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.
Enrolled graduate students interested in earning a physics graduate certificate should request to add it using the Add a Graduate Certificate form. Once this is processed, students will be notified to review the requirements in the Academic Audit. No other form or signature is needed. See full details at the Graduate School.
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.
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.
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.
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, computer, and AI methods to analyze and visualize physics problems in mechanics, electromagnetism, and quantum mechanics. Utility and potential pitfalls of these methods, basic concepts of programming, computing environments, AI engines, system libraries and computer graphics are included.
- Credits: 3.0
- Lec-Rec-Lab: (2-0-3)
- Semesters Offered: Fall
- Pre-Requisite(s): (PH 2021 or 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, in odd years
Advanced Computational Physics - Electives
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 4801
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, students will learn to design computational workflows, translate problems into programs, understand sources of errors, and debug, profile and parallelize the code. Successful completion of FOSS101 and earning its Digital Badge are required prior to registration
- Credits: 3.0
- Lec-Rec-Lab: (3-0-0)
- Semesters Offered: Fall
- 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
- 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, in even years
- 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, in even years
- Pre-Requisite(s): PH 4390
Big Data Statistics in Astrophysics - Electives (4000 level - Maximum 3 credits)
PH 4620 - Galaxies and Cosmology
Topics cover the structure and dynamics of galaxies, highlighting the roles of stellar populations and the interstellar medium, as well as the role of dark matter. The course includes galaxy formation and evolution and introduces cosmology, covering the physics of the early universe, theoretical models, large-scale structure, and observational cosmology, with emphasis on how models are connected to observables to build confidence in our physical understanding of fundamental cosmic phenomena.
- Credits: 3.0
- Lec-Rec-Lab: (3-0-0)
- Semesters Offered: Spring, in odd years
- Pre-Requisite(s): PH 1600 and PH 2400 and (MA 3520 or MA 3521 or MA 3530 or MA 3560)
PH 4630 - High-Energy Astrophysics
This course examines the physics of cosmic particle acceleration, revealed through nonthermal radiative processes and particle astrophysics. Topics include compact objects such as neutron stars and black holes, and the extreme environments around them. The course may also explore gamma-ray instrumentation, multi-messenger methods (including high-energy photons, neutrinos, and gravitational waves)m and theoretical models that describe these extreme astrophysical environments.
- Credits: 3.0
- Lec-Rec-Lab: (3-0-0)
- Semesters Offered: Spring, in even years
- 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
- 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, in odd years
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 4801
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 - Choose one of the following:
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: 3.0
- Lec-Rec-Lab: (3-0-0)
- Semesters Offered: Fall, in even years
- 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
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, in odd years
- Restrictions: Must be enrolled in one of the following Level(s): Graduate
Frontiers in Materials Physics - Electives
Only three credits at the 4000 level may count toward the certificate requirements.
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, in even years
- 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, in odd years
- Restrictions: Must be enrolled in one of the following Level(s): Graduate
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: 3.0
- Lec-Rec-Lab: (3-0-0)
- Semesters Offered: Fall, in even years
- 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
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, in even years
- 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, in even years
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 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: Fall, 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
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: On Demand
- 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: On Demand
- 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: Spring
- Restrictions: May not be enrolled in one of the following Class(es): Freshman, Sophomore
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: On Demand
- 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: On Demand
- 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, in even years
- 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, in even years
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
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
