Equations | 3 |

PHED 2 semesters | 0 | |

SAGES First and University Seminars | 10 | |

Breadth Requirements ^{4} | 12 | |

Open Electives ^{5} | 18 | |

Total Units | 127-129 |

^{1} | M-group 1, 2 and 3 are to be chosen from among approved advanced mathematics or statistics courses. |

^{2} | PHYS 303 Advanced Laboratory Physics Seminar + PHYS 352 Senior Physics Project Seminar satisfy the SAGES departmental seminar requirement. PHYS 351 Senior Physics Project is an approved SAGES capstone course. |

^{3} | Or other approved computational course. |

^{4} | The breadth requirements include 6 hours of Social Sciences and 6 hours of Arts and Humanities. This may increase by 3 credits if the required Global and Cultural Diversity course is not also one of the breadth requirement courses. Courses required for the BS in physics satisfy the 6-credit GER for Natural Sciences and Mathematics as well as the Quantitative Reasoning course requirement. |

^{5} | The number of open electives may vary, depending on the number of credits a student needs to reach the required total of 127. |

First Year | Units | |
---|---|---|

Fall | Spring | |

General Physics I - Mechanics (PHYS 121) or Physics and Frontiers I - Mechanics (PHYS 123) | 4 | |

Calculus for Science and Engineering I (MATH 121) | 4 | |

Principles of Chemistry I (CHEM 105) or Principles of Chemistry for Engineers (CHEM 111) | 3-4 | |

Physics Today and Tomorrow (PHYS 166) | 1 | |

SAGES First Seminar | 4 | |

PHED Physical Education Activities | 0 | |

General Physics II - Electricity and Magnetism (PHYS 122) or Physics and Frontiers II - Electricity and Magnetism (PHYS 124) | 4 | |

Calculus for Science and Engineering II (MATH 122) | 4 | |

Principles of Chemistry II (CHEM 106) or Chemistry of Materials (ENGR 145) | 3-4 | |

Elementary Computer Programming (ENGR 131) | 3 | |

University Seminar | 3 | |

Humanities/Social Science Elective | 3 | |

PHED Physical Education Activities | 0 | |

Year Total: | 16-17 | 20-21 |

Second Year | Units | |

Fall | Spring | |

Analog and Digital Electronics (PHYS 203) | 4 | |

Introduction to Modern Physics (PHYS 221) | 3 | |

Calculus for Science and Engineering III (MATH 223) | 3 | |

University Seminar | 3 | |

Humanities/Social Science Elective | 3 | |

Computational Methods in Physics (PHYS 250) | 3 | |

Classical Mechanics (PHYS 310) | 3 | |

Elementary Differential Equations (MATH 224) | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Year Total: | 16 | 15 |

Third Year | Units | |

Fall | Spring | |

Advanced Laboratory Physics I (PHYS 301) | 3 | |

Advanced Laboratory Physics Seminar (PHYS 303) | 1 | |

Thermodynamics and Statistical Mechanics (PHYS 313) | 3 | |

Methods of Mathematical Physics I (PHYS 349) | 3 | |

Quantum Mechanics I (PHYS 481) | 3 | |

Humanities/Social Science Elective | 3 | |

Methods of Mathematical Physics II (PHYS 350) | 3 | |

Quantum Mechanics II (PHYS 482) | 3 | |

Global and Cultural Diversity Elective | 3 | |

Advanced Mathematics Elective | 3 | |

Electricity and Magnetism I (PHYS 324) | 3 | |

Year Total: | 16 | 15 |

Fourth Year | Units | |

Fall | Spring | |

Senior Physics Project (PHYS 351) | 2 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Condensed Matter Physics Elective | 3 | |

Advanced Mathematics Elective | 3 | |

Electricity and Magnetism II (PHYS 325) | 3 | |

Open Elective | 4 | |

Senior Physics Project (PHYS 351) | 2 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Particle/Astrophysics Elective | 3 | |

Advanced Mathematics Elective | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 4 | |

Year Total: | 16 | 16 |

Total Units in Sequence: | 130-132 |

This concentration is directed towards students interested in the combined study of biology and physics. The degree is a track within the standard BS in physics, in which four physics courses and certain open electives are replaced by a “biogroup” of five courses and a technical elective. All substitutions must be approved by a physics faculty committee.

The following table illustrates the requirements for the Bachelor of Science in physics with biophysics concentration.

PHYS 121 | General Physics I - Mechanics | 4 |

or PHYS 123 | Physics and Frontiers I - Mechanics | |

PHYS 122 | General Physics II - Electricity and Magnetism | 4 |

or PHYS 124 | Physics and Frontiers II - Electricity and Magnetism | |

PHYS 221 | Introduction to Modern Physics | 3 |

PHYS 203 | Analog and Digital Electronics | 4 |

PHYS 204 | Advanced Instrumentation Laboratory | 4 |

PHYS 250 | Computational Methods in Physics | 3 |

PHYS 310 | Classical Mechanics | 3 |

PHYS 301 | Advanced Laboratory Physics I | 3 |

PHYS 303 | Advanced Laboratory Physics Seminar ^{1} | 1 |

PHYS 313 | Thermodynamics and Statistical Mechanics | 3 |

PHYS 331 | Introduction to Quantum Mechanics I | 3 |

PHYS 324 | Electricity and Magnetism I | 3 |

PHYS 325 | Electricity and Magnetism II | 3 |

Technical Elective ^{2} | 3 | |

PHYS 351 | Senior Physics Project (PHYS 351 is taken twice for 2 credit hours each) ^{1} | 4 |

PHYS 352 | Senior Physics Project Seminar (PHYS 352 is taken twice for 1 credit hour each) ^{1} | 2 |

CHEM 105 | Principles of Chemistry I | 3-4 |

or CHEM 111 | Principles of Chemistry for Engineers | |

CHEM 106 | Principles of Chemistry II | 3-4 |

or ENGR 145 | Chemistry of Materials | |

CHEM 113 | Principles of Chemistry Laboratory | 2 |

ENGR 131 | Elementary Computer Programming ^{3} | 3 |

MATH 121 | Calculus for Science and Engineering I | 4 |

MATH 122 | Calculus for Science and Engineering II | 4 |

or MATH 124 | Calculus II | |

MATH 223 | Calculus for Science and Engineering III | 3 |

or MATH 227 | Calculus III | |

MATH 224 | Elementary Differential Equations | 3 |

B-Group 1 ^{4} | 3-4 | |

B-Group 2 ^{4} | 3-4 | |

B-Group 3 ^{4} | 3 | |

B-Group 4 ^{4} | 3 | |

B-Group 5 ^{4} | 3-4 | |

PHED 2 Semesters | 0 | |

SAGES First and University Seminars | 10 | |

Breadth Requirements ^{5} | 12 | |

Open Electives ^{6} | 15 | |

Total Units | 127-132 |

^{1} | |

^{2} | Suggested technical electives include PHYS 315 Introduction to Solid State Physics, PHYS 316 Introduction to Nuclear and Particle Physics, PHYS 326 Physical Optics, PHYS 327 Laser Physics, PHYS 328 Cosmology and the Structure of the Universe, PHYS 336 Modern Cosmology, PHYS 365 General Relativity. |

^{3} | Or other approved computational course. |

^{4} | B-group 1-5 are to be chosen from among approved biology, biophysics, biochemistry, and biomedical engineering courses, including certain prerequisites as needed (e.g., chemistry). BIOL 214 Genes, Evolution and Ecology and BIOL 215 Cells and Proteins are suggested for B-group 1 and 2. The listing of credits includes numbers for the most likely choices of courses and, in parentheses, possible alternatives. |

^{5} | The breadth requirements include 6 hours of Social Sciences and 6 hours of Arts and Humanities. This may increase by 3 credits if the required Global and Cultural Diversity course is not also one of the breadth requirement courses. Courses required for the B.S. in physics satisfy the 6-credit GER for Natural Sciences and Mathematics as well as the Quantitative Reasoning course requirement. |

^{6} | The number of open electives may vary, depending on the number of credits a student needs to reach the required total of 127. |

First Year | Units | |
---|---|---|

Fall | Spring | |

General Physics I - Mechanics (PHYS 121) or Physics and Frontiers I - Mechanics (PHYS 123) | 4 | |

Calculus for Science and Engineering I (MATH 121) | 4 | |

Principles of Chemistry I (CHEM 105) or Principles of Chemistry for Engineers (CHEM 111) | 3-4 | |

Principles of Chemistry Laboratory (CHEM 113) | 2 | |

Physics Today and Tomorrow (PHYS 166) | 1 | |

SAGES First Seminar | 4 | |

PHED Physical Education Activities | 0 | |

General Physics II - Electricity and Magnetism (PHYS 122) or Physics and Frontiers II - Electricity and Magnetism (PHYS 124) | 4 | |

Calculus for Science and Engineering II (MATH 122) | 4 | |

Principles of Chemistry II (CHEM 106) or Chemistry of Materials (ENGR 145) | 3-4 | |

Elementary Computer Programming (ENGR 131) | 3 | |

Biogroup Elective | 4 | |

PHED Physical Education Activities | 0 | |

Year Total: | 18-19 | 18-19 |

Second Year | Units | |

Fall | Spring | |

Analog and Digital Electronics (PHYS 203) | 4 | |

Introduction to Modern Physics (PHYS 221) | 3 | |

Calculus for Science and Engineering III (MATH 223) | 3 | |

Biogroup Elective | 3 | |

University Seminar | 3 | |

Advanced Instrumentation Laboratory (PHYS 204) | 4 | |

Computational Methods in Physics (PHYS 250) | 3 | |

Classical Mechanics (PHYS 310) | 3 | |

Elementary Differential Equations (MATH 224) | 3 | |

University Seminar | 3 | |

Year Total: | 16 | 16 |

Third Year | Units | |

Fall | Spring | |

Advanced Laboratory Physics I (PHYS 301) | 3 | |

Advanced Laboratory Physics Seminar (PHYS 303) | 1 | |

Thermodynamics and Statistical Mechanics (PHYS 313) | 3 | |

Introduction to Quantum Mechanics I (PHYS 331) | 3 | |

Biogroup Elective | 4 | |

Humanities/Social Science Elective | 3 | |

Electricity and Magnetism I (PHYS 324) | 3 | |

Biogroup Elective | 3 | |

Global and Cultural Diversity Elective | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Year Total: | 17 | 15 |

Fourth Year | Units | |

Fall | Spring | |

Electricity and Magnetism II (PHYS 325) | 3 | |

Senior Physics Project (PHYS 351) | 2 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Physics Elective | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Senior Physics Project (PHYS 351) | 2 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Biogroup Elective | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Year Total: | 15 | 12 |

Total Units in Sequence: | 127-129 |

The engineering physics major allows students with strong interests in both physics and engineering to concentrate their studies in the common areas of these disciplines. The major prepares students to pursue careers in industry, either directly after undergraduate studies, or following graduate study in engineering or physics. Many employers value the unique problem-solving approach of physics, especially in industrial research and development.

Students majoring in engineering physics complete the Engineering Core as well as a rigorous course of study in physics. Students select a concentration area from an engineering discipline, and must complete a sequence of at least four courses in this discipline. In addition, a senior research project under the guidance of a faculty member is required. The project includes a written report and participation in the senior seminar and symposium.

First Year | Units | |
---|---|---|

Fall | Spring | |

General Physics I - Mechanics (PHYS 121)^{2} | 4 | |

Calculus for Science and Engineering I (MATH 121)^{1} | 4 | |

Principles of Chemistry for Engineers (CHEM 111) | 4 | |

SAGES First Seminar | 4 | |

PHED Physical Education Activities | 0 | |

General Physics II - Electricity and Magnetism (PHYS 122)^{2} | 4 | |

Calculus for Science and Engineering II (MATH 122)^{1} | 4 | |

Elementary Computer Programming (ENGR 131) | 3 | |

Chemistry of Materials (ENGR 145) | 4 | |

University Seminar | 3 | |

PHED Physical Education Activities | 0 | |

Year Total: | 16 | 18 |

Second Year | Units | |

Fall | Spring | |

Introduction to Modern Physics (PHYS 221) | 3 | |

Calculus for Science and Engineering III (MATH 223) | 3 | |

Statics and Strength of Materials (ENGR 200) | 3 | |

Introduction to Circuits and Instrumentation (ENGR 210) | 4 | |

University Seminar | 3 | |

Instrumentation and Signal Analysis Laboratory (PHYS 208) | 4 | |

Computational Methods in Physics (PHYS 250) | 3 | |

Classical Mechanics (PHYS 310) | 3 | |

Elementary Differential Equations (MATH 224) | 3 | |

Thermodynamics, Fluid Dynamics, Heat and Mass Transfer (ENGR 225) | 4 | |

Year Total: | 16 | 17 |

Third Year | Units | |

Fall | Spring | |

Advanced Laboratory Physics Seminar (PHYS 303) | 1 | |

Thermodynamics and Statistical Mechanics (PHYS 313) | 3 | |

Engineering Physics Laboratory I (PHYS 317) | 3 | |

Introduction to Quantum Mechanics I (PHYS 331) | 3 | |

Engineering Concentration^{3} | 3 | |

Humanities/Social Science Elective | 3 | |

Engineering Physics Laboratory II (PHYS 318) | 4 | |

Electricity and Magnetism I (PHYS 324) | 3 | |

Professional Communication for Engineers (ENGL 398) & Professional Communication for Engineers (ENGR 398) | 3 | |

Humanities/Social Science Elective | 3 | |

Engineering Concentration^{3} | 3 | |

Year Total: | 16 | 16 |

Fourth Year | Units | |

Fall | Spring | |

Introduction to Solid State Physics (PHYS 315) | 3 | |

Electricity and Magnetism II (PHYS 325) | 3 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Senior Engineering Physics Project (PHYS 353) | 2 | |

Engineering Concentration^{3} | 3 | |

Humanities/Social Science Elective | 3 | |

Senior Physics Project Seminar (PHYS 352) | 1 | |

Senior Engineering Physics Project (PHYS 353) | 2 | |

Applied Quantum Mechanics^{4} | 3 | |

Engineering Concentration^{3} | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

Year Total: | 15 | 15 |

Total Units in Sequence: | 129 |

^{1} | Selected students may be invited to take MATH 123, 124, 227, and 228 in place of MATH 121, 122, 223, and 224. |

^{2} | Selected students may be invited to take PHYS 123, 124 (Physics and Frontiers I, II Honors) in place of PHYS 121, 122. |

^{3} | Engineering physics concentration courses are flexible, but they must be in a specific engineering discipline or study area and approved by an advisor. Possible concentration areas include aerospace engineering, biomedical engineering “hardware,” biomedical engineering “software,” chemical engineering, civil engineering (solid mechanics, structural and geotechnical, environmental), computer science, computer systems hardware, computer systems software, control systems and automation, electrical engineering, macromolecular science, materials science and engineering, mechanical engineering, signal processing, systems analysis and decision making. |

^{4} | PHYS 332, PHYS 327/427, EEAP 321, EEAP 420, EMSE 314, or EMSE. Students may choose to fulfill this requirement in their third year. |

MATH 121 | Calculus for Science and Engineering I | 4 |

MATH 122 | Calculus for Science and Engineering II | 4 |

or MATH 124 | Calculus II | |

PHYS 121 | General Physics I - Mechanics | 4 |

or PHYS 123 | Physics and Frontiers I - Mechanics | |

PHYS 122 | General Physics II - Electricity and Magnetism | 4 |

or PHYS 124 | Physics and Frontiers II - Electricity and Magnetism | |

CHEM 105 | Principles of Chemistry I ^{1} | 3-4 |

or CHEM 111 | Principles of Chemistry for Engineers | |

CHEM 106 | Principles of Chemistry II ^{1} | 3-4 |

or ENGR 145 | Chemistry of Materials | |

ENGR 131 | Elementary Computer Programming ^{2} | 3 |

PHYS 221 | Introduction to Modern Physics | 3 |

MP Group 1 ^{3} | 3 | |

MATH 223 | Calculus for Science and Engineering III | 3 |

or MATH 227 | Calculus III | |

MATH 224 | Elementary Differential Equations | 3 |

MATH 307 | Introduction to Abstract Algebra I | 3 |

MATH 308 | Introduction to Abstract Algebra II | 3 |

PHYS 310 | Classical Mechanics | 3 |

PHYS 313 | Thermodynamics and Statistical Mechanics | 3 |

PHYS 331 | Introduction to Quantum Mechanics I | 3 |

or PHYS 481 | Quantum Mechanics I | |

PHYS 332 | Introduction to Quantum Mechanics II | 3 |

or PHYS 482 | Quantum Mechanics II | |

MP Group 2 ^{3} | 3 | |

MP Group 3 ^{3} | 3 | |

MATH 321 | Fundamentals of Analysis I | 3 |

MATH 322 | Fundamentals of Analysis II | 3 |

MATH 324 | Introduction to Complex Analysis | 3 |

Advanced Physics Elective ^{4} | 3 | |

MP Group 4 ^{3} | 3 | |

Either MATH 351 or PHYS 351 will be taken twice | ||

MATH 351 | Senior Project for the Mathematics and Physics Program | 2 |

PHYS 351 | Senior Physics Project ^{5} | 2 |

Choose PHYS 423 or both PHYS 324 & PHYS 325 | 3 | |

Classical Electromagnetism | ||

Electricity and Magnetism I | ||

Electricity and Magnetism II | ||

PHYS 472 | Graduate Physics Laboratory | 3 |

SAGES Dept Seminar ^{6} | 3 | |

PHED 2 semesters | 0 | |

SAGES First and University Seminars | 10 | |

Breadth Requirements ^{7} | 12 | |

Open Electives ^{8} | 15 | |

Total Units | 126-128 |

^{1} | Other science sequence courses may be substituted if approved by the mathematics and physics (MP) committee. |

^{2} | Or other approved computational course |

^{3} | The “MP group” of four courses corresponds to two physics courses and two mathematics courses. The physics courses are chosen from PHYS 250 Computational Methods in Physics, PHYS 349 Methods of Mathematical Physics I, and PHYS 350 Methods of Mathematical Physics II. The mathematics courses are subject to approval by the MP committee and are hence referred to as “approved electives.” They may be chosen from the general list of mathematics courses at the 300 level or higher. It may also be possible to choose a course outside the mathematics and physics departments as a substitute in the MP group, subject to approval by the committee. |

^{4} | An advanced physics course to be selected from the following list: PHYS 315 Introduction to Solid State Physics, PHYS 316 Introduction to Nuclear and Particle Physics, PHYS 326 Physical Optics,PHYS 327 Laser Physics, PHYS 328 Cosmology and the Structure of the Universe, PHYS 336 Modern Cosmology, PHYS 365 General Relativity. |

^{5} | PHYS 303 Advanced Laboratory Physics Seminar +PHYS 352 Senior Physics Project Seminar satisfy the SAGES departmental seminar requirement. PHYS 351 Senior Physics Project is an approved SAGES capstone course. |

^{6} | Students may take either the math or physics SAGES departmental seminar, but must take their SAGES capstone course from the same department. The physics version consists of 1 credit of PHYS 303 Advanced Laboratory Physics Seminar plus two credits of PHYS 352 Senior Physics Project Seminar. |

^{7} | The breadth requirements include 6 hours of Social Sciences and 6 hours of Arts and Humanities. This may increase by 3 credits if the required Global and Cultural Diversity course is not also one of the breadth requirement courses. Courses required for the BS in mathematics and physics satisfy the 6-credit GER for Natural Sciences and Mathematics as well as the Quantitative Reasoning course requirement. |

^{8} | The number of open electives may vary, depending on how many credits the student needs to reach the required total of 126. |

First Year | Units | |
---|---|---|

Fall | Spring | |

General Physics I - Mechanics (PHYS 121) or Physics and Frontiers I - Mechanics (PHYS 123) | 4 | |

Calculus for Science and Engineering I (MATH 121) | 4 | |

Principles of Chemistry I (CHEM 105) or Principles of Chemistry for Engineers (CHEM 111) | 3-4 | |

Physics Today and Tomorrow (PHYS 166) | 1 | |

SAGES First Seminar | 4 | |

PHED Physical Education Activities | 0 | |

General Physics II - Electricity and Magnetism (PHYS 122) or Physics and Frontiers II - Electricity and Magnetism (PHYS 124) | 4 | |

Calculus for Science and Engineering II (MATH 122) | 4 | |

Principles of Chemistry II (CHEM 106) or Chemistry of Materials (ENGR 145) | 3-4 | |

Elementary Computer Programming (ENGR 131) | 3 | |

University Seminar | 3 | |

PHED Physical Education Activities | 0 | |

Year Total: | 16-17 | 17-18 |

Second Year | Units | |

Fall | Spring | |

Introduction to Modern Physics (PHYS 221) | 3 | |

Calculus for Science and Engineering III (MATH 223) or Calculus III (MATH 227) | 3 | |

Introduction to Abstract Algebra I (MATH 307) | 3 | |

University Seminar | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 2 | |

Classical Mechanics (PHYS 310) | 3 | |

Elementary Differential Equations (MATH 224) | 3 | |

Introduction to Abstract Algebra II (MATH 308) | 3 | |

MATH/PHYS Elective | 3 | |

Humanities/Social Science Elective | 3 | |

Year Total: | 17 | 15 |

Third Year | Units | |

Fall | Spring | |

Thermodynamics and Statistical Mechanics (PHYS 313) | 3 | |

Introduction to Quantum Mechanics I (PHYS 331) or Quantum Mechanics I (PHYS 481) | 3 | |

Fundamentals of Analysis I (MATH 321) | 3 | |

MATH/PHYS Elective | 3 | |

Humanities/Social Science Elective | 3 | |

Open Elective | 3 | |

SAGES Departmental Seminar | 3 | |

Introduction to Quantum Mechanics II (PHYS 332) or Quantum Mechanics II (PHYS 482) | 3 | |

Fundamentals of Analysis II (MATH 322) | 3 | |

Introduction to Complex Analysis (MATH 324) | 3 | |

Global and Cultural Diversity Elective | 3 | |

Year Total: | 18 | 15 |

Fourth Year | Units | |

Fall | Spring | |

SAGES Capstone | 4 | |

Physics Elective | 3 | |

Classical Electromagnetism (PHYS 423) | 3 | |

MATH/PHYS Elective | 3 | |

Open Elective | 3 | |

Graduate Physics Laboratory (PHYS 472) | 3 | |

MATH/PHYS Elective | 3 | |

Open Elective | 3 | |

Open Elective | 3 | |

Year Total: | 16 | 12 |

Total Units in Sequence: | 126-128 |

**PHYS 101. Distinguishing Science from Pseudo-Science. 3 Units.**

There are many current issues arising in popular discourse, ranging from the believability of ESP to reincarnation, to "free energy" machines, which can benefit from simple physical analyses. This course will provide an introduction to the use of basic principles of physics to explore the viability of these ideas. A seminar format will be utilized with specific topics presented by students and by the instructor. Recommended preparation: PHYS 100, PHYS 115, PHYS 121, or PHYS 123.

**PHYS 113A. Principles of Physics Laboratory - Mechanics. 1 Unit.**

The laboratory portion of first semester introductory physics.

**PHYS 113B. Principles of Physics Laboratory - Electricity and Magnetism. 1 Unit.**

The laboratory portion of the second semester of physics.

**PHYS 115. Introductory Physics I. 4 Units.**

First part of a two-semester sequence directed primarily towards students working towards a B.A. in science, with an emphasis on the life sciences. Kinematics; Newton's laws; gravitation; simple harmonic motion; mechanical waves; fluids; ideal gas law; heat and the first and second laws of thermodynamics. This course has a laboratory component.

**PHYS 116. Introductory Physics II. 4 Units.**

Electrostatics, Coulomb's law, Gauss's law; capacitance and resistance; DC circuits; magnetic fields; electromagnetic induction; RC and RL circuits; light; geometrical optics; interference and diffraction; special relativity; introduction to quantum mechanics; elements of atomic, nuclear and particle physics. This course has a laboratory component.
Prereq: PHYS 115.

**PHYS 121. General Physics I - Mechanics. 4 Units.**

Particle dynamics, Newton's laws of motion, energy and momentum conservation, rotational motion, and angular momentum conservation. This course has a laboratory component. Recommended preparation: MATH 121 or MATH 123 or MATH 125 or one year of high school calculus.

**PHYS 122. General Physics II - Electricity and Magnetism. 4 Units.**

Electricity and magnetism, emphasizing the basic electromagnetic laws of Gauss, Ampere, and Faraday. Maxwell's equations and electromagnetic waves, interference, and diffraction. This course has a laboratory component.
Prereq: PHYS 121 or PHYS 123. Prereq or Coreq: MATH 122 or MATH 124 or MATH 126.

**PHYS 123. Physics and Frontiers I - Mechanics. 4 Units.**

The Newtonian dynamics of a particle and of rigid bodies. Energy, momentum, and angular momentum conservation with applications. A selection of special frontier topics as time permits, including fractals and chaos, special relativity, fluid mechanics, cosmology, quantum mechanics. This course has a laboratory component. Admission to this course is by invitation only.

**PHYS 124. Physics and Frontiers II - Electricity and Magnetism. 4 Units.**

Time-independent and time-dependent electric and magnetic fields. The laws of Coulomb, Gauss, Ampere, and Faraday. Microscopic approach to dielectric and magnetic materials. Introduction to the usage of vector calculus; Maxwell's equations in integral and differential form. The role of special relativity in electromagnetism. Electromagnetic radiation. This course has a laboratory component.
Prereq: PHYS 123. Prereq or Coreq: MATH 122 or MATH 124.

**PHYS 166. Physics Today and Tomorrow. 1 Unit.**

This course will provide students with an opportunity to learn about the most exciting and timely research areas in physics, as well as other topics germane to being a professional physicist. These discussions will cover fields such as nanoscience, ultrafast optics, exotic materials, biophysics, cosmology, string theory and the role of physicists in developing new technologies. Each week a member of the faculty will meet with students to discuss a topic of current interest, how a physicist approaches the problem, and how physicists interact with others to find a solution. Other topics germane to being a professional physicist also will be discussed, including the relationship among academic, industrial, and governmental laboratories; ethics, and non-traditional careers for students trained in physics.

**PHYS 203. Analog and Digital Electronics. 4 Units.**

Elements of both analog and digital electronics from the practical viewpoint of the experimental scientist; AC circuits, linear and non-linear operation of op-amps, logic gates, flip-flops, counters, display, memory, transducers, A/D and D/A conversion. Laboratory work involves quantitative investigation of the operation of all these elements, together with projects that explore their combination. Recommended preparation: PHYS 122 or PHYS 124.

**PHYS 203A. Analog and Digital Electronics for B.A.. 2 Units.**

This course is the first half of the laboratory requirement for the B.A. degree in Physics and is the first half of PHYS 203. Elements of both analog and digital electronics from the practical viewpoint of the experimental scientist; AC circuits, linear and non-linear operation of op-amps, digital circuits including logic gates. This course includes weekly lecture and laboratory work in electronics; it may also include an additional weekly lecture, associated with PHYS 301, on topics such as error analysis, technical writing and oral presentations. Recommended preparation: PHYS 116, PHYS 122, or PHYS 124.

**PHYS 204. Advanced Instrumentation Laboratory. 4 Units.**

Principles of experimental design; limits of resolution via band-width, thermal noise, background signals; data acquisition and control by computer; computer simulation; signal processing techniques in frequency and time domains, FFT, correlations, and other transform methods; counting techniques. Applications include lock-in amplifiers, digitizing oscilloscopes and data acquisition systems. Recommended preparation: PHYS 203 and PHYS 221.

**PHYS 208. Instrumentation and Signal Analysis Laboratory. 4 Units.**

AC circuit theory, Fourier series, discrete Fourier series. Fourier integral, discrete Fourier integral; analysis in time and frequency domains, correlation, cross-correlation and other transform techniques; computer control of experiments via IEEE488 interface; advanced instrumentation; DMM, arbitrary waveform generator, multiplexing and digitizing oscilloscopes; experimental design, noise; design, construction, and testing of a lock-in amplifier. Recommended preparation: PHYS 221.

**PHYS 221. Introduction to Modern Physics. 3 Units.**

Concepts in special relativity, statistical mechanics and quantum mechanics. Applications to atomic structure, and selected topics in nuclear, condensed matter physics, particle physics, and cosmology.
Prereq: PHYS 116 or PHYS 122 or PHYS 124.

**PHYS 250. Computational Methods in Physics. 3 Units.**

Numerical methods, data analysis, and error analysis applied to physical problems. Use of personal computers in the solution of practical problems encountered in physics. Interpolation, roots of equations, integration, differential equations, Monte Carlo techniques, propagation of errors, maximum likelihood, convolution, Fourier transforms.
Prereq: ENGR 131. Prereq or Coreq: MATH 224.

**PHYS 301. Advanced Laboratory Physics I. 3 Units.**

Problem solving approach with a range of available experiments in classical and modern physics. Emphasis on experimental techniques, data and error analysis, and the formal presentation of the work performed. Recommended preparation: PHYS 204.
Coreq: PHYS 303.

**PHYS 301B. Advanced Laboratory Physics for B.A.. 2 Units.**

This course is the second half of the laboratory requirement for the B.A. degree in Physics and is the second half of PHYS 301. Problem solving approach with a range of available experiments in classical and modern physics. Emphasis on experimental technique and data and error analysis, and the formal presentation of the work performed. Recommended preparation: PHYS 203 or PHYS 203A and concurrent enrollment in PHYS 303.

**PHYS 302. Advanced Laboratory Physics II. 4 Units.**

Several projects using research-quality equipment in contemporary fields of experimental physics. Each requires reading appropriate literature, choosing appropriate instrumentation, performing data acquisition and analysis, and writing a technical paper. Topics include particle counting techniques, neutron activation, gamma-ray spectroscopy, a range of condensed matter experiments including temperature dependent properties between 10 and 350 K, modern optics, ultrahigh vacuum surface science. Recommended preparation: PHYS 301.

**PHYS 303. Advanced Laboratory Physics Seminar. 1 Unit.**

Students will discuss various issues associated with physics research. These include how to judge the quality of an experiment and data (error analysis), how to present your work in written and oral formats, safety and ethical concerns in the laboratory. Recommended preparation: PHYS 250. Counts as SAGES Departmental Seminar.

**PHYS 310. Classical Mechanics. 3 Units.**

Lagrangian formulation of mechanics and its application to central force motion, scattering theory, rigid body motion, and systems of many degrees of freedom. Recommended preparation: PHYS 221 and either MATH 223 or MATH 227.

**PHYS 313. Thermodynamics and Statistical Mechanics. 3 Units.**

Thermodynamic laws, entropy, and phase transitions from the quantum mechanical viewpoint. Gibbs and Boltzmann factors. Ideal, degenerate fermion, degenerate boson, photon, and phonon gases. Correlation functions and transport phenomena. Applications ranging from solid state physics to astrophysics.
Prereq: PHYS 221.

**PHYS 315. Introduction to Solid State Physics. 3 Units.**

Characterization and properties of solids; crystal structure, thermal properties of lattices, quantum statistics, electronic structure of metals and semiconductors. PHYS 415 for graduate students in engineering and science. (May not be taken for departmental credit by graduate students in the Department of Physics.) Prerequisite may be waived with consent of department. Recommended preparation for PHYS 415: PHYS 331. Offered as PHYS 315 and PHYS 415.
Prereq: PHYS 331 or PHYS 481.

**PHYS 316. Introduction to Nuclear and Particle Physics. 3 Units.**

The physics of nuclei and elementary particles; experimental methods used to determine their properties; models and theories developed to describe their structure.
Prereq: PHYS 331 or PHYS 481.

**PHYS 317. Engineering Physics Laboratory I. 3 Units.**

Laboratory course for engineering physics majors. Emphasis is on experimental techniques, data and error analysis, and written and oral presentation of work. Four experiments drawn from classical and modern physics are carried out. These emphasize condensed matter, material and optical physics. Experiments include electric fields, resistivity of materials, optical interference, chaotic systems, and spectroscopy. Design of data analysis systems and software is required.
Prereq: PHYS 208. Coreq: PHYS 303.

**PHYS 318. Engineering Physics Laboratory II. 4 Units.**

Laboratory course for engineering physics majors. Several projects using research-quality equipment in contemporary fields of experimental physics. Open-ended experiments each require reading appropriate literature, designing the experiment, performing data analysis, and writing a technical paper. Topics are drawn from areas of modern physics, and concentrate on condensed matter, material, and optical physics.
Prereq: PHYS 317.

**PHYS 324. Electricity and Magnetism I. 3 Units.**

First half of a sequence that constitutes a detailed study of the basics of electromagnetic theory and many of its applications. Electrostatics and magnetostatics of free space, conductors, dielectric and magnetic materials; basic theory illustrated with applications drawn from condensed matter physics, optics, plasma physics, and physical electronics.
Prereq: PHYS 116 or PHYS 122 or PHYS 124.

**PHYS 325. Electricity and Magnetism II. 3 Units.**

(Continuation of PHYS 324.) Electrodynamics, Maxwell's equations, electromagnetic waves, electromagnetic radiation and its interaction with matter, potential formulation of electromagnetism, and relativity.
Prereq: PHYS 324.

**PHYS 326. Physical Optics. 3 Units.**

Geometrical optics and ray tracing, wave propagation, interaction of electromagnetic radiation with matter, interference, diffraction, and coherence. Supplementary current topics from modern optics such as nonlinear optics, holography, optical trapping and optical computing. Prerequisite(s) may be waived with consent of department. Offered as PHYS 326 and PHYS 426.
Prereq: PHYS 122 or PHYS 124.

**PHYS 327. Laser Physics. 3 Units.**

An introduction to theoretical and practical quantum electronics covering topics in quantum optics, laser physics, and nonlinear optics. Topics to be addressed include the physics of two-level quantum systems including the density matrix formalism, rate equations, and semiclassical radiation theory; laser operation including oscillation, gain, resonator optics, transverse and longitudinal modes, Q-switching, mode-locking, and coherence; and nonlinear optics including the nonlinear susceptibility, parametric interactions, stimulated processes, and self-action. Recommended preparation for PHYS 427: PHYS 331 or PHYS 481. Offered as PHYS 327 and PHYS 427.
Prereq: PHYS 331 or PHYS 481.

**PHYS 328. Cosmology and the Structure of the Universe. 3 Units.**

Distances to galaxies. The content of the distant universe. Large scale structure and galaxy clusters. Physical cosmology. Structure and galaxy formation and evolution. Testing cosmological models. Offered as ASTR 328, PHYS 328, ASTR 428, and PHYS 428.
Prereq: ASTR 222.

**PHYS 329. Independent Study. 1 - 4 Unit.**

An individual reading course in any topic of mutual interest to the student and the faculty supervisor.

**PHYS 331. Introduction to Quantum Mechanics I. 3 Units.**

Quantum nature of energy and angular momentum, wave nature of matter, Schroedinger equation in one and three dimensions; matrix methods; Dirac notation; quantum mechanical scattering. Two particle wave functions.
Prereq: PHYS 221.

**PHYS 332. Introduction to Quantum Mechanics II. 3 Units.**

Continuation of PHYS 331. Spin and fine structure; Dirac equation; symmetries; approximation methods; atomic and molecular spectra; time dependent perturbations; quantum statistics; applications to electrons in metals and liquid helium.
Prereq: PHYS 331.

**PHYS 336. Modern Cosmology. 3 Units.**

An introduction to modern cosmology and an exploration of current topics in the field. The first half of the course will cover the mathematical and physical basis of cosmology, while the second will delve into current questions and the observations that constrain them. Offered as PHYS 336 and PHYS 436.
Prereq: PHYS 221.

**PHYS 339. Seminar. 1 - 3 Unit.**

Conducted in small sections with presentation of papers by students and informal discussion. Special problem seminars and research seminars offered according to interest and need, often in conjunction with one or more research groups.

**PHYS 349. Methods of Mathematical Physics I. 3 Units.**

Analysis of complex functions: singularities, residues, contour integration; evaluation and approximation of sums and integrals; exact and approximate solution of ordinary differential equations; transform calculus; Sturm-Liouville theory; calculus of variations. Additional work required for graduate students. Offered as PHYS 349 and PHYS 449.
Prereq: MATH 224.

**PHYS 350. Methods of Mathematical Physics II. 3 Units.**

(Continuation of PHYS 349/449.) Special functions, orthogonal polynomials, partial differential equations, linear operators, group theory, tensors, selected specials topics. Additional work required for graduate students.
Prereq: PHYS 349.

**PHYS 351. Senior Physics Project. 2 Units.**

A two semester course required for senior BS and BA physics majors. Students pursue a project based on experimental, theoretical or teaching research under the supervision of a physics faculty member, a faculty member from another CWRU department or a research scientist or engineer from another institution. A departmental Senior Project Committee must approve all project proposals and this same committee will receive regular oral and written progress reports. Final results are presented at the end of the second semester as a paper in a style suitable for publication in a professional journal as well as an oral report in a public symposium. Counts as SAGES Senior Capstone.
Prereq: PHYS 303. Coreq: PHYS 352.

**PHYS 352. Senior Physics Project Seminar. 1 Unit.**

This two semester seminar is taken concurrently with the student's two semester senior project. Students meet weekly to discuss their projects and the research experience. The class will include dialogues about professional issues such as ethics, graduate school, jobs, funding, professional organizations, public obligations, writing and speaking. Assignments include proposals, progress reports and posters. Counts as SAGES Departmental Seminar.
Coreq: PHYS 351 or PHYS 353.

**PHYS 353. Senior Engineering Physics Project. 2 Units.**

A two semester course required for BSE Engineering Physics majors. Students are expected to complete a research project in their concentration area under the supervision of a faculty member in science, engineering, or, with approval, a researcher at another institution or company. The project may be calculational, experimental or theoretical, and will address both the underlying physics and appropriate engineering and design principles. A program Senior Project Committee must approve all project proposals and will receive regular oral and written progress reports. Final results are presented at the end of the second semester as a paper in a style suitable for publication in a professional journal as well as an oral report in a public symposium. Counts as SAGES Senior Capstone.
Prereq: PHYS 318. Coreq: PHYS 352.

**PHYS 365. General Relativity. 3 Units.**

This is an introductory course in general relativity. The techniques of tensor analysis will be developed and used to describe the effects of gravity and Einstein's theory. Consequences of the theory as well as its experimental tests will be discussed. An introduction to cosmology will be given. Additional work required for graduate students. Offered as PHYS 365 and PHYS 465.

**PHYS 390. Undergraduate Research in Physics. 3 - 6 Units.**

Research conducted under the supervision of a faculty member in the Department of Physics. Arrangements must be made with a faculty member and a written description of these arrangements must be submitted to and approved by the department before a permit will be issued to register for this course. A final report must be supplied to the department at the end of the semester.

**PHYS 413. Classical and Statistical Mechanics I. 3 Units.**

An integrated approach to classical and statistical mechanics. Lagrangian and Hamiltonian formulations, conservation laws, kinematics and dynamics, Poisson brackets, continuous media, derivation of laws of thermodynamics, the development of the partition function. To be followed by PHYS 414.

**PHYS 414. Classical and Statistical Mechanics II. 3 Units.**

A continuation of PHYS 413. Noninteracting systems, statistical mechanics of solids, liquids, gases, fluctuations, irreversible processes, phase transformations. Recommended preparation: PHYS 413 or consent of department.

**PHYS 415. Introduction to Solid State Physics. 3 Units.**

Characterization and properties of solids; crystal structure, thermal properties of lattices, quantum statistics, electronic structure of metals and semiconductors. PHYS 415 for graduate students in engineering and science. (May not be taken for departmental credit by graduate students in the Department of Physics.) Prerequisite may be waived with consent of department. Recommended preparation for PHYS 415: PHYS 331. Offered as PHYS 315 and PHYS 415.

**PHYS 423. Classical Electromagnetism. 3 Units.**

Electromagnetic theory in the classical limit. Gauge invariance and special relativity. Applications to electrostatic, magnetostatic, and radiation problems using advanced mathematical techniques. Dielectric, magnetic, and conducting materials. Wave propagation in open and confined geometries. Radiation from accelerating charges. Cherenkov, synchrotron, and transition radiation.

**PHYS 426. Physical Optics. 3 Units.**

Geometrical optics and ray tracing, wave propagation, interaction of electromagnetic radiation with matter, interference, diffraction, and coherence. Supplementary current topics from modern optics such as nonlinear optics, holography, optical trapping and optical computing. Prerequisite(s) may be waived with consent of department. Offered as PHYS 326 and PHYS 426.

**PHYS 427. Laser Physics. 3 Units.**

An introduction to theoretical and practical quantum electronics covering topics in quantum optics, laser physics, and nonlinear optics. Topics to be addressed include the physics of two-level quantum systems including the density matrix formalism, rate equations, and semiclassical radiation theory; laser operation including oscillation, gain, resonator optics, transverse and longitudinal modes, Q-switching, mode-locking, and coherence; and nonlinear optics including the nonlinear susceptibility, parametric interactions, stimulated processes, and self-action. Recommended preparation for PHYS 427: PHYS 331 or PHYS 481. Offered as PHYS 327 and PHYS 427.

**PHYS 428. Cosmology and the Structure of the Universe. 3 Units.**

Distances to galaxies. The content of the distant universe. Large scale structure and galaxy clusters. Physical cosmology. Structure and galaxy formation and evolution. Testing cosmological models. Offered as ASTR 328, PHYS 328, ASTR 428, and PHYS 428.

**PHYS 431. Physics of Imaging. 3 Units.**

Description of physical principles underlying the spin behavior in MR and Fourier imaging in multi-dimensions. Introduction of conventional, fast, and chemical-shift imaging techniques. Spin echo, gradient echo, and variable flip-angle methods. Projection reconstruction and sampling theorems. Bloch equations, T1 and T2 relaxation times, rf penetration, diffusion and perfusion. Flow imaging, MR angiography, and functional brain imaging. Sequence and coil design. Prerequisite may be waived with consent of instructor. Recommended preparation: PHYS 122 or PHYS 124 or EBME 410. Offered as EBME 431 and PHYS 431.

**PHYS 436. Modern Cosmology. 3 Units.**

An introduction to modern cosmology and an exploration of current topics in the field. The first half of the course will cover the mathematical and physical basis of cosmology, while the second will delve into current questions and the observations that constrain them. Offered as PHYS 336 and PHYS 436.

**PHYS 441. Physics of Condensed Matter I. 3 Units.**

Crystal structure, x-ray diffraction, band theory and applications. Free electron theory of metals and electrons in magnetic fields.

**PHYS 442. Physics of Condensed Matter II. 3 Units.**

Continuation of PHYS 441. Lattice vibrations, thermal properties of solids, semiconductors, magnetic properties of solids, and superconductivity. Prerequisite may be waived with consent of department. Recommended preparation: PHYS 441.

**PHYS 449. Methods of Mathematical Physics I. 3 Units.**

Analysis of complex functions: singularities, residues, contour integration; evaluation and approximation of sums and integrals; exact and approximate solution of ordinary differential equations; transform calculus; Sturm-Liouville theory; calculus of variations. Additional work required for graduate students. Offered as PHYS 349 and PHYS 449.

**PHYS 451. Empirical Foundations of the Standard Model. 3 Units.**

The experimental basis for modeling the electroweak and strong interactions in terms of fundamental fermions, quarks and leptons, and gauge bosons, photons, the weak bosons, and gluons; particle accelerators and detection techniques; phenomenology of particle reactions, decays and hadronic structure; space, time and internal symmetries; symmetries; symmetry breaking.

**PHYS 460. Advanced Topics in NMR Imaging. 3 Units.**

Frontier issues in understanding the practical aspects of NMR imaging. Theoretical descriptions are accompanied by specific examples of pulse sequences, and basic engineering considerations in MRI system design. Emphasis is placed on implications and trade-offs in MRI pulse sequence design from real-world versus theoretical perspectives. Recommended preparation: EBME 431 or PHYS 431. Offered as EBME 460 and PHYS 460.
Prereq: Graduate standing or Undergraduate with Junior or Senior standing and a cumulative GPA of 3.2 or above.

**PHYS 465. General Relativity. 3 Units.**

This is an introductory course in general relativity. The techniques of tensor analysis will be developed and used to describe the effects of gravity and Einstein's theory. Consequences of the theory as well as its experimental tests will be discussed. An introduction to cosmology will be given. Additional work required for graduate students. Offered as PHYS 365 and PHYS 465.

**PHYS 472. Graduate Physics Laboratory. 3 Units.**

A series of projects designed to introduce the student to modern research techniques such as automated data acquisition. Students will be assessed as to their individual needs and a sequence of projects will be established for each individual. Topics may include low temperature phenomena, nuclear gamma ray detection and measurement and optics.

**PHYS 481. Quantum Mechanics I. 3 Units.**

Quantum mechanics with examples of applications. Schroedinger method; matrix and operator methods. Approximation methods including WKB, variational and various perturbation methods. Applications to atomic, molecular and nuclear physics including both bound states and scattering problems. Applications of group theory to quantum mechanics.

**PHYS 482. Quantum Mechanics II. 3 Units.**

Continuation of PHYS 481, including quantum field theory. Prerequisite may be waived with consent of department. Recommended preparation: PHYS 481 or consent of department.

**PHYS 491. Modern Physics for Innovation I. 3 Units.**

The first half of a two-semester sequence providing an understanding of physics as a basis for successfully launching new high-tech ventures. The course will examine physical limitations to present technologies, and the use of physics to identify potential opportunities for new venture creation. The course will provide experience in using physics for both identification of incremental improvements, and as the basis for alternative technologies. Case studies will be used to illustrate recent commercially successful (and unsuccessful) physics-based venture creation, and will illustrate characteristics for success.

**PHYS 492. Modern Physics for Innovation II. 3 Units.**

Continuation of PHYS 491, with an emphasis on current and prospective opportunities for Physics Entrepreneurship. Longer term opportunities for Physics Entrepreneurship in emerging areas including, but not limited to, nanoscale physics and nanotechnology; biophysics and applications to biotechnology; physics-based opportunities in the context of information technology. Recommended preparation: PHYS 491.

**PHYS 493. Feasibility and Technology Analysis. 3 Units.**

This course provides the tools scientists need to determine whether a technology is ready for commercialization. These tools include (but are not limited to): financial analysis, market analysis, industry analysis, technology analysis, intellectual property protection, the entrepreneurial process and culture, an introduction to entrepreneurial strategy and new venture financing. Deliverables will include a technology feasibility analysis on a possible application in the student's scientific area. Offered as BIOL 493, CHEM 493, and PHYS 493.

**PHYS 494. Technology-Based Venture Creation. 3 Units.**

This course provides the advanced tools needed to develop, articulate, and launch a venture plan for a technology identified as likely to be successful through a feasibility analysis. Additional topics include: entrepreneurial strategy, communication, sales, negotiation, entrepreneurial finance, and leadership in an entrepreneurial environment. Guest speakers will be featured in nearly every class session.
Prereq: BIOL 493 or CHEM 493 or PHYS 493.

**PHYS 539. Special Topics Seminar. 1 - 3 Unit.**

Individual or small group instruction on topics of interest to the department. Topics include, but are not limited to, particle physics, astrophysics, optics, condensed matter physics, biophysics, imaging. Several such courses may run concurrently.

**PHYS 566. Cosmology. 3 Units.**

Introduction to our current understanding of the origin and evolution of the Universe and connection between our understanding of elementary particle physics and cosmology. Specific topics will include: General Parameters of Cosmology: Expansion, Lifetime, and Density of the Universe. The Early Universe, Constraints on Elementary Particles, Dark Matter and Dark Energy, Nucleosynthesis, Cosmic Microwave Background, Inflation, Stellar Evolution, Gravitational Waves, Baryogenesis. Some background in general relativity and particle physics phenomenology is recommended.

**PHYS 581. Quantum Mechanics III. 3 Units.**

Continuation of PHYS 482. The methods of quantum field theory applied to the nonrelativistic many-body problem, radiation theory, and relativistic particle physics. Second quantization using canonical and path integration techniques, constrained systems, and gauge theories. Graphical perturbative methods and graphs summation approaches. Topological aspects of field theories. Recommended preparation: PHYS 482 and consent of department.

**PHYS 591. Gauge Field Theory I. 3 Units.**

Noether's theorem, symmetries and conserved currents, functional integral techniques, quantization, Feynman rules, anomalies, QED, electroweak interactions, QCD, renormalization, renormalization group, asymptotic freedom and assorted other topics.
Prereq: PHYS 581.

**PHYS 601. Research in Physics. 1 - 9 Unit.**

**PHYS 651. Thesis M.S.. 1 - 9 Unit.**

**PHYS 666. Frontiers in Physics. 0 Units.**

Weekly colloquia given by eminent physicists from around the world on topics of current interest in physics.

**PHYS 701. Dissertation Ph.D.. 1 - 9 Unit.**

Prereq: Predoctoral research consent or advanced to Ph.D. candidacy milestone.