APAM 1601 Introduction to computational mathematics and physics. 3 points.

Lect: 3.

Introduction to computational methods in applied mathematics and physics. Students develop solutions in a small number of subject areas to acquire experience in the practical use of computers to solve mathematics and physics problems. Topics change from year to year. Examples include elementary interpolation of functions, solution of nonlinear algebraic equations, curve-fitting and hypothesis testing, wave propagation, fluid motion, gravitational and celestial mechanics, and chaotic dynamics. Basic requirement for this course is one year of college-level calculus and physics; programming experience is not required.

APAM 4901 Seminar: Problems in Applied Mathematics. 0 points.

0 pts. Lect: 1.

This course is required for, and can be taken only by, all applied mathematics majors in the junior year. Prerequisites or corequisites: APMA E4200 and E4204 or their equivalents. Introductory seminars on problems and techniques in applied mathematics. Typical topics are nonlinear dynamics, scientific computation, economics, operations research, etc.

APAM E3105 Programming Methods for Scientists and Engineers. 3 points.

Lect: 2.5. Lab: 1.Not offered during 2017-18 academic year.

Introduction to modern techniques of computer programming for the numerical solutions to familiarity with basic and advanced concepts of modern numerical programming and acquire practical experience solving representative problems in math and physics.

APAM E3999 Undergraduate Fieldwork. 1 point.

Prerequisites: Obtained internship and approval from faculty advisor.

May be repeated for credit, but no more than 3 total points may be used toward the 128credit degree requirement. Only for APAM undergraduate students who include relevant off-campus work experience as part of their approved program of study. Final report and letter of evaluation required. Fieldwork credits may not count toward any major core, technical, elective, and nontechnical requirements. May not be taken for pass/fail credit or audited.

APAM E4999 Supervised internship. 1 point.

1-3 pts.

Only for master's students in the Department of Applied Physics and Applied Mathematics who may need relevant work experience a part of their program of study. Final report required. This course may not be taken for pass/fail or audited. 

APAM E6650 Research project. 1 point.

1-6 pts.

Prerequisites: Written permission from instructor and approval from adviser.

Written permission from instructor and approval from adviser. This course may be repeated for credit. A special investigation of a problem in nuclear engineering, medical physics, applied mathematics, applied physics, and/or plasma physics consisting of independent work on the part of the student and embodied in a formal report.

Spring 2017: APAM E6650
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 6650 001/14326  
William Bailey 1 0/10
APAM 6650 002/62220  
Guillaume Bal 1 0/10
APAM 6650 003/28838  
Katayun Barmak 1 0/10
APAM 6650 004/72611  
Daniel Bienstock 1 0/10
APAM 6650 005/74909  
Simon Billinge 1 0/10
APAM 6650 006/65119  
Allen Boozer 1 0/10
APAM 6650 007/24725  
Mark Cane 1 0/10
APAM 6650 008/66811  
Siu-Wai Chan 1 0/10
APAM 6650 009/75846  
Chengjun Chen 1 0/10
APAM 6650 010/18617  
Andrew Cole 1 0/10
APAM 6650 011/66426  
Qiang Du 1 0/10
APAM 6650 012/20680  
Alexander Gaeta 1 2/10
APAM 6650 013/69380  
OLEG GANG 1 0/10
APAM 6650 014/11961  
Irving Herman 1 2/10
APAM 6650 015/61589  
James Im 1 0/10
APAM 6650 016/21916  
Kyle Mandli 1 1/10
APAM 6650 017/60787  
Chris Marianetti 1 0/10
APAM 6650 018/23995  
Michael Mauel 1 2/10
APAM 6650 019/11677  
Gerald Navratil 1 0/10
APAM 6650 020/72014  
Ismail Noyan 1 0/10
APAM 6650 021/21315  
Richard Osgood 1 0/10
APAM 6650 022/11464  
Aron Pinczuk 1 0/10
APAM 6650 023/11047  
Lorenzo Polvani 1 1/10
APAM 6650 024/73045  
Lorenzo Polvani 1 0/10
APAM 6650 025/70890  
Amiya Sen 1 0/10
APAM 6650 026/11770  
Adam Sobel 1 0/10
APAM 6650 027/70387  
Marc Spiegelman 1 0/10
APAM 6650 028/71960  
Michael Tippett 1 0/10
APAM 6650 029/28841  
Latha Venkataraman 1 0/10
APAM 6650 030/23582  
Francesco Volpe 1 0/10
APAM 6650 031/25669  
Michael Weinstein 1 0/10
APAM 6650 032/27401  
Chris Wiggins 1 0/10
APAM 6650 033/29052  
Shalom Wind 1 0/10
APAM 6650 034/22614  
Cheng Wuu 1 0/10
APAM 6650 035/16413  
Yuan Yang 1 0/10
APAM 6650 036/14269  
Nanfang Yu 1 1/10
APAM 6650 037/12372  
Pat Zanzonico 1 0/10
Fall 2017: APAM E6650
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 6650 001/73755  
William Bailey 1 0/10
APAM 6650 002/71430  
Guillaume Bal 1 0/10
APAM 6650 003/18314  
Katayun Barmak 1 0/10
APAM 6650 004/65411  
Daniel Bienstock 1 0/10
APAM 6650 005/11918  
Simon Billinge 1 0/10
APAM 6650 006/11840  
Allen Boozer 1 0/10
APAM 6650 007/17816  
Mark Cane 1 0/10
APAM 6650 008/62165  
Siu-Wai Chan 1 0/10
APAM 6650 009/12831  
Chengjun Chen 1 0/10
APAM 6650 010/63739  
Andrew Cole 1 1/10
APAM 6650 011/19053  
Qiang Du 1 1/10
APAM 6650 012/77288  
Peter Esser 1 0/10
APAM 6650 013/63490  
Alexander Gaeta 1 1/10
APAM 6650 014/17808  
OLEG GANG 1 0/10
APAM 6650 015/71294  
Eitan Grinspun 1 0/10
APAM 6650 016/61513  
Irving Herman 1 0/10
APAM 6650 017/61285  
James Im 1 0/10
APAM 6650 018/14095  
Kyle Mandli 1 0/10
APAM 6650 019/65609  
Chris Marianetti 1 0/10
APAM 6650 020/19286  
Michael Mauel 1 0/10
APAM 6650 021/23386  
Gerald Navratil 1 3/10
APAM 6650 022/25325  
Ismail Noyan 1 0/10
APAM 6650 023/10632  
Richard Osgood 1 1/10
APAM 6650 024/13903  
Aron Pinczuk 1 0/10
APAM 6650 025/60596  
Lorenzo Polvani 1 0/10
APAM 6650 026/76412  
Amiya Sen 1 0/10
APAM 6650 027/26559  
Adam Sobel 1 0/10
APAM 6650 028/11298  
Marc Spiegelman 1 0/10
APAM 6650 029/75929  
Michael Tippett 1 0/10
APAM 6650 030/20827  
Latha Venkataraman 1 0/10
APAM 6650 031/21050  
Francesco Volpe 1 0/10
APAM 6650 032/23733  
Michael Weinstein 1 0/10
APAM 6650 033/10318  
Renata Wentzcovitch 1 0/10
APAM 6650 034/22550  
Chris Wiggins 1 0/10
APAM 6650 035/23747  
Shalom Wind 1 0/10
APAM 6650 036/19487  
Cheng Wuu 1 1/10
APAM 6650 037/21474  
Yuan Yang 1 0/10
APAM 6650 038/28819  
Nanfang Yu 1 2/10

APAM E9301 Doctoral research. 0 points.

0-15 pts.

Prerequisite: the qualifying examination for the doctorate. Required of doctoral candidates.

Spring 2017: APAM E9301
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 9301 001/61066  
William Bailey 0 0/10
APAM 9301 002/23498  
Guillaume Bal 0 1/10
APAM 9301 003/69371  
Katayun Barmak 0 1/10
APAM 9301 004/70466  
Daniel Bienstock 0 0/10
APAM 9301 005/70206  
Simon Billinge 0 2/10
APAM 9301 006/70090  
Allen Boozer 0 0/10
APAM 9301 007/10100  
Mark Cane 0 0/10
APAM 9301 008/74256  
Siu-Wai Chan 0 0/10
APAM 9301 009/69169  
Andrew Cole 0 1/10
APAM 9301 010/61998  
Qiang Du 0 2/10
APAM 9301 011/70547  
Alexander Gaeta 0 0/10
APAM 9301 012/72480  
OLEG GANG 0 0/10
APAM 9301 013/70196  
Irving Herman 0 2/10
APAM 9301 014/27519  
James Im 0 0/10
APAM 9301 015/21994  
Kyle Mandli 0 1/20
APAM 9301 016/22163  
Chris Marianetti 0 1/10
APAM 9301 017/76240  
Michael Mauel 0 3/10
APAM 9301 018/23795  
Gerald Navratil 0 1/10
APAM 9301 019/68576  
Ismail Noyan 0 0/10
APAM 9301 020/60624  
Ismail Noyan 0 0/10
APAM 9301 021/69154  
Richard Osgood 0 2/10
APAM 9301 022/27751  
Aron Pinczuk 0 0/10
APAM 9301 023/11868  
Lorenzo Polvani 0 3/10
APAM 9301 024/28745  
Amiya Sen 0 0/10
APAM 9301 025/20600  
Adam Sobel 0 1/10
APAM 9301 026/20916  
Marc Spiegelman 0 2/10
APAM 9301 027/61801  
Latha Venkataraman 0 4/10
APAM 9301 028/60178  
Francesco Volpe 0 2/10
APAM 9301 029/24122  
Michael Weinstein 0 2/10
APAM 9301 030/73439  
Chris Wiggins 0 1/10
APAM 9301 031/75739  
Shalom Wind 0 0/10
APAM 9301 032/19576  
Cheng Wuu 0 0/10
APAM 9301 033/62548  
Yuan Yang 0 1/10
APAM 9301 034/25157  
Nanfang Yu 0 4/10
APAM 9301 035/29802  
Eitan Grinspun 0 1/10
Fall 2017: APAM E9301
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 9301 001/61142  
William Bailey 0 0/10
APAM 9301 002/68187  
Guillaume Bal 0 0/10
APAM 9301 003/67599  
Katayun Barmak 0 2/10
APAM 9301 004/16090  
Daniel Bienstock 0 0/10
APAM 9301 005/70776  
Simon Billinge 0 4/10
APAM 9301 006/65260  
Allen Boozer 0 0/10
APAM 9301 007/71977  
Mark Cane 0 0/10
APAM 9301 008/65088  
Siu-Wai Chan 0 0/10
APAM 9301 009/63734  
Andrew Cole 0 0/10
APAM 9301 010/16777  
Qiang Du 0 2/10
APAM 9301 011/70871  
Alexander Gaeta 0 2/10
APAM 9301 012/76769  
OLEG GANG 0 1/10
APAM 9301 013/26901  
Eitan Grinspun 0 1/10
APAM 9301 014/75427  
Irving Herman 0 2/10
APAM 9301 015/76526  
James Im 0 2/10
APAM 9301 016/60319  
Kyle Mandli 0 2/10
APAM 9301 017/73905  
Chris Marianetti 0 2/10
APAM 9301 018/70113  
Michael Mauel 0 3/10
APAM 9301 019/76604  
Gerald Navratil 0 1/10
APAM 9301 020/14282  
Ismail Noyan 0 1/10
APAM 9301 021/13324  
Richard Osgood 0 2/10
APAM 9301 022/71162  
Aron Pinczuk 0 1/10
APAM 9301 023/16986  
Lorenzo Polvani 0 3/10
APAM 9301 024/69666  
Amiya Sen 0 0/10
APAM 9301 025/27161  
Adam Sobel 0 2/10
APAM 9301 026/65494  
Marc Spiegelman 0 2/10
APAM 9301 027/10344  
Latha Venkataraman 0 3/10
APAM 9301 028/65774  
Francesco Volpe 0 0/10
APAM 9301 029/63361  
Michael Weinstein 0 1/10
APAM 9301 030/64515  
Renata Wentzcovitch 0 1/10
APAM 9301 031/13737  
Chris Wiggins 0 1/10
APAM 9301 032/12818  
Shalom Wind 0 1/10
APAM 9301 033/21987  
Cheng Wuu 0 0/10
APAM 9301 034/13552  
Yuan Yang 0 0/10
APAM 9301 035/63838  
Nanfang Yu 0 5/10

APAM E9800 Doctoral research instruction. 3 points.

3, 6, 9, or 12 pts.

A candidate for the Eng.Sc.D. degree must register for 12 points of doctoral research instruction. Registration for APAM E9800 may not be used to satisfy the minimum residence requirement for the degree.

Spring 2017: APAM E9800
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 9800 001/27002  
William Bailey 3 0/10
APAM 9800 002/67013  
Guillaume Bal 3 0/10
APAM 9800 003/24384  
Katayun Barmak 3 0/10
APAM 9800 004/26927  
Daniel Bienstock 3 0/10
APAM 9800 005/27568  
Simon Billinge 3 0/10
APAM 9800 006/64619  
Allen Boozer 3 0/10
APAM 9800 007/19413  
Mark Cane 3 0/10
APAM 9800 008/72690  
Siu-Wai Chan 3 0/10
APAM 9800 009/67750  
Andrew Cole 3 0/10
APAM 9800 010/74887  
Qiang Du 3 0/10
APAM 9800 011/75376  
Alexander Gaeta 3 0/10
APAM 9800 012/26274  
OLEG GANG 3 0/10
APAM 9800 013/15678  
Irving Herman 3 0/10
APAM 9800 014/15639  
James Im 3 0/10
APAM 9800 015/10988  
Kyle Mandli 3 0/10
APAM 9800 016/76975  
Chris Marianetti 3 0/10
APAM 9800 017/69204  
Michael Mauel 3 0/10
APAM 9800 018/75278  
Gerald Navratil 3 0/10
APAM 9800 019/66530  
Ismail Noyan 3 0/10
APAM 9800 020/10505  
Ismail Noyan 3 0/10
APAM 9800 021/77735  
Richard Osgood 3 0/10
APAM 9800 022/63536  
Aron Pinczuk 3 0/10
APAM 9800 023/27332  
Lorenzo Polvani 3 0/10
APAM 9800 024/14109  
Amiya Sen 3 0/10
APAM 9800 025/74487  
Adam Sobel 3 0/10
APAM 9800 026/17647  
Marc Spiegelman 3 0/10
APAM 9800 027/28794  
Latha Venkataraman 3 0/10
APAM 9800 028/69821  
Francesco Volpe 3 0/10
APAM 9800 029/70490  
Michael Weinstein 3 0/10
APAM 9800 030/17681  
Chris Wiggins 3 0/10
APAM 9800 031/28073  
Shalom Wind 3 0/10
APAM 9800 032/25339  
Cheng Wuu 3 0/10
APAM 9800 033/62102  
Yuan Yang 3 0/10
APAM 9800 034/15389  
Nanfang Yu 3 0/10
Fall 2017: APAM E9800
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 9800 001/76180  
William Bailey 3 0/10
APAM 9800 002/71942  
Guillaume Bal 3 0/10
APAM 9800 003/72598  
Katayun Barmak 3 0/10
APAM 9800 004/25968  
Daniel Bienstock 3 0/10
APAM 9800 005/11766  
Simon Billinge 3 0/10
APAM 9800 006/74758  
Allen Boozer 3 0/10
APAM 9800 007/22379  
Mark Cane 3 0/10
APAM 9800 008/29908  
Siu-Wai Chan 3 0/10
APAM 9800 009/75437  
Andrew Cole 3 0/10
APAM 9800 010/71879  
Qiang Du 3 0/10
APAM 9800 011/65456  
Alexander Gaeta 3 0/10
APAM 9800 012/70217  
OLEG GANG 3 0/10
APAM 9800 013/29826  
Eitan Grinspun 3 0/10
APAM 9800 014/68962  
Irving Herman 3 0/10
APAM 9800 015/65356  
James Im 3 0/10
APAM 9800 016/18833  
Kyle Mandli 3 0/10
APAM 9800 017/63138  
Chris Marianetti 3 0/10
APAM 9800 018/65195  
Michael Mauel 3 0/10
APAM 9800 019/66355  
Gerald Navratil 3 0/10
APAM 9800 020/76924  
Ismail Noyan 3 0/10
APAM 9800 021/64027  
Richard Osgood 3 0/10
APAM 9800 022/77578  
Aron Pinczuk 3 0/10
APAM 9800 023/15127  
Lorenzo Polvani 3 0/10
APAM 9800 024/69442  
Amiya Sen 3 0/10
APAM 9800 025/24416  
Adam Sobel 3 0/10
APAM 9800 026/16409  
Marc Spiegelman 3 0/10
APAM 9800 027/70287  
Latha Venkataraman 3 0/10
APAM 9800 028/71361  
Francesco Volpe 3 0/10
APAM 9800 029/77506  
Michael Weinstein 3 0/10
APAM 9800 030/21449  
Renata Wentzcovitch 3 0/10
APAM 9800 031/29996  
Chris Wiggins 3 0/10
APAM 9800 032/64474  
Shalom Wind 3 0/10
APAM 9800 033/61147  
Cheng Wuu 3 0/10
APAM 9800 034/22818  
Yuan Yang 3 0/10
APAM 9800 035/62436  
Nanfang Yu 3 0/10

APAM E9900 Doctoral dissertation. 0 points.

0 pts.

A candidate for the doctorate may be required to register for this course every term after the coursework has been completed, and until the dissertation has been accepted.

Spring 2017: APAM E9900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 9900 001/10148  
William Bailey 0 0/10
APAM 9900 002/16939  
Guillaume Bal 0 0/10
APAM 9900 003/26249  
Katayun Barmak 0 0/10
APAM 9900 004/21454  
Daniel Bienstock 0 0/10
APAM 9900 005/27439  
Simon Billinge 0 0/10
APAM 9900 006/70067  
Allen Boozer 0 0/10
APAM 9900 007/61556  
Mark Cane 0 0/10
APAM 9900 008/70993  
Siu-Wai Chan 0 0/10
APAM 9900 009/27365  
Andrew Cole 0 0/10
APAM 9900 010/72182  
Qiang Du 0 0/10
APAM 9900 011/23529  
Alexander Gaeta 0 0/10
APAM 9900 012/60260  
OLEG GANG 0 0/10
APAM 9900 013/63329  
Irving Herman 0 0/10
APAM 9900 014/11352  
James Im 0 0/10
APAM 9900 015/72366  
Kyle Mandli 0 0/10
APAM 9900 016/28353  
Chris Marianetti 0 0/10
APAM 9900 017/73115  
Michael Mauel 0 0/10
APAM 9900 018/15011  
Gerald Navratil 0 0/10
APAM 9900 019/63500  
Ismail Noyan 0 0/10
APAM 9900 020/63707  
Ismail Noyan 0 0/10
APAM 9900 021/76676  
Richard Osgood 0 0/10
APAM 9900 022/16767  
Aron Pinczuk 0 0/10
APAM 9900 023/64096  
Lorenzo Polvani 0 0/10
APAM 9900 024/19901  
Amiya Sen 0 0/10
APAM 9900 025/12049  
Adam Sobel 0 0/10
APAM 9900 026/19031  
Marc Spiegelman 0 0/10
APAM 9900 027/67035  
Latha Venkataraman 0 0/10
APAM 9900 028/77022  
Francesco Volpe 0 0/10
APAM 9900 029/71321  
Michael Weinstein 0 0/10
APAM 9900 030/68404  
Chris Wiggins 0 0/10
APAM 9900 031/20308  
Shalom Wind 0 0/10
APAM 9900 032/60900  
Cheng Wuu 0 0/10
APAM 9900 033/22229  
Yuan Yang 0 0/10
APAM 9900 034/26617  
Nanfang Yu 0 0/10
Fall 2017: APAM E9900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 9900 001/71513  
William Bailey 0 0/10
APAM 9900 002/22901  
Guillaume Bal 0 0/10
APAM 9900 003/74461  
Katayun Barmak 0 0/10
APAM 9900 004/67557  
Daniel Bienstock 0 0/10
APAM 9900 005/23626  
Simon Billinge 0 0/10
APAM 9900 006/16069  
Allen Boozer 0 0/10
APAM 9900 007/15830  
Mark Cane 0 0/10
APAM 9900 008/12083  
Siu-Wai Chan 0 0/10
APAM 9900 009/64994  
Andrew Cole 0 0/10
APAM 9900 010/24866  
Qiang Du 0 0/10
APAM 9900 011/12743  
Alexander Gaeta 0 0/10
APAM 9900 012/60559  
OLEG GANG 0 0/10
APAM 9900 013/26016  
Eitan Grinspun 0 0/10
APAM 9900 014/11779  
Irving Herman 0 0/10
APAM 9900 015/73460  
James Im 0 0/10
APAM 9900 016/25565  
Kyle Mandli 0 0/10
APAM 9900 017/26391  
Chris Marianetti 0 0/10
APAM 9900 018/61006  
Michael Mauel 0 0/10
APAM 9900 019/65527  
Gerald Navratil 0 0/10
APAM 9900 020/61863  
Ismail Noyan 0 0/10
APAM 9900 021/17381  
Richard Osgood 0 0/10
APAM 9900 022/10350  
Aron Pinczuk 0 0/10
APAM 9900 023/66595  
Lorenzo Polvani 0 0/10
APAM 9900 024/73413  
Amiya Sen 0 0/10
APAM 9900 025/28996  
Adam Sobel 0 0/10
APAM 9900 026/65140  
Marc Spiegelman 0 0/10
APAM 9900 027/67504  
Latha Venkataraman 0 0/10
APAM 9900 028/10732  
Francesco Volpe 0 0/10
APAM 9900 029/21082  
Michael Weinstein 0 0/10
APAM 9900 030/76985  
Renata Wentzcovitch 0 0/10
APAM 9900 031/65023  
Chris Wiggins 0 0/10
APAM 9900 032/73174  
Shalom Wind 0 0/10
APAM 9900 033/29750  
Cheng Wuu 0 0/10
APAM 9900 034/68396  
Yuan Yang 0 0/10
APAM 9900 035/12502  
Nanfang Yu 0 0/10

APBM E4650 Anatomy for physicists and engineers. 3 points.

Lect: 3.

Prerequisites: Engineering or physics background

Systemic approach to the study of the human body from a medical imaging point of view: skeletal, respiratory, cardiovascular, digestive, and urinary systems, breast and women's issues, head and neck, and central nervous system. Lectures are reinforced by examples from clinical two- and three-dimensional and functional imaging (CT, MRI, PET, SPECT, U/S, etc.).

Fall 2017: APBM E4650
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APBM 4650 001/10567 T Th 4:10pm - 5:25pm
1-303 Presbyterian Hospital
Monique Katz, Anna Rozenshtein 3 16/24

APCH E4080 Soft Condensed Matter. 3 points.

Lect: 3.Not offered during 2017-18 academic year.

Prerequisites: (MSAE E3111) and (CHEN E3010) or (CHEN E3120) or equivalent.

Course is aimed at senior undergraduate and graduate students. Introduces fundamental ideas, concepts and approaches in soft condensed matter with emphasis on biomolecular systems. Covers the broad range of molecular, nanoscale and colloidal phenomena with revealing their mechanisms and physical foundations. The relationship between molecular architecture and interactions, and macroscopic behavior are discussed for the broad range of soft and biological matter systems, from surfactants and liquid crystals to polymers, nanoparticles and biomolecules. Modern characterization methods for soft materials, including x-ray scattering, molecular force probing and electron microcopy are reviewed. Example problems, drawn from the recent scientific literature, link the studied material to the actively developed research areas. Course grade based on midterm and final exams, weekly homework assignments, and final individual/team project.

Fall 2017: APCH E4080
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APCH 4080 001/69259 T Th 1:10pm - 2:25pm
545 Seeley W. Mudd Building
OLEG GANG 3 15/45

APMA E Multivariable Calculus for Engineers and Applied Scientists. 0 points.

APMA E2101 Introduction to Applied Mathematics. 3 points.

Lect: 3.

Prerequisites: Calculus III.

A unified, single-semester introduction to differential equations and linear algebra with emphases on (1) elementary analytical and numerical technique and (2) discovering the analogs on the continuous and discrete sides of the mathematics of linear operators: superposition, diagonalization, fundamental solutions. Concepts are illustrated with applications using the language of engineering, the natural sciences, and the social sciences. Students execute scripts in Mathematica and MATLAB (or the like) to illustrate and visualize course concepts (programming not required).

Spring 2017: APMA E2101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 2101 001/60085 T Th 1:10pm - 2:25pm
309 Havemeyer Hall
Michael Tippett 3 124/164

APMA E3101 Linear Algebra. 3 points.

Lect: 3.

Matrix algebra, elementary matrices, inverses, rank, determinants. Computational aspects of solving systems of linear equations: existence-uniqueness of solutions, Gaussian elimination, scaling, ill-conditioned systems, iterative techniques. Vector spaces, bases, dimension. Eigenvalue problems, diagonalization, inner products, unitary matrices.

Fall 2017: APMA E3101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 3101 001/72178 T Th 11:40am - 12:55pm
503 Hamilton Hall
Michael Tippett 3 39/52

APMA E3102 Partial Differential Equations. 3 points.

Lect: 3.

Prerequisites: (MATH UN2030) or the equivalent

Introduction to partial differential equations; integral theorems of vector calculus. Partial differential equations of engineering in rectangular, cylindrical, and spherical coordinates. Separation of the variables. Characteristic-value problems. Bessel functions, Legendre polynomials, other orthogonal functions; their use in boundary value problems. Illustrative examples from the fields of electromagnetic theory, vibrations, heat flow, and fluid mechanics.

Spring 2017: APMA E3102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 3102 001/13709 T Th 4:10pm - 5:25pm
517 Hamilton Hall
Vincent Quenneville-Belair 3 39/70

APMA E3900 Undergraduate Research in Applied Mathematics. 0 points.

0-4 pts.

Prerequisites: Written permission from instructor and approval from adviser.

This course may be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for the B.S. degree may conduct an investigation in applied mathematics or carry out a special project under the supervision of the staff. Credit for the course is contingent upon the submission of an acceptable thesis or final report.

Spring 2017: APMA E3900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 3900 001/27800  
Guillaume Bal 0 0/10
APMA 3900 002/22758  
Daniel Bienstock 0 0/10
APMA 3900 003/20108  
Mark Cane 0 0/10
APMA 3900 004/15640  
Qiang Du 0 0/10
APMA 3900 005/16370  
Eitan Grinspun 0 0/20
APMA 3900 006/16778  
Kyle Mandli 0 1/10
APMA 3900 007/25000  
Lorenzo Polvani 0 0/10
APMA 3900 008/64666  
Adam Sobel 0 0/10
APMA 3900 009/25789  
Marc Spiegelman 0 0/10
APMA 3900 010/16824  
Michael Tippett 0 2/10
APMA 3900 011/21219  
Michael Weinstein 0 0/10
APMA 3900 012/72537  
Chris Wiggins 0 3/10
Fall 2017: APMA E3900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 3900 001/67793  
Guillaume Bal 0 0/10
APMA 3900 002/18009  
Daniel Bienstock 0 0/10
APMA 3900 003/25288  
Mark Cane 0 0/10
APMA 3900 004/19448  
Qiang Du 0 0/10
APMA 3900 005/13260  
Eitan Grinspun 0 0/10
APMA 3900 006/28598  
Kyle Mandli 0 0/10
APMA 3900 007/63915  
Lorenzo Polvani 0 0/10
APMA 3900 008/68408  
Adam Sobel 0 1/10
APMA 3900 009/68289  
Marc Spiegelman 0 0/10
APMA 3900 010/20164  
Michael Tippett 0 0/10
APMA 3900 011/14946  
Michael Weinstein 0 0/10
APMA 3900 012/75006  
Chris Wiggins 0 2/10

APMA E4001 Principles of Applied Mathematics. 3 points.

Lect: 3.

Prerequisites: Introductory Linear Algebra required. Ordinary Differential Equations recommended.

Review of finite-dimensional vector spaces and elementary matrix theory. Linear transformations, change of basis, eigenspaces. Matrix representation of linear operators and diagonalization. Applications to difference equations, Markov processes, ordinary differential equations, and stability of nonlinear dynamical systems. Inner product spaces, projection operators, orthogonal bases, Gram-Schmidt orthogonalization. Least squares method, pseudo-inverses, singular value decomposition. Adjoint operators, Hermitian and unitary operators, Fredholm Alternative Theorem. Fourier series and eigenfunction expansions. Introduction to the theory of distributions and the Fourier Integral Transform. Green's functions. Application to Partial Differential Equations.

Spring 2017: APMA E4001
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4001 001/12742 T Th 1:10pm - 2:25pm
503 Hamilton Hall
Marc Spiegelman 3 54/70

APMA E4101 Introduction to Dynamical Systems. 3 points.

Lect: 3.

Prerequisites: (APMA E2101) and (APMA E3101)

An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and classification of flows in the plane (Poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stable and unstable manifolds; bifurcations, e.g. Andronov-Hopf; sensitive dependence and chaotic dynamics; selected applications.

Fall 2017: APMA E4101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4101 001/11085 T Th 8:40am - 9:55am
545 Seeley W. Mudd Building
Marc Spiegelman 3 64/75

APMA E4150 Applied Functional Analysis. 3 points.

Prerequisites: Advanced calculus and course in basic analysis, or instructor's permission.

Introduction to modern tools in functional analysis that are used in the analysis of deterministic and stochastic partial differential equations and in the analysis of numerical methods: metric and normed spaces. Banach space of continuous functions, measurable spaces, the contraction mapping theorem, Banach and Hilbert spaces bounded linear operators on Hilbert spaces and their spectral decomposition, and time permitting distributions and Fourier transforms.

Fall 2017: APMA E4150
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4150 001/19239 M 1:10pm - 3:40pm
214 Seeley W. Mudd Building
Michael Weinstein 3 21/35

APMA E4200 Partial Differential Equations. 3 points.

Prerequisites: Course in ordinary differential equations.

Techniques of solution of partial differential equations. Separation of the variables. Orthogonality and characteristic functions, nonhomogeneous boundary value problems. Solutions in orthogonal curvilinear coordinate systems. Applications of Fourier integrals, Fourier and Laplace transforms. Problems from the fields of vibrations, heat conduction, electricity, fluid dynamics, and wave propagation are considered.

Fall 2017: APMA E4200
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4200 001/23047 M 7:00pm - 9:30pm
301 Pupin Laboratories
Donsub Rim 3 55/120

APMA E4204 Functions of a Complex Variable. 3 points.

Prerequisites: (MATH UN1202) or the equivalent.

Complex numbers, functions of a complex variable, differentiation and integration in the complex plane. Analytic functions, Cauchy integral theorem and formula, Taylor and Laurent series, poles and residues, branch points, evaluation of contour integrals. Conformal mapping, Schwarz-Christoffel transformation. Applications to physical problems.

Fall 2017: APMA E4204
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4204 001/29408 T Th 5:40pm - 6:55pm
834 Seeley W. Mudd Building
Maxence Cassier 3 34/40

APMA E4300 Computational Math: Introduction to Numerical Methods. 3 points.

Lect: 3.

Prerequisites: (MATH UN1201) and (MATH UN2030) and (APMA E3101) and (ENGI E1006) or their equivalents. Programming experience in Python extremely useful.

Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. Designed to give a fundamental understanding of the building blocks of scientific computing that will be used in more advanced courses in scientific computing and numerical methods for PDEs (e.g. APMA E4301, E4302). Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, optimization, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODE's. All programming exercises will be in Python.

Fall 2017: APMA E4300
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4300 001/70726 T Th 1:10pm - 2:25pm
428 Pupin Laboratories
Kyle Mandli 3 142/147

APMA E4301 Numerical Methods for Partial Differential Equations. 3 points.

Lect: 3.

Prerequisites: (APMA E4300) and (APMA E3102) or (APMA E4200) or or equivalents.

Numerical solution of differential equations, in particular partial differential equations arising in various fields of application. Presentation emphasizes finite difference approaches to present theory on stability, accuracy, and convergence with minimal coverage of alternate approaches (left for other courses). Method coverage includes explicit and implicit time-stepping methods, direct and iterative solvers for boundary-value problems.

Spring 2017: APMA E4301
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4301 001/24399 T Th 11:40am - 12:55pm
1024 Seeley W. Mudd Building
Kyle Mandli 3 14/70

APMA E4302 Methods in Computational Science. 3 points.

Lect: 3.

Prerequisites: (APMA E4300) and application and knowledge in C, Fortran or similar complied language.

Introduction to the key concepts and issues in computational science aimed at getting students to a basic level of understanding where they can run simulations on machines aimed at a range of applications and sizes from a single workstation to modern super-computer hardware. Topics include but are not limited to basic knowledge of UNIX shells, version control systems, reproducibility, Open MP, MPI, and many-core technologies. Applications will be used throughout to demonstrate the various use cases and pitfalls of using the latest computing hardware.

Fall 2017: APMA E4302
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4302 001/68963 W 10:10am - 12:40pm
233 Seeley W. Mudd Building
Qiang Du 3 16/35

APMA E4400 Introduction to Biophysical Modeling. 3 points.

Lect: 3.

Prerequisites: (PHYS UN1401) and (APMA E2101) or (MATH UN2030) or or equivalent.

Introduction to physical and mathematical models of cellular and molecular biology. Physics at the cellular scale (viscosity, heat, diffusion, statistical mechanics). RNA transcription and regulation of genetic expression. Genetic and biochemical networks. Bioinformatics as applied to reverse-engineering of naturally-occurring networks and to forward-engineering of synthetic biological networks. Mathematical and physical aspects of functional genomics.

APMA E4901 Seminar: Problem in Applied Mathematics. 0 points.

Lect: 1.

Prerequisites: (APMA E4200) and (APMA E4204) or their equivalents.
Corequisites: APMA E4200,APMA E4204

This course is required for, and can be taken only by, all applied mathematics majors in the junior year. Introductory seminars on problems and techniques in applied mathematics. Typical topics are nonlinear dynamics, scientific computation, economics, operation research, etc.

Fall 2017: APMA E4901
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4901 001/64865 W 11:40am - 12:55pm
633 Seeley W. Mudd Building
Chris Wiggins 0 40/50

APMA E4903 Seminar: Problems in Applied Mathematics. 3 points.

3-4 pts. Lect: 1

Prerequisites: (APMA E4200) and (APMA E4204) or their equivalents.
Corequisites: APMA E4200,APMA E4204

For 4 pts. credit, term paper required. This course is required for all applied mathematics majors in the senior year. Examples of problem areas are nonlinear dynamics, asymptotics, approximation theory, numerical methods, etc. Approximately three problem areas are studies per term. 

Fall 2017: APMA E4903
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4903 001/12394 M W 11:40am - 12:55pm
633 Seeley W. Mudd Building
Chris Wiggins 3 28/50

APMA E4990 Special Topics in Applied Mathematics. 1 point.

1-3 pts. Lect: 3.

Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.

This course may be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, biological sciences, and other fields.

Spring 2017: APMA E4990
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4990 001/23717 F 10:10am - 12:40pm
310 Fayerweather
Jacob Hofman 1 52/85
APMA 4990 002/29285 Th 7:00pm - 9:30pm
327 Seeley W. Mudd Building
Dorian Goldman 1 30/39

APMA E6100 Research Seminar. 0 points.

Lect: 3. Not offered during 2017-18 academic year.

Prerequisites: (MATH UN3027) or (APMA E4101) or (MATH UN3028) or (APMA E4200) or (MATH UN2010) or (APMA E3101) or their equivalents.
Corequisites: MATH UN3027
APMA E4101
MATH UN3028
APMA E4200
MATH UN2010
APMA E3101

This course is an M.S. degree requirement. Students attend at least three Applied Mathematics research seminars within the Department of Applied Physics and Applied Mathematics and submit reports on each. 

APMA E6209 Approximation Theory. 3 points.

Lect: 2.Not offered during 2017-18 academic year.

Prerequisites: (MATH GU4061) or or some knowledge of modern analysis.

Theory and application of approximate methods of analysis from the viewpoint of functional analysis. Approximate numerical and analytical treatment of linear and nonlinear algebraic, differential, and integral equations. Topics include function spaces, operators in normed and metric spaces, fixed point theorems and their applications.

APMA E6301 Analytic methods for partial differential equations. 3 points.

Lect: 2.

Prerequisites: (APMA E3101) and (APMA E4200) or their equivalents, Advanced calculus, basic concepts in analysis, or instructor's permission.

Introduction to analytic theory of PDEs of fundamental and applied science; wave (hyperbolic), Laplace and Poisson equations (elliptic), heat (parabolic) and Schroedinger (dispersive) equations; fundamental solutions, Green's functions, weak/distribution solutions, maximum principle, energy estimates, variational methods, method of characteristics; elementary functional analysis and applications to PDEs; introduction to nonlinear PDEs, shocks; selected applications.

Spring 2017: APMA E6301
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 6301 001/25816 M 1:10pm - 3:40pm
1024 Seeley W. Mudd Building
Michael Weinstein 3 9/70

APMA E6302 Numerical analysis of partial differential equations. 3 points.

Lect: 2.

Prerequisites: (APMA E3102) or (APMA E4200)

Numerical analysis of initial and boundary value problems for partial differential equations. Convergence and stability of the finite difference method, the spectral method, the finite element method and applications to elliptic, parabolic, and hyperbolic equations.

Spring 2017: APMA E6302
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 6302 001/70734 T 10:10am - 12:40pm
327 Seeley W. Mudd Building
Qiang Du 3 9/70

APMA E6304 Integral transforms. 3 points.

Lect: 2.Not offered during 2017-18 academic year.

Prerequisites: (APMA E4204) and (MATH UN2030) or their equivalents.

Laplace, Fourier, Hankel, and Mellin transforms. Selection of suitable transform for a given partial differential equation boundary value problem. Operational properties of transforms. Inversion theorems. Approximate evaluation of inversion integrals for small and large values of parameter. Application to the solution of integral equations.

APMA E6901 Special topics in applied mathematics. 3 points.

Lect: 3.

Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.

This course may be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For students in engineering, physical sciences, biological sciences, and other fields.

APMA E8308 Asymptotic methods in applied mathematics. 3 points.

Lect: 2. Not offered in 2016-2017.Not offered during 2017-18 academic year.

Prerequisites: (APMA E4204) or or the equivalent.

Asymptotic treatment of ordinary and partial differential equations in problems arising in applied mathematics. Asymptotic series. Asymptotic evaluation of integrals. Expansion of solutions of ordinary differential equations: connection problem and turning points. Stoke's phenomenon. Differential equations with a parameter: "boundary layer" phenomenon. Application to partial differential equations: problems from fluid dynamics, wave propagation theory, electromagnetic theory.

APMA E9101 Research. 1 point.

1-4 pts.

Prerequisites: Prerequisite: the permission of the supervising faculty member.

This course may be repeated. Advanced study in a special area.

Fall 2017: APMA E9101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 9101 001/23237  
Guillaume Bal 1 0/10
APMA 9101 002/70525  
Daniel Bienstock 1 0/10
APMA 9101 003/75700  
Mark Cane 1 0/10
APMA 9101 004/75696  
Eitan Grinspun 1 0/10
APMA 9101 006/16041  
Kyle Mandli 1 0/10
APMA 9101 007/29298  
Lorenzo Polvani 1 0/10
APMA 9101 008/12391  
Adam Sobel 1 0/10
APMA 9101 009/72657  
Marc Spiegelman 1 0/10
APMA 9101 010/66299  
Michael Weinstein 1 0/10
APMA 9101 011/29500  
Chris Wiggins 1 0/10

APMA E9102 Research. 1 point.

1-4 pts.

Prerequisites: Prerequisite: the permission of the supervising faculty member.

This course may be repeated. Advanced study in a special area.

Spring 2017: APMA E9102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 9102 001/69570  
Guillaume Bal 1 0/10
APMA 9102 002/28735  
Daniel Bienstock 1 0/10
APMA 9102 003/65986  
Mark Cane 1 0/10
APMA 9102 004/27892  
Qiang Du 1 1/10
APMA 9102 005/10233  
Eitan Grinspun 1 0/20
APMA 9102 006/69233  
Kyle Mandli 1 0/10
APMA 9102 007/70107  
Lorenzo Polvani 1 0/10
APMA 9102 008/74952  
Adam Sobel 1 0/10
APMA 9102 009/77681  
Marc Spiegelman 1 0/10
APMA 9102 010/73847  
Michael Weinstein 1 0/10
APMA 9102 011/28216  
Chris Wiggins 1 0/10

APMA E9810 SEAS colloquium in climate science. 0 points.

0 pts. Lect: 1.

Prerequisites: Instructor's permission.

Current research in problems at the interface between applied mathematics and earth and environmental sciences.

Spring 2017: APMA E9810
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 9810 001/76778 Th 2:45pm - 3:45pm
214 Seeley W. Mudd Building
Lorenzo Polvani 0 0/35
Fall 2017: APMA E9810
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 9810 001/21787 Th 2:45pm - 3:45pm
214 Seeley W. Mudd Building
Lorenzo Polvani 0 0/0

APMA E9815 Geophysical fluid dynamics seminar. 1-3 points.

May be repeated for up to 10 points of credit. Not offered during 2017-18 academic year.

Prerequisites: Instructor's permission.

Problems in the dynamics of geophysical fluid flows.

APPH E3100 Introduction to quantum mechanics. 3 points.

Lect: 3.

Prerequisites: (PHYS UN1403) or the equivalent, and differential and integral calculus.
Corequisites: APMA E3101

Basic concepts and assumptions of quantum mechanics, Schrodinger's equation, solutions for one-dimensional problems including square wells, barriers and the harmonic oscillator, introduction to the hydrogen atom, atomic physics and x-rays, electron spin.

Spring 2017: APPH E3100
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3100 001/26436 M W 1:10pm - 2:25pm
825 Seeley W. Mudd Building
Irving Herman 3 10/35

APPH E3200 Mechanics: fundamentals and applications. 3 points.

Lect: 3

Prerequisites: (PHYS UN1402) and (MATH UN2030) or or equivalent.

Basic non-Euclidean coordinate systems, Newtonian Mechanics, oscillations, Green's functions, Newtonian graviation, Lagrangian mechanics, central force motion, two-body collisions, noninertial reference frames, rigid body dynamics. Applications, including GPS and feedback control systems, are emphasized throughout.

Fall 2017: APPH E3200
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3200 001/76256 M W 10:10am - 11:25am
327 Seeley W. Mudd Building
Andrew Cole 3 10/35

APPH E3300 Applied electromagnetism. 3 points.

Lect: 3.

Corequisites: APMA E3102

Vector analysis, electrostatic fields, Laplace's equation, multipole expansions, electric fields in matter: dielectrics, magnetostatic fields, magnetic materials, and superconductors. Applications of electromagnetism to devices and research areas in applied physics.

Spring 2017: APPH E3300
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3300 001/11287 M W 10:10am - 11:25am
327 Seeley W. Mudd Building
Latha Venkataraman 3 11/35

APPH E3400 Physics of the human body. 3 points.

Lect: 3.

Prerequisites: (PHYS UN1201) or (PHYS UN1401) and (MATH UN1101)
Corequisites: PHYS UN1202,PHYS UN1402,MATH UN1102

This introductory course analyzes the human body from the basic principles of physics. Topics covered include the energy balance in the body, the mechanics of motion, fluid dynamics of the heart and circulation, vibrations in speaking and hearing, muscle mechanics, gas exchange and transport in the lungs, vision, structural properties and limits, electrical properties and the development and sensing of magnetic fields, and the basics of equilibrium and regulatory control. In each case, a simple model of the body organ, property, or function will be derived and then applied. 

APPH E3900 Undergraduate research in applied physics. 0 points.

0-4 pts.

Prerequisites: Written permission from instructor and approval from adviser.

This course may be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for the B.S. degree may conduct an investigation in applied physics or carry out a special project under the supervision of the staff. Credit for the course is contingent upon the submission of an acceptable thesis or final report.

Spring 2017: APPH E3900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3900 001/18752  
Allen Boozer 0 0/10
APPH 3900 002/13649  
Andrew Cole 0 0/10
APPH 3900 003/10120  
Alexander Gaeta 0 0/10
APPH 3900 004/66686  
OLEG GANG 0 0/10
APPH 3900 005/17839  
Irving Herman 0 0/10
APPH 3900 006/60398  
Michael Mauel 0 0/10
APPH 3900 007/63645  
Gerald Navratil 0 0/10
APPH 3900 008/71582  
Richard Osgood 0 0/10
APPH 3900 009/77322  
Aron Pinczuk 0 0/10
APPH 3900 010/11250  
Amiya Sen 0 0/10
APPH 3900 011/20378  
Latha Venkataraman 0 0/10
APPH 3900 012/25621  
Francesco Volpe 0 3/10
APPH 3900 013/63257  
Yuan Yang 0 0/10
APPH 3900 014/72056  
Nanfang Yu 0 0/10
Fall 2017: APPH E3900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3900 001/18436  
Allen Boozer 0 0/10
APPH 3900 002/71179  
Andrew Cole 0 0/10
APPH 3900 003/22772  
Alexander Gaeta 0 0/10
APPH 3900 004/75207  
OLEG GANG 0 0/10
APPH 3900 005/15692  
Irving Herman 0 2/10
APPH 3900 006/23120  
Michael Mauel 0 0/10
APPH 3900 007/68560  
Gerald Navratil 0 1/10
APPH 3900 008/63069  
Richard Osgood 0 0/10
APPH 3900 009/27629  
Aron Pinczuk 0 0/10
APPH 3900 010/64895  
Amiya Sen 0 0/10
APPH 3900 011/12125  
Latha Venkataraman 0 0/10
APPH 3900 012/60098  
Renata Wentzcovitch 0 0/10
APPH 3900 013/18700  
Francesco Volpe 0 1/10
APPH 3900 014/24489  
Nanfang Yu 0 0/10
APPH 3900 015/63187  
Yuan Yang 0 0/10

APPH E4008 Introduction to atmospheric science. 3 points.

Lect: 3

Prerequisites: Advanced calculus and general physics, or instructor's permission.

Basic physical processes controlling atmospheric structure: thermodynamics; radiation physics and radiative transfer; principles of atmospheric dynamics; cloud processes; applications to Earth's atmospheric general circulation, climatic variations, and the atmosphere of the other planets.

APPH E4010 Introduction to nuclear science. 3 points.

Lect: 3.

Prerequisites: (MATH UN1202) and (MATH UN2030) and (PHYS UN1403) or or equivalents.

This introductory course is for individuals with an interest in medical physics and other branches of radiation science. Topics covered include: basic concepts, nuclear models, semi-empirical mass formula, interaction of radiation with matter, nuclear detectors, nuclear structure and instability, radioactive decay process and radiation, particle accelerators, and fission and fusion processes and technologies.

Fall 2017: APPH E4010
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4010 001/72938 T 6:30pm - 9:00pm
214 Seeley W. Mudd Building
Stephen Ostrow 3 21/35

APPH E4018 Applied physics laboratory. 2 points.

Lab: 4.

Prerequisites: (ELEN E3401) or or equivalent.

Typical experiments are in the areas of plasma physics, microwaves, laser applications, optical spectroscopy physics, and superconductivity.

Spring 2017: APPH E4018
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4018 001/14127  
Francesco Volpe 2 15/35

APPH E4090 Nanotechnology. 3 points.

Lect: 3.

Prerequisites: (APPH E3100) and (MSAE E3103) or or their equivalents with instructor's permission.

The science and engineering of creating materials, functional structures and devices on the nanometer scale. Carbon nanotubes, nanocrystals, quantum dots, size dependent properties, self-assembly, nanostructured materials. Devices and applications, nanofabrication. Molecular engineering, bionanotechnology. Imaging and manipulating at the atomic scale. Nanotechnology in society and industry.

APPH E4100 Quantum physics of matter. 3 points.

Lect: 3.

Prerequisites: (APPH E3100)
Corequisites: APMA E3102

Basic theory of quantum mechanics, well and barrier problems, the harmonic oscillator, angular momentum identical particles, quantum statistics, perturbation theory and applications to the quantum physics of atoms, molecules, and solids.

Fall 2017: APPH E4100
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4100 001/66688 T Th 10:10am - 11:25am
524 Seeley W. Mudd Building
Latha Venkataraman 3 17/35

APPH E4110 Modern optics. 3 points.

Lect: 3.

Prerequisites: (APPH E3300)

Ray optics, matrix formulation, wave effects, interference, Gaussian beams, Fourier optics, diffraction, image formation, electromagnetic theory of light, polarization and crystal optics, coherence, guided wave and fiber optics, optical elements, photons, selected topics in nonlinear optics.

Spring 2017: APPH E4110
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4110 001/15740 T Th 11:40am - 12:55pm
524 Seeley W. Mudd Building
Nanfang Yu 3 10/35

APPH E4112 Laser physics. 3 points.

Lect: 3.

Prerequisites: Recommended but not required: APPH E3100 and APPH E3300 or their equivalents.

Optical resonators, interaction of radiation and atomic systems, theory of laser oscillation, specific laser systems, rate processes, modulation, detection, harmonic generation, and applications.

APPH E4130 Physics of solar energy. 3 points.

Lect: 3.

Prerequisites: (PHYS UN1403) or (PHYS UN1602) and (MATH UN1202) or (MATH UN2030) or instructor's permission.

The physics of solar energy including solar radiation, the analemma, atmospheric efforts, thermodynamics of solar energy, physics of solar cells, energy storage and transmission, and physics and economics in the solar era.

Fall 2017: APPH E4130
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4130 001/68774 M W 1:10pm - 2:25pm
524 Seeley W. Mudd Building
Chengjun Chen 3 23/35

APPH E4200 Physics of fluids. 3 points.

Lect: 3.

Prerequisites: (APMA E3102) or (PHYS UN1401) or (PHYS UN1601) or or equivalent.

 An introduction to the physical behavior of fluids for science and engineering students. Derivation of basic equations of fluid dynamics: conservation of mass, momentum, and energy. Dimensional analysis. Vorticity. Laminar boundary layers. Potential flow. Effects of compressibility, stratification, and rotation. Waves on a free surface; shallow water equations. Turbulence.

Fall 2017: APPH E4200
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4200 001/16451 T Th 1:10pm - 2:25pm
1024 Seeley W. Mudd Building
Francesco Volpe 3 6/35

APPH E4210 Geophysical fluid dynamics. 3 points.

Lect: 3.

Prerequisites: (APMA E3101) and (APMA E3102) and (APPH E4200) or equivalents or permission from instructor.

Fundamental concepts in the dynamics of rotating, stratified flows. Geostrophic and hydrostatic balances, potential vorticity, f and beta plane approximations, gravity and Rossby waves, geostrophic adjustment and quasigeostrophy, baroclinic and barotropic instabilities, Sverdrup balance, boundary currents, Ekman layers.

Spring 2017: APPH E4210
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4210 001/70312 Th 4:10pm - 6:40pm
417 Schermerhorn Hall
Lorenzo Polvani 3 0/35

APPH E4300 Applied electrodynamics. 3 points.

Lect: 3.

Prerequisites: (APPH E3300)

Overview of properties and interactions of static electric and magnetic fields. Study of phenomena of time dependent electric and magnetic fields including induction, waves, and radiation as well as special relativity. Applications are emphasized.

Fall 2017: APPH E4300
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4300 001/77028 M W 2:40pm - 3:55pm
327 Seeley W. Mudd Building
Alexander Gaeta 3 21/35

APPH E4301 Introduction to plasma physics. 3 points.

Lect: 3.

Prerequisites: (PHYS UN3008) or (APPH E3300)

Definition of a plasma. Plasmas in laboratories and nature, plasma production. Motion of charged particles in electric and magnetic fields, adiabatic invariants. Heuristic treatment of collisions, diffusion, transport, and resistivity. Plasma as a conducting fluid. Electrostatic and magnetostatic equilibria of plasmas. Waves in cold plasmas. Demonstration of laboratory plasma behavior, measurement of plasma properties. Illustrative problems in fusion, space, and nonneutral or beam plasmas.

APPH E4330 Radiobiology for medical physicists. 3 points.

Lect: 3.

Prerequisites: (APPH E4010) or equivalent or
Corequisites: APPH E4010

Interface between clinical practice and quantitative radiation biology.  Microdosimetry, dose-rate effects and biological effectiveness thereof; radiation biology data, radiation action at the cellular and tissue level; radiation effects on human populations, carcinogenesis, genetic effects; radiation protection; tumor control, normal-tissue complication probabilities; treatment plan optimization.

Spring 2017: APPH E4330
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4330 001/60369 M 5:00pm - 7:00pm
Room TBA
Marco Zaider 3 6/35

APPH E4500 Health physics. 3 points.

Lect: 3.

Prerequisites: (APPH E4600) or
Corequisites: APPH E4600

Fundamental principles and objectives of health physics (radiation protection), the quantities of radiation dosimetry (the absorbed dose, equivalent dose, and effective dose) used to evaluate human radiation risks, elementary shielding calculations and protection measures for clinical environments, characterization and proper use of health physics instrumentation, and regulatory and administrative requirements of health physics programs in general and as applied to clinical activities.

Fall 2017: APPH E4500
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4500 001/67941 Th 6:30pm - 9:00pm
202a Hammer Hlth Sciences Center
Thomas Morgan 3 10/35

APPH E4501 Medical health physics tutorial. 0 points.

0 pts.

Prerequisites: Permission of the course coordinator.

Required for, and limited to, MS degree candidates in the Medical Physics Program. Course addresses procedures for personnel and area monitoring, radiation and contamination surveys, instrument calibration, radioactive waste disposal, radiation safety compliance, licensure requirements and other matters contributing to professional competence in the field of medical health physics. Course includes lectures, seminars, tours, and hands-on experience. This two-week tutorial is offered immediately following spring semester final examinations and is taken for Pass/Fail only.

Spring 2017: APPH E4501
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4501 001/67241  
Thomas Morgan 0 4/35

APPH E4550 Medical physics seminar. 0 points.

0 pts. Lect: 1.

Required for all graduate students in the medical physics program. Practicing professionals and faculty in the field present selected topics in medical physics.

Spring 2017: APPH E4550
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4550 001/10780 Th 4:10pm - 5:15pm
214 Seeley W. Mudd Building
Cheng Wuu 0 4/35

APPH E4600 Fundamentals of radiological physics and radiation dosimetry. 3 points.

Lect: 3.

Prerequisites: (APPH E4010) or or equivalent
Corequisites: APPH E4010

Basic radiation physics: radioactive decay, radiation producing devices, characteristics of the different types of radiation (photons, charged and uncharged particles) and mechanisms of their interactions with materials. Essentials of the determination, by measurement and calculation, of absorbed doses from ionizing radiation sources used in medical physics (clinical) situations and for health physics purposes.

Fall 2017: APPH E4600
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4600 001/12794 W 4:10pm - 6:40pm
834 Seeley W. Mudd Building
Jerome Meli 3 14/35

APPH E4710 Radiation instrumentation and measurement laboratory, I. 3 points.

Lect: 1. Lab: 4.

Prerequisites: (APPH E4010) or
Corequisites: APPH E4010

Lab fee: $50. Theory and use of alpha, beta, gamma, and X-ray detectors and associated electronics for counting, energy spectroscopy, and dosimetry; radiation safety; counting statistics and error propagation; mechanisms of radiation emission and interaction. (Topic coverage may be revised.)

Fall 2017: APPH E4710
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4710 001/72574 M 5:00pm - 10:00pm
214 Seeley W. Mudd Building
Stephen Ostrow 3 11/35

APPH E4711 Radiation instrumentation and measurement laboratory, II. 3 points.

Lect: 1. Lab: 4.

Prerequisites: (APPH E4010) or
Corequisites: APPH E4010

Lab fee: $50. Additional detector types; applications and systems including coincidence, low-level, and liquid scintillation counting; neutron activation; TLD dosimetry; gamma camera imaging. (Topic coverage may be revised.)

APPH E4901 Seminar: problems in applied physics. 1 point.

Lect: 1.

This course is required for, and can be taken only by, all applied physics majors and minors in the junior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Topics change yearly.

Fall 2017: APPH E4901
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4901 001/73069 M W 11:40am - 12:55pm
337 Seeley W. Mudd Building
Irving Herman 1 12/35

APPH E4903 Seminar: problems in applied physics. 2 points.

Lect: 1. Tutorial:1.

This course is required for, and can be taken only by, all applied physics majors in the senior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Formal presentation of a term paper required. Topics change yearly.

Fall 2017: APPH E4903
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4903 001/24332 M W 11:40am - 12:55pm
337 Seeley W. Mudd Building
Irving Herman 2 12/35

APPH E4990 Special topics in applied physics. 1-3 points.

Not offered during 2017-18 academic year.

Prerequisites: Instructor's permission.

This course may be repeated for credit. Topics and instructors change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, and other fields.

Spring 2017: APPH E4990
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4990 001/62035 W 1:10pm - 3:40pm
1106b Seeley W. Mudd Building
Alexander Gaeta 1-3 13/14

APPH E6081 Solid state physics, I. 3 points.

Lect: 3.

Prerequisites: (APPH E3100) or the equivalent. Knowledge of statistical physics on the level of MSAE E3111 or PHYS GU4023 strongly recommended.

Crystal structure, reciprocal lattices, classification of solids, lattice dynamics, anharmonic effects in crystals, classical electron models of metals, electron band structure, and low-dimensional electron structures.

Fall 2017: APPH E6081
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6081 001/71660 M W 1:10pm - 2:25pm
644 Seeley W. Mudd Building
Aron Pinczuk 3 8/35

APPH E6082 Solid state physics, II. 3 points.

Lect: 3.Not offered during 2017-18 academic year.

Prerequisites: (APPH E6081) or the instructor's permission.

Semiclassical and quantum mechanical electron dynamics and conduction, dielectric properties of insulators, semiconductors, defects, magnetism, superconductivity, low-dimensional structures, and soft matter.

APPH E6085 Computing the electronic structure of complex materials. 3 points.

Lect: 3Not offered during 2017-18 academic year.

Prerequisites: (APPH E3100) or equivalent.

Basics of density functional theory (DFT) and its application to complex materials. Computation of electronics and mechanical properties of materials. Group theory, numerical methods, basis sets, computing, and running open source DFT codes. Problem sets and a small project.

APPH E6091 Magnetism and magnetic materials. 3 points.

Lect. 3. Not offered during 2017-18 academic year.

Prerequisites: (MSAE E4206) or (APPH E6081) or equivalent.

Types of magnetism. Band theory of ferromagnetism. Magnetic metals, insulators, and semiconductors. Magnetic nanostructures: ultrathin films, superlattices, and particles. Surface magnetism and spectroscopies. High speed magnetization dynamics. Spin electronics.

APPH E6101 Plasma physics, I. 3 points.

Lect: 3.

Prerequisites: (APPH E4300)

Debye screening. Motion of charged particles in space- and time-varying electromagnetic fields. Two-fluid description of plasmas. Linear electrostatic and electromagnetic waves in unmagnetized and magnetized plasmas. The magnetohydrodynamic (MHD) model, including MHD equilibrium, stability, and MHD waves in simple geometries. 

Fall 2017: APPH E6101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6101 001/71671 M W 1:10pm - 2:25pm
834 Seeley W. Mudd Building
Gerald Navratil 3 8/35

APPH E6102 Plasma physics, II. 3 points.

Lect: 3.

Prerequisites: (APPH E6101)

Magnetic coordinates. Equilibrium, stability, and transport of torodial plasmas. Ballooning and tearing instabilities. Kinetic theory, including Vlasov equation, Fokker-Planck equation, Landau damping, kinetic transport theory.  Drift instabilities.

Spring 2017: APPH E6102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6102 001/69721 M W 2:40pm - 3:55pm
214 Seeley W. Mudd Building
Andrew Cole 3 5/35

APPH E6110 Laser interactions with matter. 3 points.

Lect: 3.

Prerequisites: (APPH E4112) or equivalent, and quantum mechanics.

Principles and applications of laser-matter coupling, non-linear optics, three- and four-wave mixing, harmonic generation, laser processing of surfaces, laser probing of materials, spontaneous and stimulated light scattering, saturation spectroscopy, multiphoton excitation, laser isotope separation, transient optical effects.

APPH E6319 Clinical nuclear medicine physics. 3 points.

Lect: 3.

Prerequisites: (APPH E4010) or equivalent.

Introduction to the instrumentation and physics used in clinical nuclear medicine and PET with an emphasis on detector systems, tomography and quality control. Problem sets, papers and term project.

Spring 2017: APPH E6319
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6319 001/73975 T 7:10pm - 9:40pm
834 Seeley W. Mudd Building
Pat Zanzonico 3 4/35

APPH E6330 Diagnostic radiology physics. 3 points.

Lect: 3.

Prerequisites: (APPH E4600)

Physics of medical imaging.  Imaging techniques: radiography, fluoroscopy, computed tomography, mammography, ultrasound, magnetic resonance.  Includes conceptual, mathematical/theoretical, and practical clinical physics aspects.

Spring 2017: APPH E6330
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6330 001/12891 W 5:30pm - 8:20pm
Room TBA
Sachin Jambawalikar, Yongguang Liang 3 4/35

APPH E6333 Radiation therapy physics practicum. 3 points.

Prerequisites: Grade of B+ or better in APPH E6335 and instructor's permission.

Students spend two to four days per week studying the clinical aspects of radiation therapy physics. Projects on the application of medical physics in cancer therapy within a hospital environment are assigned; each entails one or two weeks of work and requires a laboratory report.  Two areas are emphasized: 1. computer-assisted treatment planning (design of typical treatment plans for various treatment sites including prostate, breast, head and neck, lung, brain, esophagus, and cervix) and 2. clinical dosimetry and calibrations (radiation measurements for both photon and electron beams, as well as daily, monthly, and part of annual QA).

Fall 2017: APPH E6333
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6333 001/27745  
Cheng Wuu 3 3/20

APPH E6335 Radiation therapy physics. 3 points.

Lect: 3.

Prerequisites: (APPH E4600) APPH E4330 recommended.

Review of X-ray production and fundamentals of nuclear physics and radioactivity. Detailed analysis of radiation absorption and interactions in biological materials as specifically related to radiation therapy and radiation therapy dosimetry. Surveys of use of teletherapy isotopes and X-ray generators in radiation therapy plus the clinical use of interstitial and intracavitary isotopes. Principles of radiation therapy treatment planning and isodose calculations. Problem sets taken from actual clinical examples are assigned.

Spring 2017: APPH E6335
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6335 001/71483 Th 5:30pm - 8:20pm
Room TBA
Cheng Wuu 3 8/35

APPH E6336 Advanced Topics in Radiation Therapy. 3 points.

Lect: 3.

Prerequisites: (APPH E6335)

Advanced technology applications in radiation therapy physics, including intensity modulated, image guided, stereotactic, and hypofractionated radiation therapy.  Emphasis on advanced technological, engineering, clinical, and quality assurance issues associated with high technology radiation therapy and the special role of the medical physicist in the safe clinical application of these tools.

APPH E6340 Diagnostic radiology practicum. 3 points.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E6330 and instructor's permission.

Practical applications of diagnostic radiology for various measurements and equipment assessments. Instruction and supervised practice in radiation safety procedures, image quality assessments, regulatory compliance, radiation dose evaluations and calibration of equipment. Students participate in clinical QC of the following imaging equipment: radiologic units (mobile and fixed), fluoroscopy units (mobile and fixed), angiography units, mammography units, CT scanners, MRI units and ultrasound units. The objective is familiarization in routine operation of test instrumentation and QC measurements utilized in diagnostic medical physics. Students are required to submit QC forms with data on three different types of radiology imaging equipment.

Fall 2017: APPH E6340
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6340 001/74741  
Sachin Jambawalikar 3 4/20

APPH E6365 Nuclear medicine practicum. 3 points.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E6319 and instructor's permission.

Practical applications of nuclear medicine theory and application for processing and analysis of clinical images and radiation safety and quality assurance programs. Topics may include tomography, instrumentation, and functional imaging. Reports.

Fall 2017: APPH E6365
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6365 001/68871  
Klaus Hamacher 3 2/20

APPH E6380 Health physics practicum. 3 points.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E4500 and permission of the instructor, or
Corequisites: APPH E4500

Radiation protection practices and procedures for clinical and biomedical research environments. Includes design, radiation safety surveys of diagnostic and therapeutic machine source facilities, the design and radiation protection protocols for facilities using unsealed sources of radioactivity – nuclear medicine suites and sealed sources – brachytherapy suites. Also includes radiation protection procedures for biomedical research facilities and the administration of programs for compliance to professional health physics standards and federal and state regulatory requirements for the possession and use of radioactive materials and machine sources of ionizing and non ionizing radiations in clinical situations.  Individual topics are decided by the student and the collaborating Clinical Radiation Safety Officer.

Fall 2017: APPH E6380
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6380 001/23640  
Thomas Morgan 3 3/20

APPH E9142 Applied physics seminar. 3 points.

Sem: 3.Not offered during 2017-18 academic year.

These courses may be repeated for credit. Selected topics in applied physics. Topics and instructors change from year to year. 

APPH E9143 Applied physics seminar. 3 points.

Sem: 3.Not offered during 2017-18 academic year.

These courses may be repeated for credit. Selected topics in applied physics. Topics and instructors change from year to year.

CHAP E4120 Statistical mechanics. 3 points.

Lect: 3.

Prerequisites: (CHEN E3210) or equivalent thermodynamics course, or instructor's permission.

Fundamental principles and underlying assumptions of statistical mechanics. Boltzmann's entropy hypothesis and its restatement in terms of Helmholtz and Gibbs free energies and for open systems. Correlation times and lengths. Exploration of phase space and observation timescale. Correlation functions. Fermi-Dirac and Bose-Einstein statistics. Fluctuation-response theory. Applications to ideal gases, interfaces, liquid crystals, microemulsions and other complex fluids, polymers, Coulomb gas, interactions between charged polymers and charged interfaces, ordering transitions.

Fall 2017: CHAP E4120
Course Number Section/Call Number Times/Location Instructor Points Enrollment
CHAP 4120 001/19438 T 7:00pm - 9:30pm
227 Seeley W. Mudd Building
Ben O'Shaughnessy 3 46/45

COSA E9800 Data Science Doctoral Seminar. 1 point.

Not offered during 2017-18 academic year.

The Data Science Doctoral Seminar is a 1-credit course that meets weekly. The purpose is to expose the doctoral students to a breadth of ideas in data science across disciplinary domains. The syllabus combines guest lectures from academic data scientists in the greater NYC area and faculty at Columbia, along with a selection of related readings chosen by the guest lecturers. As part of this seminar, students will be expected to engage in active open discussion about the topics and readings covered in class, as well as discuss how such topics apply to their own respective research areas.