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College of Engineering  ›  Electrical and Computer Engineering  ›  Academics  ›  PhD in ECE  ›  Breadth Areas

Breadth Areas

The following courses are listed by area and are available to fulfill the PhD Breadth Requirements.

Algorithms/Complexity/Programming Languages

Course Units
10-708 Probabilistic Graphical Models 12
10-725 Optimization 12
15-750 Graduate Algorithms 12
15-751 CS Theory Toolkit (approved until F25) 12
15-812 Programming Language Semantics 12
15-814 Type Systems for Programming Languages 12
15-816 Advanced Topics in Logic: Linear Logic 12
15-849B Performance Modeling 12
15-853 Algorithms in the Real World 12
15-855 An Intensive Introduction to Computational Complexity Theory 12
15-857 Performance Modeling 12
18-645 How to Write Fast Code 12
18-645SV How to Write Fast Code 12
18-645T How to Write Fast Code 12
18-647  Computational Problem Solving for Engineers 12
18-660 Optimization  12
18-660SV Numerical Methods for Engineering Design and Optimization 12
18-667 Algorithms for Large-scale Distributed Machine Learning and Optimization 12
18-687 Analytical Performance Modeling & Design of Computer Systems 12
18-687SV Analytical Performance Modeling & Design of Computer Systems 12
18-733 Applied Cryptography 12
18-733SV Applied Cryptography 12
18-755 Networks in the Real World 12
18-779T Stochastic Optimization 12
21-690 Methods of Optimization 12
21-801 Advanced Topics in Discrete Mathematics: Sampling, Counting and Rapidly Mixing Markov Chains 12
24-785 Engineering Optimization 12

Special Topics Courses
18799 Special Topics in Signal Processing 12
Topic titles:
 Nonlinear Optimization

Artificial Intelligence, Robotics and Control

Course Units
06-708 Advanced Process Dynamics and Control 12
10-403 Deep Reinforcement Learning & Control (approved until S26)  12 
10-701 Machine Learning 12
10-703 Deep Reinforcement Learning & Control 12
10-707 Advanced Deep Learning 12
10-715 Advanced Introduction to Machine Learning 12
15-780 Advanced Artificial Intelligence Concepts 12
15-781 Machine Learning 12
15-849N Advanced Topics in Computer Systems: Machine Learning Systems (dual-categorization with Software Systems area) 12
15-882 Introduction to Artificial Neural Networks 12
15-883 Computational Models of Neural Systems 12
15-889 AI Planning, Execution, and Learning 12
16-711 Kinematics, Dynamic Systems and Control 12

16-720

 Computer Vision 12
16-721 Learning-Based Methods in Vision 12
16-722 Sensing and Sensors 12
16-745 Optimal Control and Reinforcement Learning 12
16-782 Planning and Decision-Making in Robotics 12
16-785 Social Robotics 12
16-811 Mathematical Fundamentals for Robotics 12
16-822 Geometry-based Methods in Vision 12
16-824 Visual Learning and Recognition 12
16-825 Learning for 3D Vision (previously 16889 - 16889 will count toward requirements; approved until F25) 12
16-831 Statistical Techniques in Robotics* (*offered offered through Spring 2023)  12
16-831 Introduction to Robot Learning  12
16-833 Robot Localization and Mapping (approved until F27)  12
16-883 Special Topics: Provably Safe Robotics 12
16-885 Tactile Sensing and Haptics 12
17-759 Advanced Topics in Machine Learning and Game Theory 12
18-618 Smart Grids and Future Electric Energy Systems 12
18-661 Introduction to Machine Learning for Engineers 12
18-665 Advanced Probability & Statistics for Engineers 12
18-744 Autonomous Driving  12
18-771 Linear Systems 12
18-771PP Linear Systems 12
18-771SV Linear Systems 12
18-776 Non Linear Control 12
18-777 Complex Large-Scale Dynamic Systems 12
18-782PP Machine Learning 12
18-785 Data, Inference, and Applied Machine Learning 12
18-786 Introduction to Deep Learning 12
18-875 Engineering and Economics of Electric Energy Systems 12
18-813  Foundations of Reinforcement Learning (Approved until S26)  12
24-673 Soft Robots: Mechanics, Design and Modeling 12
24-787 Machine Learning and Artificial Intelligence for Engineers 12

Special Topics Courses
18799 Special Topics in Signal Processing 12
Topic titles:  Evolutionary Algorithms in Engineering Optimization
18813 Special Topics in Artificial Intelligence 12
Topic titles: Foundations of Reinforcement Learning
18879 Special Topics in Systems and Controls 12
Topic titles: Computer Control Engineering
Optimal Control
Advanced Linear Systems and Control
Adaptive Control and Signal Processing
Logical Analysis of Hybrid Systems
Optimization in Energy Networks
Multi-Agent Systems
Engineering and Economics of Electric Power Systems
Nonlinear Dynamics, Chaos, and Control: How Systems Really Work
Electric Power Systems: Modeling, Analysis, and Control
Networked Control Systems
Stochastic Optimization
Nonlinear Systems

Circuits

Course Units
18-622 Advanced Digital Integrated Circuit Design 12
18-623 Analog Integrated Circuit Design 12
18-664 ULSI Technology Status and Roadmap for System on Chips and System in Package 12
18-721 Advanced Analog Integrated Circuits Design 12
18-723 RF IC Design and Implementation 12
18-725 Advanced Digital Integrated Circuit Design 12
18-726 Projects in Integrated Circuit Design: First Silicon 12
18-762 Circuit Simulation: Theory and Practice 12
18-764 Technology Foundations and Roadmap for System on Chip and System in Package Products 12
18-769 Design for Manufacturability in Nanometer Era 12

Special Topics Courses
18629 Special Topics in Circuits 12
Topic titles: Integrated Microsystems
Modeling and Design for Reliability – From Technology to Application
IC Design for Wireless Communication Systems
18729 Special Topics in Circuits 12
Topic titles: IC Technology: 3D System Integration (with VeSFETs)
18819 Special Topics in Applied Physics 12
Topic titles: Beyond CMOS Devices and Circuits

Computer Hardware Engineering

Course Units
15-740 Computer Architecture 12
15-745 Optimizing Compilers for Modern Architectures 12
15-843 Parallel Computing 12
18-625 ULSI Mobile Platform and Server Product Design 12
18-632 Introduction to Hardware Security 12
18-643 Reconfigurable Logic: Technology, Architecture and Applications 12
18-645 How to write fast code I 12
18-646 Low-Power System-on-Chip Architecture 12
18-663 Hardware Architectures for Machine Learning *(offered through Spring 2019) 12
18-667* Design of Integrated Embedded Systems  *(offered through Fall 2015) 12
18-740 Modern Computer Architecture and Design 12
18-742 Computer Architecture and Systems 12
18-743 Energy Aware Computing 12
18-745 Rapid Prototyping of Computer Systems 12
18-747* Wireless Device Architecture  *(offered through Fall 2019) 12
18-747* How to Write Low Power Code for the IoT *(offered through Fall 2021) 12
18-747 Data Center Computing 12
18-760 VLSI CAD: Logic to Layout 12
18-762 Circuit Simulation: Theory and Practice 12
18-765 Digital Systems Testing and Testable Design 12
18-765PP Digital Systems Testing and Testable Design 12

Special Topics Courses

Device Science and Nanofabrication

Course Units
18-610 Fundamentals of Modern CMOS Devices 12
18-614 Microelectromechanical Systems 12
18-615 Micro and Nano Systems Fabrication 12
18-616 Nano-Bio-Photonics 12
18-617 Memory Devices and Systems 12
18-669 Special Topics in IST: Micro/Nano Biomedical Devices 12
18-669 Special Topics in Integrated Systems Technology: Hacker Fab 12
18-712 Elements of Photonics for Communication Systems 12
18-715 Physics of Applied Magnetism 12
18-716 Advanced Applied Magnetism 12
18-817 Applied Physics: Fundamentals of Semiconductors and Nanostructures 12
24-615 Microfluidics 12
24-623 Molecular Simulation of Materials 12
24-628 Energy Transport and Conversion at the Nanoscale 12
24-751 Introduction to Solid Mechanics I 12
27-710 Quantum Mechanics of Materials 12
27-742 Processing and Properties of Thin Films 12
27-770 Electronic, Magnetic and Optical Properties 12
33-755 Quantum Mechanics I 12
33-759 Introduction to Mathematical Physics I 12
33-761 Classical Electrodynamics I 12
33-783 Theory of Solids I 12

Special Topics Courses
18669 Special Topics in Integrated Systems Technology 12
Topic titles: Applications Micro/Nano Biomedical Devices
Hacker Fab (Approved until F27) 
18819  Special Topics in Applied Physics  12
Topic titles: Applications of Lithographically
Introduction to Solar Arrays: Modeling, Analysis, and Design
Introduction to Quantum Computing (approved until S26)
Memory Devices and Technology
Micro and Nano Systems Fabrication
Neural Technology, Sensing, and Stimulation
Waves and Applications
Physical Sensors, Transducers and Instrumentation
Antennas for Wireless Communications
Ultrasonic Devices and Applications
Beyond CMOS Devices and Circuits
Introduction to Quantum Computing

Signal Processing and Communications

Course Units
15-862 Computational Photography 12
16-725
Medical Image Analysis
 12
42-630
Introduction to Neural Engineering (Approved until S26) 
 12
18-639 Policies of the Internet 12
18-650 Policies of Wireless Systems 12
18-690 Introduction to Neuroscience for Engineers 12
18-691 Digital Signal Processing 12
18-697 Statistical Discovery and Learning 12
18-697SV Statistical Discovery and Learning 12
18-698 Neural Signal Processing 12
18-741 Computer Networks 12
18-751 Applied Stochastic Processes 12
18-751SV Applied Stochastic Processes 12
18-752 Estimation, Detection and Learning 12
18-752PP Estimation, Detection and Learning 12
18-753 Information Theory and Coding 12
18-754 Error Control Coding 12
18-758 Wireless Communications 12
18-759 Wireless Networks 12
18-759PP Wireless Networks 12
18-781 Speech Recognition and Understanding 12
18-781SV Speech Recognition and Understanding 12
18-790 Wavelets and Multiresolution Techniques 12
18-791 Methods in Medical Imaging Analysis 12
18-792 Advanced Digital Signal Processing 12
18-793 Image and Video Processing 12
18-794 Introduction to Deep Learning and Pattern Recognition for Computer Vision 12
18-795 Bioimage Informatics 12
18-796PP Multimedia Communications: Coding, Systems, and Networking 12
18-797 Machine Learning for Signal Processing 12
18-798 Image, Video, and Multimedia 12
18-798PP Image, Video, and Multimedia 12

Special Topics Courses
18799 Special Topics in Signal Processing 12
Topic titles: Advanced Speech Lab
Design Implementation of Speech Recognition Systems
Biometric Recognition
Algebraic Signal Processing Theory
Network Science: Modeling and Inference
Compressive Sensing and Sparse Optimization
Cognitive Video
Advanced Machine Learning
Large Scale Stochastic Adaptive Systems
18858 Special Topics in Communications 6
Topic titles: Telecommunications Policy in Developing Countries
18859 Special Topics in Communications 12
Topic titles: Communication and Networking
Network Management and Control
Stochastic Geometry for Communication Networks
Emerging Topics in Wireless Networks
Wireless Networks and Mobile Systems: DARPA Spectrum Grand Challenge Edition (offered through Fall 2020)
Network Economics and Resource Allocation
18882 Special Topics in Energy Systems 12
Topic titles: Power Electronics
Microgrids and New Generation Power Systems
18883 Special Topics in Energy Systems 6
Topic titles: Photovoltaic Systems Engineering
18898 Special Topics in Signal Processing 12
Topic titles: Intro to Data-Science with Applications to Clinical Neural Data
Graph Signal Processing and Learning
18899 Special Topics in Signal Processing 6
Topic titles: Applied Time Series Analysis
Data and Inference (DI)
Applied Machine Learning (AML)
Data Science and Risk Management Applications

Software Systems and Computer Networking

Course Units
10-714 Deep Learning System (Approved until F25)  12
15-618 Parallel Computer Architecture and Programming (Approved until F25) 12
15-712 Advanced Operating Systems and Distributed Systems 12
15-721 Database System Design and Implementation 12
15-744 Computer Networks 12
15-829 Modeling and Performance Tools for Computer (Approved until S26) 12 
15-839 Mobile and Wireless Communications 12
15-849N Advanced Topics in Computer Systems: Machine Learning Systems (dual-categorization with Artificial Intelligence area)
17-755 Architectures for Software Systems 12
18-630 Introduction to Security and Policy 12
18-631 Introduction to Information Security 12
18-635 Web Application Security and Performance 12
18-636 Browser Security 12
18-637 Wireless Network Security 12
18-638 Mobile Security 12
18-641 Java for Smart Phone Development 12
18-642 Introduction to Software Engineering 12
18-644 Mobile Hardware for Software Engineers 12
18-646 How to write fast code II 12
18-647 Computational Problem Solving for Engineers (previously 18847G) 12
18-647 Connected Embedded Systems Architecture (offered through Spring 2019) 12
18-648 Real-Time Embedded Systems 12
18-649 Distributed Embedded Systems 12
18-651 Networked Cyber-Physical Systems 12
18-652 Foundations of Software Engineering 12
18-653 Software Architecture and Design 12
18-654SV Software Verification, Validation and Testing 12
18-655* Service Oriented Computing* 12
18-656SV Data Intensive Workflow Development for Software Engineers 12
18-657SV Decision Analysis and Engineering Economics for Software Engineers 12
18-658SV Software Requirements and Interaction Design 12
18-659SV Software Engineering Methods 12
18-709 Advanced Cloud Computing 12
18-713PP Optical Networks 12
18-730 Introduction to Computer Security 12
18-731 Network Security 12
18-732 Secure Software Systems 12
18-734 Foundations of Privacy 12
18-741

Computer Networks

12
18-744

Autonomous Driving 

12
18-746 Storage Systems 12
18-747 How to Write Low Power Code for the IoT 12
18-748 Wireless Sensor Networks 12
18-749 Building Reliable Distributed Systems 12
18750 Wireless Networking and Applications 12
18-756 Packet Switching and Computer Networks 12
18-757 Network Management and Control 12
18-759 Wireless Networks 12
18-842 Distributed Systems 12
18-843 Mobile and Pervasive Computing 12
18-845 Internet Services 12

*This course is dormant.

Special Topics Courses
15829 Special Topics in Software Systems 12
Topic titles: Programmable Networks
18739 Special Topics in Security 12
Topic titles: Foundations of Security and Privacy
Vulnerability, Defenses, and Malware Analysis
Network Security and Management
Formal Foundations of Software Security
Security and Fairness of Deep Learning
18847 Special Topics in Computer Systems 12
Topic titles: Foundations of Cloud and Machine Learning Infrastructure
Computing for Engineers
Wireless Software System Architecture
18848 Special Topics in Embedded Systems 12
Topic titles: Networked Cyber-Physical Systems
Sports Technology
18859 Special Topics in Communications 12
Topic titles: Wireless Networks and Mobile Systems: DARPA Spectrum Grand Challenge Edition (offered through Fall 2020)
Software-Defined Networking and Network Functions Virtualization
Distributed Systems and Networking

Other

Graduate courses in other departments at Carnegie Mellon may be counted for the "Other" area by petition to the GSC.

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