MASTER OF SCIENCE DEGREE REQUIREMENTS

The department of ECE offers both part-time and full-time programs. The ECE department recognizes that a student may be employed full-time while studying for a degree. Therefore, most courses are offered at times and on days that will permit a student to complete the program by taking courses either late in the day or outside normal business hours. Many employers will permit additional flexibility by releasing employees early to attend classes. The MS degree programs can generally be completed in about four years if one course is taken each quarter, but it is usually possible to take two courses per quarter, bringing completion time closer to the more common duration of two years. For part-time students who are working in industry positions and who have chosen the thesis option, a topic related to the job function may be acceptable as the thesis research topic. Furthermore, a qualified staff member at the place of employment may be approved to serve as an adjunct faculty on the thesis committee.

Students not interested in pursuing a degree but interested in taking an occasional course may register as special status students by following an abbreviated admissions process. However, only 15 quarter hours earned as a special status student may be applied toward a MS or PhD degree.

Minimum Credit Requirements
Every candidate for the MS degree must complete 45 quarter hour of credit, at least 36 of which must be completed at the University of Denver.

Master of Science in Computer Engineering, Electrical Engineering, Mechatronic Systems Engineering, or Engineering
The Master of Science in computer engineering (MSCpE), electrical engineering (MSEE), mechatronic systems engineering (MSMSE) or engineering (MSENGE) is designed to advance the student's knowledge in several areas of engineering. Each degree provides breadth while permitting the student to achieve depth in one of several specialization areas. These specialization areas, with thematic sequences of courses, have been selected to coincide with those of high current interest as well as those emerging technologies that hold promise of increasing importance for the future. The purpose of these programs is to serve the profession of engineering and the Colorado community through advanced study in computer, electrical engineering and related fields. Each program prepares the student for academic and industrial advancement. All programs offer a thesis and a non-thesis option.

Program Structure
Candidates may elect either the thesis or non-thesis option. This choice may be made at any time, although a delay in declaration may impact the completion date. Students who are GTAs or who receive financial support from a University research grant, such as GRAs, are required to elect the thesis option. These programs are designed to be completed in about seven quarters if two courses (usually eight quarter hours) are taken each quarter.

Non-Thesis Option
The non-thesis option is the more flexible of the two options. This program is designed with the working professional in mind. For this option, a grade of B or better must be obtained in each course in order for that course to count toward the requirement of 45 quarter hours. An overall minimum GPA of 3.0 is also required for graduation. Students may only take up to eight quarter hours of independent study to be counted toward the degree.  Each student must take a minimum of 24 quarter hours at the 4000-level. The basic structure of the minimum 45 quarter hours for the non-thesis option is as follows:

Core Requirement Based on Degree                                             Minimum Quarter hours
Each degree program has two required                                                  8 Quarter hours classes, please see program for specifics  
Depth Requirement - Specialization Area                                              20 Quarter hours
Additional Mathematics Requirement                                                    3 Quarter hours*    
Requires one approved course at                       
3000-level or higher
Breadth Requirement                                                                            14 Quarter hours           Total Quarter hours, non-thesis option                              45 Quarter hours

(*) This indicates minimum number of quarter hours. Any credits over the required three quarter hours from the mathematics courses will count toward the breadth requirement.

Thesis Option
A thesis permits a candidate to obtain depth in an area of study and it is especially useful for individuals who seek to pursue a subsequent degree, for example, a PhD degree. Thesis candidates work closely with a thesis advisor. The thesis option is required for all GRAs and GTAs. For this option, a grade of C or better must be obtained in each course in order for that course to count toward the 45 quarter hours hour requirements. An overall minimum GPA of 3.0 is also required for graduation. Students may only take up to eight quarter hours of independent study to be counted toward the degree. Each student must take a minimum of 16 quarter hours at the 4000-level.The basic structure of the minimum 45 quarter hours for the thesis option is as follows:

Core Requirement based on Degree   Minimum Quarter hours
Each degree program has two required                                               8 Quarter hours classes
Please see program for specifics  
Depth Requirement- Specialization Area                                         16 Quarter hours
Breadth Requirement                                                                       6 Quarter hours (*)
Thesis                                                                                            15 Quarter hours
 Total Quarter hours thesis option                                                  45 Quarter hours
     
(*) This indicates minimum number of credit hours. Any credits over the required 3 quarter hours from the mathematics courses will count toward the breadth requirement.

If a student who has elected to pursue a thesis option, then at any time thereafter elects to change to a non-thesis option, all requirements for the non-thesis must be met.  Any independent research taken may be forfeited and students must adhere to the grade requirements of the non-thesis option.  

Breadth Requirement (Non-Thesis and Thesis Option)
Breadth Requirement courses (each with not less than three quarter hours of credit) may be chosen from courses offered in other specialization areas. A course that appears in more than one specialization area may only be counted toward either the specialization requirement or the breadth requirement. The remaining courses are chosen from appropriate courses numbered 3000 or higher, offered by the department mechanical and materials engineering, department of computer science or NSM (Natural Sciences and Mathematics). Prior approval by the student's advisor is required.

Computer Engineering

The MSCpE program offers one area of specialization:
      • Intelligent Information System Design

Each student must choose the area of specialization.  The student's degree program will be a combination of the core courses, specialization area (depth requirement) and the breadth requirement.  Each student is required to complete the two core courses.  Students may choose from any of the courses from their area of specialization but should keep in mind the 4000-level requirement of the degree.
Core courses for all Computer Engineering Students
The following courses are required for all computer engineering students regardless of area of specialization:

 ENCE 4110 Modern Digital Systems Design
 ENGR 3620 Advanced Engineering Mathematics
Specialization in Intelligent Information System Design
This area of specialization prepares students with fundamental and working knowledge of methods for analysis, design and implementation of intelligent systems (IS). Particular attention is given to signal and information processing in IS, design of IS, and implementation of IS using state-of-the-art technology. This is accomplished through several theoretical courses and applied courses.  Students must choose from the following courses: 

 ENEE 3670 Introduction to Digital Signal Processing
 ENCE 4501 Advanced VSLI Design
 ENCE 4250 Advanced Hardware Description Language (HDL) Modeling and Synthesis
 ENCE 3321 Network Design
 ENCE 4620 Advanced Computer Vision

Electrical Engineering

The MSEE program offers four areas of specialization:
• Control System Analysis and Synthesis
• Electric Power and Energy Systems
• Microelectronics, Microsystems and Nanotechnology
• Modern Communications System Design

Each student must choose an area of specialization.  The student's degree program will be a combination of the core courses, specialization areas (depth requirement) and the breadth requirement.  Each student is required to complete the two core courses.  Students may choose from any of the courses from their area of specialization but should keep in mind the 4000-level requirement of the degree. 
Core courses for all Electrical Engineering Students
The following courses are required for all electrical engineering students regardless of area of specialization:

 ENEE 4640 Electromagnetic Compatibility
 ENGR 3620 Advanced Engineering Mathematics

Specialization in Control System Analysis and Synthesis
This area of specialization prepares students for basic and applied research and development of complex systems, including, electrical, mechanical, bio-inspired, mechatronic, and robotic systems, as well as unmanned systems. This is accomplished through several theoretical courses and applied courses.  Students must choose from the following courses:
     
      ENCE 4231 Embedded Systems Programming
      ENEE 3670 Introduction to Digital Signal Processing
      ENGR 3721/3722 Controls and Controls Systems Laboratory
      ENEE 4630 Optical Networking
      ENGR 4730 Introduction to Robotics

Specialization in Electric Power and Energy
This area of specialization prepares students with the basic foundation and advanced knowledge, required for the research and development in the area of power systems, renewable energy systems, and power electronic devices. This is accomplished through several theoretical courses and applied courses.  Students must choose from the following courses: 

ENGR 3510 Renewable and Efficient Power and Energy Systems
ENGR 3540 Electric Power Systems
ENGR 3721/3722 Controls and Controls Systems Laboratory
ENGR 4530 Introduction to Power and Energy
ENGR 4560 Power Generation Operation and Control
ENGR 4545 Electric Power Economy

Specialization in Microelectronics, Microsystems & Nanotechnology
This area of specialization prepares students for careers in design, fabrication, and characterization of microelectronic devices and integrated circuits, MEMS and microsystems, as well as the emerging nano-electro-mechanical technologies.  

ENEE 4030 Optoelectronics
ENEE 4035 Nanophotonics
ENGR 4200 Introduction to Nanotechnology
ENGR 4220 Introduction to MEMS and Microsystems
ENCE 4250 Advanced Hardware Description Language (HDL) Modeling and Synthesis
Specialization in Modern Communications Design

This area of specialization prepares students for research, development and design of devices and systems that operate using wave theory: laser, optics and light wave devices, electromagnetic theory, waveguides and antennas. This is accomplished through several theoretical courses and applied courses.  Students must choose from the following courses:
 
ENCE 3321 Network DesignENEE 4030 Optoelectronics  
ENEE 4035 Nanophotonics
ENEE 4620 Advanced Optical Fiber Communication

Mechatronic Systems Engineering

This program is designed to meet the needs of industry and federal research laboratories for engineers with multidisciplinary experience and ability to design and integrate complex systems requiring knowledge from diverse engineering disciplines. Said differently, mechatronics involves integration of mechanical, electrical, and computer engineering to design complex systems that perform real-world tasks. This program includes a broad set of common course requirements along with a selection of appropriate technical electives providing both breadth and depth of knowledge in a student's area of interest.

The MSE program offers one area of specialization:
• Mechatronic System Design

This program is a combination of core courses, specialization area (depth requirement) and technical electives (breadth requirement). Each student is required to complete two core courses.  Students, along with their advisor, should develop a plan of study choosing thematic sequences of courses from different specialization areas, but they should keep in mind the 4000-level requirement of the degree. 

Core courses for all Mechatronic Systems Engineering StudentsThe following courses are required for all mechatronic systems engineering students
ENEE 4641 Electromagnetic Compatibility OR
ENCE 4110 Modern Digital Systems Design
ENGR 3620 Advanced Engineering Mathematics
Specialization in Mechatronic System Design
ENMT 4220 Mechatronics II
ENGR  4730 Introduction to Robotics
ENCE 4620 Advanced Computer Vision
ENCE 4250 Advanced Hardware Description Language (HDL) Modeling and Synthesis
ENCE 4231 Embedded Systems Programming
ENCE 4900 Machine Learning

Engineering - Concentration in Engineering Management

This program allows students to pursue a concentration in engineering management. The concentration in engineering management is designed to meet the increasing needs of students to enhance their career opportunities as managers or as entrepreneurs by supplementing advanced engineering knowledge with a fundamental understanding of business principles within the context of technology enterprises.  Drawing upon the strengths of both the School of Engineering and Computer Science (SECS) and the Daniels College of Business (DCB), the program provides relevant content for graduates to lead technology enterprises. There is only a non-thesis option available for this program. The program structure is as follows:

 Engineering Focus (depth requirement)                                           Minimum Quarter hours
• A minimum of four 4000-level courses                                                     24 Quarter hours
• At the time of admission students must choose
an Engineering Focus from the following: computer,
electrical, or mechanical engineering.  This focus
area should be  mentioned in the Statement of
Purpose
• At least 6 courses must be in the Engineering
Focus Area of either computer, electrical, or
mechanical engineering. Student will be assigned
to an engineering advisor which students must
consult.
Engineering Mathematics Requirement                                                     3 Quarter hours  
Must be at the 4000-level and have                                                      
 advisor's approval
Management Focus                                                                                   18 Quarter hours
Students may choose any 4000-level management
courses offered by the Daniels College of Business
Total Quarter hours                                                                                  45 Quarter hours

The engineering focus must consist of a set of coordinated and related engineering courses designed to give the student depth in a particular engineering discipline (CpE, EE or ME). Students must choose and follow an area of specialization from a given discipline (the specializations are listed above), but this requirement may be waived with approval by the student's engineering advisor if the student wishes to pursue a coherent inter-disciplinary curriculum.

Additional Mathematics Requirement:
All MS non-thesis candidates must complete an advanced mathematics requirement. Students may choose from the following courses:

ENGR 3620  Advanced Engineering Mathematics
ENGR 4620   Optimization
ENEE 3670/4800  Introduction to DSP
ENGR 4810   Advanced Topics: Linear Systems
ENGR 3630   Finite Element Methods
ENGR 4740    Principles of Adaptive and Optimal Control Systems
ENGR 4745    Advanced Non-Linear Control System
ENGR 4350   Reliability
ENME 4020   Advanced Finite Element Analysis
ENGR 3800   Topics in Engineering: Numerical Methods
MATH 3120   Introduction to Topology
MATH 3151   Advanced Linear Algebra
MATH 3152   Linear Algebra II
MATH 3161   Introduction to Real Analysis
MATH 3166   Group Theory
MATH 3400   Introduction to Geometry
MATH 3705   Topics in Mathematics
MATH 3720   Coding Theory
MATH 3851   Functions Complex Variable I
MATH 3852   Functions Complex Variable II
F DENVER

DOCTOR OF PHILOSOPHY IN ELECTRICAL AND COMPUTER ENGINEERING OR MECHATRONIC SYSTEMS ENGINEERING DEGREE REQUIREMENTS

The objective of the PhD in ECE or MSE degree programs is to provide an educational environment that encourages students to develop the ability to contribute to the advancement of science, engineering and technology, through independent research. The PhD students of the 21st century may pursue academic, research, entrepreneurial, and/or industrial careers. We offer opportunities to develop individualized plans of study based on the students' previous experience and desired research areas. The plan of study allows students to work on interdisciplinary research, while also satisfying the PhD in ECE or MSE degree requirements.

Program Structure
Research requires an in-depth study of engineering problems with a broad knowledge base in science and engineering. Therefore, advanced courses are offered to strengthen the fundamentals and to broaden the engineering and science perspective. The minimum credit requirements are different for individuals entering a program with a closely related master's degree and for those entering with a bachelor's only. All requirements for the degree must be completed within seven years (eight years without a master's degree) from admission to candidacy. A grade of C or better must be obtained in each course in order for that course to count toward the credit hour requirements. An overall minimum GPA of 3.0 is also required for graduation.

PhD in ECE
The PhD in ECE is appealing to students because it offers the much needed specialization component and the 'degree identity' required to be competitive in the job market. Graduates from this program will be well equipped to follow academic careers, or be hired in federal laboratories, industry and the private sector.

PhD in MSE
The PhD in MSE is at the forefront and intersection of the coupled disciplines of electrical, mechanical, computer engineering, and computer science. This unique degree is appealing to students because they will acquire the knowledge and ability to deal with and solve highly complex problems where integration is a key component. This degree provides a holistic approach to graduate education focusing on the ability to cover both breadth and depth of knowledge. Graduates of this program will lay the foundation for the modern engineering departments of the future, where 'integration' will be the key ingredient of studies.
Program requirements
All PhD students who have been admitted to the PhD in ECE or MSE programs must successfully complete three milestones before the PhD degree can be conferred. These milestones refer to:
• Demonstrating that the student is qualified to begin PhD studies
• Demonstrating that the student may identify and formulate a research problem
• Demonstrating that the student can defend her/his dissertation
These three milestones are referred to as the PhD qualifying exam the comprehensive exam (also known as the PhD proposal), and the dissertation defense.

Qualifying Examination
Each student must demonstrate sufficient breadth and depth of basic engineering knowledge relevant to electrical and computer engineering. Each student must demonstrate ability to organize and present her/his thoughts in a convincing manner. The PhD qualifying exam achieves this through three components: a written common exam of basic engineering knowledge (breadth), two written specific area exams (depth), and an oral design exam (breadth, depth, organization and presentation). Failure to pass any component of the PhD qualifying exam will prevent the student from continuing in the PhD program.

All students admitted into the PhD program must take all three components of the PhD qualifying exam within one year of admission. All students must pass the PhD qualifying exam within two years of admission to the PhD program.

A student may take the PhD qualifying exam at most twice. If a student fails in any component(s) of the exam the first time, she/he must take the same component(s) during the second attempt. Appeals for a third attempt may be considered on an individual basis, but they are rarely granted. They will be reviewed by the entire faculty of the department with clear, convincing evidence supporting the reasons for the appeal. The time table for such third attempts shall be determined by the department. In general, third attempts will not be permitted.

A student shall be considered to have passed the PhD qualifying exam only after all three components have been successfully completed within the time constraints specified.

Common Exam: The common exam is a two-hour written exam. Each student, in consultation with her/his advisor, must choose one of three options for the common exam:
• Engineering Mathematics (Calculus, Engineering Analysis, Linear Algebra)
• Circuits and Electronics
• Digital Design, Computer Organization, and HDL

Specific Area Exams: The PhD qualifying specific area exam component is designed to demonstrate depth in two chosen areas of expertise. Each specific area exam is two hours in length. The two areas of expertise must be chosen at the time of the first attempt of the PhD qualifier and cannot be changed. Specific areas for the PhD qualifier include, but are not limited to:

* Digital Design, Computer Organization, and HDL (only if NOT taken for the common component)
* Circuits and Electronics (only if NOT taken for the common component)
* Microprocessors
* Data Structures, Algorithms, & Operating Systems
* Control, Signals & Systems
* Electromagnetics
* Physical Electronics
* Power ElectronicsPower & Energy Systems
* Optoelectronics
* Optical Fiber Communication
* Communication & DSP
* Robotics
* Image Processing & Computer Vision
* Pattern Recognition
* Control, Signals & Systems
* MEMS

Specialization Design Exam:  Design is the cornerstone of engineering. Every PhD student will be required to demonstrate ability to follow a sound design approach toward an engineering problem in her/his area of expertise and to convincingly defend her/his design in written and oral communication.  The specialization design exam will be an open-ended design problem, developed by the candidate's advisor with the candidate's area of study in mind. The candidate must complete the design exam in one week. The results of the candidate's design exercise will be evaluated by a committee of three faculty, in both oral and written form. The candidate will have five days to complete and submit a written report of her/his design solution and an additional two days to prepare an oral defense of the design. Upon submission of a sufficient written report, the committee will schedule the oral defense of the design.

The purpose of this design examination is to demonstrate the candidate's ability to follow good design procedures at the level of an undergraduate senior design course and to explain/justify the tradeoffs that are tantamount to design. For the purposes of this examination, "good design procedures" shall include the following steps as outlined in the DU ENGR 3313/3323/3333 sequence in the undergraduate curriculum:
* Conceptual Design
* Requirements Analysis
* Specification
* Brainstorming
* Architectural Design
* Detailed Design
* Test and Validation
* Maintenance and Support

In general, it will not be possible to fully execute a design solution to an open-ended design problem in one week. The emphasis of this exam is on the candidate's ability to complete the above steps to some convincing level of detail, the candidate's ability to explain/justify the tradeoffs considered at each step of the process, and the candidate's ability to communicate the completeness of the design exercise to the committee at a level appropriate for a beginning graduate student in engineering. As part of this exercise, comparisons to the existing body of literature are expected.

The examining committee for the specialization design exam shall consist of the candidate's advisor and two other faculty members. At least one of these other faculty members must be from the ECE department. Final constitution of the committee must be approved by the student's advisor. If the student's advisor is unavailable, the Department Chair will assign the committee based on recommendations provided by the advisor, if possible.

Comprehensive Examination
The purpose of the comprehensive examination is to ascertain the potential of the student for PhD quality research.  At least two quarters prior to the final defense, the student shall schedule and take the comprehensive examination.  This oral and written examination will be attended by a minimum of three faculty members, the same faculty who will attend the student's final dissertation defense.   The comprehensive exam may be open to other students based on the requirements of the student's advisor.  The student is expected to make a 30 to 40 minute concise presentation on her/his dissertation topic. The oral and written presentation will highlight previous work in this area, demonstrate a need for the given research, and explain how the given research will contribute to the advancement of the area. The student will also present completed work and results, anticipated work and results, and a detailed plan for project completion. In addition, the student will be expected to answer general fundamental questions in the area of her/his concentration and detailed questions in the area of the student's graduate course work.

The PhD qualifying examination must be taken and passed prior to the student taking the comprehensive examination. The comprehensive examination can be taken two times.  If the student does not pass the comprehensive exam on the second try, the student will be terminated from the program. The comprehensive exam will be graded on a pass/fail system, revisions maybe required. 

Dissertation
The student is required to complete and defend a dissertation of publishable quality based on the student's original research. The dissertation must be completed in written form in accordance with the University's graduate school guidelines. A summary of the dissertation must be presented in a public seminar and subsequently defended by the student in the final oral examination. The examining committee will consist of the student's entire PhD committee.

Residence Requirement
One year of full-time graduate work and two consecutive years of part-time graduate work satisfy the minimum residency requirement at the University of Denver. For those applicants from industry with established special degree programs with the School of Engineering and Computer Science (SECS), the residency requirement can be waived by the dean of SECS.

PhD Committee
The PhD committee should consist of at least four faculty members. Three faculty members must be from within the student's specialty area; this committee should include the student's advisor, other faculty in that degree program and, if necessary (with university approval), off-campus experts. Finally, for the final oral defense of the dissertation, an oral defense chair, who must be a tenured faculty member outside the department of electrical and computer engineering and mechanical and materials engineering, needs to be identified in consultation with the DU Graduate Studies Office. The PhD committee must approve the student's plan of study and research plan and must be in place before the PhD comprehensive exam.

Minimum credit requirements

Students with a Bachelor of Science in Engineering/Science
For students admitted to the PhD program with a bachelor's degree, 90 quarter hours are required, 72 of which must be completed at the University of Denver. A minimum of 48 quarter hours must be at the 4000-level or higher and may include as many dissertation research hours (independent research and independent study) as considered appropriate by the advisor. The student with his/her advisor will develop an appropriate plan of study with core requirements, an area of specialization (depth requirement), breadth requirement and advanced mathematics. The core will consist of 8 quarter hours of coursework. The area of specialization will consist of 16 quarter hours of coursework.  An additional six quarter hours of coursework (excluding independent research) is required as related breadth requirement. The student must complete a minimum of 16 quarter hours at the 4000-level courses, excluding independent research. Prior to completion of the comprehensive exam, the plan of study must be approved by the student's PhD committee.

Students with a Master of Science in Engineering/Science
If a student is admitted with a closely related master's degree, up to 45 hours may be transferred and applied to the doctorate degree.  A minimum of 45 quarter hours is required at the University of Denver. The student with his or her advisor will develop an appropriate program consisting of a minimum of 45 quarter hours at the 4000-level, which may include as many dissertation research hours (Independent Research and Independent Study) as considered appropriate by the advisor. The student with his or her advisor will develop an appropriate plan of study with an area of specialization, breadth requirements and advanced mathematics. Prior to completion of the comprehensive exam, the student's plan of study must be approved by the student's PhD committee.