Department of Electrical and Computer Engineering



  • H. Vincent Poor (acting) (fall)
  • James C. Sturm

Associate Chair

  • Claire F. Gmachl

Director of Undergraduate Studies

  • Prateek Mittal

Director of Graduate Studies

  • Niraj K. Jha

Executive Committee

  • Claire F. Gmachl, Electrical & Comp Engineering
  • Andrew A. Houck, Electrical & Comp Engineering
  • Sharad Malik, Electrical & Comp Engineering
  • Peter J. Ramadge, Electrical & Comp Engineering
  • James C. Sturm, Electrical & Comp Engineering
  • Naveen Verma, Electrical & Comp Engineering


  • Ravindra N. Bhatt
  • Stephen Y. Chou
  • Jason W. Fleischer
  • Claire F. Gmachl
  • Andrea J. Goldsmith
  • Andrew A. Houck
  • Niraj K. Jha
  • Antoine Kahn
  • Sanjeev R. Kulkarni
  • Sun-Yuan Kung
  • Stephen A. Lyon
  • Sharad Malik
  • Prateek Mittal
  • H. Vincent Poor
  • Paul R. Prucnal
  • Peter J. Ramadge
  • Mansour Shayegan
  • James C. Sturm
  • Naveen Verma
  • Pramod Viswanath

Associate Professor

  • Jason D. Lee
  • Barry P. Rand
  • Alejandro W. Rodriguez
  • Kaushik Sengupta
  • Jeffrey D. Thompson
  • Hakan E. Türeci
  • Mengdi Wang
  • David Wentzlaff
  • Gerard Wysocki
  • Nathalie P. de Leon

Assistant Professor

  • Maria Apostolaki
  • Minjie Chen
  • Jaime Fernandez Fisac
  • Tian-Ming Fu
  • Yasaman Ghasempour
  • Sarang Gopalakrishnan
  • Chi Jin
  • Saien Xie

Associated Faculty

  • Amir Ali Ahmadi, Oper Res and Financial Eng
  • Craig B. Arnold, Mechanical & Aerospace Eng
  • David I. August, Computer Science
  • Jianqing Fan, Oper Res and Financial Eng
  • Kyle A. Jamieson, Computer Science
  • Gillat Kol, Computer Science
  • Kai Li, Computer Science
  • Lynn Loo, Chemical and Biological Eng
  • Margaret R. Martonosi, Computer Science
  • Jason Petta, Physics
  • Jennifer Rexford, Computer Science


  • Hossein Valavi

Visiting Associate Professor

  • Tirza S. Routtenberg

Visiting Lecturer

  • Jonathan Hodges
  • Ali Javadi-Abhari
  • Hamed Rahmani
For a full list of faculty members and fellows please visit the department or program website.

Program Information

Information and Departmental Plan of Study

The Department of Electrical and Computer Engineering offers an academic program of study spanning a wide range of disciplines, connecting the broad fields of information, data, communication, and computing systems to circuits, energy, and the physical world. To prepare students for a future beyond Princeton, the three main themes of the program are (i) a broad foundation, (ii) depth and expertise in a concentration, and (iii) independent work and design. 

All students begin with a unifying foundation, after which areas of specialization range from information and data sciences, computing systems, privacy and security, and communication technology, to robotics and autonomous cyberphysical systems, to semiconductor electronic and optoelectronic devices, materials and nanotechnology, photonics and optics, and quantum computing, to circuits with energy and biomedical applications. Students may select one of a set of suggested concentrations, or tailor their own in consultation with their faculty adviser to suit special interests. The ECE program is accredited by the Engineering Accreditation Commission of ABET.

Students enter the department with a variety of career objectives in mind. Some intend to enter industry directly upon graduation or to continue their studies in graduate school. Others wish to use the electrical and computer engineering program as background for careers in other fields ranging from business to law to medicine. Flexibility in the undergraduate program allows a wide variety of objectives to be achieved and to allow a student to see a wide cross-section of electrical and computer engineering before deciding on an area of concentration. Similarly, students may also formally combine electrical and computer engineering with studies in a wide range of disciplines outside of ECE, from other engineering and science fields to broader topics connecting to society in many ways. (See Interdisciplinary Programs below.)

General Requirements

All candidates for the B.S.E. are required to satisfy the general University requirements and the School of Engineering and Applied Science requirements. The SEAS computing requirement should be fulfilled in the first year if possible.

Each student's academic program must have depth in at least one area plus a reasonable degree of breadth to produce a sound basis for future development. All programs are required to have a strong design component and a strong engineering science component. The specific plan of study is determined in consultation with the student's academic adviser, taking into account ABET program guidelines. All such plans must include the following:

1. Foundations: Electrical and Computer Engineering 201, 203, and at least one of 206 or 308. This requirement is normally satisfied by the end of  sophomore year, although 206 and 308 can be delayed if foundational courses in related disciplines make this difficult. These courses are all open to all qualified first-year students.

2. Core: Electrical and Computer Engineering 302. This requirement is normally satisfied by the end of junior year.

3. Mathematics: At least one upper-level mathematics course. This may include: MAE305/MAT301, MAE306/MAT302, ORF309/MAT309, COS 340 or any other 300-/400-level mathematics course. The course selected to satisfy this requirement may not be counted toward the concentration requirement, toward the breadth requirement, or as a departmental. 

4. Concentration: Three courses in a chosen concentration. (See Program of Study.)

5. Breadth: At least one 300-/400-level ECE elective course in an area distinct from the area of concentration. Some COS and PHY courses are also possible. Note: ORF 309 cannot be used to satisfy this requirement.

6. Engineering science: An engineering course with a significant scientific component must be taken outside of ECE to satisfy this requirement. Many courses can be used to satisfy this requirement; note, however, that a course comprised largely of mathematics or applied mathematics does not satisfy the requirement. The course used to satisfy the engineering science requirement cannot also be used to satisfy the concentration requirement or the breadth requirement, nor can it be counted as a departmental requirement. The following is a non-exhaustive list of possibilities: COS 217, 226, 320, 402, 423, 425, 451, 487; MAE 206, 221, 222, 324, 328, 344, 345, 433, 434; CEE 205, 207, 305, 471; MSE 301, 302; CBE 245, 246, 341, 415, 447; ORF 307, 311, 405, 406, 417.

7. Design: At least one upper-level electrical and computer engineering course with substantial design content beyond ECE 302 must be selected. These courses include ECE 375, 404, 458, 462, 475, 482 and COS 426, 436. This requirement may also be satisfied through junior work or a senior thesis with a substantial design component.

8. Balance and completeness: ECE students must take at least two upper-level (300- or 400-level) technical courses in each of the last four terms, called "departmental" courses. Of the eight departmental courses, at least five must be ECE courses and normally include 302 and the senior thesis (497, 498). The remaining three courses can be taken in CEE, CHM, CBE, COS, EEB, ECE, ENE, MAE, MAT, MOL, MSE, NEU, ORF, or PHY. Courses in or cross-listed with electrical and computer engineering counted toward this requirement must be closely related to the student's academic program.

Note: Junior independent work (397, 398) and the senior thesis (497, 498) cannot be used to fulfill the breadth or concentration requirements.

9. Senior thesis: A two-term senior thesis is required. Students must enroll in ECE 497 (fall) and ECE 498 (spring). A grade will be given at the end of each term. A senior thesis must include an oral presentation to the faculty at the end of each term.

10. Oral presentation: This requirement is normally satisfied by the senior thesis presentation at the end of the senior year. The midyear thesis presentation does not satisfy the requirement.

Program of Study

After the foundational courses, each student must develop depth in a coherent area of concentration. Concentrations may be interdisciplinary and include courses from other departments in the School of Engineering and Applied Science, as well as from related fields such as biology, chemistry, neuroscience, physics, and others. However, the courses must form a coherent theme, and normally, two of the courses will be ECE courses or designated equivalents. ORF 309/MAT 380 may be used to satisfy either the upper-level mathematics requirement or the concentration requirement, but not both. The current list of standard concentrations may be found at

Graduate courses (500 level) are open to undergraduates after the completion of a permission form containing the signatures of the instructor and director of undergraduate studies.

Independent Work

Independent projects outside normal, structured lecture or laboratory courses are a valuable educational experience, and are most like what a student will experience in life after academia. Most students find them intellectually challenging but also extremely fulfilling. The projects may be done in collaboration with a faculty member's research program, or they may be "self-driven." Each student doing independent work will be required to give a presentation during a department-organized session given at the end of each term. Sophomore and junior independent work is highly encouraged (ECE 297, 298, 397, 398) and a two-semester thesis is required.

Interdisciplinary Programs. Interested students may combine their work in electrical and computer engineering with that in other departments through interdisciplinary certificate programs such as robotics and intelligent systems, computing applications, optimization and quantitative decision science, engineering physics, materials science and engineering, neuroscience, engineering biology, environmental studies, applied and computational mathematics, sustainable energy, and technology and society. Students fulfilling a certificate program will receive a special certificate upon graduation. Concentrators should consult with their advisers to develop an ECE program that best combines their ECE interest with the interdisciplinary program. Additional materials on a certificate program may be obtained by contacting the director of the program.

Further Information. Additional information on the departmental academic program and requirements is given in the electrical and computer engineering handbook, available from the departmental undergraduate office, Room B304, Engineering Quadrangle, or online at Prospective concentrators in electrical and computer engineering should consult the director of undergraduate studies as early as possible for purposes of planning an academic program.


ECE 102 New Eyes for the World: Hands-On Optical Engineering (also
EGR 103
) Not offered this year SEL

This lab course introduces students to modern topics of engineering optics. Teams of students will carry out four different projects: holography, lasers, free-space optical communication, and nanotechnology. Teaches the foundations and broader societal issues of these technologies. The laboratory sessions involve hands-on training as well as experimentation and exploration. Skills acquired in this course include computer programming of user interfaces, data acquisition and interpretation, wet chemical processing, and electronics design assembly. One 90-minute lecture, one three-hour laboratory. Instructed by: C. Gmachl

ECE 201 Information Signals Spring SEL

Signals that carry information, e.g. sound, images, sensors, radar, communication, robotic control, play a central role in technology and engineering. This course teaches mathematical tools to analyze, manipulate, and preserve information signals. We discuss how continuous signals can be perfectly represented through sampling, leading to digital signals. Major focus points are the Fourier transform---how, when, and why to use it, linear time-invariant systems, modulation, and stability. We use MATLAB for design projects. Prerequisite: knowledge of elementary calculus. Three lectures, one laboratory. Instructed by: Staff

ECE 203 Electronic Circuit Design, Analysis and Implementation Spring SEL

Introduction to electronic circuits and systems. Methods of circuit analysis to create functions from devices, including resistors, capacitors, inductors, diodes, and transistors, in conjunction with op-amps. Quantitative focus on DC and higher-frequency signals using linear systems theory. A major emphasis on intuition, with labs organized as mini projects (1. Touch-screen controller, 2. Radio, 3. Brain-machine interface), where students pursue design (using op-amps and micro controllers), simulations (using SPICE), and analysis (both by hand and using Python). Instructed by: Staff

ECE 206 Contemporary Logic Design (also
COS 306
) Fall SEL

Logic circuits are at the heart of modern computing and communication chips. These deliver valuable societal solutions in several key areas: in information retrieval and processing using smart phones and cloud computing; in smart sensing and control as in emerging chips for human health care; and in critical security applications such as protecting infrastructures like the internet and energy production/distribution systems. Foundational aspects of logic design; contemporary design principles and practices. Three lectures, one laboratory. Prerequisite: an introductory programming course, or equivalent programming experience. Instructed by: S. Malik

ECE 218 Learning Theory and Epistemology (See PHI 218)

ECE 222A The Computing Age (also
EGR 222A
) Not offered this year

The past several decades have seen an exponential growth in computing as reflected in modern computers as well as consumer products such as music/video players and cell phones. This course will explore the reasons for this growth through studying the core principles of computing. It will cover representation of information including video and music, the design of computers and consumer devices, and their efficient implementation using computer chips. Finally, it will examine the technological factors that will likely limit future growth and discuss the societal impact of this outcome. Two 90-minute lectures, one preceptorial. Instructed by: Staff

ECE 222B The Computing Age (also
EGR 222B
) Not offered this year SEL

The past several decades have seen an exponential growth in computing as reflected in modern computers as well as consumer products such as music/video players and cell phones. This course will explore the reasons for this growth through studying the core principles of computing. It will cover representation of information including video and music, the design of computers and consumer devices, and their efficient implementation using computer chips. Finally, it will examine the technological factors that will likely limit future growth and discuss the societal impact of this outcome. Two 90-minute lectures, one three-hour laboratory. Instructed by: Staff

ECE 301 Designing Real Systems Not offered this year

This course focuses on the science, engineering, and design of the highly integrated systems that dominate many of today's devices. Analysis of systems, subsystems, and basic principles will be covered, with an emphasis on hardware-software optimization, sampling and digitization, signal and noise, feedback and control, and communication. Prerequisites: ELE 201, ELE 203, ELE 206. Instructed by: Staff

ECE 302 Robotic and Autonomous Systems Lab Spring

Comprehensive laboratory-based course in electronic system design and analysis. Covers formal methods for the design and analysis of moderately complex real-world electronic systems. Course is centered around a semester-long design project involving a computer-controlled vehicle designed and constructed by teams of two students. Integrates microprocessors, communications, and control. Three lectures, one laboratory; open laboratory during final month. Prerequisites: 201 and 203 or permission of instructor. Instructed by: Staff

ECE 308 Electronic and Photonic Devices Fall SEL

Explores ways in which semiconductor devices harness and control electrons and photons to generate, store or transmit information. The basics of semiconductor electronics and photonics are introduced. Discusses diodes, transistors, LEDs, solar-cells, and lasers, which form the foundations of integrated circuits, microchips, displays, cameras, etc. Nanotechnology, a recent addition to devices and systems, is introduced. Laboratory: fundamentals of micro-and nano-fabrication, fabrication of Si integrated circuits, semiconductor light emitters, quantum devices. Prerequisites: CHM 201 or 203. Co-requisite: PHY 102 or 104 or EGR 153. Instructed by: A. Kahn

ECE 341 Solid-State Devices Not offered this year

The physics and technology of solid-state devices. Topics include: p-n junctions and two terminal devices, transistors, silicon controlled rectifiers, field effect devices, silicon vidicon and storage tubes, metal-semiconductor contacts and Schottky barrier devices, microwave devices, junction lasers, liquid crystal devices, and fabrication of integrated circuits. Three hours of lectures. Prerequisite: 308 or the equivalent. Instructed by: Staff

ECE 342 Principles of Quantum Engineering Spring

Fundamental principles of solid-state and optoelectronic device operation. Principles of quantum mechanics (Schroedinger equation, operator and matrix methods) important to a basic understanding of solid-state and quantum electronics. Topics in statistical mechanics, including distribution functions, density of states, Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. Applications to atoms, molecules, lasers, and solids, with special emphasis on semiconductors. Three hours of lectures. Prerequisites: PHY 103/105 and 104/106 or EGR 151/153. Instructed by: R. Bhatt

ECE 345 Introduction to Robotics (See MAE 345)

ECE 351 Foundations of Modern Optics Fall

This course should provide the students with a broad and solid background in electromagnetics, including both statics and dynamics, as described by Maxwell's equations. Fundamental concepts of diffraction theory, Fourier optics, polarization of light, and geometrical optics will be discussed. Emphasis will be on basic engineering principles, and applications will be discussed throughout. Examples include cavities, waveguides, antennas, fiber optic communications, and imaging. Prerequisite: PHY 104 or EGR 153. Instructed by: H. Türeci, G. Wysocki

ECE 352 Physical Optics Not offered this year

Fundamental and practical aspects of physical optics. Lenses and ray optics, lens maker's formula, wave propagation, Fourier optics, Gaussian beams are all considered. Design and use of practical optical systems including optical beam steering in medicine, fiber optics. Three hours of lectures. Prerequisite: PHY 104. Instructed by: J. Fleischer

ECE 375 Computer Architecture and Organization (See COS 375)

ECE 381 Networks: Friends, Money and Bytes (also
COS 381
) Not offered this year

This course is oriented around 20 practical questions in the social, economic, and technological networks in our daily lives. How does Google sell ad spaces and rank webpages? How does Netflix recommend movies and Amazon rank products? How do I influence people on Facebook and Twitter? Why doesn't the Internet collapse under congestion, and does it have an Achilles heel? Why does each gigabyte of mobile data cost $10, but Skype is free? How come Wi-Fi is slower at hotspots than at home, and what is inside the cloud of iCloud? In formulating and addressing these questions, we introduce the fundamental concepts behind the networking industry. Instructed by: Staff

ECE 386 Cyber Security (also
EGR 386
) Not offered this year SEN

The technology underlying secure transactions and safe interactions in a public Internet and wireless world. Humans interact daily with each other, with information, and with services through cyberspace. Topics include policy, economic, and social issues related to cyber security needs such as confidentiality, data integrity, user authentication, trust, non-repudiation, availability, privacy and anonymity, case studies in electronic commerce, denial of service attacks, viruses and worms, digital rights management, surveillance, and cyber-terrorism. Two 90-minute lectures. Instructed by: Staff

ECE 391 The Wireless Revolution: Telecommunications for the 21st Century (also
EGR 391
) Not offered this year SEN

This interdisciplinary course addresses technological, regulatory, economic, and social issues arising in the rapidly developing field of wireless communications. The course introduces students to a major technological trend that will be a significant force in worldwide commercial and social development throughout the 21st century. Prerequisites: MAT 103 or permission of instructor. Two 90-minute lectures. Instructed by: Staff

ECE 396 Introduction to Quantum Computing (also
COS 396
) Fall

This course will introduce the matrix form of quantum mechanics and discuss the concepts underlying the theory of quantum information. Some of the important algorithms will be discussed, as well as physical systems which have been suggested for quantum computing. Prerequisite: Linear algebra at the level of MAT 202, 204, 217, or the equivalent. Instructed by: H. Türeci

ECE 397 Junior Independent Work Fall

Provides an opportunity for a student to concentrate on a "state-of-the-art" project in electrical engineering. Topics may be selected from suggestions by faculty members or proposed by the student. The final choice must be approved by the faculty member. Instructed by: P. Prucnal

ECE 398 Junior Independent Work Spring

Provides an opportunity for a student to concentrate on a "state-of-the-art" project in electrical engineering. Topics may be selected from suggestions by faculty members or proposed by the student. The final choice must be approved by the faculty member. Instructed by: P. Prucnal

ECE 404 Mixed-signal Circuits and Systems Not offered this year

Start by analyzing biological systems to understand the origins of some of the signals that they present. Develop circuit models of these systems to determine what instrumentation circuits are required at the interface so that the signals can be reliably acquired. Study analog circuit topologies based on MOSFETs for low-noise instrumentation and processing of the signals. Study digital topologies based on MOSFETs for extensive computations on the biological signals. Analyze the trade-offs between the analog and digital topologies. Emphasis is on design and analysis using circuit simulators. Instructed by: Staff

ECE 411 Sequential Decision Analytics and Modeling (See ORF 411)

ECE 431 Solar Energy Conversion (See ENE 431)

ECE 432 Information Security (See COS 432)

ECE 441 Solid-State Physics I (also
ENE 441
) Fall

An introduction to the properties of solids. Theory of free electrons--classical and quantum. Crystal structure and methods of determination. Electron energy levels in a crystal: weak potential and tight-binding limits. Classification of solids--metals, semiconductors, and insulators. Types of bonding and cohesion in crystals. Lattice dynamics, phonon spectra, and thermal properties of harmonic crystals. Three hours of lectures. Prerequisite: 342, or PHY 208 and 305, or equivalent. Instructed by: M. Shayegan

ECE 442 Solid-State Physics II (also
ENE 442
) Not offered this year

Electronic structure of solids. Electron dynamics and transport. Semiconductors and impurity states. Surfaces and interfaces. Dielectric properties of insulators. Electron-electron, electron-phonon, and phonon-phonon interactions. Anharmonic effects in crystals. Magnetism. Superconductivity. Alloys. Three hours of lectures. Prerequisites: 441 or equivalent. Instructed by: Staff

ECE 453 Optical and Quantum Electronics Fall

Electromagnetic waves. Gaussian beams. Optical resonators. Interaction of light and matter. Lasers. Mode locking and Q-switching in lasers. Three hours of lectures. Prerequisites: ELE 351 or PHY 304 or permission of instructor. Instructed by: Staff

ECE 455 Optical and Photonic Systems for Environmental Sensing (also
CEE 455
MAE 455
MSE 455
) Spring

This course is designed to give juniors, seniors, and interested graduate students a comprehensive and interdisciplinary introduction into mid-infrared sensing, its applications, and its technological foundations. Topics include: materials, light sources, lasers and detectors for the mid-infrared; spectroscopy and sensing; sensing systems and sensor networks. It addresses such important issues as global warming, policy making, engineering solutions to global challenges, environmental sensing, breath analysis and health applications, and sensing in homeland security. Two 90-minute lectures. Instructed by: Staff

ECE 458 Photonics and Light Wave Communications Fall

Introduction to fiber-optic communication systems. Optical detectors and receivers. Design and performance of direct detection systems. Coherent light wave systems. Multichannel WDM communication systems. Optical amplifiers. Soliton communication systems. Three hours of lectures. Prerequisite: 351 or 352. Instructed by: P. Prucnal

ECE 461 Design with Nanotechnologies Not offered this year

Introduction to nanotechnologies; threshold logic/majority logic and their applications to RTDs, QCA and SETs; nanowire based crossbars and PLAs; carbon nanotube based circuits; double-gate CMOS-based circuits; reversible logic for quantum computing; non-volatile memory; nanopipelining; testing; and defect tolerance. Two 90-minute lectures. Prerequisite: ELE 206. Instructed by: Staff

ECE 462 Design of Very Large-Scale Integrated (VLSI) Systems (also
COS 462
) Fall

Analysis and design of digital integrated circuits using deep sub-micron CMOS technologies as well as emerging and post-CMOS technologies (Si finFETs, III-V, carbon). Emphasis on design, including synthesis, simulation, layout and post-layout verification. Analysis of energy, power, performance, area of logic-gates, interconnect and signaling structures. Instructed by: H. Valavi

ECE 465 Switching and Sequential Systems Not offered this year

Theory of digital computing systems. Topics include logic function decomposition, reliability and fault diagnosis, synthesis of synchronous circuits and iterative networks, state minimization, synthesis of asynchronous circuits, state-identification and fault detection, finite-state recognizers, definite machines, information lossless machines. Three hours of lectures. Prerequisite: 206. Instructed by: S. Kung

ECE 466 Digital System Testing Not offered this year

Component-level issues related to testing and design/synthesis for testability of digital systems. Topics include test generation for combinational and sequential circuits, design and synthesis for testability, and built-in self-test circuits. Three hours of lectures. Prerequisite 206. Instructed by: Staff

ECE 469 Human-Computer Interface Technology (See COS 436)

ECE 475 Computer Architecture (also
COS 475
) Spring

An in-depth study of the fundamentals of modern processor and system design. Students will develop a strong practical and theoretical background in the technical and economic issues that govern the design of computer architectures and implementations. The course will emphasize the skills required to design and evaluate current and future systems. Three hours of lectures. Prerequisites: 206, 375. Instructed by: D. Wentzlaff

ECE 482 Digital Signal Processing

The lectures will cover: (1) Basic principles of digital signal processing. (2) Design of digital filters. (3) Fourier analysis and the fast Fourier transform. (4) Roundoff errors in digital signal processing. (5) Applications of digital signal processing. Instructed by: S. Kung

ECE 486 Transmission and Compression of Information (also
APC 486

An introduction to lossless data compression algorithms, modulation/demodulation of digital data, error correcting codes, channel capacity, lossy compression of analog and digital sources. Three hours of lectures. Prerequisites: 301, ORF 309. Instructed by: Staff

ECE 488 Image Processing Not offered this year

Introduction to the basic theory and techniques of two- and three-dimensional image processing. Topics include image perception, 2-D image transforms, enhancement, restoration, compression, tomography and image understanding. Applications to HDTV, machine vision, and medical imaging, etc. Three hours of lectures, one laboratory. Instructed by: P. Ramadge

ECE 491 High-Tech Entrepreneurship (See EGR 491)

ECE 497 Senior Independent Work Fall

Senior Thesis Course. The student has the opportunity to do a self driven project by proposing a topic and finding a faculty member willing to supervise the work, or, the student may do a project in conjunction with a faculty member's research. A second reader will be required for both the midterm report and final thesis report. Students will be required to enroll in ELE 498 in the spring. Instructed by: P. Prucnal

ECE 498 Senior Independent Work Spring

Senior Thesis Course. A senior thesis presentation will be held at the end of spring semester. The unbound senior thesis must be turned in to the ELE Undergraduate Office on the University's established senior thesis submission deadline. Instructed by: P. Prucnal