Applied Physics and Applied Mathematics

200 S. W. Mudd, MC 4701
212-854-4457
Applied Physics and Applied Mathematics: apam.columbia.edu
Materials Science and Engineering: matsci.apam.columbia.edu

The Department of Applied Physics and Applied Mathematics includes undergraduate and graduate studies in the fields of applied physics, applied mathematics, and materials science and engineering. The graduate program in applied physics includes plasma physics and controlled fusion; solid-state physics; optical and laser physics and medical physics. The graduate program in applied mathematics includes research in applied analysis, data science, and atmospheric, oceanic, and earth physics. The graduate programs in materials science and engineering are described here.

Furthermore, the Department has a leadership role in development and support of Columbia Shared Computing resources and has access to multiple HPC clusters. In addition, the research of the Plasma Lab is supported by a dedicated data acquisition/data analysis system. Researchers in the department are using supercomputing facilities at the National Center for Atmospheric Research; the San Diego Supercomputing Center; the National Energy Research Supercomputer Center in Berkeley, California; the National Leadership Class Facility at Oak Ridge, Tennessee; various allocations via ACCESS; and others. The Amazon Elastic Compute Cloud (EC2) is also utilized to supplement computing resources in times of high demand.

Current Research Activities in the Department

Applied Physics

Plasma physics and fusion energy. In plasma physics, research is being conducted on:

  1. equilibrium, stability, and transport in tokamak plasmas
  2. modeling and optimization of stellarator plasmas
  3. enabling technology of fusion such as superconducting magnets, blankets, and fuel cycle
  4. the development of new plasma measurement techniques
  5. fundamental plasma physics

The results from our fusion science experiments are used as a basis for collaboration with large national and international projects and support the growing commercial fusion startup sector. This program is closely coupled to the new Columbia Fusion Research Center which enables members to advance fundamental plasma physics, collaborate closely with industry, and broaden participation in this field.

Optical and laser physics. Active areas of research include quantum science and technology, flat optics, metasurfaces, silicon nanophotonics, superconducting circuits, nonlinear photonics, ultrafast optics, and photon integrated circuits.

Solid-state physics. Research in solid-state physics covers nanoscience and nanoparticles, electronic transport and inelastic light scattering in low-dimensional correlated electron systems, heterostructure physics and applications, grain boundaries and interfaces, nucleation in thin films, molecular electronics, nanostructure analysis, and electronic structure calculations.

Applied physics is part of the Columbia Quantum Initiative. Research opportunities also exist within the Columbia Nano Initiative (CNI), including the NSF Materials Research Science and Engineering Center, which focuses on low dimensional materials.

Applied and Computational Mathematics. The program in Applied Mathematics encompasses both methodological approaches in applied and computational math, which are fundamental to modern applications, and domain specific applied mathematics in classical and emergent new field of physics, engineering, bio-engineering, bio-physics, and social sciences. Current research encompasses analytical and numerical analysis of deterministic and stochastic partial differential equations, numerical analysis, large-scale scientific computation, fluid dynamics, dynamical systems and chaos, inverse problems, algorithms for data and machine learning, and their applications. Physical science applications include quantum and condensed-matter physics, materials science, electromagnetics, optics and photonics, plasma physics, medical imaging, and the earth sciences (atmospheric, oceanic, climate science, and solid earth geophysics).

Atmospheric, oceanic, and earth physics. Current research focuses on the dynamics of the atmosphere and the ocean, climate modeling, cloud physics, radiation transfer, remote sensing, geophysical/geological fluid dynamics, and geochemistry. Five faculty members share appointments with the Department of Earth and Environmental Sciences.

The Applied Mathematics Program has extensive connections (through joint and affiliated faculty, postdoctoral fellows and research scientists) in departments and centers at the School of Engineering and Applied Sciences (SEAS), Arts and Sciences, and the Columbia University Irving Medical Center (CUIMC) as well as in Columbia Institutes, such as the Data Science Institute (DSI), NASA Goddard Institute for Space Studies, Lamont-Doherty Earth Observatory. There are also extensive collaborations with national research centers, such as the Geophysical Fluid Dynamics Laboratory and the National Center for Atmospheric Research, and with national laboratories of the U.S. Department of Energy, custodians of the nation's most powerful supercomputers.

Laboratory and Computational Facilities in Applied Physics and Applied Mathematics

The Plasma Physics Laboratory, founded in 1961, is one of the leading university laboratories for the study of fusion and plasma physics in the United States. Within it, there are several experimental facilities. The Columbia High-Beta Tokamak (HBT-EP) supports the national program to develop controlled fusion energy. It utilizes high voltage, pulsed power systems, and laser and magnetic diagnostics to study the properties of high-performance plasmas and the use of advanced control schemes and is also being used to explore novel plasma configurations. The Columbia Stellarator Experiment (CSX) is developing high-temperature superconducting non-planar magnets and their application to the stellarator magnetic confinement concept. The Columbia University Tokamak for Education (CUTE) is a device targeting student engagement in developing and demonstrating tokamak pulse designs. The Pellets at Columbia (PAC) experiment is testing the science and technology of cryogenic material injection into high-temperature plasma. The Columbia plasma physics group also performs work at off-site Department of Energy user facilities, such as the DIII-D National Fusion Facilities in California and the National Spherical Torus Experiment Upgrade in New Jersey. The Plasma Physics Laboratory is an essential component of the Columbia Fusion Research Center. More information can be found at fusion.columbia.edu.

Experimental research in solid-state physics and laser physics is conducted within the department and also in association with the Columbia Nano Initiative. Facilities include laser processing and spectroscopic apparatus, ultrahigh vacuum chambers for surface analysis, picosecond and femtosecond lasers, and a clean room that includes photo-lithography and thin film fabrication systems. Within this field, the Laser Diagnostics and Solid State Physics Laboratory conducts studies in laser spectroscopy of nanomaterials and semiconductor thin films, and laser diagnostics of thin film processing. The Laser Lab focuses on the study of laser surface chemical processing and new semiconductor structures. Research is also conducted in the shared characterization laboratories and clean room operated by CNI.

Current Research Activities and Laboratory Facilities in Materials Science and Engineering

See Current Research Activities and Laboratory Facilities in Materials Science and Engineering.

Chair

Marc W. Spiegelman
208 S. W. Mudd

Department Administrator

Marri Davis

Professors

Katayun Barmak
Daniel Bienstock, Industrial Engineering and Operations Research
Simon J. L. Billinge
Allen H. Boozer
Liliana Borcea
Mark A. Cane, Professor Emeritus, Earth and Environmental Sciences
Siu-Wai Chan
Qiang Du
Alexander Gaeta
Oleg Gang, Chemical Engineering
Irving P. Herman, Professor Emeritus
James S. Im
Michal Lipson, Electrical Engineering
Chris A. Marianetti
Michael E. Mauel
Gerald A. Navratil
Ismail C. Noyan
Lorenzo M. Polvani, Earth and Environmental Sciences
Kui Ren
Christopher H. Scholz, Professor Emeritus, Earth and Environmental Sciences
Adam Sobel, Earth and Environmental Sciences
Marc W. Spiegelman, Earth and Environmental Sciences
Latha Venkataraman
Wen I. Wang, Electrical Engineering
Michael I. Weinstein, Mathematics
Renata M. Wentzcovitch, Earth and Environmental Sciences

Associate Professors

William E. Bailey
Carlos Paz-Soldan
Michael K. Tippett
Chris H. Wiggins, Systems Biology
Yuan Yang
Nanfang Yu

Assistant Professors

Aravind Devarakonda
Xuenan Li
Curtiss Lyman
Elizabeth Paul
Michele Simoncelli
Xueyue (Sherry) Zhang

Lecturer in Discipline

Drew Youngren

Adjunct Associate Professors

Brian Cairns
Yuan He
Anastasia Romanou

Senior Research Scientists

Steven A. Sabbagh

Adjunct Senior Research Scientists

John Marshall

Research Scientists

Jacek Chowdhary
Gregory Elsaesser
Igor Geogdzhayev
Christopher J. Hansen
Jeffrey Levesque
Nikolas C. Logan
Catherine Naud

Associate Research Scientists

Mikhail Alexandrov
Robert Field
Jeremy Hanson
Paul Lerner
Nils Leuthold
A. Oak Nelson
Ian G. Stewart
Francesca Turco
Veronika Zamkovska

Medical Physics Faculty

Zohaib Ahmad
Sean L. Berry
Peter F. Caracappa
C. Julian Chen
Perry S. Gerard
Monique C. Katz
Stephen L. Ostrow
Boyu Peng
Anna Rozenshtein
Cheng-Shie Wuu, Radiation Oncology
Marco Zaider
Pat Zanzonico

Course Descriptions

AMCS E4302 PARALLEL SCI COMPUTING. 3.00 points.

APAM E3899 Research Training. 0.00 points.

Prerequisites: Instructor's permission.
Research training course. Recommended in preparation for laboratory related research

APAM E3999 UNDERGRADUATE FIELDWORK. 1.00-2.00 points.

1-2 pts.

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.

Summer 2025: APAM E3999
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 3999 001/11947  
Marc Spiegelman 1.00-2.00 2/5
APAM 3999 002/12018  
Qiang Du 1.00-2.00 1/5

APAM E4114 Quantum and Nonlinear Photonics. 3.00 points.

Quantum and Nonlinear Photonics is an advanced senior-level/MS/PhD course that describes the interaction of laser light with matter in both the classical and quantum domains. The first half of the course introduces the microscopic origin of optical nonlinearities through formal derivation of the nonlinear susceptibilities, with emphasis on second- and third-order optical processes. These susceptibilities are incorporated into Maxwell's wave equation, and nonlinear optical processes such as second-harmonic, difference-frequency generation, four-wave mixing and self-phase modulation are described. Various applications of these processes are discussed including frequency conversion, and optical parametric amplifiers and oscillators. The second half of the course describes two-level atomic systems and quantization of the electromagnetic field. Descriptions of coherent, Fock, and squeezed states of light are discussed and techniques to generate such states are outlined

APAM E4899 Research Training. 0.00 points.

Prerequisites: Instructor's permission.
Research training course. Recommended in preparation for laboratory related research

APAM E4901 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 E4999 SUPERVISED INTERNSHIP. 1.00-3.00 points.

1-3 pts.

Prerequisites: Obtained internship and approval from adviser.
Only for masters 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. May not be taken for pass/fail or audited

Summer 2025: APAM E4999
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 4999 001/12126  
Kui Ren 1.00-3.00 2/5
APAM 4999 003/12947  
Klaus Hamacher 1.00-3.00 0/2

APAM E6650 RESEARCH PROJECT. 1.00-6.00 points.

Prerequisites: Written permission from instructor and approval from adviser.
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 2025: APAM E6650
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 6650 004/18997  
Aravind Devarakonda 1.00-6.00 2/5
APAM 6650 006/18470  
Alexander Gaeta 1.00-6.00 1/5
APAM 6650 008/18998  
Xueyue Zhang 1.00-6.00 3/5
APAM 6650 012/18471  
Elizabeth Paul 1.00-6.00 0/5
APAM 6650 013/18469  
Carlos Paz Soldan 1.00-6.00 3/5
APAM 6650 014/18932  
Lorenzo Polvani 1.00-6.00 1/5
APAM 6650 015/20751  
Kui Ren 1.00-6.00 2/8
APAM 6650 016/18468  
Adam Sobel 1.00-6.00 1/5
Fall 2025: APAM E6650
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 6650 006/15627  
Kui Ren 1.00-6.00 0/10

APAM E9301 DOCTORAL RESEARCH. 0.00-15.00 points.

0-15 pts.

Prerequisites: Qualifying examination for the doctorate.
Required of doctoral candidates

Spring 2025: APAM E9301
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 9301 002/18446  
Daniel Bienstock 0.00-15.00 1/5
APAM 9301 005/18477  
Liliana Borcea 0.00-15.00 1/5
APAM 9301 006/18450  
Aravind Devarakonda 0.00-15.00 0/5
APAM 9301 007/18447  
Qiang Du 0.00-15.00 5/5
APAM 9301 008/18448  
Alexander Gaeta 0.00-15.00 6/8
APAM 9301 011/18449  
Michal Lipson 0.00-15.00 4/5
APAM 9301 012/20643  
Chris Marianetti 0.00-15.00 0/5
APAM 9301 013/18459  
Michael Mauel 0.00-15.00 4/5
APAM 9301 015/18458  
Elizabeth Paul 0.00-15.00 4/5
APAM 9301 016/18457  
Carlos Paz Soldan 0.00-15.00 9/10
APAM 9301 018/18451  
Lorenzo Polvani 0.00-15.00 2/5
APAM 9301 019/18456  
Kui Ren 0.00-15.00 6/5
APAM 9301 020/18455  
Steven Sabbagh 0.00-15.00 4/5
APAM 9301 022/18454  
Marc Spiegelman 0.00-15.00 1/5
APAM 9301 025/18453  
Michael Weinstein 0.00-15.00 4/5
APAM 9301 028/18452  
Nanfang Yu 0.00-15.00 5/5
APAM 9301 029/20478  
Michele Simoncelli 0.00-15.00 1/5
Fall 2025: APAM E9301
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APAM 9301 001/14769  
Daniel Bienstock 0.00-15.00 0/10
APAM 9301 004/14770  
Liliana Borcea 0.00-15.00 0/10
APAM 9301 005/14771  
Aravind Devarakonda 0.00-15.00 0/10
APAM 9301 007/14772  
Alexander Gaeta 0.00-15.00 0/10
APAM 9301 009/14775  
Michal Lipson 0.00-15.00 0/10
APAM 9301 011/14776  
Michael Mauel 0.00-15.00 0/10
APAM 9301 012/14777  
Gerald Navratil 0.00-15.00 0/10
APAM 9301 013/14778  
Elizabeth Paul 0.00-15.00 0/10
APAM 9301 014/14779  
Carlos Paz Soldan 0.00-15.00 0/10
APAM 9301 015/14780  
Lorenzo Polvani 0.00-15.00 1/10
APAM 9301 016/14781  
Kui Ren 0.00-15.00 0/10
APAM 9301 017/14782  
Steven Sabbagh 0.00-15.00 0/10
APAM 9301 018/14783  
Michele Simoncelli 0.00-15.00 0/10
APAM 9301 019/14784  
Adam Sobel 0.00-15.00 0/10
APAM 9301 020/14785  
Marc Spiegelman 0.00-15.00 0/10
APAM 9301 022/14786  
Michael Weinstein 0.00-15.00 0/10
APAM 9301 024/14787  
Nanfang Yu 0.00-15.00 0/10
APAM 9301 025/14788  
Xueyue Zhang 0.00-15.00 0/10

APAM E9800 DOCTORAL RESEARCH INSTRUCTION. 3.00-12.00 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

APAM E9900 DOCTORAL DISSERTATION. 0.00 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

APBM E4650 ANATOMY FOR PHYSICISTS & ENGR. 3.00 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 womens 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 2025: APBM E4650
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APBM 4650 001/14285 T Th 4:00pm - 5:20pm
Room TBA
Zohaib Ahmad, Perry Gerard, Anna Rozenshtein, Monique Katz 3.00 0/24

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

APMA E2000 MULTV. CALC. FOR ENGI & APP SCI. 4.00 points.

Lect: 3.

Differential and integral calculus of multiple variables. Topics include partial differentiation; optimization of functions of several variables; line, area, volume, and surface integrals; vector functions and vector calculus; theorems of Green, Gauss, and Stokes; applications to selected problems in engineering and applied science

Spring 2025: APMA E2000
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 2000 001/14583 T Th 8:40am - 9:55am
331 Uris Hall
Drew Youngren 4.00 49/48
APMA 2000 002/14584 T Th 1:10pm - 2:25pm
428 Pupin Laboratories
Drew Youngren 4.00 123/147
Fall 2025: APMA E2000
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 2000 001/12748 T Th 8:40am - 9:55am
Room TBA
4.00 5/86
APMA 2000 002/12749 T Th 1:10pm - 2:25pm
Room TBA
Drew Youngren 4.00 58/125
APMA 2000 003/12750 T Th 5:40pm - 6:55pm
Room TBA
Drew Youngren 4.00 18/100

APMA E2001 MULTV. CALC. FOR ENGI & APP SCI. 0.00 points.

Required recitation session for students enrolled in APMA E2000

Spring 2025: APMA E2001
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 2001 R01/14585 F 2:40pm - 3:30pm
707 Hamilton Hall
Yinxi Pan 0.00 28/30
APMA 2001 R02/14586 Th 4:10pm - 5:00pm
602 Northwest Corner
Jackson Turner 0.00 31/30
APMA 2001 R03/14587 F 10:10am - 11:00am
337 Seeley W. Mudd Building
Yinxi Pan 0.00 30/30
APMA 2001 R04/14588 Th 4:10pm - 5:00pm
C01 Knox Hall
Yin Zhou 0.00 30/30
APMA 2001 R05/14589 Th 5:10pm - 6:00pm
C01 Knox Hall
Yin Zhou 0.00 25/30
APMA 2001 R06/14590 Th 11:40am - 12:30pm
601b Fairchild Life Sciences Bldg
Jackson Turner 0.00 30/30
Fall 2025: APMA E2001
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 2001 R01/12751 Th 2:40pm - 3:30pm
Room TBA
0.00 19/40
APMA 2001 R02/12752 Th 4:10pm - 5:00pm
Room TBA
0.00 5/32
APMA 2001 R03/12753 F 10:10am - 11:00am
Room TBA
0.00 2/36
APMA 2001 R04/12754 Th 11:40am - 12:30pm
Room TBA
0.00 5/30
APMA 2001 R05/12755 Th 4:10pm - 5:00pm
Room TBA
0.00 2/34
APMA 2001 R06/12756 F 2:40pm - 3:30pm
Room TBA
0.00 3/36
APMA 2001 R07/12757 Th 2:40pm - 3:30pm
Room TBA
0.00 3/40
APMA 2001 R08/12758 Th 11:40am - 12:30pm
Room TBA
0.00 7/35
APMA 2001 R09/12761 F 1:10pm - 2:00pm
Room TBA
0.00 8/30

APMA E2101 INTRO TO APPLIED MATHEMATICS. 3.00 points.

Lect: 3.

Prerequisites: MATH V1201
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 2025: APMA E2101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 2101 001/14591 M W 10:10am - 11:25am
833 Seeley W. Mudd Building
Yuan He 3.00 117/123
Fall 2025: APMA E2101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 2101 001/12762 T Th 1:10pm - 2:25pm
Room TBA
Yuan He 3.00 93/125

APMA E3101 APPLIED MATH I: LINEAR ALGEBRA. 3.00 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 2025: APMA E3101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 3101 001/12763 T Th 10:10am - 11:25am
Room TBA
Yuan He 3.00 34/52

APMA E3102 APPLIED MATHEMATICS II: PDE'S. 3.00 points.

Lect: 3.

Prerequisites: (MATH UN2030) MATH V2030; or 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 2025: APMA E3102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 3102 001/14601 T Th 1:10pm - 2:25pm
825 Seeley W. Mudd Building
Michael Tippett 3.00 34/44

APMA E3900 UNDERGRAD RES IN APPLIED MATH. 0.00-4.00 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 2025: APMA E3900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 3900 001/18825  
Lorenzo Polvani 0.00-4.00 3/5
APMA 3900 002/20668  
Marc Spiegelman 0.00-4.00 0/5

APMA E4001 PRINCIPLES OF APPLIED MATH. 3.00 points.

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. Greens functions. Application to Partial Differential Equations

APMA E4007 APPLIED LINEAR ALGEBRA. 3.00 points.

Prerequisites: Cannot be taken together with APMA E3101
Fundamentals of Linear Algebra including vector and Matrix algebra, solution of linear systems, existence and uniqueness, gaussian elimination, gauss-jordan elimination, the matrix inverse, elementary matrices and the LU factorization, computational cost of solutions. Vector spaces and subspaces, linear independence, basis and dimension. The 4 fundamental subspaces of a matrix. Orthogonal projection onto a subspace and solution of Linear Least Squares problems, unitary matrices, inner products, orthogonalization algorithms and the QR factorization, applications. Determinants and applications. Eigen problems including diagonalization, symmetric matrices, positive-definite systems, eigen factorization and applications to dynamical systems and iterative maps. Introduction to the singular value decomposition and its applications

Fall 2025: APMA E4007
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4007 001/12764 T Th 1:10pm - 2:25pm
Room TBA
Michael Tippett 3.00 1/90

APMA E4008 Advanced and Applied Linear Algebra. 3.00 points.

Prerequisites: APMA E3101 AND APMA E4007; After the approval of APMA E4007, it could also serve as a pre-requisite to 4008.
Advanced topics in linear algebra with applications to data analysis, algorithms, dynamics and differential equations, and more. (1) General vector spaces, linear transformations, spaces isomorphisms; (2) spectral theory - normal matrices and their spectral properties, Rayleigh quotient, Courant-Fischer Theorem, Jordan forms, eigenvalue perturbations; (3) least squares problem and the Gauss-Markov Theorem; (4) singular value decomposition, its approximation properties, matrix norms, PCA and CCA

Spring 2025: APMA E4008
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4008 001/14610 M W 1:10pm - 2:25pm
633 Seeley W. Mudd Building
Yuan He 3.00 45/70
APMA 4008 V01/17990  
Yuan He 3.00 3/99

APMA E4100 Applied Analysis. 3.00 points.

Prerequisites: Strong background in multivariate calculus is required. Knowledge in elementary analysis such as the delta-epsilon definition of continuity, convergence of sequences of real numbers, topocontinuity of real-valued functions

Elementary introduction to fundamental concepts and techniques in classical analysis; applications of such techniques in different topics in applied mathematics. Brief review of essential concepts and techniques in elementary analysis; elementary properties of metric and normed spaces; completeness, compactness, and their consequences; continuous functions and their properties; Contracting Mapping Theorem and its applications; elementary properties of Hilbert and Banach spaces; bounded linear operators in Hilbert spaces; Fourier series and their applications.

Fall 2025: APMA E4100
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4100 001/12765 M W 2:40pm - 3:55pm
Room TBA
Liliana Borcea 3.00 15/50

APMA E4101 APPL MATH III:DYNAMICAL SYSTMS. 3.00 points.

Lect: 3.

Prerequisites: (APMA E2101) and (APMA E3101) or their equivalents, or instructor's permission.
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

Spring 2025: APMA E4101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4101 001/14623 M W 8:40am - 9:55am
702 Hamilton Hall
Xuenan Li 3.00 71/86
APMA 4101 V01/17991  
Xuenan Li 3.00 6/99

APMA E4150 APPLIED FUNCTIONAL ANALYSIS. 3.00 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

Spring 2025: APMA E4150
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4150 001/14632 M W 2:40pm - 3:55pm
327 Seeley W. Mudd Building
Michael Weinstein 3.00 20/39

APMA E4200 PARTIAL DIFFERENTIAL EQUATIONS. 3.00 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

Spring 2025: APMA E4200
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4200 001/14641 T Th 1:10pm - 2:25pm
1127 Seeley W. Mudd Building
Liliana Borcea 3.00 36/70
APMA 4200 V01/17995  
Liliana Borcea 3.00 7/99
Fall 2025: APMA E4200
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4200 001/12766 M W 11:40am - 12:55pm
Room TBA
Kui Ren 3.00 39/70

APMA E4204 FUNCTNS OF A COMPLEX VARIABLE. 3.00 points.

Prerequisites: (MATH UN1202) MATH V1202; or 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 2025: APMA E4204
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4204 001/12767 M W 1:10pm - 2:25pm
Room TBA
Xuenan Li 3.00 53/55

APMA E4300 COMPUT MATH:INTRO-NUMERCL METH. 3.00 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 ODEs. All programming exercises will be in Python

Spring 2025: APMA E4300
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4300 001/14647 T Th 10:10am - 11:25am
833 Seeley W. Mudd Building
Kui Ren 3.00 64/120
APMA 4300 V01/17998  
Kui Ren 3.00 4/99
Fall 2025: APMA E4300
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4300 001/12768 T Th 10:10am - 11:25am
Room TBA
Marc Spiegelman 3.00 1/120

APMA E4301 NUMERICAL METHODS/PDE'S. 3.00 points.

Lect: 3.

Prerequisites: (APMA E4300) and (APMA E3102) or (APMA E4200) or APMA E3102 AND APMA E4200 AND APMA E4300; 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 2025: APMA E4301
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4301 001/14654 T Th 11:40am - 12:55pm
1024 Seeley W. Mudd Building
Kossi Amenoagbadji 3.00 33/40
APMA 4301 V01/17999  
Kossi Amenoagbadji 3.00 1/99

APMA E4302 METHODS IN COMPUTATIONAL SCI. 3.00 points.

Lect: 3.

Prerequisites: (APMA E4300) and 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

APMA E4306 Applied Stochastic Analysis. 3.00 points.

Prerequisites: Elementary probability theory IEOR E3658 or above, stochastic process the first part of IEOR E4106 or STAT G4264, knowledge on analysis MATH GU4601 or above, differential equations APMA E4200, numerical methods APMA E4300 & programming skills
Provides elementary introduction to fundamental ideas in stochastic analysis for applied mathematics. Core material includes: (i) review of probability theory (including limit theorems), and introduction to discrete Markov chains and Monte Carlo methods; (ii) elementary theory of stochastic process, Ito's stochastic calculus and stochastic differential equations; (iii) introductions to probabilistic representation of elliptic partial differential equations (the Fokker-Planck equation theory); (iv) stochastic approximation algorithms; and (v) asymptotic analysis of SDEs

Spring 2025: APMA E4306
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4306 001/14667 M W 10:10am - 11:25am
545 Seeley W. Mudd Building
Shanyin Tong 3.00 22/39
APMA 4306 V01/18000  
Shanyin Tong 3.00 6/99

APMA E4400 INTRO TO BIOPHYSICAL MODELING. 3.00 points.

Lect: 3.

Prerequisites: (PHYS UN1401) and (APMA E2101) or (MATH UN2030) or or equivalents.
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 SEM-PROBLEMS IN APPLIED MATH. 0.00-1.00 points.

Lect: 1.

Prerequisites: MATH V3027, V3028, and V2010, or their equivalents. May be taken before or concurrently with this course.
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 2025: APMA E4901
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4901 001/12769 M W 11:40am - 12:55pm
Room TBA
Chris Wiggins 0.00-1.00 43/85

APMA E4903 SEM-PROBLEMS IN APPLIED MATH. 3.00-4.00 points.

3-4 pts. Lect: 1

Prerequisites: MATH V3007, V3028, and V2010, or their equivalents. May be taken before or concurrently with this course.
Required for all applied mathematics majors in the senior year. Term paper required. Examples of problem areas are nonlinear dynamics, asymptotics, approximation theory, numerical methods, etc. Approximately three problem areas are studied per term

Fall 2025: APMA E4903
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4903 001/12770 M W 11:40am - 12:55pm
Room TBA
Chris Wiggins 3.00-4.00 59/70

APMA E4904 SEM-PROBLEMS IN APPLIED MATH. 3.00-4.00 points.

APMA E4990 SPEC TOPICS IN APPLIED MATH. 3.00 points.

1-3 pts. Lect: 3.

Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.
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. Examples of topics include multi-scale analysis and Applied Harmonic Analysis

Spring 2025: APMA E4990
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4990 001/14691 M W 11:40am - 12:55pm
327 Seeley W. Mudd Building
James Scott 3.00 11/39
APMA 4990 002/14692 M W 10:10am - 11:25am
141 Uris Hall
Madison Ihrig 3.00 8/20
Fall 2025: APMA E4990
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 4990 001/12771 T Th 10:10am - 11:25am
Room TBA
Michael Weinstein 3.00 0/35

APMA E6100 RESEARCH SEMINAR. 0.00 points.

Lect: 3. Not offered during 2023-2024 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

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

Fall 2025: APMA E6100
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 6100 001/12772 T 4:10pm - 5:00pm
Room TBA
Kui Ren 0.00 4/50

APMA E6301 ANALYTIC METHODS FOR PDE'S. 3.00 points.

Lect: 2.

Prerequisites: (APMA E3101) and (APMA E4200) 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, Greens 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

APMA E6302 NUMERICAL ANALYSIS OF PDE'S. 3.00 points.

Lect: 2.

Prerequisites: (APMA E3102) or (APMA E4200) 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

Fall 2025: APMA E6302
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APMA 6302 001/12773 T Th 10:10am - 11:25am
Room TBA
Qiang Du 3.00 13/35

APMA E6901 SPECIAL TOPICS IN APPLIED MATH. 3.00 points.

Lect: 3.

Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.
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 E9101 RESEARCH I. 1.00-4.00 points.

1-4 pts.

Prerequisites: Permission of the supervising faculty member.
May be repeated. Advanced study in a special area

APMA E9102 RESEARCH II. 1.00-4.00 points.

1-4 pts.

Prerequisites: Permission of the supervising faculty member.
May be repeated. Advanced study in a special area

APMA E9810 MATHEMATICAL EARTH SCIENCE SEM. 0.00 points.

0 pts. Lect: 1.

Prerequisites: Instructor's permission.
Current research in problems at the interface between applied mathematics and earth and environmental sciences

APPH E1300 PHYSICS OF THE HUMAN BODY. 3.00 points.

APPH E3100 INTRO TO QUANTUM MECHANICS. 3.00 points.

Lect: 3.

Prerequisites: (PHYS UN1403) or PHYS W1403; APMA E3101; or 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 2025: APPH E3100
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3100 001/14668 M W 1:10pm - 2:25pm
644 Seeley W. Mudd Building
Aravind Devarakonda 3.00 18/35
Fall 2025: APPH E3100
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3100 001/13568 T Th 2:40pm - 3:55pm
Room TBA
Aravind Devarakonda 3.00 6/35

APPH E3200 MECHANICS:FUND & APPLICATIONS. 3.00 points.

Lect: 3

Prerequisites: (PHYS UN1402) and (MATH UN2030) or MATH V2030 AND PHYS C1402; or equivalent.
Basic non-Euclidean coordinate systems, Newtonian Mechanics, oscillations, Greens 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 2025: APPH E3200
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3200 001/12777 M W 10:10am - 11:25am
Room TBA
Elizabeth Paul 3.00 12/35

APPH E3300 APPLIED ELECTROMAGNETISM. 3.00 points.

Lect: 3.

Prerequisites: APMA E3102
Corequisites: APMA E3102
Vector analysis, electrostatic fields, Laplaces 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 2025: APPH E3300
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3300 001/14669 M W 10:10am - 11:25am
414 Pupin Laboratories
Xueyue Zhang 3.00 19/30

APPH E3400 PHYSICS OF THE HUMAN BODY. 3.00 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 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 UNDERGRAD RESRCH-APPLD PHYSICS. 0.00-4.00 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 2025: APPH E3900
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 3900 003/20873  
Aravind Devarakonda 0.00-4.00 0/5
APPH 3900 010/18933  
Elizabeth Paul 0.00-4.00 1/5
APPH 3900 011/18934  
Carlos Paz Soldan 0.00-4.00 4/5
APPH 3900 013/20517  
Nanfang Yu 0.00-4.00 1/5

APPH E4010 INTRODUCTN TO NUCLEAR SCIENCE. 3.00 points.

Prerequisites: APMA E2000 AND MATH V1202 AND MATH V2030 AND PHYS W1403; or equivalents.
Introductory course is for individuals with an interest in medical physics and other branches of radiation science. Topics 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 2025: APPH E4010
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4010 001/13411 T 6:30pm - 9:00pm
Room TBA
Stephen Ostrow 3.00 6/25

APPH E4018 APPLIED PHYSICS LABORATORY. 3.00 points.

Prerequisites: (ELEN E3401) or APPH E3300 AND ELEN E3401; or equivalent.

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

Spring 2025: APPH E4018
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4018 001/14670  
Michael Mauel 3.00 18/35

APPH E4100 QUANTUM PHYSICS OF MATTER. 3.00 points.

Lect: 3.

Prerequisites: (APPH E3100) APPH E3100; APMA E3102
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 2025: APPH E4100
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4100 001/13412 T Th 10:10am - 11:25am
Room TBA
Alexander Gaeta 3.00 13/45

APPH E4110 MODERN OPTICS. 3.00 points.

Lect: 3.

Prerequisites: (APPH E3300) 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 2025: APPH E4110
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4110 001/14671 T Th 11:40am - 12:55pm
545 Seeley W. Mudd Building
Nanfang Yu 3.00 18/35
APPH 4110 V01/18832  
Nanfang Yu 3.00 2/99

APPH E4112 LASER PHYSICS. 3.00 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

Fall 2025: APPH E4112
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4112 001/13413 T Th 11:40am - 12:55pm
Room TBA
Nanfang Yu 3.00 7/35

APPH E4114 Quantum and Nonlinear Photonics. 3.00 points.

Prerequisites: APPH E3300 AND PHYS W3008
Advanced senior-level/MS/PhD course covering interaction of laser light with matter in both classical and quantum domains. First half introduces microscopic origin of optical nonlinearities through formal derivation of nonlinear susceptibilities, emphasis on second- and third-order optical processes. Topics include Maxwell's wave equation, and nonlinear optical processes such as second-harmonic, difference frequency generation, four-wave mixing, and self-phase modulation, including various applications of processes such as frequency conversion, and optical parametric amplifiers and oscillators. Second half describes two-level atomic systems and quantization of electromagnetic field. Descriptions of coherent, Fock, and squeezed states of light discussed and techniques to generate such states outlined

Spring 2025: APPH E4114
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4114 001/14672 W 1:10pm - 3:40pm
545 Seeley W. Mudd Building
Alexander Gaeta 3.00 9/30
APPH 4114 V01/18833  
Alexander Gaeta 3.00 3/99

APPH E4130 SOLAR ENERGY & STORAGE. 3.00 points.

Lect: 3.

Prerequisites: (PHYS UN1403) or (PHYS UN1602) and (MATH UN1202) or (MATH UN2030) General physics PHYS C1401x, C1402y, C1403x, C1601x, and C1602y, freshman mathematics including ordinary differential equations MATH V1201 and MATH V1202, MATH E1210. Familiarity in thermodynamics, electromagnetism, quantum mechanics, solid-state

Nature of solar radiation as electromagnetic waves and photons. Availability of solar radiation at different times and at various places in the world. Thermodynamics of solar energy. Elements of quantum mechanics for the understanding of solar cells, photosynthesis, and electrochemistry. Theory, design, manufacturing, and installation of solar cells. Lithium-ion rechargeable batteries and other energy-storage devices. Architecture of buildings to utilize solar energy

Fall 2025: APPH E4130
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4130 001/13414 M W 1:10pm - 2:25pm
Room TBA
Julian Chen 3.00 4/35

APPH E4164 Electric Field Effects in Catalysis. 1.50 point.

Real-time exposition of an emerging area of study at the interface between chemistry, physics, engineering, and biology to understand and control how electric fields can be used to catalyze chemical transformations. Taught by a cross-disciplinary group of faculty. Topics covered: (1) theoretical underpinnings for catalysis in nanoscale electrical environments, (2) experimental tools used to study these chemical transformations, (3) experimental demonstrations of catalysis in electric fields. Each topic will draw on elements of organometallic/organic catalysis, quantum mechanics, enzymatic catalysis, and nano electronics to form the basis for understanding this new branch of catalytic science

APPH E4200 PHYSICS OF FLUIDS. 3.00 points.

Lect: 3.

Prerequisites: (APMA E3102) or (PHYS UN1401) or (PHYS UN1601) or or equivalents.
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 2025: APPH E4200
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4200 001/13569 Th 4:10pm - 6:40pm
Room TBA
Lorenzo Polvani 3.00 9/35

APPH E4210 GEOPHYSICAL FLUID DYNAMICS. 3.00 points.

Lect: 3.

Prerequisites: (APMA E3101) and (APMA E3102) and (APPH E4200) APMA E3101 AND APMA E3102 AND APPH E4200; or equivalents or instructor's permission.
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

APPH E4300 APPLIED ELECTRODYNAMICS. 3.00 points.

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 2025: APPH E4300
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4300 001/13570 W 4:10pm - 6:40pm
Room TBA
Carlos Paz Soldan 3.00 14/35

APPH E4301 INTRO TO PLASMA PHYSICS. 3.00 points.

Lect: 3.

Prerequisites: (PHYS UN3008) or (APPH E3300) APPH E3300 AND PHYS W3008
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 MED PHYS. 3.00 points.

Lect: 3.

Prerequisites: (APPH E4010) APPH E4010; or equivalent.
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

Fall 2025: APPH E4330
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4330 001/11105 Th 5:00pm - 7:00pm
Room TBA
Marco Zaider 3.00 0/13

APPH E4500 HEALTH PHYSICS. 3.00 points.

Lect: 3.

Prerequisites: (APPH E4600) APPH E4600 OR APPH E6380
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

Spring 2025: APPH E4500
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4500 001/15009 M 5:30pm - 8:00pm
252 Georgian (Nursing)
Peter Caracappa 3.00 6/10

APPH E4501 MEDICAL HLTH PHYS TUTORIAL. 0.00 points.

APPH E4550 MEDICAL PHYSICS SEMINAR. 0.00 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 2025: APPH E4550
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4550 001/15025 M 9:00am - 10:15am
612 Martin Luther King Building
Cheng Wuu 0.00 7/10

APPH E4600 FUNDAMENTALS OF DOSIMETRY. 3.00 points.

Lect: 3.

Prerequisites: (APPH E4010) or APPH E4010 OR APPH E4500; 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

APPH E4710 RAD INSTRUMENT/MEASUREMENT LAB. 3.00 points.

Lect: 1. Lab: 4.

Prerequisites: (APPH E4010) or APPH E4010
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.)

APPH E4711 RAD INSTRUMENT/MEASUREMENT LAB. 3.00 points.

Lect: 1. Lab: 4.

Prerequisites: (APPH E4010) or APPH E4710
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 SEM-PROBLMS IN APPLIED PHYSICS. 1.00 point.

Lect: 1.

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 2025: APPH E4901
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4901 001/13666 M W 11:40am - 12:55pm
Room TBA
1.00 11/35

APPH E4903 SEM-PROBLMS IN APPLIED PHYSICS. 2.00 points.

Lect: 1. Tutorial:1.

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 2025: APPH E4903
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4903 001/13667 M W 11:40am - 12:55pm
Room TBA
2.00 12/35

APPH E4990 SPEC TOPICS IN APPLIED PHYSICS. 3.00 points.

Prerequisites: Instructor's permission.
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 2025: APPH E4990
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 4990 001/14673 M 4:10pm - 6:40pm
227 Seeley W. Mudd Building
Piero Martin, Carlos Paz Soldan 3.00 14/35

APPH E6081 SOLID STATE PHYSICS I. 3.00 points.

Lect: 3.

Prerequisites: (APPH E3100) 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

APPH E6091 Magnetism and magnetic materials. 3 points.

Lect. 3. Not offered during 2023-2024 academic year.

Prerequisites: (MSAE E4206) or (APPH E6081) MSAE E4206, 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. 3.00 points.

Lect: 3.

Prerequisites: (APPH E4300) 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 2025: APPH E6101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6101 001/13415 M W 1:10pm - 2:25pm
Room TBA
Gerald Navratil 3.00 4/35

APPH E6102 PLASMA PHYSICS II. 3.00 points.

Lect: 3.

Prerequisites: (APPH E6101) 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 2025: APPH E6102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6102 001/14674 M W 1:10pm - 2:25pm
327 Seeley W. Mudd Building
Carlos Paz Soldan 3.00 14/35

APPH E6319 CLIN NUCLEAR MEDICINE PHYSICS. 3.00 points.

Lect: 3.

Prerequisites: (APPH E4010) 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 2025: APPH E6319
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6319 001/15011 T 5:30pm - 8:00pm
406 Hamilton Hall
Pat Zanzonico 3.00 9/10

APPH E6330 DIAGNOSTIC RADIOLOGY PHYSICS. 3.00 points.

Lect: 3.

Prerequisites: (APPH E4600) 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 2025: APPH E6330
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6330 001/15014 W 5:30pm - 8:30pm
612 Martin Luther King Building
Boyu Peng 3.00 9/10

APPH E6333 RADIATION THERAPY PHYS PRACT. 3.00 points.

Prerequisites: APPH E6335; 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 2025: APPH E6333
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6333 001/11106  
Cheng Wuu 3.00 0/10

APPH E6335 RADIATION THERAPY PHYSICS. 3.00 points.

Lect: 3.

Prerequisites: (APPH E4600) 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 2025: APPH E6335
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6335 001/15023 Th 5:00pm - 8:00pm
612 Martin Luther King Building
Cheng Wuu 3.00 8/10

APPH E6336 ADV TPCS IN RADIATION THERAPY. 3.00 points.

Lect: 3.

Prerequisites: (APPH E6335) 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

Fall 2025: APPH E6336
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6336 001/11111 Th 2:00pm - 5:00pm
Room TBA
Cheng Wuu 3.00 0/10

APPH E6340 DIAGNOSTIC RADIOL PRACTICUM. 3.00 points.

Lab: 6.

Prerequisites: APPH6330; 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 2025: APPH E6340
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6340 001/11107  
Boyu Peng 3.00 0/10

APPH E6365 NUCLEAR MEDICINE PRACTICUM. 3.00 points.

Lab: 6.

Prerequisites: APPH E6319; 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 2025: APPH E6365
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6365 001/11108  
Klaus Hamacher 3.00 0/3

APPH E6380 HEALTH PHYSICS PRACTICUM. 3.00 points.

Lab: 6.

Prerequisites: APPH E4500; Grade of B+ or better in APPH E4500 and instructor's permission.
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 2025: APPH E6380
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 6380 001/11109  
Peter Caracappa 3.00 0/10

APPH E9143 APPLIED PHYSICS SEMINAR. 3.00 points.

Sem: 3.Not offered during 2023-2024 academic year.

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

Spring 2025: APPH E9143
Course Number Section/Call Number Times/Location Instructor Points Enrollment
APPH 9143 001/14676 T Th 2:40pm - 3:55pm
227 Seeley W. Mudd Building
Elizabeth Paul 3.00 8/35

APCH E4080 SOFT CONDENSED MATTER. 3.00 points.

Prerequisites: CHEE E3010 AND MSAE E3111; 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 materials to the actively developed research areas. Course grade based on midterm and final exams, weekly homework assignments, and final individual/team project

CHAP E4120 STATISTICAL MECHANICS AND COMP METHODS. 3.00 points.

Lect: 3.

Prerequisites: (CHEN E3210) Elementary statistics, thermodynamics, some familiarity with Python, or instructor's permission.
Boltzmann’s entropy hypothesis and its restatement to calculate the Helmholtz and Gibbs free energies and the grand potential. Applications to interfaces, liquid crystal displays, polymeric materials, crystalline solids, heat capacity and electrical conductivity of crystalline materials, fuel cell solid electrolytes, rubbers, surfactants, molecular self assembly, ferroelectricity. Computational methods for molecular systems. Monte Carlo (MC) and molecular dynamics (MD) simulation methods. MC method applied to liquid-gas and ferromagnetic phase transitions. Deterministic MD simulations of isolated gases and liquids. Stochastic MD simulation methods

Spring 2025: CHAP E4120
Course Number Section/Call Number Times/Location Instructor Points Enrollment
CHAP 4120 001/15144 T 5:40pm - 8:25pm
326 Uris Hall
Ben O'Shaughnessy 3.00 22/85

PSAM UN3707 Persuasion at scale: causal inference, machine learning, and evidence-based understanding of the information environment. 3.00 points.

By employing statistical and computational methods, including randomized controlled trials, natural experiments, and machine learning techniques, students will engage directly with real-world data to uncover the intricacies of persuasion across different sectors, including but not limited to quantifying the effects of partisan media, social media, and political campaigns. The course will also delve into the historical evolution of these persuasive techniques, providing students with a rich contextual background to better understand current trends and anticipate future developments. This course fulfills the quantitative methods requirement for the Political Science major

Spring 2025: PSAM UN3707
Course Number Section/Call Number Times/Location Instructor Points Enrollment
PSAM 3707 001/17626 M W 11:40am - 12:55pm
313 Fayerweather
Chris Wiggins, Eunji Kim 3.00 61/70

HSAM UN2901 DATA:PAST, PRESENT AND FUTURE. 3.00 points.

Lect: 1.5. Lab: 1.5.

Data-empowered algorithms are reshaping our professional, personal, and political realities, for good--and for bad. Data: Past, Present, and Future moves from the birth of statistics in the 18th century to the surveillance capitalism of the present day, covering racist eugenics, World War II cryptography, and creepy personalized advertising along the way. Rather than looking at ethics and history as separate from the science and engineering, the course integrates the teaching of algorithms and data manipulation with the political whirlwinds and ethical controversies from which those techniques emerged. We pair the introduction of technical developments with the shifting political and economic powers that encouraged and benefited from new capabilities. We couple primary and secondary readings on the history and ethics of data with computational work done largely with user-friendly Jupyter notebooks in Python

EESC UN3109 CLIMATE PHYSICS. 3.00 points.

This is a calculus-based treatment of climate system physics and the mechanisms of anthropogenic climate change. By the end of this course, students will understand: how solar radiation and rotating fluid dynamics determine the basic climate state, mechanisms of natural variability and change in climate, why anthropogenic climate change is occurring, and which scientific uncertainties are most important to estimates of 21st century change. This course is designed for undergraduate students seeking a quantitative introduction to climate and climate change science. EESC V2100 (Climate Systems) is not a prerequisite, but can also be taken for credit if it is taken before this course

Spring 2025: EESC UN3109
Course Number Section/Call Number Times/Location Instructor Points Enrollment
EESC 3109 001/13558 T Th 10:10am - 11:25am
555 Ext Schermerhorn Hall
Adam Sobel 3.00 15/25