Department of Chemical and Biological Engineering

  • Chair

    Athanassios Z. Panagiotopoulos

  • Departmental Representative

    A. James Link

  • Director of Graduate Studies

    Rodney D. Priestley

  • Professor

    Ilhan A. Aksay

    Jay B. Benziger

    Pablo G. Debenedetti

    Bruce E. Koel

    A. James Link

    Lynn Loo

    Celeste M. Nelson

    Athanassios Z. Panagiotopoulos

    Robert K. Prud'homme

    Richard A. Register

    Stanislav Y. Shvartsman, also Lewis-Sigler Institute for Integrative Genomics

    Sankaran Sundaresan

  • Associate Professor

    Clifford P. Brangwynne

    Mark P. Brynildsen

    Rodney D. Priestley

  • Assistant Professor

    José L. Avalos, also Andlinger Center for Energy and the Environment

    Pierre-Thomas Brun

    Sujit S. Datta

    Michele L. Sarazen

  • Associated Faculty

    Ian C. Bourg, Civil and Environmental Engineering, Princeton Environmental Institute

    Emily A. Carter, Mechanical and Aerospace Engineering, Applied and Computational Mathematics

    Daniel J. Cohen, Mechanical and Aerospace Engineering

    Sabine Petry, Molecular Biology

    Daniel A. Steingart, Mechanical and Aerospace Engineering, Andlinger Center for Energy and the Environment

    Howard A. Stone, Mechanical and Aerospace Engineering

    Jared E. Toettcher, Molecular Biology

    Claire E. White, Civil and Environmental Engineering

    Martin Wühr, Molecular Biology, Lewis-Sigler Institute for Integrative Genomics

  • Visiting Professor

    Nancy Lape, William R. Kenan, Jr., Visiting Professor for Distinguished Teaching

Information and Departmental Plan of Study

Prerequisites

The first-year program in engineering or its equivalent.

General Requirements

In order to qualify for the B.S.E. degree in the Department of Chemical and Biological Engineering, a student must satisfy the requirements of the School of Engineering and Applied Science and must choose courses during the sophomore, junior, and senior years to provide a core knowledge of chemical and biological engineering and advanced knowledge in an area of concentration. The advanced science and core chemical and biological engineering courses in the sophomore and junior years provide the fundamental tools of thermodynamics, transport processes, and reactor analysis. In the spring semester of the junior year, students take a laboratory-based course that utilizes core chemical and biological engineering knowledge. In the senior year, students undertake an in-depth design analysis with state-of-the-art design and optimization tools. Students can tailor their specific interests in chemical and biological engineering by pursuing an area of concentration that culminates with a senior thesis project. The areas of concentration, reflective of the practice of modern chemical and biological engineering, include bioengineering and biotechnology; materials and product engineering; energy and environmental engineering; optimization, dynamics, and information technology; entrepreneurship and management; and science and engineering for new technologies. The program of study is accredited as a program in chemical engineering by the Engineering Accreditation Commission of ABET, http://www.abet.org. Students with special interests should consult the section on special programs and options. Total courses: 36.

Departmental Requirements

Chemical and Biological Engineering Core

The nine courses listed below are required of all chemical and biological engineering majors:

245 Introduction to Chemical and Biochemical Engineering Principles
246 Thermodynamics
250 Separations in Chemical Engineering and Biotechnology
341 Mass, Momentum, and Energy Transport
346 Chemical Engineering Laboratory
441 Chemical Reaction Engineering
442 Design, Synthesis, and Optimization of Chemical Processes
451, 452 Independent Work or 454 Senior Thesis

Most students carry out a two-term senior thesis. Students must complete a two-term thesis for departmental honors. Students who elect one term of independent work are required to take an additional chemical and biological engineering elective at the 300 level or above.

Mathematics Requirement

MAE 305 Mathematics in Engineering I

Chemistry Requirement

CHM 201 General Chemistry I, or CHM 207 Advanced General Chemistry: Materials Chemistry
CHM 202 General Chemistry II, or CHM 215 Advanced General Chemistry: Honors Course
CHM 301 Organic Chemistry I: Biological Emphasis

Molecular Biology Requirement

MOL 214 Introduction to Cellular and Molecular Biology

Advanced Science Requirements

Advanced Chemistry. The advanced chemistry course provides a greater depth in the underlying science of chemistry. The course may be any 300-level-or-above chemistry course, including those cross-listed by the chemistry department. With the approval of the departmental representative, the advanced chemistry requirement may be selected from another science department.

Advanced Chemical and Biological Engineering. One advanced chemical engineering course is also required. This can be any 300-level-or-above course (excluding independent work) offered by the Department of Chemical and Biological Engineering.

Societal Impact Requirement

Of the seven required Humanities and Social Science electives, undergraduates in chemical and biological engineering must take at least one course in the Ethical Thought and Moral Values area (EM)

Program of Study

In addition to the requirements above, students are required to designate an area of concentration and take three courses from the approved lists below in that area of concentration. The senior independent work is usually undertaken within the area of concentration. In addition, students are required to take at least one course each from two of the advanced areas outside their area of concentration to provide technical diversity. (Note: An asterisk indicates one-time-only courses.)

ABET requires chemical engineering students to complete a minimum of 12 engineering topic courses. This is satisfied by completing the nine CBE core courses (including the double credit thesis), plus the following: the required advanced chemical engineering course, and at least two program electives chosen from CBE, CEE, COS, EGR*,ELE, MAE, MSE, or ORF that are on the approved list of courses in the areas of concentration.

*EGR courses that are non-credit do not count for this requirement.

Bioengineering and Biotechnology

CBE 419 Enzymes
CBE 433 Introduction to the Mechanics and Dynamics of Soft Living Matter
CBE 438/MOL 438 Biomolecular Engineering
CBE 439 Quantitative Physiology and Tissue Design
CBE 440 The Physical Basis of Human Disease
CBE 447 Metabolic Engineering
CHM 440 Drug Discovery in the Genomics Era
CHM 538 Topics in Biological Chemistry - Chemistry Tools to Study Biological Systems
CHM 542 Principles of Macromolecular Structure: Protein Folding, Structure and Design
CHM 544/ENV 544 Metals in Biology
EEB 320/MOL 330 Molecular Evolutionary Genetics
EEB 325 Mathematical Modeling in Biology and Medicine
EEB 327/MOL327 Immune Systems: From Molecules to Populations
ENE 318/ CBE 318 Fundamentals of Biofuels
GEO 428 Biological Oceanography
ISC 326/EEB 326/MOL 326 Human Genomics: The Past, Present, and Future of the Human Genome
MAE 344 Biomechanics and Biomaterials: From Cells to Organisms
MOL 340 Molecular and Cellular Immunology
MOL 342 Genetics
MOL 345/CHM 345 Biochemistry
MOL 348 Cell and Developmental Biology
MOL 433/CBE 434 Biotechnology
MOL 459 Viruses: Strategy and Tactics
MOL 423 Molecular Basis of Cancer
NEU 201/PSY 258 Fundamentals of Neuroscience
NEU 202/PSY 259 Introduction to Cognitive Neuroscience
NEU 408/MOL 408/PSY 404 Cellular and Systems Neuroscience
NEU 437/MOL 437/PSY 437 Computational Neuroscience
PSY 406 Functional Neuroanatomy
PSY 407 Developmental Neuroscience
QCB 511/CBE 511 Modeling Tools for Cell and Developmental Biology
QCB 455/COS 455 Introduction to Genomics and Computational Molecular Biology

Entrepreneurship and Management

CBE 260/EGR 260 Ethics and Technology: Engineering in the Real World
CEE 334/ WWS 452/ ENV 334/ ENE 334 Global Environmental Issues
CEE 460 Risk Assessment and Management
CHV 331/ WWS 372 Ethics and Public Health
COS 432 Information Security
ECO 310 Microeconomic Theory: A Mathematical Approach
ECO 311 Macroeconomics: A Mathematical Approach
EGR 437/MAE 437/ELE 437 Innovation Process Leadership
EGR 492 Radical Innovation in Global Markets
EGR 494 Leadership Development for Business
EGR 495 Special Topics in Entrepreneurship
EGR 497 Entrepreneurial Leadership
ELE 491 High-Tech Entrepreneurship
ENV 324 Environmental Entrepreneurship
GEO 366/ENV 339/WWS 451/ ENE 366 Climate Change: Scientific Basis, Policy Implications
ORF 245 Fundamentals of Engineering Statistics
ORF 335 Introduction to Financial Engineering
ORF 360 Decision Modeling in Business Analytics
ORF 435 Financial Risk Management
WWS 327/CHM 443 Pharmaceutical Research and Health Policy

Energy and Environmental Technology

AST 309/MAE 309/PHY 309 Science and Technology of Nuclear Energy: Fission and Fusion
CBE 335/ MAE 338/ ENV 335 The Energy Water Nexus
CEE 207/ENV 207 Introduction to Environmental Engineering
CEE 304/ ENE 304/ ENV 300 Environmental Implications of Energy Technology
CEE 306 Hydrology
CEE 308 Environmental Engineering Laboratory
CEE 311/CHM 311/GEO 311 Global Air Pollution
CEE 334/ WWS 452/ ENV 334/ ENE 334 Global Environmental Issues
CEE 471 Introduction to Water Pollution Technology
CEE 474/ENV 474 Special Topics in Civil and Environmental Engineering - Design and Construction of Environmental Sensors
CEE 477/ ENE 477 Engineering Design for Sustainable Development
CHM 333/ENV 333 Chemistry of the Environment
ECO 429 Issues in Environmental and Natural Resource Economics
ELE 431 Solar Energy Conversion
ENE 414 Renewable Energy Systems
ENE 318/ CBE 318 Fundamentals of Biofuels
ENV 201a, 201b Fundamentals of Environmental Studies: Population, Land Use, Biodiversity, Energy
ENV 202a, 202b Fundamentals of Environmental Studies: Climate, Air Pollution, Toxics, and Water
ENV 204 Global Warming: Causes, Consequences, Policy Responses
ENV 305 Topics in Environmental Studies- Hormonally Active Pollutants
ENV 324 Environmental Entrepreneurship
ENV 531/GEO 531/CEE 583 Topics in Energy and the Environment: Intro to Petroleum Engineering
GEO 220a or 220b Weather and Climate
GEO 322 Biogeochemical Cycles and Global Change
GEO 360/ ENV 356 Geochemistry of the Human Environment
GEO 363/CHM 331/ENV 331 Environmental Geochemistry: Chemistry of the Natural Systems
GEO 364/ CHM 364 Earth Chemistry: Majors Realms of the Planet
GEO 366/ENV 339/ WWS 451/ ENE 366 Climate Change: Scientific Basis, Policy Implications
GEO 418/CHM 418 Environmental Aqueous Geochemistry
GEO 423/CEE 423 Dynamic Meterology
GEO 424/CEE 424/ENE 425 Introductory Seismology
GEO 470/CHM 470 Environmental Chemistry of Soils
MAE 328/EGR 328/ENV 328 Energy for a Greenhouse-Constrained World
MAE 424/ ENE 424 Energy Storage Systems
MAE 427 Energy Conversion and the Environment: Transportation Applications

Materials and Product Engineering

CBE 415/CHM 415 Polymers
CBE 422 Molecular Modeling Methods
CBE 433 Introduction to the Mechanics and Dynamics of Soft Living Matter
CBE 526/ CHM 527/ MSE 526 Surface Science: Processes and Probes
CEE 364 Materials in Civil Engineering
CHM 403 Advanced Organic Chemistry
CHM 409 Structural Solid State Chemistry
ELE 341 Solid-State Devices
ELE 342 Principles of Quantum Engineering
ELE 441/ENE 441 Solid-State Physics I
ELE 442/ENE 442 Solid-State Physics II
ELE 449 Materials and Solid-State Device Laboratory
GEO 378 Mineralogy
MAE 324 Structure and Properties of Materials
MAE 334 Materials Selection and Design
MSE 301 Materials Science and Engineering
MSE 302 Laboratory Techniques in Materials Science and Engineering
MSE 504/CHM 560/PHY 512/CBE 520 Monte Carlo and Molecular Simulation in Statistical Physics & Material Science
MSE 531/ELE 531 Introduction to Nano/Microfabrication

Optimization, Dynamics, and Information Technology

CBE 422 Molecular Modeling Methods
CBE 520 Molecular Simulation Methods
CBE 527 Nonlinear and Mixed-Integer Optimization
COS 217 Introduction to Programming Systems
COS 226 Algorithms and Data Structures
COS 323 Computing for the Physical and Social Sciences
COS 333 Advanced Programming Techniques
COS 340 Reasoning About Computation
COS 343 Algorithms in Computational Biology
COS 402 Artificial Intelligence
COS 424 Interacting with Data
EEB 355/MOL 355 Introduction to Statistics for Biology
ORF 245 Fundamentals of Engineering Statistics
ORF 307 Optimization
ORF 309/EGR 309/MAT 380 Probability and Stochastic Systems
ORF 311 Optimization Under Uncertainty
ORF 360 Decision Modeling in Business Analytics
ORF 406 Statistical Design of Experiments
ORF 409 Introduction to Monte Carlo Simulation
ORF 411 Operations and Information Engineering
ORF 417 Dynamic Programming

Science and Engineering for New Technologies

Transport Phenomena
MAE 306/MAT 392 Mathematics in Engineering II
MAE 336 Viscous Flows
MAE 423 Heat Transfer

Chemical Technology
CBE 421/CHM 421 Catalytic Chemistry
CHM 302 Organic Chemistry II: Biological Emphasis
CHM 304 Organic Chemistry II: Foundations of Chemical Reactivity and Synthesis
CHM 305 The Quantum World
CHM 306 Physical Chemistry: Chemical Thermodynamics and Kinetics
CHM 403 Advanced Organic Chemistry
CHM 405 Advanced Physical Chemistry: Quantum Mechanics
CHM 406 Advanced Physical Chemistry: Chemical Dynamics and Thermodynamics
CHM 407 Inorganic Chemistry: Structure and Bonding
CHM 408 Inorganic Chemistry: Reactions and Mechanisms

Engineering Physics
PHY 203 Classical Mechanics A, or PHY 205 Classical Mechanics B
PHY 208 Principles of Quantum Mechanics
PHY 301 Thermal Physics
PHY 304 Advanced Electromagnetism
PHY 305 Introduction to Quantum Theory

Electronic Materials Processing
ELE 206/COS 306 Introduction to Logic Design
ELE 208 Integrated Circuits: Practice and Principles
ELE 341 Solid-State Devices
ELE 342 Physical Principles of Electronic Devices
ELE 441/ENE 441 Solid-State Physics I
ELE 442/ENE 442 Solid-State Physics II

The advanced chemistry course requirement and the advanced chemical engineering course requirement can both be satisfied by electives in the areas of concentration.

Special Programs and Options. The flexibility built into the chemical and biological engineering curriculum provides an opportunity for students to obtain a thorough education in the fundamentals of chemical and biological engineering science and at the same time pursue a cognate field (a track) such as biology, business, medicine, chemistry, or physics. Students simply elect as few or as many courses in the cognate field as they desire. While some students may concentrate all their electives in a single field, others may prefer to divide their time between two tracks--for example, chemistry and the biological sciences, or physics and mathematics. The following listing suggests the many tracks available.

Applied and Computational Mathematics: Elective courses in mathematics, modeling, and applications.

Applied Mathematics and Computer Technology: Elective courses in statistical studies, mathematics, electrical engineering, computer science, mechanical and aerospace engineering, and civil engineering and operations research.

Applied Physics: Elective courses in physics, mathematics, and chemical and biological engineering.

Biotechnology: Elective courses in chemical and biological engineering, molecular biology, and chemistry.

Business and Finance: Elective courses in decision theory, engineering administration, and economics.

Chemistry: Additional courses in chemistry and the biological sciences beyond those required in the regular program.

Energy Conversion and Resources: Elective courses with emphasis on conversion of energy as given by the Departments of Mechanical and Aerospace Engineering, Chemical and Biological Engineering, and Physics.

Environmental Studies: Elective courses in ecology and evolutionary biology, molecular biology, chemistry, chemical and biological engineering, and civil and environmental engineering.

Materials Science: Elective courses in materials science and engineering, mechanical and aerospace engineering, chemical and biological engineering, and civil and environmental engineering.

Premedical: Elective courses in ecology and evolutionary biology, molecular biology, and chemistry.

Princeton University offers several special programs called certificate programs. Unlike the tracks described above, these certificate programs have formal requirements. They are described elsewhere in this announcement (for example, see the programs in engineering physics, engineering biology, materials science and engineering, sustainable energy, and environmental studies).

Courses

CBE 215 Quantitative Principles in Cell and Molecular Biology (See MOL 215)
CBE 228 Energy Technologies in the 21st Century (See MAE 228)
CBE 245 Introduction to Chemical and Biochemical Engineering Principles Fall STN Application of the principles of conservation of mass and energy to the design and analysis of chemical processes. Elementary treatment of single and multiphase systems. First law of thermodynamics for closed and open systems. Steady state and transient analysis of reacting and nonreacting systems. Three lectures, one preceptorial. Prerequisite: CHM 201. M. Brynildsen
CBE 246 Thermodynamics Spring STN Basic concepts governing the equilibrium behavior of macroscopic fluid and solid systems of interest in modern chemical engineering. Applications of the first law (energy conservation) and second law (temperature, entropy, reversibility) to open and closed systems. Thermodynamic properties of pure substances and mixtures. Phase equilibrium and introduction to reaction equilibrium. Introduction to the molecular basis of thermodynamics. Applications include thermodynamics of protein stability, the Earth's energy balance, energy conversion schemes, and the binding of ligands to proteins. Prerequisites: CBE 245 and MAT 201. R. Register
CBE 250 Separations in Chemical Engineering and Biotechnology Fall STN Fundamental thermodynamic principles and transport processes that govern separations in biotechnology and chemical processing. Staged operations, such as distillation and chromatography, are developed based on coupling phase equilibrium with mass balances. Transport processes driven by electric fields, centrifugal fields, or hydrodynamics provide the basis for understanding ultracentrifugation, membrane process, and electrophoresis. Three lectures. Prerequisites: CBE 245 and CBE 246. MAE 305 and CHM 301 may be taken concurrently. N. Lape
CBE 260 Ethics and Technology: Engineering in the Real World (also
EGR 260
) Fall EM
An examination of engineering as a profession and the professional responsibilities of engineers. The ethics of engineering will be considered through case studies (e.g., automobile safety, pollution control), and the social responsibilities of engineering will be distinguished from those of science and business. Quantitative decision-making concepts, including risk-benefit analysis, are introduced and weighed against ethical considerations to compare technology options. Ethical conflicts between utilitarian theories and duty theories will be debated. Two lectures and one preceptorial. J. Benziger, B. Francis
CBE 305 Mathematics in Engineering I (See MAE 305)
CBE 341 Mass, Momentum, and Energy Transport Fall STN Survey of modeling and solution methods for the transport of fluids, heat, and chemical species in response to differences in pressure, temperature, and concentration. Steady state and transient behavior will be examined. Topics include fluid statics; conservation equations for mass, momentum and energy; dimensional analysis; viscous flow at high and low Reynolds number; thermal conduction; convective heat and mass transfer, correlations; diffusion and interphase mass transfer. Working knowledge of calculus, linear algebra and ordinary differential equations is assumed. Prerequisites: CBE 245, CBE 246 & MAE 305. Can take MAE 305 concurrently. P. Brun
CBE 342 Fluid Mechanics Not offered this year Elements of fluid mechanics relevant to simple and complex fluids. Topics include macroscopic balances; derivation of differential balance equations and applications to unidirectional flows; treatment of nearly unidirectional flows through the lubrication approximation; introduction to turbulent flow; flow through porous media; capillary flows; dispersed two-phase flows; and hydrodynamic stability. Three lectures. Prerequisite: CBE 341. S. Sundaresan
CBE 346 Chemical Engineering Laboratory Spring STL An intensive hands-on practice of engineering. Experimental work in the areas of separations, heat transfer, fluid mechanics, process dynamics and control, materials processing and characterization, chemical reactors. Development of written and oral technical communication skills. One lecture, two three-hour laboratories. Prerequisites: CBE 246 and CBE 341 or equivalents. S. Sundaresan, J. Nunes, L. Loo
CBE 351 Junior Independent Work Fall Subjects chosen by the student with the approval of the faculty for independent study. A written report, examination, or other evidence of accomplishment will be required. A. Link
CBE 352 Junior Independent Work Spring Subjects chosen by the student with the approval of the faculty for independent study. A written report, examination, or other evidence of accomplishment will be required. A. Link
CBE 415 Polymers (also
CHM 415
/
MSE 425
) Fall
Broad introduction to polymer science and technology, including polymer chemistry (major synthetic routes to polymers), polymer physics (solution and melt behavior, solid-state morphology and properties), and polymer engineering (overview of reaction engineering and melt processing methods). Two lectures. Prerequisites: CHM 301 or 303, which may be taken concurrently, and MAT 104, or permission of the instructor. R. Register
CBE 421 Catalytic Chemistry (also
CHM 421
/
ENE 421
) Not offered this year
Concepts of heterogeneous catalysis applied to chemical processes. Major industrial processes based on heterogeneous catalysis, including ammonia synthesis, partial oxidation, petroleum refining, and environmental control. The major classes of heterogeneous catalysts, such as solid acids and transition metals, and the classes of chemical reactions catalyzed by these materials. Processing conditions and reactor design are considered. Fundamentals of surface reactivity will be explored. Two lectures. Prerequisite: CHM 303 organic chemistry. J. Benziger
CBE 432 The Cell as a Chemical Reactor Not offered this year Presents a framework for the analysis of cellular responses, such as proliferation, migration, and differentiation. Emphasis on mechanistic models of biotransformation, signal transduction, and cell-cell communication in tissues. Focuses first on unit operations of cell physiology transcription, translation, and signal transduction. Models of these processes will rely on tools of reaction engineering and transport. Process dynamics and control will then be used to analyze the regulatory structure of networks of interacting genes and proteins. Prerequisites: MOL 214 and MAE 305 or their equivalents. S. Shvartsman
CBE 434 Biotechnology (See MOL 433)
CBE 438 Biomolecular Engineering (also
MOL 438
) Fall
This course will focus on the design and engineering of biomacromolecules. After a brief review of protein and nucleic acid chemistry and structure, we will delve into rational, evolutionary, and computational methods for the design of these molecules. Specific topics to be covered include aptamers, protein and RNA-based switches and sensors, unnatural amino acids and nucleotides, enzyme engineering, and the integration of these parts via synthetic biology efforts. Two lectures. A. Link
CBE 441 Chemical Reaction Engineering Spring STN Stoichiometry and mechanisms of chemical reaction rates, both homogeneous and catalytic; adsorption, batch, continuous flow, and staged reactors; coupling between chemical reaction rates and mass, momentum, and energy transport; stability; optimization of reactor design. Application to environmental and industrial problems. Two lectures, one preceptorial. Prerequisites: CBE 246 and CBE 341. J. Avalos
CBE 442 Design, Synthesis, and Optimization of Chemical Processes Fall STL Introduction to chemical process flow-sheeting; process design, sizing and cost estimation of total processes; process economics; introduction to optimization, linear programming, integer programming, and nonlinear programming; heat integration methods, minimum utility cost, minimum number of units, network optimization. Two lectures, one laboratory. Prerequisites: CBE 341, CBE 346, and CBE 441. A. Panagiotopoulos, C. Smith
CBE 445 Process Control Not offered this year A quantitative study of the principles of process dynamics and control. Dynamic behavior of chemical process elements; analysis and synthesis of linear feedback control systems with special emphasis on frequency response techniques and scalar systems. Two lectures. Prerequisite: MAE 305, which may be taken concurrently. S. Sundaresan
CBE 447 Metabolic Engineering (also
GHP 457
) Not offered this year STN
Introduction to engineering metabolism. The objective of this course is to introduce students to current techniques and challenges within the field of metabolic engineering. Specific topics include introduction to metabolism, transcriptional regulation, signal transduction, flux balance analysis, and metabolic flux analysis. Designed for upper division students in engineering, chemistry, and molecular biology. Two lectures. Prerequisites: MOL 214 or MOL 215, or equivalent. M. Brynildsen
CBE 451 Senior Independent Work Fall A one semester study of an important problem or topic in chemical and biological engineering. Projects may be experimental, computational, or theoretical. Topics selected by the students from suggestions by the faculty. Written report required. A. Link
CBE 452 Senior Independent Work Spring A one semester study of an important problem or topic in chemical and biological engineering. Projects may be experimental, computational, or theoretical. Topics selected by the students from suggestions by the faculty. Written report required. A. Link
CBE 454 Senior Thesis Spring A full year study of an important problem or topic in chemical and biological engineering culminating in a senior thesis. Projects may be experimental, computational, or theoretical. Topics selected by the students from suggestions by the faculty. Written thesis, poster presentation, and oral defense required. The senior thesis is recorded as a double course in the spring. Departmental permission required. A. Link