PROGRAM

OVERVIEW
Quantum Engineering is an interdisciplinary program that seeks to equip students for careers in emerging technologies based on quantum entanglement. It encompasses a wide range of disciplines that includes physics, materials science, computer science, electrical engineering, chemistry, and mathematics, and is necessarily a collaborative effort among many Mines departments.
 

Two Master’s degrees and one professional certificate are offered. For both degrees and the professional certificate, Quantum Engineering has two tracks.

  • Quantum Engineering Hardware (QEH) track focuses on experimental techniques relevant to quantum technology.
  • Quantum Engineering Software (QES) track focuses on theory, algorithms, and simulation.
A track must be chosen to complete the program, but courses from both tracks may be taken provided that the prerequisite requirements are met.
 
An interdisciplinary minor in Quantum Engineering is also offered. Details may be found in the Minor section and in the course catalog.
MS THESIS

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective #13
Elective #23
Elective #33
Elective #43

PHGN707 GRADUATE THESIS / DISSERTATION RESEARCH CREDIT. 1-15 SEMESTER HR.

PHGN707. GRADUATE THESIS / DISSERTATION RESEARCH CREDIT. 1-15 SEMESTER HR. (I, II, S) Research credit hours required for completion of a Masters-level thesis or Doctoral dissertation. Research must be carried out under the direct supervision of the student's faculty advisor. Variable class and semester hours. Repeatable for credit.
9
30 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532/PHGN532 Low Temperature Microwave Measurements for Quantum Applications

EENG532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective #13
Elective #23
Elective #33
Elective #43

PHGN707 GRADUATE THESIS / DISSERTATION RESEARCH CREDIT. 1-15 SEMESTER HR.

PHGN707. GRADUATE THESIS / DISSERTATION RESEARCH CREDIT. 1-15 SEMESTER HR. (I, II, S) Research credit hours required for completion of a Masters-level thesis or Doctoral dissertation. Research must be carried out under the direct supervision of the student's faculty advisor. Variable class and semester hours. Repeatable for credit.
9
30 Total

MS NON-THESIS

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective #13
Elective #23
Elective #33
Elective #43
Elective #53
Elective #63
Elective #73
30 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532/PHGN532 Low Temperature Microwave Measurements for Quantum Applications

EENG532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective #13
Elective #23
Elective #33
Elective #43
Elective #53
Elective #63
Elective #73
30 Total

GRADUATE CERTIFICATE

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective3
12 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532/PHGN532 Low Temperature Microwave Measurements for Quantum Applications

EENG532/PHGN532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective3
12 Total

GRADUATE ELECTIVES

 

Beyond the required courses for each track, students will take one or more additional electives chosen from an extensive list of relevant courses (courses meant for the other track can also be used for these electives). This following list is continuously updated as the curricula of the participating departments evolve.

Note

  • Independent study and electives not on the list require approval from Dr. Eliot Kapit, the QE Program Director.
  • Beginning Fall 2024, for incoming students, 400-level courses no longer count toward a Master’s degree.

Course Information
Physics

PHGN520/521 Quantum Mechanics

PHGN520. QUANTUM MECHANICS I. 3.0 SEMESTER HRS. (II) Schroedinger equation, uncertainty, change of representation, one-dimensonal problems, axioms for state vectors and operators, matrix mechanics, uncertainty relations, time-independent perturbation theory, time-dependent perturbations, harmonic oscillator, angular momentum; semiclassical methods, variational methods, two-level system, sudden and adiabatic changes, applications. Prerequisite: PHGN511 and PHGN320 or equivalent. 3 hours lecture; 3 semester hours.

PHGN521. QUANTUM MECHANICS II. 3.0 SEMESTER HRS. (I) Review of angular momentum, central potentials and applications. Spin; rotations in quantum mechanics. Formal scattering theory, Born series, partial wave analysis. Addition of angular momenta, Wigner-Eckart theorem, selection rules, identical particles. Prerequisite: PHGN520. 3 hours lecture; 3 semester hours.

PHGN530 Statistical Mechanics

PHGN530. STATISTICAL MECHANICS. 3.0 SEMESTER HRS. (I) Review of thermodynamics; equilibrium and stability; statistical operator and ensemblesl ideal systems; phase transitions; non-equilibrium systems. Prerequisite: PHGN341 or equivalent and PHGN520. Co-requisite: PHGN521. 3 hours lecture; 3 semester hours.

PHGN550 Nanoscale Physics and Technology

PHGN550. NANOSCALE PHYSICS AND TECHNOLOGY. 3.0 SEMESTER HRS. An introduction to the basic physics concepts involved in nanoscale phenomena, processing methods resulting in engineered nanostructures, and the design and operation of novel structures and devices which take advantage of nanoscale effects. Students will become familiar with interdisciplinary aspects of nanotechnology, as well as with current nanoscience developments described in the literature. Prerequisites: PHGN320, PHGN341, co-requisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN566 Modern Optical Engineering

PHGN566. MODERN OPTICAL ENGINEERING. 3.0 SEMESTER HRS. Provides students with a comprehensive working knowledge of optical system design that is sufficient to address optical problems found in their respective disciplines. Topics include paraxial optics, imaging, aberration analysis, use of commercial ray tracing and optimazation, diffraction, linear systems and optical transfer functions, detectors, and optical system examples. Prerequisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN581 Laser Physics

PHGN581. LASER PHYSICS. 3.0 SEMESTER HRS. Theory, modeling, and experimental work with: absorption and emission of light from atoms, Gaussian beams, optical resonator theory and design, laser oscillation and pulsing dynamics, introduction to nonlinear optics and ultrafast pulses. Full scope of PHGN480 with more advanced homework, experimental analysis/modeling, and final project.

PHGN585 Nonlinear Optics

PHGN585. NONLINEAR OPTICS. 3.0 SEMESTER HRS. An exploration of the nonlinear response of a medium (semiclassical and quantum descriptions) and nonlinear wave mixing and propagation. Analytic and numeric techniques to treat nonlinear dynamics are developed. Applications to devices and modern research areas are discussed, including harmonic and parametric wave modulation, phase conjugation, electro-optic modulation. Prerequiste: PHGN462 or equivalent, PHGN520. 3 hours lecture; 3 semester hours.
Computer Science

CSCI542 Simulation

CSCI542. SIMULATION. 3.0 Semester Hrs. Equivalent with MACS542, (I) Advanced study of computational and mathematical techniques for modeling, simulating, and analyzing the performance of various systems. Simulation permits the evaluation of performance prior to the implementation of a system; it permits the comparison of various operational alternatives without perturbing the real system. Topics to be covered include simulation techniques, random number generation, Monte Carlo simulations, discrete and continuous stochastic models, and point/interval estimation. Offered every other year. Prerequisite: CSCI 262 (or equivalent) and MATH 323 (or MATH 530 or equivalent). 3 hours lecture; 3 semester hours.

CSCI561 Theory of Computation

CSCI561. THEORY OF COMPUTATION. 3.0 SEMESTER HRS. (I) An introduction to abstract models of computation and computability theory; including finite automata (finite state machines), pushdown automata, and Turing machines. Language models, including formal languages, regular expressions, and grammars. Decidability and undecidability of computational problems. 3 hours lecture; 3 semester hours. Prerequisite: CSCI406.

CSCI563 Parallel Computing for Scientists and Engineers

CSCI563. PARALLEL COMPUTING FOR SCIENTISTS AND ENGINEERS. 3.0 Semester Hrs.(I) Students are taught how to use parallel computing to solve complex scientific problems. They learn how to develop parallel programs, how to analyze their performance, and how to optimize program performance. The course covers the classification of parallel computers, shared memory versus distributed memory machines, software issues, and hardware issues in parallel computing. Students write programs for state of the art high performance supercomputers, which are accessed over the network. Prerequisite: Programming experience in C. 3 hours lecture; 3 semester hours.

CSCI564 Advanced Computer Architecture

CSCI564. ADVANCED COMPUTER ARCHITECTURE. 3.0 Semester Hrs. The objective of this class is to gain a detailed understanding about the options available to a computer architect when designing a computer system along with quantitative justifications for the options. All aspects of modern computer architectures including instruction sets, processor design, memory system design, storage system design, multiprocessors, and software approaches will be discussed. Prerequisite: CSCI341. 3 hours lecture; 3 semester hours.

CSCI571 Artificial Intelligence

CSCI571. ARTIFICIAL INTELLIGENCE. 3.0 Semester Hrs. (I) Artificial Intelligence (AI) is the subfield of computer science that studies how to automate tasks for which people currently exhibit superior performance over computers. Historically, AI has studied problems such as machine learning, language understanding, game playing, planning, robotics, and machine vision. AI techniques include those for uncertainty management, automated theorem proving, heuristic search, neural networks, and simulation of expert performance in specialized domains like medical diagnosis. This course provides an overview of the field of Artificial Intelligence. Particular attention will be paid to learning the LISP language for AI programming. Prerequisite: CSCI262. 3 hours lecture; 3 semester hours.

CSCI574 Theory of Cryptography

CSCI574. THEORY OF CRYPTOGRAPHY. 3.0 SEMESTER HRS. Equivalent with MATH574, (I) Students will draw upon current research results to design, implement and analyze their own computer security or other related cryptography projects. The requisite mathematical background, including relevant aspects of number theory and mathematical statistics, will be covered in lecture. Students will be expected to review current literature from prominent researchers in cryptography and to present their findings to the class. Particular focus will be given to the application of various techniques to real-life situations. The course will also cover the following aspects of cryptography: symmetric and asymmetric encryption, computational number theory, quantum encryption, RSA and discrete log systems, SHA, steganography, chaotic and pseudo-random sequences, message authentication, digital signatures, key distribution and key management, and block ciphers. Prerequisite: CSCI262. 3 hours lecture, 3 semester hours.

CSCI575 Advanced Machine Learning

CSCI575. ADVANCED MACHINE LEARNING. 3.0 Semester Hrs. Equivalent with MACS575, (II) The goal of machine learning research is to build computer systems that learn from experience and that adapt to their environments. Machine learning systems do not have to be programmed by humans to solve a problem; instead, they essentially program themselves based on examples of how they should behave, or based on trial and error experience trying to solve the problem. This course will focus on the methods that have proven valuable and successful in practical applications. The course will also contrast the various methods, with the aim of explaining the situations in which each is most appropriate. Prerequisites: CSCI262 and MATH201. 3 hours lecture; 3 semester hours.

CSCI580 Advanced High-Performance Computing

CSCI580. ADVANCED HIGH PERFORMANCE COMPUTING. 3.0 Semester Hrs. This course provides students with knowledge of the fundamental concepts of high performance computing as well as hands-on experience with the core technology in the field. The objective of this class is to understand how to achieve high performance on a wide range of computational platforms. Topics will include sequential computers including memory hierarchies, shared memory computers and multicore, distributed memory computers, graphical processing units (GPUs), cloud and grid computing, threads, OpenMP, message passing (MPI), CUDA (for GPUs), parallel file systems, and scientific applications. 3 hours lecture; 3 semester hours.
Electrical Engineering

EENG509 Sparse Signal Processing

EENG509. SPARSE SIGNAL PROCESSING. 3.0 Semester Hrs. Equivalent with EGGN509, (II) This course presents a mathematical tour of sparse signal representations and their applications in modern signal processing. The classical Fourier transform and traditional digital signal processing techniques are extended to enable various types of computational harmonic analysis. Topics covered include time-frequency and wavelet analysis, filter banks, nonlinear approximation of functions, compression, signal restoration, and compressive sensing. Prerequisites: EENG411 and EENG515. 3 hours lecture; 3 semester hours.

EENG517 Modern Control Design

EENG517. THEORY AND DESIGN OF ADVANCED CONTROL SYSTEMS. 3.0 Semester Hrs. Equivalent with EGGN517, (II) This course will introduce and study the theory and design of multivariable and nonlinear control systems. Students will learn to design multivariable controllers that are both optimal and robust, using tools such as state space and transfer matrix models, nonlinear analysis, optimal estimator and controller design, and multi-loop controller synthesis. Spring semester of even years. Prerequisites: EENG417. 3 hours lecture; 3 semester hours.

EENG526 Advanced Electromagnetics

EENG526. ADVANCED ELECTROMAGNETICS. 3.0 SEMESTER HRS. (II) In this course the fundamental theorems of electromagnetics are developed rigorously. Wave solutions are developed in Cartesian, cylindrical, and spherical coordinate systems for bounded and unbounded regions. Prerequisite: EENG386. 3 hours lecture; 3 semester hours.

EENG528 Computational Electromagnetics

EENG528. COMPUTATIONAL ELECTROMAGNETICS. 3.0 Semester Hrs. (II) In this course the fundamental theorems of electromagnetics are developed rigorously. Wave solutions are developed in Cartesian, cylindrical, and spherical coordinate systems for bounded and unbounded regions. Prerequisite: EENG386. 3 hours lecture; 3 semester hours.

EENG529 Active RF and Microwave Devices

EENG529. ACTIVE RF & MICROWAVE DEVICES. 3.0 Semester Hrs. (II) This course introduces the basics of active radio-frequency (RF) and microwave circuits and devices which are the building blocks of modern communication and radar systems. The topics that will be studied are RF and microwave circuit components, resonant circuits, matching networks, noise in active circuits, switches, RF and microwave transistors and amplifiers. Additionally, mixers, oscillators, transceiver architectures, RF and monolithic microwave integrated circuits (RFICs and MMICs) will be introduced. Moreover, students will learn how to model active devices using professional CAD software, how to fabricate printed active microwave devices, how a vector network analyzer (VNA) operates, and how to measure active RF and microwave devices using VNAs. Prerequisites: EEBG385. 3 hours lecture; 3 semester hours.

EENG530 Passive RF and Microwave Devices

EENG530. PASSIVE RF & MICROWAVE DEVICES. 3.0 Semester Hrs. (I) This course introduces the basics of passive radio-frequency (RF) and microwave circuits and devices which are the building blocks of modern communication and radar systems. The topics that will be studied are microwave transmission lines and waveguides, microwave network theory, microwave resonators, power dividers, directional couplers, hybrids, RF/microwave filters, and phase shifters. Students will also learn how to design and analyze passive microwave devices using professional CAD software. Moreover, students will learn how to fabricate printed passive microwave devices and test them using a vector network analyzer. Prerequisites: EENG386. 3 hours lecture; 3 semester hours.

EENG617 Intelligent Control Systems

EENG617. INTELLIGENT CONTROL SYSTEMS. 3.0 Semester Hrs. Equivalent with EGGN617, Fundamental issues related to the design on intelligent control systems are described. Neural networks analysis for engi neering systems are presented. Neural-based learning, estimation, and identification of dynamical systems are described. Qualitative control system analysis using fuzzy logic is presented. Fuzzy mathematics design of rule-based control, and integrated human-machine intelligent control systems are covered. Real-life problems from different engineering systems are analyzed. Prerequisite: EENG517. 3 hours lecture; 3 semester hours. Taught on demand.

EENG618 Nonlinear and Adaptive Control

EENG618. NONLINEAR AND ADAPTIVE CONTROL. 3.0 Semester Hrs. Equivalent with EGGN618, This course presents a comprehensive exposition of the theory of nonlinear dynamical systems and the applications of this theory to adaptive control. It will focus on (1) methods of characterizing and understanding the behavior of systems that can be described by nonlinear ordinary differential equations, (2) methods for designing controllers for such systems, (3) an introduction to the topic of system identification, and (4) study of the primary techniques in adaptive control, including model-reference adaptive control and model predictive control. Prerequisite: EENG517. 3 hours lecture; 3 semester hours. Spring, even numbered years.
Metallurgy and Material Engineering

MTGN505 Crystallography and Diffraction

MTGN505. CRYSTALLOGRAPHY AND DIFFRACTION. 3.0 SEMESTER HRS. (I) Introduction to point symmetry operations, crystal systems, Bravais lattices, point groups, space groups, Laue classes, stereographic projections, reciprocal lattice and Ewald sphere constructions, the new International Tables for Crystallography, and, finally, how certain properties correlate with symmetry. Subsequent to the crystallography portion, the course will move into the area of diffraction and will consider the primary diffraction techniques (x-rays, electrons and neutrons) used to determine the crystal structure of materials. Other applications of diffraction such as texture and residual stress will also be considered. Prerequisites: Graduate or Senior in good standing. 3 hours lecture, 3 semester hours.

MTGN605/605L Advanced Transmission Electron Microscopy

MTGN605/605L5. .ADVANCED TRANSMISSION ELECTRON MICROSCOPY. 2.0 SEMESTER HRS. Introduction to transmission electron microscopy techniques and their application to materials characterization. Topics include electron optics, electron-specimen interactions, imaging, diffraction, contrast mechanisms, defect analyses, compositional measurements using energy dispersive x-ray spectroscopy and energy loss spectroscopy, scanning transmission electron microscopy, high angle annular dark field imaging, energy filtered TEM and high resolution phase contrast imaging. Prerequisite: MTGN 505. Co-requisite; MTGN 605L. 2 hours lecture, 2 semester hours.

MTGN656/656L Advanced Electron Microscopy

MTGN656/656L5. ADVANCED ELECTRON MICROSCOPY. 2.0 SEMESTER HRS. Advanced introduction to electron optics and the design and application of transmission and scanning electron microscopes. Interpretation of images produced by various contrast mechanisms. Electron diffraction analysis and the indexing of electron diffraction patterns. Co-requisite: MTGN656L.

MTGN573 Computational Materials

MTGN573. COMPUTATIONAL MATERIALS. 3.0 SEMESTER HRS. (II) Computational Materials is a course designed as an introduction to computational approaches and codes used in modern materials science and engineering, and to provide the hands?on experience in using massively parallel supercomputers and popular materials software packages. The main goal is to provide exposure to students to the growing and highly interdisciplinary field of computational materials science and engineering, through a combination of lectures, hands-on exercises and a series of specifically designed projects. The course is organized to cover different length scales including: atomistic (electronic structure) calculations, molecular dynamics, and phase equilibria modeling. The emerging trends in data driven materials discovery and design are also covered. Particular emphasis is placed on the validation of computational results and recent trends in integrating theory, computations and experiment. Graduate students are expected to successfully complete 4 projects while the undergraduate students are required to finish 3 out of 4 projects. 3 hours lecture; 3 semester hours.
Materials Science

MLGN502 Solid State Physics

MLGN502. SOLID STATE PHYSICS. 3.0 SEMESTER HRS. An elementary study of the properties of solids including crystalline structure and its determination, lattice vibrations, electrons in metals, and semiconductors. (Graduate students in physics may register only for PHGN440.) Prerequisite: PH320. 3 hours lecture; 3 semester hours.

MLGN515 Electrical Properties and Applications of Materials

MLGN515. ELECTRICAL PROPERTIES AND APPLICATIONS OF MATERIALS. 3.0 SEMESTER HRS. (II) Survey of the electrical properties of materials, and the applications of materials as electrical circuit components. The effects of chemistry, processing, and microstructure on the electrical properties will be discussed, along with functions, performance requirements, and testing methods of materials for each type of circuit component. The general topics covered are conductors, resistors, insulators, capacitors, energy convertors, magnetic materials, and integrated circuits. Prerequisites: PHGN200; MTGN311 or MLGN501; MTGN412/MLGN512,. 3 hours lecture; 3 semester hours.

MLGN583 Principles and Applications of Surface Analysis Techniques

MLGN583. PRINCIPLES AND APPLICATIONS OF SURFACE ANALYSIS TECHNIQUES. 3.0 SEMESTER HRS. (II) Instrumental techniques for the characterization of surfaces of solid materials. Applications of such techniques to polymers, corrosion, metallurgy, adhesion science, micro-electronics. Methods of analysis discussed: X-ray photoelectron spectroscopy (XPS), auger electron spectroscopy (AES), ion scattering spectroscopy (ISS), secondary ion mass spectroscopy (SIMS), Rutherford backscattering (RBS), scanning and transmission electron microscopy (SEM, TEM), energy and wavelength dispersive X-ray analysis; principles of these methods, quantification, instrumentation, sample preparation. Prerequisite: B.S. in metallurgy, chemistry, chemical engineering, physics. 3 hours lecture; 3 semester hours. This course taught in alternate even numbered years.

MLGN593 Bonding, Structure, and Crystallography

MLGN593. BONDING, STRUCTURE, AND CRYSTALLOGRAPHY. 3.0 SEMESTER HRS. (I) This course will be an overview of condensed matter structure from the atomic scale to the mesoscale. Students will gain a perspective on electronic structure as it relates to bonding, long range order as it relates to crystallography and amorphous structures, and extend these ideas to nanostructure and microstructure. Examples relating to each hierarchy of structure will be stressed, especially as they relate to reactivity, mechanical properties, and electronic and optical properties. Prerequisites: A 300 level or higher course in thermodynamics. 3 semester hours.
Applied Mathematics and Statistics

MATH506 Complex Analysis II

MATH506. COMPLEX ANALYSIS II. 3.0 SEMESTER HRS. (II) Analytic functions. Conformal mapping and applications. Analytic continuation. Schlicht functions. Approximation theorems in the complex domain. Taught every other year. Prerequisite: MATH454. 3 hours lecture; 3 semester hours.

MATH510 Ordinary Differential Equations and Dynamical Systems

MATH510. ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS. 3.0 SEMESTER HRS. (I) Topics to be covered: basic existence and uniqueness theory, systems of equations, stability, differential inequalities, Poincare-Bendixon theory, linearization. Other topics from: Hamiltonian systems, periodic and almost periodic systems, integral manifolds, Lyapunov functions, bifurcations, homoclinic points and chaos theory. Offered even years. Prerequisite: (MATH225 or MATH235) and (MATH332 or MATH342). 3 hours lecture; 3 semester hours.

MATH536 Advanced Statistical Modeling

MATH536. ADVANCED STATISTICAL MODELING. 3.0 SEMESTER HRS. (II) Modern extensions of the standard linear model for analyzing data. Topics include generalized linear models, generalized additive models, mixed effects models, and resampling methods. Offered every two years on odd years. 3 hours lecture; 3 semester hours. Prerequisite: MATH335, MATH424.

MATH538 Stochastic Models

MATH538. STOCHASTIC MODELS. 3.0 SEMESTER HRS. (II) An introduction to the mathematical principles of stochastic processes. Discrete- and continuous-time Markov processes, Poisson processes, Brownian motion. Offered every two years on even years. 3 hours lecture; 3 semester hours.

MATH550 Numerical Solution of Partial Differential Equations

MATH550. NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS. 3.0 SEMESTER HRS. (I) Numerical methods for solving partial differential equations. Explicit and implicit finite difference methods; stability, convergence, and consistency. Alternating direction implicit (ADI) methods. Weighted residual and finite element methods. Prerequisites: MATH225 or MATH235 and MATH332 or MATH342. GEOPHYSICS

MATH551 Computational Linear Algebra

MATH551. COMPUTATIONAL LINEAR ALGEBRA. 3.0 SEMESTER HRS. (II) Numerical analysis of algorithms for solving linear systems of equations, least squares methods, the symmetric eigenproblem, singular value decomposition, conjugate gradient iteration. Modification of algorithms to fit the architecture. Error analysis, existing software packages. 3 hours lecture; 3 semester hours. Prerequisite: MATH332, MATH 307.
Humanities, Arts, and Social Sciences

HASS523 Advanced Science Communication

HASS523. ADVANCED SCIENCE COMMUNICATION. 3.0 SEMESTER HRS. Equivalent with LAIS523, This course will examine historical and contemporary case studies in which science communication (or miscommunication) played key roles in shaping policy outcomes and/or public perceptions. Examples of cases might include the recent controversies over hacked climate science emails, nuclear power plant siting controversies, or discussions of ethics in classic environmental cases, such as the Dioxin pollution case. Students will study, analyze, and write about science communication and policy theories related to scientific uncertainty; the role of the scientist as communicator; and media ethics. Students will also be exposed to a number of strategies for managing their encounters with the media, as well as tools for assessing their communication responsibilities and capacities. 3 hours seminar; 3 semester hours.

COMBINED BS/MS
As with many other graduate programs, students enrolled in Mines’ combined undergraduate/graduate program (meaning uninterrupted registration from the time the student earns a Mines undergraduate degree to the time the student begins a Mines graduate degree) may double count up to six hours of credits which were used in fulfilling the requirements of their undergraduate degree at Mines towards their quantum engineering MS degree. Any 400+ level courses that count towards the undergraduate degree requirements as Elective Coursework, or any 500+ level course, may be used for the purposes of double counting at the discretion of the graduate advisor. These courses must have been passed with a B- or better, not be substitutes for required coursework, and meet all other University, Department, Division, and Program requirements for graduate credit.
BS Electrical Engineering / MS Quantum Engineering (please consult with your advisor)
REGISTRATION REQUIREMENTS FOR COMBINED STUDENTS
MINOR

The interdisciplinary minor in Quantum Engineering requires 18 credit hours.

QE minor students will be required to take Honors Linear Algebra (MATH342) or Linear Algebra (MATH332)

MATH342 HONORS LINEAR ALGEBRA

MATH342. HONORS LINEAR ALGEBRA. Same topics as those covered in MATH332 but with additional material and problems as well as a more rigorous presentation. 3 hours lecture; 3 semester hours. Prerequisite: MATH213, MATH223 or MATH224.

MATH332 LINEAR ALGEBRA

MATH332. LINEAR ALGEBRA. (I, II,S) Systems of linear equations, matrices, determinants and eigenvalues. Linear operators. Abstract vector spaces. Applications selected from linear programming, physics, graph theory, and other fields. 3 hours lecture; 3 semester hours. Prerequisite: MATH213, MATH223 or MATH224.

and three of the following courses: Quantum Programming (CSCI481/CSCI581), Low Temperature Microwave Measurement (EENG432/EENG532), Quantum Many-Body Physics (PHGN545), Microelectronics Processing (PHGN435), and Fundamentals of Quantum Information (PHYS519).

CSCI481/CSCI581 QUANTUM PROGRAMMING

CSCI581. QUANTUM PROGRAMMING. 3.0 SEMESTER HRS. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.

EENG432/EENG532 LOW TEMPERATURE MICROWAVE MEASUREMENTS FOR QUANTUM ENGINEERING

EENG532. LOW TEMPERATURE MICROWAVE MEASUREMENTS FOR QUANTUM ENGINEERING. 3.0 SEMESTER HRS. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Offered every Spring semester. Prerequisite: EENG385, PHGN215 or equivalent Electronics Devices & Circuits course.

PHGN441 SOLID STATE PHYSICS APPLICATIONS AND PHENOMENA

PHGN441. SOLID STATE PHYSICS APPLICATIONS AND PHENOMENA. 3.0 SEMESTER HRS. Continuation of PHGN440/ MLGN502 with an emphasis on applications of the principles of solid state physics to practical properties of materials including: optical properties, superconductivity, dielectric properties, magnetism, noncrystalline structure, and interfaces. (Graduate students in physics may register only for PHGN441.) Prerequisite: PHGN440 or MLGN502. 3 hours lecture; 3 semester hours.

PHGN435 INTERDISCIPLINARY MICROELECTRONICS PROCESSING LABORATORY

PHGN435. INTERDISCIPLINARY MICROELECTRONICS PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN535, Application of science and engineering principles to the design, fabrication, and testing of microelectronic devices. Emphasis on specific unit operations and the interrelation among processing steps. Prerequisite: MATH213 or MATH214 or MATH223 or MATH224.

PHGN519 FUNDAMENTALS OF QUANTUM INFORMATION

PHGN519. FUNDAMENTALS OF QUANTUM INFORMATION. 3.0 SEMESTER HRS. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers. Prerequisite: MATH332 (linear algebra) or an equivalent linear algebra course.

Students may select an additional 2 courses from the list above or from the list below (also available in the course catalog) to further increase specialization.

Elective Information, 3 credit hours each course
Physics

PHGN440 Solid-State Physics

PHGN440also a materials course. SOLID STATE PHYSICS. 3.0 SEMESTER HRS. An elementary study of the properties of solids including crystalline structure and its determination, lattice vibrations, electrons in metals, and semiconductors. (Graduate students in physics may register only for PHGN440.) Prerequisite: PHGN320. 3 hours lecture; 3 semester hours.

PHGN466/566 Modern Optical Engineering

PHGN466 MODERN OPTICAL ENGINEERING. 3.0 SEMESTER HRS. Provides students with a comprehensive working knowledge of optical system design that is sufficient to address optical problems found in their respective disciplines. Topics include paraxial optics, imaging, aberration analysis, use of commercial ray tracing and optimization, diffraction, linear systems and optical transfer functions, detectors and optical system examples. Prerequisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN566. MODERN OPTICAL ENGINEERING. 3.0 SEMESTER HRS. Provides students with a comprehensive working knowledge of optical system design that is sufficient to address optical problems found in their respective disciplines. Topics include paraxial optics, imaging, aberration analysis, use of commercial ray tracing and optimazation, diffraction, linear systems and optical transfer functions, detectors, and optical system examples. Prerequisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN480 Laser Physics

PHGN480. LASER PHYSICS. 3.0 SEMESTER HRS.(I) Theory and application of the following: Interaction of light with atoms: absorption, gain, rate equations and line broadening. Propagation, control and measurement of light waves: Gaussian beams, optical resonators and wave guides, interferometers. Laser design and operation: pumping, oscillation, and dynamics (Q-switching and mode-locking). Introduction to ultrafast optics. Laboratory: alignment and characterization of laser systems. Prerequisites: PHGN320. Co-requisites: PHGN462. 3 hours lecture; 3 semester hours.
Computer Science

CSCI474 Introduction to Cryptography

CSCI474. INTRODUCTION TO CRYPTOGRAPHY. 3.0 SEMESTER HRS. Equivalent with MATH474, (II) This course is primarily oriented towards the mathematical aspects of cryptography, but is also closely related to practical and theoretical issues of computer security. The course provides mathematical background required for cryptography, including relevant aspects of number theory and mathematical statistics. The following aspects of cryptography will be covered: symmetric and asymmetric encryption, computational number theory, quantum encryption, RSA and discrete log systems, SHA, steganography, chaotic and pseudo-random sequences, message authentication, digital signatures, key distribution and key management, and block ciphers. Many practical approaches and most commonly used techniques will be considered and illustrated with real-life examples. Prerequisites: CSCI262, CSCI358, MATH334 or MATH335 or MATH201. 3 hours lecture; 3 semester hours.

CSCI423 Computer Simulation

CSCI423. COMPUTER SIMULATION. 3.0 SEMESTER HRS. A first course in computer simulation using formal learning groups and emphasizing the rigorous development of simulation applications. Topics will include random number generation, Monte Carlo simulation, discrete event simulation, and the mathematics behind their proper implementation and analysis (random variates, arrival time modeling, infinite horizon statistics, batch means and sampling techniques). The course uses learning group assignments, quizzes, programming projects (using Linux) and exams for assessment. Prerequisite: CSCI274, CSCI306, MATH201.

CSCI440 Parallel Computing for Scientists and Engineers

CSCI440. Equivalent with MATH440, (II) This course is designed to introduce the field of parallel computing to all scientists and engineers. The students will be taught how to solve scientific problems using parallel computing technologies. They will be introduced to basic terminologies and concepts of parallel computing, learn how to use MPI to develop parallel programs, and study how to design and analyze parallel algorithms. Prerequisite: CSCI220 with a grade of C- or higher or CSCI262 with a grade of C- or higher, CSCI341.

CSCI470 INTRODUCTION TO MACHINE LEARNING

CSCI470. INTRODUCTION TO MACHINE LEARNING. 3.0 SEMESTER HRS. (I) The goal of machine learning is to build computer systems that improve automatically with experience, which has been successfully applied to a variety of application areas, including, for example, gene discovery, financial forecasting, and credit card fraud detection. This introductory course will study both the theoretical properties of machine learning algorithms and their practical applications. Students will have an opportunity to experiment with machine learning techniques and apply them to a selected problem in the context of term projects. Prerequisite: CSCI101 or CSCI102 or CSCI200 or CSCI261, MATH201, MATH332.
Electrical Engineering

EENG307 INTRODUCTION TO FEEDBACK CONTROL SYSTEMS

EENG307. INTRODUCTION TO FEEDBACK CONTROL SYSTEMS. 3.0 SEMESTER HRS. System modeling through an energy flow approach is presented, with examples from linear electrical, mechanical, fluid and/or thermal systems. Analysis of system response in both the time domain and frequency domain is discussed in detail. Feedback control design techniques, including PID, are analyzed using both analytical and computational methods. Prerequisite: EENG281 or EENG282 or PHGN215 (C- or better) and MATH225.

EENG383 EMBEDDED SYSTEMS

EENG383. EMBEDDED SYSTEMS. 4.0 SEMESTER HRS. (I, II) The design and implementation of systems consisting of analog and digital components with a microcontroller to perform a dedicated task. Student will implement systems using a variety of microcontroller subsystems including timers, PWM, ADC, serial communication subsystems and interrupts. Students will learn embedded systems programming techniques like, fixed-point math, direct digital synthesis, lookup tables, and row scanning. Student will program the microcontroller using a high-level programming language like C or C++. Prerequisite: EENG281 or EENG282 or PHGN215 (C-or better) and EENG284 or PHGN317 (C-or better).

EENG385 ELECTRONIC DEVICES AND CIRCUITS

EENG385. ELECTRONIC DEVICES AND CIRCUITS. 4.0 SEMESTER HRS. (I, II) Semiconductor materials and characteristics, junction diode operation, bipolar junction transistors, field effect transistors, biasing techniques, four layer devices, amplifier and power supply design, laboratory study of semiconductor circuit characteristics. Prerequisite: EENG307. 3 hours lecture; 3 hours lab; 4 semester hours.

EENG411 DIGITAL SIGNAL PROCESSING

EENG411. DIGITAL SIGNAL PROCESSING. 3.0 SEMESTER HRS. (II) This course introduces the mathematical and engineering aspects of digital signal processing (DSP). An emphasis is placed on the various possible representations for discrete-time signals and systems (in the time, z-, and frequency domains) and how those representations can facilitate the identification of signal properties, the design of digital filters, and the sampling of continuous-time signals. Advanced topics include sigma-delta conversion techniques, multi-rate signal processing, and spectral analysis. The course will be useful to all students who are concerned with information bearing signals and signal processing in a wide variety of application settings, including sensing, instrumentation, control, communications, signal interpretation and diagnostics, and imaging. Prerequisite: EENG310. 3 hours lecture; 3 semester hours.

EENG421 SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

EENG421. SEMICONDUCTOR DEVICE PHYSICS AND DESIGN. 3.0 SEMESTER HRS. (I) This course will explore the field of semiconductors and the technological breakthroughs which they have enabled. We will begin by investigating the physics of semiconductor materials, including a brief foray into quantum mechanics. Then, we will focus on understanding pn junctions in great detail, as this device will lead us to many others (bipolar transistors, LEDs, solar cells). We will explore these topics through a range of sources (textbooks, scientific literature, patents) and discuss the effects they have had on Western society. As time allows, we will conclude with topics of interest to the students (possibilities include quantum devices, MOSFETs, lasers, and integrated circuit fabrication techniques). Prerequisite: PHGN200. 3 hours lecture; 3 semester hours.

EENG428 COMPUTATIONAL ELECTROMAGNETICS

EENG428. COMPUTATIONAL ELECTROMAGNETICS. 3.0 SEMESTER HRS. (I) This course provides the basic formulation and numerical solution for static electric problems based on Laplace, Poisson and wave equations and for full wave electromagnetic problems based on Maxwell's equations. Variation principles methods, including the finite-element method and method of moments will be introduced. Field to circuit conversion will be discussed via the transmission line method. Numerical approximations based on the finite difference and finite difference frequency domain techniques will also be developed for solving practical problems. Prerequisite: EENG386. 3 hours lecture; 3 semester hours.
Metallurgy and Material Engineering

MTGN211 STRUCTURE OF MATERIALS

MTGN211. STRUCTURE OF MATERIALS. 3.0 SEMESTER HRS. (II) Principles of atomic bonding, crystallography, and amorphous structures. ii) Symmetry relationships to material properties. iii) Atomic structure determination through diffraction techniques. Prerequisite: MTGN202. Corequisite: PHGN200. 3 hours lecture; 3 semester hours.

MTGN315 ELECTRICAL PROPERTIES AND APPLICATIONS OF MATERIALS

MTGN315. ELECTRICAL PROPERTIES AND APPLICATIONS OF MATERIALS. 3.0 SEMESTER HRS. Survey of aspects of modern physics needed to understand selected properties of materials including conductivity (electrical, thermal, etc.), electronic states of materials, density of states, the nature of bands and bonding and how they arise, total and cohesive energy of solids based on filling of states, the nature of metals, semiconductors, and dielectrics and how these arise from electronic states, and the application of these concepts to understand dielectrics, magnetism, and semiconductor devices. Prerequisite: PHGN200, MATH225, MTGN211.

MTGN350 STATISTICAL PROCESS CONTROL AND DESIGN OF EXPERIMENTS

MTGN350. STATISTICAL PROCESS CONTROL AND DESIGN OF EXPERIMENTS. 3.0 SEMESTER HRS. Introduction to statistical process control, process capability analysis and experimental design techniques. Statistical process control theory and techniques developed and applied to control charts for variables and attributes involved in process control and evaluation. Process capability concepts developed and applied to the evaluation of manufacturing processes. Theory of designed experiments developed and applied to full factorial experiments, fractional factorial experiments, and multilevel experiments. Analysis of designed experiments by graphical and statistical techniques. Introduction to computer software for statistical process control and for the design and analysis of experiments.

MTGN352 METALLURGICAL AND MATERIALS KINETICS

MTGN352. METALLURGICAL AND MATERIALS KINETICS. 3.0 SEMESTER HRS. Introduction to reaction kinetics: chemical kinetics, atomic and molecular diffusion, surface thermodynamics and kinetics of interfaces and nucleation-and-growth. Applications to materials processing and performance aspects associated with gas/solid reactions, precipitation and dissolution behavior, oxidation and corrosion, purification of semiconductors, carburizing of steel, formation of p-n junctions and other important materials systems. Prerequisite: MTGN272. Co-requisite: MTGN251.

MTGN456 Electron Microscopy

MTGN456. ELECTRON MICROSCOPY. 2.0 Semester Hrs. (I, II, S) Introduction to electron optics and the design and application of transmission and scanning electron microscopes. Interpretation of images produced by various contrast mechanisms. Electron diffraction analysis and the indexing of electron diffraction patterns. Prerequisites: MTGN211 or MTGN311. Corequisite: MTGN456L. 2 hours lecture; 2 semester hours.

MTGN473 COMPUTATIONAL MATERIALS

MTGN473. COMPUTATIONAL MATERIALS. 3.0 SEMESTER HRS. (II) Computational Materials is a course designed as an introduction to computational approaches used in modern materials science and engineering, and to provide the hands-on experience in using massively parallel supercomputers and executing popular materials software packages. The main goal is to provide exposure to students to the growing and highly interdisciplinary field of computational materials science and engineering, through a combination of lectures, hands-on exercises and a series of specifically designed projects. The course is organized to cover different length scales including: atomistic (electronic structure) calculations, molecular dynamics, and phase equilibria modeling. The emerging trends in data driven materials discovery and design are also covered. Particular emphasis is placed on the validation of computational results and recent trends in integrating theory, computations and experiment. 3 hours lecture; 3 semester hours.
Applied Mathematics and Statistics

MATH436 Advanced Statistical Modeling

MATH436. ADVANCED STATISTICAL MODELING. 3.0 Semester Hrs. (II) Modern methods for constructing and evaluating statistical models. Topics include generalized linear models, generalized additive models, hierarchical Bayes methods, and resampling methods. Time series models, including moving average, autoregressive, and ARIMA models, estimation and forecasting, confidence intervals. Prerequisites: MATH335 and MATH424. 3 hours lecture; 3 semester hours.

MATH438 Stochastic Models

MATH438. STOCHASTIC MODELS. 3.0 Semester Hrs. (II) An introduction to stochastic models applicable to problems in engineering, physical science, economics, and operations research. Markov chains in discrete and continuous time, Poisson processes, and topics in queuing, reliability, and renewal theory. Prerequisite: MATH334. 3 hours lecture, 3 semester hours.

MATH454 COMPLEX ANALYSIS

MATH454. COMPLEX ANALYSIS. 3.0 SEMESTER HRS. (II) The complex plane. Analytic functions, harmonic functions. Mapping by elementary functions. Complex integration, power series, calculus of residues. Conformal mapping. Prerequisite: MATH225 or MATH235 and MATH213 or MATH223 or MATH224. 3 hours lecture, 3 semester hours.

MATH458 ABSTRACT ALGEBRA

MATH458. ABSTRACT ALGEBRA. 3.0 SEMESTER HRS. (I) This course is an introduction to the concepts of contemporary abstract algebra and applications of those concepts in areas such as physics and chemistry. Topics include groups, subgroups, isomorphisms and homomorphisms, rings, integral domains and fields. Prerequisites: MATH300. 3 hours lecture; 3 semester hours.

FAQ

Q. Are GRE scores required to apply to the Quantum Engineering (QE) Master’s program?
A. No, GRE scores are not required for either the QE Master’s Thesis or QE Master’s Non-Thesis. Submission of GRE scores is entirely optional.

Q. To whom should I submit my academic credentials?
A. Please submit all academic credentials only via the online application.

Q. Are teaching and research assistantships available?
A. Yes, teaching and research assistantships are available to qualified MS and PhD candidates in Mines’ interdisciplinary programs.

Q. Does Mines offer a Quantum Engineering PhD?
A. No. Currently PhDs go only through the QE constituent departments.

Q. Does Mines offer a Quantum Engineering Minor?
A. Yes, beginning with the Fall 2021 semester.

Q. What types of courses should I take as an undergraduate that would allow myself to be viewed most favorably for admission to the Quantum Engineering program?
A. A science or engineering degree and successful completion of college-level linear algebra are required for admission. Successful completion of a number of elective courses is required for the QE MS Thesis, MS Non-Thesis, and Graduate Certificate options. Completion of prerequisites, or comparable courses, for the electives that you intend to take, prior to entering the program, is recommended. Please see the Electives section of this document for information on the various elective courses including prerequisites.

GRAD LINKS
Grad School Important Links
Graduate Studies Website Step-by-Step Guide to Graduation
Combined Program BS/MS Cost of Attendance
Registration Requirements Degree Requirements
Master’s Along the Way Reduced Registration
Graduation Deadlines Thesis Writer’s Guide
Forms Graduate School Contacts

Comments/corrections to quantum@mines.edu

APPLICATION INFO

For more information about admission to our program, application instructions, deadlines, selection criteria, and other aspects of the process, please see the Quantum Engineering Program Overview, Quantum Engineering Minor IDM, and Quantum Engineering Minor pages, refer to the FAQs and Grad Links sections of this document, and/or contact us at quantum@mines.edu.

Please submit credentials only via the online application.