Chapter 17: Certificate Programs
General Information
Certificate programs are designed to provide an intensive background in a narrow area at the graduate level. At approximately one-third of the units required for a master’s degree, the certificate is designed to be completed in a much shorter period of time. These certificate programs are appropriate for students working in industry who wish to update their skills or for those interested in changing their career path.
Interdisciplinary
Certificate in Frugal Innovation
Advisor: Dr. Drazen Fabris
Over the past two decades, global trends have been forcing businesses to adapt to growing consumer bases in Africa, Asia, and Latin America, which are in desperate need of low-cost and high-quality solutions to the challenges that they face. The importance of these new “economic realities” is underscored by the fact that emerging markets are expected to exceed 50% of the world’s GDP in 2017 (according to IMF estimates). In order to excel professionally in such an environment, engineers will have to be equipped with the knowledge and skill sets to appropriately define, design, and implement solutions that are not merely a “stripping down” of Western products to meet the rising demand. Industry, particularly in Silicon Valley, is becoming increasingly aware of this fact and has begun to move toward a ‘Triple Bottom Line’ approach to business, which integrates environmental, societal, and financial considerations. The Certificate in Frugal Innovation is designed to give students the ability and the tools to adapt to this new model, and to expand their understanding of the impact that engineering has on society.
This program is suitable for working professionals in a wide variety of engineering disciplines. To enroll, students must have a B.S. in Engineering from an accredited institution and should maintain a GPA of at least 3.000 in order to receive the certificate.
Program Requirements
The Certificate in Frugal Innovation entails a minimum of 16 units of coursework. It consists of an eight-unit Core and a set of electives that are organized into two groups. Students are required to take four units from Group A and another four from Group B, as described below.
Required Core Classes (8 units)
- ENGR/GREN 336 Engineering for the Developing World (2 units)
- ENGR/GREN 338 Mobile Applications and Instrumentation for Emerging Markets (2 units)
- ENGR/GREN 340 Distributed and Renewable Energy for the Developing World (2 units)
- ENGR/GREN 341 Innovation, Design and Spirituality
Elective Group A (4 units)
- ENGR/GREN 304 Building Global Teams (2 units)
- ENGR/GREN 342 3D Print Technology and Society (2 units)
- ENGR 349 Ethical Decision Making for Technology Leaders (2 units)
Elective Group B (4 units)
- CENG 219 Designing for Sustainable Construction (4 units)
- CSEN 389 Energy Efficient Computing (2 units)
- ECEN 280/MECH 287 Introduction to Alternative Energy Systems (2 units)
- ECEN 288/CSEN 282 Energy Management Systems (2 units)
- ENGR/GREN 302 Managing in the Multicultural Environment (2 units)
Renewable Energy Certificate
Advisor: Dr. Maryam Khanbaghi
Renewable energy is the fastest-growing sector in California and brings together principles and practices from engineering, environmental science, and economics. Silicon Valley, the home of the world’s largest cluster of renewable energy companies and green investors, offers fertile ground to recruit career changers who wish to move into renewable energy and students who want to take advantage of the tremendous career opportunities.
The main goal of this certificate is to introduce students to the field of renewable energy. The intent is to help equip professionals in Silicon Valley with the knowledge that will help them advance in their present careers or enter the renewable energy field. To enroll in this certificate, an applicant should have a B.S. in Engineering from an accredited school and should maintain a grade point average of 3.000. As with most certificates in the Graduate School of Engineering, the requirement is 16 quarter units. Eight of these units are in Power Systems, eight units are in Renewable Energy.
Required Courses (16 units total)
Power Systems (8 units)
- ECEN 280/MECH 288 Renewable Energy (2 units)
- ECEN 281A Power Systems: Generation and Transmission (2 units)
- ECEN 281B Power Systems Distribution (2 units) or ECEN 281E (4 units)
- ECEN 285 Introduction to the Smart Grid (2 units)
Renewable Energy (8 units)
- ECEN 284 Solar Cell Technologies and Simulation Tools (2 units) or ECEN 380 Economics of Energy (2 units)
- ECEN/MECH 286 Introduction to Wind Energy Engineering (2 units)
- ECEN 287/MECH 287 Storage Device Systems (2 units)
- ENGR/GREN 272 Energy Public Policy (2 units)
Bioengineering Certificate
Online Graduate Certificate in Applied Bioengineering
Advisor: Dr. Prashanth Asuri
The primary goal of the online graduate certificate is to provide a graduate-level introduction to recent graduates and professionals wishing to explore the field of applied bioengineering. The certificate is suitable for students with bachelor's degrees in a variety of related disciplines, including but not limited to: biotechnology, bioengineering, biology, electrical engineering, mechanical engineering, and systems engineering. The program will provide a balanced foundation core and a broad array of elective courses, and addresses both theoretical and applied aspects of bioengineering.
Requirements for the Online Graduate Certificate in Applied Bioengineering
The program is offered to students with an undergraduate degree in the fields of bioengineering, biotechnology, biology, biochemistry, pharmacology, engineering, or a similar course of study, ideally with a focus on life sciences, medical, or biomedical sciences. The curriculum consists of 16 units: three required courses (6 units) and 10 units of elective courses listed below.
Foundational Courses (6 units)
- Topics in Bioengineering
- Human Anatomy and Physiology for Engineers
- Clinical Trials Methodology
Elective Courses (10 units)
Select from the following options:
- AI in Medical Imaging
- Biosignals and Medical Image Processing
- Optical Imaging and Photonics
- Biosensors and Biowearables
- Biomaterials Engineering
- Medical Device Development
- Directed Research
Please contact the Bioengineering Department to see which courses are currently being offered.
Electrical and Computer Engineering Certificates
Digital System Design
Advisor: Dr. Hoeseok Yang
This certificate program has a triple purpose: (a) to increase design skills in digital system development, (b) to strengthen fundamental knowledge of computer architecture, digital design, and embedded systems; and (c) to introduce the digital system designer to state-of-the-art tools and techniques. The program consists of the courses listed below totaling 16 units. Any change in the requirements must be approved by the academic advisor.
Required Courses (7 units)
- ECEN 501/501L (Embedded Systems) 3 units
- ECEN 511 Advanced Computer Architecture (2 units)
- ECEN 603 Logic Design Using HDL (2 units)
Elective Courses (9 units)
- ECEN 226 Machine Learning and Signal Processing Using FPGAs (2 units)
- ECEN 387 VLSI Design I (2 units)
- ECEN 388 VLSI Design II (2 units)
- ECEN 500 Logic Analysis and Synthesis (2 units)
- ECEN 502 Real Time Systems (2 units)
- ECEN 503 Hardware-Software Co-design (2 units)
- ECEN 512 Advanced Computer Architecture II (2 units)
- ECEN 513 Parallel System Architectures (2 units)
- ECEN 529 Hardware Acceleration for Machine Learning on FPGAs (2 units)
- ECEN 530 Fundamentals of System Security (2 units)
- ECEN 531 Advanced System Security (2 units)
- ECEN 601 Low Power Designs of VLSI Circuits and Systems (2 units)
- ECEN 608 Design for Testability (2 units)
- ECEN 613 SoC (System-on-Chip) Verification (2 units)
Integrated Circuit Design and Technology
Advisors: Dr. Shoba Krishnan, Dr. Cary Yang, Dr. Mahmudur Rahman
The study of integrated circuits consists of three interconnected areas: Design, Devices, and Process Technology. This certificate provides the necessary fundamentals in these areas and advanced concepts and applications in integrated circuit design, devices, and process technology. The program will also introduce the IC designer to state-of-the-art tools and techniques. The program consists of the courses listed below; students are required to complete a total of 16 units. Any change in the requirements must be approved by the academic advisor.
Required Courses (8 units)
- ECEN 252 Analog Integrated Circuits I (2 units)
- ECEN 261 Fundamentals of Semiconductor Physics (2 units)
- ECEN 270 Introduction to IC Materials (2 units)
- ECEN 387 VLSI Design I (2 units)
Elective Courses (8 units)
- ECEN 251 Transistor Models for IC Design (2 units)
- ECEN 253 Analog Integrated Circuit Design (2 units)
- ECEN 254 Advanced Analog Integrated Circuit Design
- ECEN 264 Semiconductor Device Theory I (2 units)
- ECEN 265 Semiconductor Device Theory II (2 units)
- ECEN 267 Device Electronics for IC Design (4 units)
- ECEN 271 Microsensors: Components and Systems (2 Units)
- ECEN 274 Integrated Circuit Fabrication Processes I (2 units)
- ECEN 275 Integrated Circuit Fabrication Processes II (2 units)
- ECEN 351 RF Integrated Circuit Design (2 units)
- ECEN 352 Mixed Signal IC Design for Data Communications (2 units)
- ECEN 353 DC to DC Power Conversion (2 units)
- ECEN 361 Nanoelectronics
- ECEN 388 VLSI Design II (2 units)
Digital Signal Processing and Machine Learning
Advisors: Dr. Tokunbo Ogunfunmi, Dr. Sally Wood
This certificate program provides a basic understanding of digital signal processing theory, machine learning, and modern implementation methods as well as advanced knowledge of at least one specific application area. Digital signal processing and machine learning have become important across many areas of engineering, and this certificate prepares students for traditional or novel applications. This certificate can be earned with a combination of in-person and online courses.
Required Courses (11 units minimum)
- ECEN 233 Digital Signal Processing I (2 units)
- ECEN 520 Introduction to Machine Learning (3 units)
- At least one course from: AMTH 210 Probability I or AMTH 245 Linear Algebra I or AMTH 370 Optimization Techniques (2 units)
- At least one course from: ECEN 223 Digital Signal Processing System Development (4 units) or ECEN 226 Machine Learning and Signal Processing Using FPGAs (2 units) or ECEN 234 Digital Signal Processing II (2 units) or ECEN 529 Hardware Acceleration for Machine Learning on FPGAs (2 units)
- At least one course from: ECEN 421 Speech Processing I or ECEN 640 Digital Image Processing I (2 units) or ECEN 521 Deep Learning (3 units)
- Note: ECEN 233E Digital Signal Processing I, II (4 units) is equivalent to both ECEN 233 and ECEN 234.
Elective Courses (Additional courses to make a total of 16 units) selected from the list below or from any courses in the list above that are not used to meet the specified certificate requirements:
- ECEN 241E Modern Communications(4 units)
- ECEN 244 Information Theory (2 units)
- ECEN 334 Introduction to Statistical Signal Processing (2 units)
- ECEN 422 Speech Coding II (2 units)
- ECEN 431 Adaptive Signal Processing I (2 units)
- ECEN 522 Reinforcement Learning (3 units)
- ECEN 523 Natural Language Processing with Deep Learning (2 units)
- ECEN 643 Digital Image Processing II (2 units)
- ECEN 644 Computer Vision I (2 units) or ECEN 645 Computer Vision II (2 units)
Digital Signal Processing Theory
Advisors: Dr. Tokunbo Ogunfunmi, Dr. Sally Wood
This certificate program provides a firm theoretical grounding in the fundamentals of digital signal processing (DSP) technology and its applications. It is appropriate for engineers involved with any application of DSP who want a better working knowledge of DSP theory and its applications. A novel feature of the program is a hands-on DSP hardware/software development laboratory course in which students design and build systems for various applications using contemporary DSP hardware and development software.
Required Courses (8 units)
- AMTH 308 Theory of Wavelets (2 units) or AMTH 358 Fourier Transforms (2 units)
- ECEN 233E or ECEN 233 and 234 Digital Signal Processing I, II (4 units)
- ECEN 334 Introduction to Statistical Signal Processing (2 units)
Elective Courses (8 units)
- ECEN 223 Digital Signal Processing System Development (4 units)
- ECEN 226 Machine Learning and Signal Processing Using FPGAs (2 units)
- ECEN 235 Estimation I (2 units)
- ECEN 241E Modern Communications (4 units)
- ECEN 244 Information Theory (2 units)
- ECEN 336 Detection (2 units)
- ECEN 431 Adaptive Signal Processing I (2 units)
- ECEN 640 Digital Image Processing I (2 units)
- ECEN 641 Image and Video Compression (2 units)
- ECEN 643 Digital Image Processing II (2 units
Fundamentals of Electrical and Computer Engineering
Advisor: Dr. Shoba Krishnan
This certificate has been designed for those individuals who have significant work experience in some area of electrical and computer engineering and wish to take graduate-level courses but may lack some prerequisite knowledge because they have not earned a BS degree in electrical and/or computer engineering. This one-year program consists of 16 to 28 units, depending on the background of the individual student, and covers electrical and computer engineering core areas. Units from courses at or above the 200 level may be credited toward the Master of Science Degree in Electrical and Computer Engineering after successful completion of the certificate.
The specific required courses for a certificate are selected with the help of the program advisor according to the student’s background.
- ECEN 21 Introduction to Logic Design (4 units)
- ECEN 50 Electric Circuits I (4 units)
- ECEN 100 Electric Circuits II (4 units)
- ECEN 104 Electromagnetics I (4 units)
- ECEN 110 Linear Systems (4 units) or ECEN 210 (2 units)
- ECEN 115 Electronic Circuits I (4 units) or ECEN 250 (2 units)
- ECEN 120 Microprocessor System Design (4 units)
RF and Applied Electromagnetics
Advisor: Dr. Kurt Schab
The purpose of this certificate is to meet the increasing need for knowledge in microwave, antenna, and RF integrated circuits in existing electronic products. This program is offered to students who have a B.S. in Electrical Computer Engineering. Students are expected to have knowledge of multivariate calculus and preferably partial differential equations and they must ensure that they have prerequisites for the courses in their program.
The curriculum consists of 16 units: two required courses (4 units) and 12 units of elective courses listed below:
Required Courses (4 units)
- ECEN 201 Electromagnetic Field Theory I (2 units)
- ECEN 701 Microwave System Architecture (2 units)
Elective Courses (12 units)
- ECEN 202 Computational Electromagnetics (2 units)
- ECEN 203 Bio-Electromagnetics (2 units)
- ECEN 204 Magnetic Circuits for Electric and Autonomous Vehicles (2 units)
- ECEN 351 RF Integrated Circuit Design or ECEN 354 Advanced RFIC Design (2 units each)
- ECEN 624 Signal Integrity in IC and PCB Systems (2 units)
- ECEN 706 Microwave Circuit Analysis and Design (2 units) (Passive Component)
- ECEN 711 Active Microwave Devices I or ECEN 712 Active Microwave Devices II (2 units each) (Active Components)
- ECEN 715 Antennas I or ECEN 716 Antennas II (2 units each)
- ECEN 726 Microwave Measurements, Theory and Tech (3 units) (Laboratory Oriented)
Substitutions for these courses are only possible with the approval of the certificate advisor and the chair.
Mechanical Engineering Certificates
Department Chair: Dr. Michael Taylor
The Department of Mechanical Engineering offers certificates in: Design and Manufacturing; Dynamics and Controls; Mechanics and Materials; Mechatronic Systems Engineering; and Thermofluids and Energy. g. The certificate program is designed for working professionals, who would like to deepen their understanding in disciplinary-specific subjects and apply the knowledge to real engineering problems. One can receive a certificate in Mechanical Engineering by taking 16 units of Mechanical Engineering graduate courses with a minimum GPA of 3.00 and a grade of C or better in each course. Students must take at least 8 units of core courses associated with their chosen emphasis area as specified below. Applicants must have completed an accredited bachelor’s degree program in Mechanical Engineering or a closely related field of engineering. Up to 16 units earned in a certificate can be transferred toward another advanced degree program at SCU if they are accepted to the M.S. program.
Design and Manufacturing
Advisors: Dr. Michael Abbott, Dr. Sthanu Mahadev, Dr. Panthea Sepehrband, Dr. Jun Wang, Dr. Peter Woytowitz, Dr. Xiaoou Yang
The Design & Manufacturing (DM) certificate allows students to develop abilities and skills in mechanical design and aspects of manufacturing in achieving competence in product development.
Core Courses (Students need to take at least 8 units out of these courses)
- MECH 251 Finite Element Methods I (4 units)
- MECH 275 Design for Competitiveness (2 units)
- MECH 281 Elasticity, Fracture, and Fatigue (4 units)
- MECH 285 Computer-Aided Design of Mechanisms (2 units)
- MECH 325 Computational Geometry for Computer-Aided Design and Manufacture (2 units)
- MECH 415 Optimization in Mechanical Design (2 units)
Elective Courses (8 units)
- Any graduate-level MECH courses
Dynamics and Controls
Advisors: Dr. Mohammad Ayoubi, Dr. Christopher Kitts
The Dynamics and Controls (D&C) certificate in the Department of Mechanical Engineering provides a foundation for students to utilize physics-based or data-driven techniques to model, identify, analyze, and regulate the behavior of dynamical systems. The important feature is to achieve the specified objectives in an optimal fashion while coping with the disturbances and model uncertainties.
Core Courses (Students need to take at least 8 units out of these courses)
- MECH 214 Advanced Dynamics* (4 units) or
- MECH 305 Advanced Vibrations* (4 units)
- MECH 323/324 Modern Control Systems I, II (2 units each)
- MECH 429/430 Optimal Control I, II (2 units each)
Elective Courses (8 units)
- Any graduate-level MECH courses
Mechanics and Materials
Advisors: Dr. Sthanu Mahadev, Dr. Robert Marks, Dr. On Shun Pak, Dr. Panthea Sepehrband, Dr. Michael Taylor, Dr. Peter Woytowitz
The Mechanics & Materials (MM) certificate allows students to explore the science of materials and how those materials move and deform in response to thermomechanical loading.
Core Courses (Students need to take at least 8 units out of these courses)
- MECH 251 Finite Element Methods I (4 units)
- MECH 281 Elasticity, Fracture, and Fatigue (4 units)
- MECH 330 Atomic Bonding, Crystal Structure, and Material Properties (4 units)
- MECH 331 Equilibrium Thermodynamics and Phase Transformations (4 units)
- MECH 377 Continuum Mechanics (4 units)
Elective Courses (8 units)
- Any graduate-level MECH courses
Mechatronic Systems Engineering
Advisors: Dr. Michael Abbott, Dr. Christopher Kitts, Dr. Michael Neumann
The Mechatronic Systems Engineering (MSE) certificate focuses on the methods and techniques relating to the design, control, and operation of complex modern engineering systems.
Core Courses (Students must complete 10 units of coursework as specified below in requirements A, B, and C.)
(A) Mechatronics: Students will need to complete the 6-unit graduate mechatronic sequence:
- MECH 207 and 208 Advanced Mechatronics I, II (3 units each)
(B) Systems: In addition, students will need to complete a minimum of 2 units of coursework from the following list of “systems” courses; additional courses may apply based on approval from faculty in the emphasis area.
- MECH 292 Special Topics in Mechatronic Systems Engineering (2-4 units)
(Tentative Topics: UAV Systems; Marine Systems) - MECH 311 Design and Control of Telerobotic Systems (4 units)
- MECH 337/338 Robotics I, II (2 units each)
- MECH 371/372 Space Systems Design and Engineering I, II (4 units each)
- MECH 379 Satellite Operations (1 unit)
(C) Design Process: Students must also complete a 2-unit course in systems development. Some of these options may be used to also satisfy the degree’s enrichment requirement. Courses that satisfy this requirement include:
- MECH 275 Design for Competitiveness (2 units)
- EMGT 380 Introduction to Systems Engineering Management (2 units)
Elective Courses (6 units)
- Any graduate-level MECH courses
Thermofluids and Energy
Advisors: Dr. Drazen Fabris, Dr. Godfrey Mungal, Dr. On Shun Pak
The ThermoFluids and Energy (TFE) certificate explores mechanisms and application of fluid motion at various scales and energy conversion.
Core Courses (Students need to take at least 8 units out of these courses)
- MECH 228 Energy Conversion and Conservation (4 units)
- MECH 242 Advanced Heat Transfer (4 units)
- MECH 266 Fundamentals of Fluid Mechanics (2 units)
- MECH 268 Computational Fluid Dynamics (2 units)
- MECH 270 Viscous Flow (2 units)
- MECH 274 Microfabrication and Microfluidics (4 units) and MECH 274L (1 unit)
- MECH 287 Energy Storage Systems (2 units)
- MECH 377 Continuum Mechanics (4 units)
Elective Courses (8 units)
- Any graduate-level MECH courses
Robotics and Automation Certificate Program
Advisor: Dr. Christopher Kitts
This certificate program provides a graduate-level introduction to the theoretical knowledge and the practical skills necessary to excel in the growing, interdisciplinary fields of robotics, autonomous systems, intelligent machines, and smart products. The program is offered to students with an undergraduate degree in a field of engineering or related area. Students should also have an academic background or demonstrate proficiency in computer programming, basic electrical circuit design, basic mechanical design, system dynamics, and mathematics at least at a level of differential equations. The Certificate is ideal for professionals wishing to enhance their knowledge of this emerging engineering area. It is also ideal for students interested in completing the Certificate as a step toward enrolling in the full M.S. Degree in Robotics and Automation; Certificate courses may be applied to the M.S. program.
The curriculum consists of 16 units: three required courses (7 units) and 9 units of elective courses listed below:
Required Courses (7 units)
- MECH 207/ECEN 460 Advanced Mechatronics I (3 units)
- MECH/ECEN 337 Robotics I (2 units)
- MECH/ECEN 338 Robotics II (2 units)
Elective Courses (9 units)
- BIOE 277 Biosensors (2 units)
- CSEN 266 Artificial Intelligence (4 units)
- CSEN 344 /ECEN 644 Computer Vision I (2 units)
- CSEN 345 /ECEN 645 Computer Vision II (2 units)
- ECEN 331(L) Autonomous Driving Systems (2 units w/optional 1-unit Lab)
- ECEN 520(L) Intro to Machine Learning (2 units w/optional 1-unit Lab)
- MECH 208 / ECEN 461 Adv Mechatronics II (3 units)
- MECH 323 Modern Control Systems I (2 units)
- MECH 324 Modern Control Systems II (2 units)
- Up to 2 units of experiential research and design work: MECH 290 Graduate Research Project (1-2 units)
- Up to 4 units of mathematics selected from the following courses:
(1) AMTH 245 Linear Algebra I (2 units)
(2) AMTH 246 Linear Algebra II (2 units)
(3) AMTH 247 Linear Algebra I & II (4 units)
(4) AMTH 210 Probability I (2 units)
(5) AMTH 211 Probability II (2 units)
(6) AMTH 212 Probability I & II (4 units) - Up to 2 units of coursework relating to business, societal and/or ethical issues:
(1) CSEN 288 Software Ethics (2 units)
(2) EMGT 292 Managing Capital Assets in the Smart Machine Era (2 units)
(3) ENGR/GREN 342 3D Print Technology and Society (2 units)
(4) ENGR /GREN 344 Artificial Intelligence and Ethics (2 units)
Substitutions for these courses are possible with the approval of the certificate advisor.
Online Graduate Certificate in Robotics and Automation
Advisor: Dr. Christopher Kitts
This certificate program provides a graduate-level introduction to the theoretical knowledge and practical skills necessary to excel in the growing, interdisciplinary fields of robotics, autonomous systems, intelligent machines, and smart products. The program is offered to students with an undergraduate degree in a field of engineering or related area. Students should also have an academic background or demonstrate proficiency in computer programming, basic electrical circuit design, basic mechanical design, system dynamics, and mathematics at least at a level of differential equations. The Certificate is ideal for professionals wishing to enhance their knowledge of this emerging engineering area. It is also ideal for students interested in completing the Certificate as a step toward enrolling in the full M.S. Degree in Robotics and Automation; Certificate courses may be applied to the M.S. program.
The curriculum consists of 16 units: three required courses (7 units) and 9 units of elective courses listed below. This is an online version of the Certificate in Robotics and Automation, intended to support the needs of remote and international students. Courses may be taken online or in person. For students who are completely remote, 4 units of coursework will generally be available during each quarter of the academic year, and only a subset of the elective courses listed below may be available:
Required Courses (7 units):
- MECH 207/ECEN 460 Advanced Mechatronics l (3 units)
- MECH/ECEN 337 Robotics l (2 units)
- MECH/ECEN 338 Robotics II (2 units)
Elective Courses (9 units):
- BIOE 277 Biosensors (2 units)
- CSEN 266 Artificial Intelligence (4 units)
- CSEN 344/ECEN 644 Computer Vision I (2 units)
- CSEN 345/ ECEN 645 Computer Vision II (2 units)
- ECEN 331(L) Autonomous Driving Systems (2 units w/optional 1 unit Lab)
- ECEN 520(L) Intro to Machine Learning (2 units w/optional 1 unit Lab)
- MECH 217 Introduction to Control Systems (2 units)
- MECH 208 / ECEN 461 Adv Mechatronics II (3 units)
- MECH 323 Modern Control Systems I (2 units)
- MECH 324 Modern Control Systems II (2 units)
- MECH 379 Satellite Operations (1 unit)
- Up to 2 units of experiential research and design work: MECH 290 Graduate Research Project (1-2 units)
- Up to 4 units of mathematics selected from the following courses:
(1) AMTH 245 Linear Algebra I (2 units)
(2) AMTH 246 Linear Algebra II (2 units)
(3) AMTH 247 Linear Algebra I & II (4 units)
(4) AMTH 210 Probability I (2 units)
(5) AMTH 211 Probability II (2 units)
(6) AMTH 212 Probability I & II (4 units) - Up to 2 units of coursework relating to business, societal and/or ethical issues:
(1) CSEN 288 Software Ethics (2 units)
(2) ENGR/GREN 342 3D Print Technology and Society (2 units)
(3) ENGR 344/GREN Artificial Intelligence and Ethics (2 units)
(4) EMGT 292 Managing Capital Assets in the Smart Machine Era (2 units)
Substitutions for these courses are possible with the approval of the certificate advisor.