Graduate Certificates

Prepare yourself to explore future science and technology with our interdisciplinary graduate certificate program. These certificates allow students to learn beyond their graduate research. Current graduate students can also earn these credentials simultaneously with their degrees.

Researcher at computer

Advanced Computational Physics

Numerical programming and computer simulations are ubiquitous through all subjects in physics. Thus, computational physics has grown to be an appealing field for those who wish to acquire advanced and modern skills to solve interdisciplinary problems.

The graduate certificate in Advanced Computational Physics develops a foundation in programming, UNIX computing environment, system libraries, and computer graphics, to enable you to start exploring more advanced computational topics. You will learn basic and advanced numerical algorithms, develop and implement numerical methods and computer simulations using these new skills, and explore the application of advanced computation to scientific problems in your research area.

High-Altitude Water Cherenkov Gamma-Ray Observatory

Big Data Statistics in Astrophysics

Astronomy and astrophysics data are undergoing dramatic growth in size and complexity as detectors, telescopes, and computers become ever more powerful. Modern telescopes produce terabytes of data per observation, and over the next decade the data volume is expected to enter the petabyte domain.

The graduate certificate Big Data Statistics in Astrophysics will help you to develop a foundation of statistical analysis, data mining, and machine learning; understand how to implement algorithms; how to use databases to manage the data; and how to learn from the data with machine learning tools. You will develop and implement new machine learning methods for problems in astrophysics. Based on these skills, you can explore applications of statistical techniques and machine learning tools to analyze and interpret astrophysical data.

Scientists with lab equipment

Frontiers in Materials Physics

Experimental materials physics is an indispensable field for advanced electronic, photonic, energy devices, and future quantum computation and communication. This growing area is expected to meet many academic and industrial needs.

The graduate certificate in Frontiers in Materials Physics aims to help you develop foundational knowledge and techniques in the areas of: low-dimensional materials, quantum and topological materials, energy materials, and atmospheric particles and nanomaterials. You may also explore applications for spectroscopy, photovoltaics, optoelectronic devices, and environmental optics.

Microscopic view of proton filaments

Frontiers in Optics and Photonics

Optical and photonic physics are emerging fields for telecommunication, optical
computing, biophotonics, quantum sensing/communication and computing. This growing field is expected to meet many academic and industrial needs.

The graduate certificate in Frontiers in Optics and Photonics will develop your foundation in integrated photonics, nano optics, computational electromagnetics, quantum optics, and optical wave propagation in complex media. Based on these skills, you can explore applications in telecommunications, biophotonics, quantum computing, sensing and imaging.

Certificate Requirements

Each certificate is comprised of at least one required course, with the remainder of the 9 credits selected from a list of elective courses. The program advisor will help you select courses that fit your interests and skills.

Advanced Computational Physics - Required

PH 4390 - Computational Methods in Physics

An overview of numerical and computer methods to analyze and visualize physics problems in mechanics, electromagnetism, and quantum mechanics. Utility and potential pitfalls of these methods, basic concepts of programming, UNIX computing environment, system libraries and computer graphics are included.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-3)
  • Semesters Offered: Fall
  • Pre-Requisite(s): PH 2020 and PH 3410

PH 5395 - Computer Simulation in Physics

Role of computer simulation in physics with emphasis on methodologies, data and error analysis, approximations, and potential pitfalls. Methodologies may include Monte Carlo simulation, molecular dynamics, and first-principles calculations for materials, astrophysics simulation, and biophysics simulations.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-3)
  • Semesters Offered: Spring

Advanced Computational Physics - Electives

CS 5841 - Machine Learning

This course will explore the foundational techniques of machine learning. Topics are pulled from the areas of unsupervised and supervised learning. Specific methods covered include naive Bayes, decision trees, support vector machine (SVMs), ensemble, and clustering methods.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring
  • Restrictions: Permission of instructor required; May not be enrolled in one of the following Class(es): Freshman, Sophomore, Junior
  • Pre-Requisite(s): CS 4821

EE 5841 - Machine Learning

This course will explore the foundational techniques of machine learning. Topics are pulled from the areas of unsupervised and supervised learning. Specific methods covered include naive Bayes, decision trees, support vector machine (SVMs), ensemble, and clustering methods.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring
  • Restrictions: Permission of instructor required; May not be enrolled in one of the following Class(es): Freshman, Sophomore, Junior

UN 5390 - Scientific Computing

Set in a Linux environment, course offers exposure to Foss tools for developing computational and visualization workflows. Students will learn to translate problems into programs, understand sources of errors, and debug, improve the performance of and parallelize the code.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall, Spring
  • Restrictions: Permission of instructor required; Must be enrolled in one of the following Level(s): Graduate

CS 5821 - Computational Intelligence - Theory and Application

This course covers the four main paradigms of Computational Intelligence, viz., fuzzy systems, artificial neural networks, evolutionary computing, and swarm intelligence, and their integration to develop hybrid systems. Applications of Computational Intelligence include classification, regression, clustering, controls, robotics, etc.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: On Demand
  • Restrictions: Permission of instructor required; Must be enrolled in one of the following Level(s): Graduate

EE 5821 - Computational Intelligence - Theory and application

This course covers the four main paradigms of Computational Intelligence, viz., fuzzy systems, artificial neural networks, evolutionary computing, and swarm intelligence, and their integration to develop hybrid systems. Applications of Computational Intelligence include classification, regression, clustering, controls, robotics, etc.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: On Demand
  • Restrictions: Permission of instructor required; Must be enrolled in one of the following Level(s): Graduate

MA 5761 - Computational Statistics

Introduction to computationally intensive statistical methods. Topics include resampling methods, Monte Carlo simulation methods, smoothing technique to estimate functions, and methods to explore data structure. This course will use the statistical software R.

  • Credits: 3.0
  • Lec-Rec-Lab: (0-3-0)
  • Semesters Offered: Fall, Spring
  • Pre-Requisite(s): MA 4770(C) or (MA 4700 and MA 5701)

PH 5396 - Statistics, Data Mining and Machine Learning in Astronomy

The course focuses on modern problem solving in Astronomy and Astrophysics through statistical inference, machine learning algorithms and data mining techniques. Students will be presented with data sets and research problems in astrophysics and will learn how to formulate solutions.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-3)
  • Semesters Offered: Spring
  • Co-Requisite(s): PH 4395
  • Pre-Requisite(s): PH 4390

Big Data Statistics in Astrophysics - Required

PH 5396 - Statistics, Data Mining and Machine Learning in Astronomy

The course focuses on modern problem solving in Astronomy and Astrophysics through statistical inference, machine learning algorithms and data mining techniques. Students will be presented with data sets and research problems in astrophysics and will learn how to formulate solutions.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-3)
  • Semesters Offered: Spring
  • Co-Requisite(s): PH 4395
  • Pre-Requisite(s): PH 4390

Big Data Statistics in Astrophysics - Electives (4000 level - Maximum 3 credits)

PH 4610 - Stellar Astrophysics

Topics include an overview of observational astrophysics, stellar atmospheres, stellar structure, atomic properties of matter, radiation and energy transport in stellar interiors, and stellar evolution to and from the main sequence. Course offered every third year beginning 2008-09.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2008-2009 academic year
  • Pre-Requisite(s): PH 1600 and PH 2400 and (MA 3520 or MA 3521 or MA 3530 or MA 3560)

PH 4620 - Galactic Astrophysics

Topics include the composition and dynamics of our galaxy, dynamics of stellar encounters, spiral density wave theory, clusters of galaxies, theoretical cosmology, physics of the early universe, and observational cosmology. Course offered every third year beginning 2009-10.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2009-2010 academic year
  • Pre-Requisite(s): PH 1600 and PH 2400 and (MA 3520 or MA 3521 or MA 3530 or MA 3560)

PH 4630 - Particle Astrophysics

Introduction to the twin fields of elementary particle physics and high energy astrophysics. Topics include an overview of particles and interactions, the expanding universe, conservation laws, dark matter and dark energy, large scale structure, and cosmic particles. Course offered every third year beginning 2007-08.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2007-2008 academic year
  • Pre-Requisite(s): PH 2400 and (MA 3520 or MA 3521 or MA 3530 or MA 3560)

Big Data Statistics in Astrophysics - Electives (5000 level)

MA 5761 - Computational Statistics

Introduction to computationally intensive statistical methods. Topics include resampling methods, Monte Carlo simulation methods, smoothing technique to estimate functions, and methods to explore data structure. This course will use the statistical software R.

  • Credits: 3.0
  • Lec-Rec-Lab: (0-3-0)
  • Semesters Offered: Fall, Spring
  • Pre-Requisite(s): MA 4770(C) or (MA 4700 and MA 5701)

PH 5395 - Computer Simulation in Physics

Role of computer simulation in physics with emphasis on methodologies, data and error analysis, approximations, and potential pitfalls. Methodologies may include Monte Carlo simulation, molecular dynamics, and first-principles calculations for materials, astrophysics simulation, and biophysics simulations.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-3)
  • Semesters Offered: Spring

CS 5841 - Machine Learning

This course will explore the foundational techniques of machine learning. Topics are pulled from the areas of unsupervised and supervised learning. Specific methods covered include naive Bayes, decision trees, support vector machine (SVMs), ensemble, and clustering methods.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring
  • Restrictions: Permission of instructor required; May not be enrolled in one of the following Class(es): Freshman, Sophomore, Junior
  • Pre-Requisite(s): CS 4821

EE 5841 - Machine Learning

This course will explore the foundational techniques of machine learning. Topics are pulled from the areas of unsupervised and supervised learning. Specific methods covered include naive Bayes, decision trees, support vector machine (SVMs), ensemble, and clustering methods.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring
  • Restrictions: Permission of instructor required; May not be enrolled in one of the following Class(es): Freshman, Sophomore, Junior

CS 5821 - Computational Intelligence - Theory and Application

This course covers the four main paradigms of Computational Intelligence, viz., fuzzy systems, artificial neural networks, evolutionary computing, and swarm intelligence, and their integration to develop hybrid systems. Applications of Computational Intelligence include classification, regression, clustering, controls, robotics, etc.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: On Demand
  • Restrictions: Permission of instructor required; Must be enrolled in one of the following Level(s): Graduate

EE 5821 - Computational Intelligence - Theory and application

This course covers the four main paradigms of Computational Intelligence, viz., fuzzy systems, artificial neural networks, evolutionary computing, and swarm intelligence, and their integration to develop hybrid systems. Applications of Computational Intelligence include classification, regression, clustering, controls, robotics, etc.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: On Demand
  • Restrictions: Permission of instructor required; Must be enrolled in one of the following Level(s): Graduate

Frontiers in Materials Physics - Required

PH 4510 - Introduction to Solid State Physics

Crystal structures, X-ray diffraction, phonons, free electron theory of metals, rudiments of band theory, an overview of semiconductors, and other topics in solid-state physics.

  • Credits: 2.0
  • Lec-Rec-Lab: (2-0-0)
  • Semesters Offered: Fall
  • Pre-Requisite(s): (PH 2300 or PH 1360) and PH 2400 and (CH 1150 and CH 1151) and (MA 3520 or MA 3521 or MA 3530 or MA 3560)

PH 5530 - Selected Topics in Nanoscale Science and Technology

Presentation and discussion of selected topics in nanoscale science and engineering. Topics include growth, properties, applications, and societal implication of nanoscale materials. Evaluation: attendance and assignment.

  • Credits: 2.0
  • Lec-Rec-Lab: (2-0-0)
  • Semesters Offered: On Demand
  • Restrictions: May not be enrolled in one of the following Class(es): Freshman, Sophomore, Junior

Frontiers in Materials Physics - Electives

PH 5510 - Theory of Solids

Free electron theory, Bloch's theorem, electronic band structure theory, Fermi surfaces, electron transport in metals and semiconductors. Lattice vibrations and phonons, other topics as time permits.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2000-2001 academic year
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate
  • Pre-Requisite(s): PH 5320 and PH 5410

PH 5520 - Materials Physics

Materials classification and structures; phase diagrams; lattice imperfections; quasiparticles; boundaries and interfaces; mechanical, electronic, optical, magnetic and superconducting properties of materials.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2001-2002 academic year
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate

PH 5151 - Quantum Field Theory for Photonics and Materials

This course will review the basics of quantum mechanics and second quantization, and cover quantum field theoretical methods, including Wick's theorem and Feynman diagram techniques, for absolute zero and non-zero temperatures (Matsubara frequencies) and their application in photonics, properties of materials and condensed matter physics.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2020-2021 academic year
  • Pre-Requisite(s): PH 3410 and PH 3411(C)

MSE 5151 - Quantum Field Theory for Photonics and Materials

This course will review the basics of quantum mechanics and second quantization, and cover quantum field theoretical methods, including Wick's theorem and Feynman diagram techniques, for absolute zero and non-zero temperatures (Matsubara frequencies) and their application in photonics, properties of materials and condensed matter physics.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2020-2021 academic year

EE 5430 - Electronic Materials

A study of the physical principles of electronic materials, their applications in solid-state devices, and future trends in their development.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate

EE 5490 - Solar Photovoltaic Science and Engineering

Solar photovoltaic materials, the device physics of photovoltaic cells and practical applications of solar electric systems engineering.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: On Demand
  • Restrictions: Permission of instructor required; Must be enrolled in one of the following Level(s): Graduate

EE 5471 - Microfabrication Laboratory

A hands-on laboratory experience in which the students fabricate devices with micro-and nano- scale dimensions. Lecture component covers safety training, background on microfabrication processes and systems, and facility tours to observe additional systems.

  • Credits: 2.0
  • Lec-Rec-Lab: (1-0-3)
  • Semesters Offered: Fall, Spring
  • Restrictions: Permission of instructor required; Must be enrolled in one of the following Level(s): Graduate

EE 5460 - Solid State Devices

A study of the physical principles and evolution of solid-state devices, such as transistors: from conventional to novel types utilizing hetero-junctions and quantum effects; light emitting devices, semiconductor lasers; and displays of various types.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring
  • Restrictions: May not be enrolled in one of the following Class(es): Freshman, Sophomore, Junior

MSE 5130 - Crystallography & Diffraction

Crystallographic concepts and diffraction analyses in materials science.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-3)
  • Semesters Offered: Spring
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate

MSE 5550 - Transmission Electron Microscopy

Practical aspects of materials characterization by transmission electron microscopy.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-3)
  • Semesters Offered: On Demand
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate

Additionally, a maximum of one credit of the following can be counted toward the Frontiers in Material Physics Certificate:

PH 4292 - Light and Photonic Materials

Material properties controlling light wave propagation in optical crystals and optical waveguides. Photonic crystals and photonic devices based on electrical, magnetic, and strain effects.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Pre-Requisite(s): PH 2200(C)

MSE 4292 - Light and Photonic Materials

Material properties controlling light wave propagation in optical crystals and optical wave guides. Photonic crystals and photonic devices based on electrical, magnetic, and strain effects.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Major(s): Physics, Applied Physics, Electrical Engineering, Materials Science and Engrg; Must be enrolled in one of the following Class(es): Junior, Senior
  • Pre-Requisite(s): PH 2200 or EE 2190 or EE 3140

MSE 4530 - Scanning Electron Microscopy and X-ray Microanalysis

Topics include electron beam and image formation, beam- specimen interactions, and x-ray microanalysis. Course content is relevant to students of the physical sciences, engineering, and related disciplines. Includes a laboratory experience that provides hands-on practical training sufficient to enable independent use of the SEM.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-3)
  • Semesters Offered: Fall, Spring
  • Restrictions: Must be enrolled in one of the following Class(es): Junior, Senior

Frontiers in Optics and Photonics - Required

PH 4292 - Light and Photonic Materials

Material properties controlling light wave propagation in optical crystals and optical waveguides. Photonic crystals and photonic devices based on electrical, magnetic, and strain effects.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Pre-Requisite(s): PH 2200(C)

MSE 4292 - Light and Photonic Materials

Material properties controlling light wave propagation in optical crystals and optical wave guides. Photonic crystals and photonic devices based on electrical, magnetic, and strain effects.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Major(s): Physics, Applied Physics, Electrical Engineering, Materials Science and Engrg; Must be enrolled in one of the following Class(es): Junior, Senior
  • Pre-Requisite(s): PH 2200 or EE 2190 or EE 3140

Frontiers in Optics and Photonics - Electives

PH 5210 - Electrodynamics I

Electrostatics and magnetostatics, boundary value problems, multipoles, Maxwell's equations, time-dependent fields, propagating wave solutions, radiation.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate
  • Pre-Requisite(s): PH 5320

PH 5151 - Quantum Field Theory for Photonics and Materials

This course will review the basics of quantum mechanics and second quantization, and cover quantum field theoretical methods, including Wick's theorem and Feynman diagram techniques, for absolute zero and non-zero temperatures (Matsubara frequencies) and their application in photonics, properties of materials and condensed matter physics.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2020-2021 academic year
  • Pre-Requisite(s): PH 3410 and PH 3411(C)

MSE 5151 - Quantum Field Theory for Photonics and Materials

This course will review the basics of quantum mechanics and second quantization, and cover quantum field theoretical methods, including Wick's theorem and Feynman diagram techniques, for absolute zero and non-zero temperatures (Matsubara frequencies) and their application in photonics, properties of materials and condensed matter physics.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2020-2021 academic year

PH 5410 - Quantum Mechanics I

Study of the postulates of quantum mechanics framed in Dirac notation, the Heisenberg uncertainty relations, simple problems in one dimension, the harmonic oscillator, the principles of quantum dynamics, rotational invariance and angular momentum, spherically symmetric potentials including the hydrogen atom, and spin.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate

EE 5520 - Fourier Optics

Analysis and modeling of diffraction effects on optical systems, emphasizing frequency-domain analytic and computational approaches. Presents wave propagation, imaging, and optical information processing applications.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate; Must be enrolled in one of the following Major(s): Electrical Engineering, Electrical Engineering, Electrical & Computer Engineer
  • Pre-Requisite(s): EE 3190

EE 5410 - Engineering Electromagnetics

A mathematically rigorous study of dynamic electromagnetic fields, beginning with Maxwell's equations. Topics include scalar and vector potentials, waves, and radiation.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate; Must be enrolled in one of the following Major(s): Electrical Engineering, Electrical Engineering, Electrical & Computer Engineer
  • Pre-Requisite(s): EE 3140

EE 5526 - Microwave Engineering

Basics of microwave engineering. Topics include: microwave sources; wave equations and their solutions; wave propagation; reflection, and guiding; transmission line theory and practice; microwave network analysis and impedance matching; microwave resonators, filters, and dividers; left-handed materials and devices.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Fall, Spring
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate
  • Pre-Requisite(s): EE 3140 or EE 5140

EE 5528 - Antenna Engineering

Topics include: basics of radiation theory, Hertzian dipole and loop antennas, near and far fields, bandwidth, gain and other antenna parameters, Yagi-Uda, bow-tie, cavity-backed and traveling wave antennas, microstrip solutions, miniaturization, substrates and superstrates.

  • Credits: 3.0
  • Lec-Rec-Lab: (3-0-0)
  • Semesters Offered: Spring - Offered alternate years beginning with the 2013-2014 academic year
  • Pre-Requisite(s): EE 5526

Contacts


Issei Nakamura
Elena Giusarma
Jae Yong Suh
Ramy El-Ganainy
Mauricio Reyes Hurtado

Issei Nakamura

Advanced Computational Physics

Elena Giusarma

Big Data Statistics in Astrophysics

Jae Yong Suh

Frontiers in Materials Physics

Ramy El-Ganainy

Frontiers in Optics and Photonics

Mauricio Reyes Hurtado

Graduate Program Coordinator