Physics
Departmental Office: 704 Pupin; 2128543348
http://www.columbia.edu/cu/physics
Director of Undergraduate Studies: Dr. Jeremy Dodd, 924 Pupin; 2128543969; dodd@phys.columbia.edu
The physics major offers a rigorous preparation in the intellectual developments of modern physics, along with extensive exposure to the mathematical and experimental techniques required to conduct basic and applied research in physics.
For the major, the department offers a set of required courses wellsuited to prepare students for the most rigorous course of graduate study. These can be supplemented by elective courses in a variety of advanced topics. Although most majors go on to graduate work in physics, the intellectual skills acquired in the study of physics can also provide the basis for work in a variety of other scientific and nonscientific areas.
The physics concentration is for students who are interested in physics but are uncertain about graduate study in physics; for those who want to explore other subjects along with physics; for those who want to find a physics or technologyrelated job after graduation; or for those who are considering a professional school such as law or medicine. The department helps concentrators custom design programs to ensure maximum flexibility in meeting students’ intellectual needs and career goals. With appropriate selection of courses, the concentrator can explore other subjects yet maintain the option of graduate study in physics.
Research is an extremely important component of the Columbia physics experience. Because the department has a very small studenttofaculty ratio, essentially all physics majors and concentrators engage in experimental, computational, or theoretical research under the close supervision of a faculty member during part, if not all, of their time at Columbia.
Registration for Introductory Courses
The department offers a standalone onesemester course for nonscience majors, one introductory sequence in physics intended primarily for preprofessional students, and three introductory sequences in physics for engineering and physical science majors. Students are given credit for courses from only one of the different sequence groups.
Mixing courses across the sequences is strongly discouraged; however, physics majors who begin their studies with PHYS UN1401 Introduction To Mechanics and Thermodynamics  PHYS UN1402 Introduction To Electricity, Magnetism, and Optics should take PHYS UN2601 Physics, III: Classical and Quantum Waves as the thirdsemester course.
Introductory Sequences
Nonscience Majors:
Code  Title  Points 

PHYS UN1001  Physics for Poets 
Preprofessional Students:
Code  Title  Points 

PHYS UN1201  PHYS UN1202 
General Physics I and General Physics II 

Accompanying laboratory course:  
PHYS UN1291  PHYS UN1292 
General Physics Laboratory and General Physics Laboratory II 
Engineering and Physical Science Majors:
Code  Title  Points 

Select one of the following sequences with accompanying laboratory course:  
Sequence A:


Introduction To Mechanics and Thermodynamics and Introduction To Electricity, Magnetism, and Optics and Introduction to Classical and Quantum Waves 

Sequence B:


Physics, I: Mechanics and Relativity and Physics, II: Thermodynamics, Electricity, and Magnetism and Physics, III: Classical and Quantum Waves 

Sequence C:


Accelerated Physics I and Accelerated Physics II 
Sequence A is a selfcontained group of three courses, while Sequences B and C anticipate more course work in the Physics Department. Students considering a physics major are strongly encouraged to begin one of these sequences in their first year.
Laboratory
Many of the introductory courses include a laboratory, as indicated. A $75 per term laboratory fee is charged for all 1000level and 2000level laboratories.
Advanced Placement
Students may earn a maximum of 6 credits in physics. The department grants 6 credits for a score of 4 or 5 on the AP Physics B exam, but the student is not entitled to any exemptions. The amount of credit is reduced to 3 if the student takes a 1000level physics course.
The department grants 3 credits for a score of 4 or 5 on the AP Physics C/MECH exam, but the student is not entitled to any exemptions. The amount of credit is reduced to 0 if the student takes PHYS UN1001, PHYS UN1201, PHYS UN1401 or PHYS UN1601.
The department grants 3 credits for a score of 4 or 5 on the AP Physics C/E&M exam, but the student is not entitled to any exemptions. The amount of credit is reduced to 0 if the student takes PHYS UN1001, PHYS UN1202,PHYS UN1402 or PHYS UN1602.
Professors
 Igor Aleiner
 Boris Altshuler
 Elena Aprile
 Dmitri Bassov
 Andrei Beloborodov
 Allan Blaer (emeritus)
 Gustaaf Brooijmans
 Norman Christ
 Brian Cole
 Frederik Denef
 Richard Friedberg (Barnard emeritus)
 Brian Greene (Mathematics)
 Miklos Gyulassy (emeritus)
 Charles J. Hailey
 Timothy HalpinHealy (Barnard)
 Sven Hartmann (emeritus)
 Emlyn Hughes
 Lam Hui
 Laura Kay (Barnard Astronomy)
 Tsung Dao Lee (emeritus)
 Szabolcs Marka
 Robert Mawhinney
 Andrew Millis
 Alfred H. Mueller
 Reshmi Mukherjee (Barnard)
 John Parsons
 Aron Pinczuk (Applied Physics)
 Malvin Ruderman
 Frank Sciulli (emeritus)
 Michael Shaevitz
 Michael Tuts (Chair)
 Yasutomo Uemura
 Erick Weinberg
 William Zajc
Associate Professors
 Janna Levin (Barnard)
 Alberto Nicolis
 Abhay Pasupathy
 Ozgur Sahin (Biology)
 Tanya Zelevinsky
Assistant Professors
 Cory Dean
 Brian Humensky
 Bradley Johnson
 Georgia Karagiorgi
 Brian Metzger
 Rachel Rosen
 Sebastian Will
Senior Lecturer in Discipline
 Jeremy Dodd
Adjunct Professor
 Morgan May
Lecturer
 Burton Budick
 Joel Gersten
On Leave
Tony Heinz
Amber Miller
Guidelines for all Physics Majors, Concentrators, and Interdepartmental Majors
Majors and concentrators should plan their programs of study with the director of undergraduate studies before the beginning of the junior year.
Prospective physics majors are strongly encouraged to begin one of the introductory physics sequences in their first year. Majors should aim to acquire as extensive a background in mathematics as possible.
The department considers laboratory experience to be an essential part of the physics curriculum. Majors and concentrators can gain such experience in the intermediatelevel laboratories, the electronics laboratory, and through experimental research in faculty research groups.
Grading
A grade of C or better must be obtained for a course to count toward the majors or the concentration. The grade of P is not acceptable, but a course that was taken P/D/F may be counted if and only if the P is uncovered by the Registrar's deadline.
Major in Physics
Physics Courses
The major in physics requires a minimum of 41 points in physics courses, including:
Code  Title  Points 

Introductory Sequences  
Select one of the following sequences:  
Sequence A: Students with a limited background in high school physics may elect to take:


Introduction To Mechanics and Thermodynamics and Introduction To Electricity, Magnetism, and Optics and Physics, III: Classical and Quantum Waves 

Sequence B:


Physics, I: Mechanics and Relativity and Physics, II: Thermodynamics, Electricity, and Magnetism and Physics, III: Classical and Quantum Waves 

Sequence C: Students with advanced preparation in both physics and mathematics may be eligible to take:


Accelerated Physics I and Accelerated Physics II 

Core Physics Courses  
Mechanics  
Electricity and Magnetism  
Electromagnetic Waves and Optics  
Quantum Mechanics  
Quantum Mechanics II  
Thermal and Statistical Physics  
Elective Courses  
Select at least six points of the following courses:  
From Quarks To the Cosmos: Applications of Modern Physics  
Advanced Mechanics  
Particle Astrophysics and Cosmology  
SolidState Physics  
Mathematical Methods of Physics  
PHYS GU4040


Introduction to Particle Physics  
With the permission of the Director of Undergraduate Studies, 4000 or 6000level courses offered in this or other science departments


Laboratory Work at the Intermediate Level ^{*}  
Select one of the following options:  
Option 1:


Intermediate Laboratory Work (two semesters)  
Electronics Laboratory  
Option 2:


Intermediate Laboratory Work (three semesters)  
Senior Seminar  
PHYS UN3072  Seminar in Current Research Problems 
* 
Approved experimental work with a faculty research group may satisfy one semester of the laboratory requirement. 
Mathematics Courses
Calculus through MATH UN1202 Calculus IV or MATH UN1208 Honors Mathematics B; and MATH UN3027 Ordinary Differential Equations or the equivalent.
Recommended cognate courses: MATH UN2010 Linear Algebra, MATH UN3007 Complex Variables, and MATH UN3028 Partial Differential Equations.
Concentration in Physics
The concentration in physics requires a minimum of 24 points in physics, including one of the introductory sequences.
Interdisciplinary Major
It is also possible to major in astrophysics, biophysics, and chemical physics. Students interested in these areas should consult with the director of undergraduate studies and with cognate departments (astronomy, biological sciences, chemistry).
PHYS UN1001 Physics for Poets. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: high school algebra.
This course does not fulfill the physics requirement for admission to medical school. No previous background in physics is expected. An introduction to physics taught through the exploration of the scientific method, and the application of physical principles to a wide range of topics from quantum mechanics to cosmology.
Spring 2017: PHYS UN1001


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1001  001/22892  M W 2:40pm  3:55pm 428 Pupin Laboratories 
Szabolcs Marka  3  127/140 
PHYS UN1018 Weapons of Mass Destruction. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: high school science and math.
A review of the history and environmental consequences of nuclear, chemical, and biological weapons of mass destruction (WMD); of how these weapons work, what they cost, how they have spread, how they might be used, how they are currently controlled by international treaties and domestic legislation, and what issues of policy and technology arise in current debates on WMD. What aspects of the manufacture of WMD are easily addressed, and what aspects are technically challenging? It may be expected that current events/headlines will be discussed in class.
Spring 2017: PHYS UN1018


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1018  001/76198  T Th 2:40pm  3:55pm 301 Pupin Laboratories 
Szabolcs Marka  3  153/140 
PHYS UN1201 General Physics I. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: some basic background in calculus or be concurrently taking MATH V1101x Calculus I.,The accompanying laboratory is PHYS UN1291UN1292
The course will use elementary concepts from calculus. The accompanying laboratory is PHYS W1291xW1292y. Basic introduction to the study of mechanics, fluids, thermodynamics, electricity, magnetism, optics, special relativity, quantum mechanics, atomic physics, and nuclear physics.
Spring 2017: PHYS UN1201


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1201  001/18383  T Th 6:10pm  7:25pm 301 Pupin Laboratories 
Cory Dean  3  108/140 
Fall 2017: PHYS UN1201


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
PHYS 1201  001/22186  M W 10:10am  11:25am Room TBA 
Michael Shaevitz  3  160/160 
PHYS 1201  002/23538  M W 10:10am  11:25am Room TBA 
Bradley Johnson  3  43/130 
PHYS 1201  003/19467  T Th 6:10pm  7:25pm Room TBA 
Burton Budick  3  49/130 
PHYS UN1202 General Physics II. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: This couse will use elementary concepts from calculus. Students should therefore have had some high school calculus, or be cuncurrently enrolled in MATH V1101.
Corequisites: Taken with accompanying lab PHYS V12912, the sequence PHYS V12012 satisfies requirements for medical school.
Electricity, magnetism, optics, and modern physics.
Spring 2017: PHYS UN1202


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1202  001/60626  M W 10:10am  11:25am 301 Pupin Laboratories 
Michael Shaevitz  3  162/160 
PHYS 1202  002/63885  M W 10:10am  11:25am 428 Pupin Laboratories 
Jeremy Dodd  3  99/130 
PHYS 1202  003/25739  T Th 6:10pm  7:25pm 428 Pupin Laboratories 
Burton Budick  3  50/130 
PHYS UN1291 General Physics Laboratory. 1 point.
Same course as PHYS W1291x, but given offsequence.
Corequisites: PHYS W1201y.
This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.
Spring 2017: PHYS UN1291


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1291  001/61966  M 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  13/15 
PHYS 1291  002/76375  M 4:10pm  7:10pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  9/15 
PHYS 1291  003/74858  T 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  12/15 
PHYS 1291  004/64480  T 7:30pm  10:30pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  9/15 
PHYS 1291  005/17809  W 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  12/15 
PHYS 1291  006/64268  W 7:30pm  10:30pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  5/15 
PHYS 1291  007/61869  Th 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  14/15 
PHYS 1291  008/74156  Th 7:30pm  10:30pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  9/15 
PHYS 1291  009/67925  F 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  6/15 
Fall 2017: PHYS UN1291


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
PHYS 1291  001/21452  M 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  002/10062  M 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  003/67323  M 4:10pm  7:10pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  004/22799  M 4:10pm  7:10pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  005/75863  M 7:30pm  10:30pm Room TBA 
Giuseppina Cambareri  1  13/15 
PHYS 1291  006/68967  M 7:30pm  10:30pm Room TBA 
Giuseppina Cambareri  1  2/15 
PHYS 1291  007/72385  T 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  008/29961  T 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  009/16186  T 4:10pm  7:10pm Room TBA 
Giuseppina Cambareri  1  8/15 
PHYS 1291  010/64117  T 4:10pm  7:10pm Room TBA 
Giuseppina Cambareri  1  4/15 
PHYS 1291  011/23167  T 7:30pm  10:30pm Room TBA 
Giuseppina Cambareri  1  8/15 
PHYS 1291  012/27691  T 7:30pm  10:30pm Room TBA 
Giuseppina Cambareri  1  0/15 
PHYS 1291  013/74065  W 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  014/28513  W 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  015/13394  W 4:10pm  7:10pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  016/11326  W 4:10pm  7:10pm Room TBA 
Giuseppina Cambareri  1  6/15 
PHYS 1291  017/67817  W 7:30pm  10:30pm Room TBA 
Giuseppina Cambareri  1  6/15 
PHYS 1291  018/19821  W 7:30pm  10:30pm Room TBA 
Giuseppina Cambareri  1  0/15 
PHYS 1291  019/68973  Th 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  15/15 
PHYS 1291  020/29005  Th 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  13/15 
PHYS 1291  021/75327  Th 4:10pm  7:10pm Room TBA 
Giuseppina Cambareri  1  5/15 
PHYS 1291  022/69519  Th 4:10pm  7:10pm Room TBA 
Giuseppina Cambareri  1  1/15 
PHYS 1291  023/14769  Th 7:30pm  10:30pm Room TBA 
Giuseppina Cambareri  1  8/15 
PHYS 1291  024/28004  Th 7:30pm  10:30pm Room TBA 
Giuseppina Cambareri  1  2/15 
PHYS 1291  025/12938  F 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  10/15 
PHYS 1291  026/23661  F 1:00pm  4:00pm Room TBA 
Giuseppina Cambareri  1  1/15 
PHYS UN1292 General Physics Laboratory II. 1 point.
Corequisites: PHYS W1201xW1202y.
This course is the laboratory for the corequisite lecture course (PHYS W1201xW1202y) and can be taken only during the same term as the corresponding lecture.
Spring 2017: PHYS UN1292


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1292  001/25415  M 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  14/15 
PHYS 1292  002/64628  M 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  15/15 
PHYS 1292  003/74037  M 4:10pm  7:10pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  14/15 
PHYS 1292  004/77349  M 4:10pm  7:10pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  13/15 
PHYS 1292  005/64687  M 7:30pm  10:30pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  14/15 
PHYS 1292  006/10789  M 7:30pm  10:30pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  7/15 
PHYS 1292  007/26909  T 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  15/15 
PHYS 1292  008/64016  T 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  14/15 
PHYS 1292  009/21826  T 4:10pm  7:10pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  11/15 
PHYS 1292  010/67061  T 4:10pm  7:10pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  11/15 
PHYS 1292  011/75591  T 7:30pm  10:30pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  13/15 
PHYS 1292  013/28570  W 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  15/15 
PHYS 1292  014/28837  W 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  13/15 
PHYS 1292  015/63092  W 4:10pm  7:10pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  16/15 
PHYS 1292  016/70747  W 4:10pm  7:10pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  15/15 
PHYS 1292  017/29301  W 7:30pm  10:30pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  14/15 
PHYS 1292  018/66164  Th 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  15/15 
PHYS 1292  019/13901  Th 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  12/15 
PHYS 1292  020/67374  Th 4:10pm  7:10pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  15/15 
PHYS 1292  022/16213  Th 7:30pm  10:30pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  14/15 
PHYS 1292  023/12305  F 1:00pm  4:00pm 5th Flr Pupin Laboratories 
Giuseppina Cambareri  1  12/15 
PHYS UN1401 Introduction To Mechanics and Thermodynamics. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Corequisites: MATH V1101 or the equivalent.
Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, temperature and heat, gas laws, the first and second laws of thermodynamics.
Fall 2017: PHYS UN1401


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1401  001/18908  M W 1:10pm  2:25pm Room TBA 
William Zajc  3  33/160 
PHYS 1401  002/13337  T Th 10:10am  11:25am Room TBA 
3  8/140 
PHYS W1402 Introduction To Electricity, Magnetism, and Optics. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: PHYS W1401.
Corequisites: MATH V1102 or the equivalent.
Electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves, polarization, geometrical optics, interference, and diffraction.
PHYS UN1403 Introduction to Classical and Quantum Waves. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: PHYS W1402.
Corequisites: MATH V1201 or the equivalent.
Classical waves and the wave equation, Fourier series and integrals, normal modes, waveparticle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, applications to atomic physics.
Fall 2017: PHYS UN1403


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1403  001/72043  M W 11:40am  12:55pm Room TBA 
Rachel Rosen  3  93/130 
PHYS UN1493 Introduction to Experimental Physics. 3 points.
Prerequisites: PHYS W1401 and W1402.
Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.
Fall 2017: PHYS UN1493


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1493  001/61060  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  001/61060  T 4:10pm  7:10pm Room TBA 
3  13/13  
PHYS 1493  002/21714  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  002/21714  T 7:30pm  10:30pm Room TBA 
3  13/13  
PHYS 1493  003/61205  W 1:00pm  4:00pm Room TBA 
3  13/13  
PHYS 1493  003/61205  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  004/19894  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  004/19894  W 4:10pm  7:10pm Room TBA 
3  13/13  
PHYS 1493  005/16957  T 3:00pm  3:55pm Room TBA 
3  10/13  
PHYS 1493  005/16957  W 7:30pm  10:30pm Room TBA 
3  10/13  
PHYS 1493  006/23968  Th 1:00pm  4:00pm Room TBA 
3  13/13  
PHYS 1493  006/23968  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  007/23867  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  007/23867  Th 4:10pm  7:10pm Room TBA 
3  13/13  
PHYS 1493  008/71940  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  008/71940  Th 7:30pm  10:30pm Room TBA 
3  13/13  
PHYS 1493  009/12172  F 1:00pm  4:00pm Room TBA 
3  13/13  
PHYS 1493  009/12172  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  010/67765  M 1:00pm  4:00pm Room TBA 
3  13/13  
PHYS 1493  010/67765  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  011/21701  T 3:00pm  3:55pm Room TBA 
3  13/13  
PHYS 1493  011/21701  M 4:10pm  7:10pm Room TBA 
3  13/13  
PHYS 1493  012/22577  T 3:00pm  3:55pm Room TBA 
3  4/13  
PHYS 1493  012/22577  M 7:30pm  10:30pm Room TBA 
3  4/13 
PHYS W1494 Introduction to Experimental Physics. 3 points.
Prerequisites: PHYS W1401 and W1402.
Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.
PHYS UN1601 Physics, I: Mechanics and Relativity. 3.5 points.
CC/GS: Partial Fulfillment of Science Requirement
Corequisites: MATH V1102 or the equivalent.
Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, introduction to special relativity and relativistic kinematics. The course is preparatory for advanced work in physics and related fields.
Fall 2017: PHYS UN1601


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1601  001/62274  T Th 10:10am  11:25am Room TBA 
Thomas Humensky  3.5  8/180 
PHYS UN1602 Physics, II: Thermodynamics, Electricity, and Magnetism. 3.5 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: PHYS W1601.
Corequisites: MATH V1201 or the equivalent.
Temperature and heat, gas laws, the first and second laws of thermodynamics, kinetic theory of gases, electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves. The course is preparatory for advanced work in physics and related fields.
Spring 2017: PHYS UN1602


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 1602  001/10916  T Th 10:10am  11:25am 428 Pupin Laboratories 
Thomas Humensky  3.5  119/180 
PHYS W2001 Special Relativity. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Not offered during 201718 academic year.
Prerequisites: a working knowledge of high school algebra, trigonometry, and physics. Some familiarity with calculus is useful but not essential.
This course is a comprehensive, onesemester introduction to the essential ideas and mathematical structures underlying Einstein’s Special Theory of Relativity. Among the topics covered will be: the relativity of simultaneity, time dilation, Lorentz contraction, velocity combination laws, time dilation over large distances, the Lorentz transformation, spacetime diagrams, the basic (seeming) paradoxes of special relativity, relativistic equations of motion and E = mc2.
PHYS UN2601 Physics, III: Classical and Quantum Waves. 3.5 points.
Prerequisites: PHYS W1402 or W1602.
Corequisites: MATH V1202 or the equivalent.
Classical waves and the wave equation, geometrical optics, interference and diffraction, Fourier series and integrals, normal modes, waveparticle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, the harmonic oscillator. The course is preparatory for advanced work in physics and related fields.
Fall 2017: PHYS UN2601


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 2601  001/76382  T Th 2:40pm  3:55pm Room TBA 
Jeremy Dodd  3.5  74/100 
PHYS W2699 Experiments in Classical and Modern Physics. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: PHYS W1601 (or W1401), W1602 (or W1402), and W2601.
Laboratory work associated with the three prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics.
PHYS UN2801 Accelerated Physics I. 4.5 points.
Prerequisites: Advanced Placement in physics and mathematics, or the equivalent, and the instructor's permission. (A special placement meeting is held during Orientation.)
This accelerated twosemester sequence covers the subject matter of PHYS W1601, W1602 and W2601, and is intended for those students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, PHYS W3081, in the following year.
Fall 2017: PHYS UN2801


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 2801  001/22373  T Th 10:10am  12:00pm Room TBA 
Brian Cole  4.5  6/100 
PHYS UN2802 Accelerated Physics II. 4.5 points.
Prerequisites: PHYS W2801.
This accelerated twosemester sequence covers the subject matter of PHYS W1601, W1602 and W2601, and is intended for those students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, PHYS W3081, in the following year.
Spring 2017: PHYS UN2802


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 2802  001/14518  T Th 10:10am  12:00pm 329 Pupin Laboratories 
Robert Mawhinney  4.5  36/70 
PHYS W3002 From Quarks To the Cosmos: Applications of Modern Physics. 3.5 points.
Not offered during 201718 academic year.
Prerequisites: W2601 or W2802
This course reinforces basic ideas of modern physics through applications to nuclear physics, high energy physics, astrophysics and cosmology. The ongoing Columbia research programs in these fields are used as practical examples. The course is preparatory for advanced work in physics and related fields.
PHYS UN3003 Mechanics. 3 points.
Prerequisites: general physics, and differential and integral calculus.
Newtonian mechanics, oscillations and resonance, conservative forces and potential energy, central forces, noninertial frames of reference, rigid body motion, an introduction to Lagrange's formulation of mechanics, coupled oscillators, and normal modes.
Spring 2017: PHYS UN3003


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 3003  001/75008  M W 10:10am  11:25am 329 Pupin Laboratories 
John Parsons  3  46/70 
PHYS UN3007 Electricity and Magnetism. 3 points.
Prerequisites: general physics, and differential and integral calculus.
Electrostatics and magnetostatics, Laplace's equation and boundaryvalue problems, multipole expansions, dielectric and magnetic materials, Faraday's law, AC circuits, Maxwell's equations, Lorentz covariance, and special relativity.
Fall 2017: PHYS UN3007


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 3007  001/71505  M W 11:40am  12:55pm Room TBA 
Abhay Pasupathy  3  47/100 
PHYS UN3008 Electromagnetic Waves and Optics. 3 points.
Prerequisites: PHYS W3007.
Maxwell's equations and electromagnetic potentials, the wave equation, propagation of plane waves, reflection and refraction, geometrical optics, transmission lines, wave guides, resonant cavities, radiation, interference of waves, and diffraction.
Spring 2017: PHYS UN3008


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 3008  001/20109  M W 2:40pm  3:55pm 329 Pupin Laboratories 
Bradley Johnson  3  45/70 
PHYS W3018 Weapons of Mass Destruction. 3 points.
CC/GS: Partial Fulfillment of Science Requirement, BC: Fulfillment of General Education Requirement: Reason and Value (REA).
Prerequisites: high school science and math.
A review of the history and environmental consequences of nuclear, chemical, and biological weapons of mass destruction (WMD); of how these weapons work, what they cost, how they have spread, how they might be used, how they are currently controlled by international treaties and domestic legislation, and what issues of policy and technology arise in current debates on WMD. What aspects of the manufacture of WMD are easily addressed, and what aspects are technically challenging? It may be expected that current events/headlines will be discussed in class.
PHYS UN3072 Seminar in Current Research Problems. 2 points.
May be taken for Pass/Fail credit only.
A detailed study of a selected field of active research in physics. The motivation, techniques, and results obtained to the present, as well as the difficulties and unsolved problems. For Physics majors only. Priority given to seniors; juniors by permission of the instructor.
Spring 2017: PHYS UN3072


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 3072  001/27725  M 5:30pm  6:45pm 814 Pupin Laboratories 
Alberto Nicolis  2  6/15 
PHYS 3072  002/77416  M 5:30pm  6:45pm 703 Northwest Corner 
Georgia Karagiorgi  2  12/15 
PHYS UN3081 Intermediate Laboratory Work. 2 points.
May be repeated for credit by performing different experiments. The laboratory has available fifteen individual experiments, of which two are required per 2 points.
Prerequisites: PHYS W2601 or PHYS W2802. Primarily for junior and senior physics majors; other majors must obtain the instructor's permission.
Each experiment is chosen by the student in consultation with the instructor. Each section meets one afternoon per week, with registration in each section limited by the laboratory capacity. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics.
Spring 2017: PHYS UN3081


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 3081  002/72661  Th 1:10pm  5:00pm 6th Flr Pupin Laboratories 
Elena Aprile  2  11/15 
PHYS 3081  003/68328  F 1:10pm  5:00pm 6th Flr Pupin Laboratories 
Morgan May  2  14/15 
Fall 2017: PHYS UN3081


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
PHYS 3081  001/75150  M 1:10pm  5:00pm Room TBA 
Elena Aprile  2  8/15 
PHYS 3081  002/16760  Th 1:10pm  5:00pm Room TBA 
Cory Dean  2  0/15 
PHYS 3081  003/21153  F 1:10pm  5:00pm Room TBA 
Morgan May  2  11/15 
PHYS UN3083 Electronics Laboratory. 3 points.
Enrollment limited to the capacity of the laboratory.
Prerequisites: PHYS W3003 or W3007. May be taken before or concurrently with this course.
A sequence of experiments in solidstate electronics, with introductory lectures.
Spring 2017: PHYS UN3083


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 3083  001/23354  M W 1:10pm  4:00pm 513 Pupin Laboratories 
John Parsons  3  10/12 
PHYS UN3500 Supervised Readings in Physics. 3 points.
CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: the written permission of the faculty member who agrees to act as supervisor, and the director of undergraduate studies' permission.
Readings in a selected field of physics under the supervision of a faculty member. Written reports and periodic conferences with the instructor.
Fall 2017: PHYS UN3500


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 3500  001/25373  
Jeremy Dodd  3  0 
PHYS UN3900 Supervised Individual Research. 15 points.
Prerequisites: the written permission of the faculty member who agrees to act as supervisor, and the director of undergraduate studies' permission.
For specially selected physics majors, the opportunity to do a research project in contemporary physics under the supervision of a faculty member. A detailed report on the research is presented by the student when the project is completed.
Fall 2017: PHYS UN3900


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 3900  001/71946  
Jeremy Dodd  15  0 
PHYS G4003 Advanced Mechanics. 3 points.
Lagrange’s formulation of mechanics, calculus of variations, the Action Principle, Hamilton’s formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics
PHYS GU4003 Advanced Mechanics. 3 points.
Prerequisites: differential and integral calculus, differential equations, and PHYS W3003 or the equivalent.
Lagrange's formulation of mechanics, calculus of variations and the Action Principle, Hamilton's formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics.
Spring 2017: PHYS GU4003


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 4003  001/22513  M W 1:10pm  2:25pm 329 Pupin Laboratories 
Brian Cole  3  31/45 
PHYS W4011 Particle Astrophysics and Cosmology. 3 points.
Not offered during 201718 academic year.
Prerequisites: PHYS W1403, W2601 or W2802; MATH V1202 or V1208; students are recommended but not required to have taken PHYS W3003 and W3007.
An introduction to the basics of particle astrophysics and cosmology. Particle physics  introduction to the Standard Model and supersymmetry/higher dimension theories; Cosmology – FriedmannRobertsonWalker line element and equation for expansion of universe; time evolution of energy/matter density from the Big Bang; inflationary cosmology; microwave background theory and observation; structure formation; dark energy; observational tests of geometry of universe and expansion; observational evidence for dark matter; motivation for existence of dark matter from particle physics; experimental searches of dark matter; evaporating and primordial black holes; ultrahigh energy phenomena (gammarays and cosmicrays).
PHYS GU4012 String Theory. 3 points.
Prerequisites: PHYS W3003, PHYS W3008, PHYS W4021. PHYS W4023 would be helpful but is not required. Students should have some familiarity with tools for graphical presentation and numeric problem solving such as Mathematica and/or MatLab.
This course is intended as an introduction to string theory for undergraduates. No advanced graduatelevel preparation is assumed, and the material will be covered at (no higher than) the advanced undergraduate level. Advanced topics such as supersymmetry, Tduality, and covariant quantization will not be covered. The focus will be on the dynamics of classical and quantum mechanical strings, with an emphasis on integrating undergraduate material in classical mechanics, relativity, electrodynamics and quantum mechanics.
Spring 2017: PHYS GU4012


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 4012  001/72877  M W 11:40am  12:55pm 414 Pupin Laboratories 
William Zajc  3  4/30 
PHYS GU4018 SolidState Physics. 3 points.
Prerequisites: PHYS W4021 and W4023, or the equivalent.
Introduction to solidstate physics: crystal structures, properties of periodic lattices, electrons in metals, band structure, transport properties, semiconductors, magnetism, and superconductivity.
Spring 2017: PHYS GU4018


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 4018  001/29128  T Th 2:40pm  3:55pm 420 Pupin Laboratories 
Aron Pinczuk  3  19/30 
PHYS G4019 Mathematical Methods of Physics. 3 points.
Highlights of complex analysis, differential equations, integral equations, Green’s functions, special functions, Fourier and other transforms, approximation methods, group theory and representations, differential geometry and manifolds. Emphasis on applications to physical problems
PHYS GU4019 Mathematical Methods of Physics. 3 points.
Prerequisites: differential and integral calculus; linear algebra; PHYS W3003 and PHYS W3007; or the instructor's permission.
This course will present a wide variety of mathematical ideas and techniques used in the study of physical systems. Topics will include: ordinary and partial differential equations; generalized functions; integral transforms; Green’s functions; nonlinear equations, chaos, and solitons; Hilbert space and linear operators; Feynman path integrals; Riemannian manifolds; tensor analysis; probability and statistics. There will also be a discussion of applications to classical mechanics, fluid dynamics, electromagnetism, plasma physics, quantum mechanics, and general relativity.
Fall 2017: PHYS GU4019


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 4019  001/70892  M W 10:10am  11:25am Room TBA 
Brian Metzger  3  22/100 
PHYS G4021 Quantum Mechanics. 3 points.
The formulation of quantum mechanics in terms of state vectors and linear operators, three dimensional spherically symmetric potentials, the theory of angular momentum and spin, timeindependent and timedependent perturbation theory, scattering theory, identical particles
PHYS GU4021 Quantum Mechanics. 3 points.
Prerequisites: W3003, W3007, BC3006.
Formulation of quantum mechanics in terms of state vectors and linear operators. Three dimensional spherically symmetric potentials. The theory of angular momentum and spin. Identical particles and the exclusion principle. Methods of approximation. Multielectron atoms.
Fall 2017: PHYS GU4021


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 4021  001/67220  T Th 11:40am  12:55pm Room TBA 
Emlyn Hughes  3  31/100 
PHYS GU4022 Quantum Mechanics II. 3 points.
Prerequisites:PHYS UN4021.Formulation of quantum mechanics in terms of state vectors and linear operators, threedimensional spherically symmetric potentials, the theory of angular momentum and spin, timeindependent and timedependent perturbation theory, scattering theory, and identical particles.Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models.
Spring 2017: PHYS GU4022


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 4022  001/64588  T Th 8:40am  9:55am 329 Pupin Laboratories 
Emlyn Hughes  3  53/60 
PHYS G4023 Thermal and Statistical Physics. 3 points.
Pre or corequisite: G4021. Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism
PHYS GU4023 Thermal and Statistical Physics. 3 points.
Prerequisites: PHYS W4021 or the equivalent.
Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism.
Fall 2017: PHYS GU4023


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 4023  001/27342  T Th 1:10pm  2:25pm Room TBA 
Frederik Denef  3  47/100 
PHYS W4040 Introduction to General Relativity. 3 points.
Prerequisites: PHYS W3003, PHYS W3007 or the equivalent.
Tensor algebra, tensor analysis, introduction to Riemann geometry. Motion of particles, fluid, and fields in curved spacetime. Einstein equation. Schwarzschild solution; testparticle orbits and light bending. Introduction to black holes, gravitational waves, and cosmological models.
PHYS W4050 Introduction to Particle Physics. 3 points.
Not offered during 201718 academic year.
Prerequisites: PHYS W2601 or W2802, or the equivalent.
Review of key concepts in quantum mechanics and special relativity. Conservation laws, decays, interactions, oscillations. Atoms, nuclei, hadrons (protons and neutrons) and quarks. Current theoertical and experimental challenges, including physics at the Large Hadron Collider.
PHYS GU4051 Advanced Laboratory Work. 2 points.
Prerequisites: the instructor's permission.
The laboratory has 13 available individual experiments, of which two are required per 2 points. Each experiment requires two (fourhour) laboratory sessions. Registration is limited by the laboratory capacity. May be repeated for credit with different experiment selection. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics.
Spring 2017: PHYS GU4051


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

PHYS 4051  002/69473  Th 1:10pm  5:00pm 6th Flr Pupin Laboratories 
Elena Aprile  2  0/0 
PHYS 4051  003/73559  F 1:10pm  5:00pm 6th Flr Pupin Laboratories 
Morgan May  2  0/0 
Fall 2017: PHYS GU4051


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
PHYS 4051  001/66692  M 1:10pm  5:00pm Room TBA 
Elena Aprile  2  0/0 
PHYS 4051  002/71308  Th 1:10pm  5:00pm Room TBA 
Cory Dean  2  0/0 
PHYS 4051  003/27564  F 1:10pm  5:00pm Room TBA 
Morgan May  2  0/0 
PHYS W4075 Biology at Physical Extremes. 0 points.
Prerequisites: one year each of introductory physics and biology.
This is a combined lecture/seminar course designed for graduate students and advanced undergraduates. The course will cover a series of cases where biological systems take advantage of physical phenomena in counter intuitive and surprising ways to accomplish their functions. In each of these cases, we will discuss different physical mechanisms at work. We will limit our discussions to simple, qualitative arguments. We will also discuss experimental methods enabling the study of these biological systems. Overall, the course will expose students to a wide range of physical concepts involved in biological processes.
PHYS W4080 Scientific Computing. 3 points.
Not offered during 201718 academic year.
Prerequisites: PHYS W3003, PHYS W3008, PHYS W4021, PHYS W4023 or the instructor permission.
This course is intended to provide an introduction to scientic computing for Physics and other physical science undergraduates. Methods of computing will be taught through solving a variety of physical science problems. Previous programming experience is useful, but not required. The course will introduce the C++ programming language and also make use of Python and MATLAB in class and in exercises. The first part of the course will introduce these software tools and explore basic numerical algorithms for dierential equations and matrices, emphasizing numerical stability and performance. These algorithms will then be used to explore physical phenomena, such as the equation of state for a simple gas, electromagnetic wave propgation and statistical mechanics systems. A brief discussion of parallel computing techniques will be included, with a chance to implement some parallel algorithms.
PHYS G4302 General Relativity and Black Holes. 3 points.
Special relativity and its role in physics, the Newtonian theory of gravity from Einstein’s viewpoint, the equivalence principle, differential geometry and geodesics, Einstein’s equations, light bending and gravitational lensing, Newtonian thermodynamics of black holes
PHYS G4386 Geometrical Concepts In Physics. 3 points.
Material from topology and differential geometry with illustrations of their use in electrodynamics, general relativity, and YangMills theory. In particular, topological and differential manifolds, tensors, vector bundles, connections, and Lie groups