The concentration in Engineering equips students with a solid foundation for careers in engineering, to advance the knowledge base for future technologies, and to merge teaching, scholarship, and practice in the pursuit of solutions to human needs. The concentration offers one standard Bachelor of Arts (A.B.) program and nine Bachelor of Science (Sc.B.) degree program tracks. Of these, Sc.B. programs in biomedical, chemical and biochemical, computer, electrical, materials, and mechanical engineering are accredited by the Engineering Accreditation Commission of ABET. Sc.B. degree programs in environmental engineering and engineering physics are also offered, but they are not accredited by ABET. (Note: Students interested in structural engineering entering in the class of 2017 and beyond may pursue a Structures track within the Mechanical Engineering program). Other programs leading to the Sc.B. or A.B. degrees in Engineering may be designed in consultation with a faculty advisor. These programs must meet the general requirements for concentration programs in the School of Engineering. Students interested in an individualized program should consult with an Engineering faculty member willing to serve as an advisor and obtain the approval of the Engineering Concentration Committee. Engineering students with a particular interest in using their technical skills for the public benefit might also consider the Engaged Scholars Program.
Please note that all student concentration forms must be approved by the Engineering Concentration Committee, which reviews them for compliance with all relevant program and accreditation requirements.
Mathematics
Mathematics 0190, 0200 is the preferred sequence of courses to be taken in the freshman year. Students who would prefer a more introductory level calculus course may start in MATH 0100 and take MATH 0200 or MATH 0180 in second semester. Students without one year of secondary school level preparation in calculus should take MATH 0090 , MATH 0100 in their first year, and should begin their sequence of engineering courses with ENGN 0030 in sophomore year. The courses APMA 0330 & APMA 0340 (Methods of Applied Math I, II) can be taken in the sophomore year as well.
Advanced Placement
Students who have taken Advanced Placement courses in high school and/or have shown proficiency through advanced placement examinations are often able to start at a higher level than suggested by the standard programs below. However, please note that Advanced Placement credit cannot be used to satisfy any concentration requirements. For example, our Sc.B. programs specify that students must take 4 semesters of math while enrolled here at Brown, beginning with MATH 0190 or MATH 0170. If a student comes in with advanced placement credit (e.g. placing out of MATH 0190 or MATH 0200), he/she is strongly recommended to take a higher level math course as a replacement. Examples of such courses are MATH 0520 (Linear Algebra), MATH 1260 (Complex Analysis), MATH 1610 (Probability), MATH 1620 (Statistics), APMA 1170 (Numerical Analysis), APMA 1210 (Operations Research), or APMA 1650 (Statistical Inference). However, the student with advanced placement credit for MATH 0190 orMATH 0200 also has the option of replacing the math course with an advancedlevel science course, subject to the approval of the concentration advisor.
Transfer Credit
Students who have successfully completed college courses elsewhere may apply to the University for transfer credit. (See the “Study Elsewhere” section of the University Bulletin for procedures, or contact the Dean of the College.) Transfer courses that are used to meet Engineering concentration requirements must be approved by the student’s concentration advisor, and must be described briefly on the student’s electronic concentration form. Transfer courses that are determined by the concentration advisor to be substantially equivalent to a required Brown course automatically fulfill concentration requirements. In rare cases, students may petition the concentration committee to use courses that do not have an equivalent offered at Brown to meet a concentration requirement. Substitutions of this nature can only be approved if the student’s overall program meets published educational outcomes for the concentration and has sufficient basic science, mathematics, and engineering topics courses to meet relevant accreditation requirements. Students should consult their concentration advisor for assistance with drafting a petition. The decision whether to award concentration credit is made by majority vote of the Engineering Concentration Committee.
Substitutions for Required Courses
A student may petition the Concentration Adviser to substitute a course in place of a requirement. Such substitutions can only be approved if the student's modified program continues to meet the published educational outcomes for the concentration, and has sufficient basic science, mathematics, and engineering topics courses to meet accreditation requirements. If the substitution involves taking an equal or higher level course in substantially the same area, whether at Brown or elsewhere, it can be approved by the Concentration Adviser. (For courses taken elsewhere, the credit must be officially transferred.) Students wishing to make substitutions of a broader nature should consult their Concentration Adviser for assistance with drafting their petition to the Engineering Concentration Committee, which may be approved by a majority vote.
Standard Program for the A.B. degree:
Candidates for the Bachelor of Arts (A.B.) degree with a concentration in Engineering must complete at least eight approved Engineering courses. The eight courses must include at least two 1000level Engineering courses. Of these 1000level courses, one must be a design or independent study course and the other an inclassroom experience. The set of Engineering courses must be chosen with careful attention to the prerequisites of the 1000level courses. Please note that this A.B. degree program is not accredited by ABET.
Not all engineering courses may be used to satisfy the engineering course requirement for the A.B. degree. For example, the following courses cannot be used to satisfy the engineering course requirement for the A.B. degree: ENGN 0020, ENGN 0090, ENGN 0900, ENGN 0930A, ENGN 0930C, ENGN 1010. Therefore, the program of study must be developed through consultation with the concentration advisor.
The A.B. program also requires preparation in Mathematics equivalent to MATH 0200 and APMA 0330, as well as at least one collegelevel science course from the general areas of chemistry, life sciences, physics, or geological sciences. Remedial courses, such as CHEM 0100, cannot be used to satisfy this requirement. A programming course is also recommended, but not required. The entire program is subject to approval by an Engineering Concentration Advisor and the Chair of the Engineering Concentration Committee.
Standard programs for the Sc.B. degree
All Bachelor of Science (Sc.B.) program tracks build upon a common core of engineering knowledge and skills applicable across all engineering disciplines. The goal of this engineering core curriculum is to prepared to practice engineering in an age of rapidly changing technology. Twothirds of this fouryear program consists of a core of basic mathematics, physical sciences and engineering sciences common to all branches of engineering, including a thorough grounding in programming and technical problem solving. This core provides our graduates with the basis of theory, design, and analysis that will enable them to adapt to whatever may come along during their careers.
At the same time, the core courses assist students in making informed choices in determining their areas of specialization, at the end of their sophomore year. To this end, firstyear students are given an introduction to engineering  featuring case studies from different disciplines in engineering as well as guest speakers from industry. This aspect of the program is different from that at many other schools where students are expected to select a specific branch of engineering much earlier in their academic program.
In addition, all Sc.B. programs in Engineering must be complemented by at least four courses in humanities and social sciences.The minimum fourcourse humanities and social sciences requirement for the Sc.B. in Engineering cannot be met by advanced placement credit.
Special Concentrations
In addition to the standard programs described above, students may also petition the Engineering Concentration Committee to pursue a special engineering Sc.B. degree of their own design. Such special Sc.B. programs are not ABETaccredited. Students with a special concentration will receive an Sc.B. degree in engineering, but a specific area of specialization will not be noted on their transcript. A special Sc.B. concentration is intended to prepare graduates for advanced study in engineering or for professional practice, but in an area that is not covered by one of the existing Sc.B. programs. Accordingly, special concentration programs are expected to consist of a coherent set of courses with breadth, depth and rigor comparable to an accredited degree. A total of 21 engineering, mathematics, and basic science courses are required. The program must include at least 3 courses in mathematics, at least 2 courses in physical or life sciences; and at least 12 courses in engineering. At least five of the engineering courses must be upper level courses, and one must be a capstone design course or independent study, which must be advised or coadvised by a member of the regular engineering faculty. Note that not all engineering courses may be used to meet Sc.B. requirements: for example, the courses not allowed to count toward the A.B., will not qualify. Petitions should be prepared in consultation with an engineering faculty adviser, who will submit the petition to the Engineering Concentration Committee. Petitions must include: (i) a statement of the objectives of the degree program, and an explanation of how the courses in the program meet these objectives; (ii) course descriptions for any courses in the program that are not part of standard ScB engineering concentrations; (iii) a detailed description of any independent study courses used for concentration credit, signed by the faculty adviser for this course; and (iv) an uptodate internal transcript.
Professional Tracks
While we do not give course credit for internships, we officially recognize their importance via the optional Professional Tracks. The requirements for the professional tracks include all those of the standard tracks, as well as the following: Students must complete two fulltime professional experiences, lasting two to four months each (or two parttime experiences of equivalent total effort), doing work that is related to their concentration programs. Such work is normally done within an industrial organization, but may also be done at a university under the supervision of a faculty member. For the work to be considered related to a concentration program, the job responsibilities must make use of the material from one or more courses of the concentration (regardless of whether the student has taken those courses or not at the time of the internship). On completion of each professional experience, the student must write and upload to ASK a reflective essay about the experience addressing the following prompts:

Describe the organization you worked in and the nature of your responsibilities.

Which courses were put to use in your work? Which topics, in particular, were important?

In retrospect, which courses should you have taken before embarking on your work experience?

What are the topics from these courses that would have helped you if you had been more familiar with them?

What topics would have been helpful in preparation for this work experience that you did not learn at Brown?

What did you learn from the experience that probably could not have been picked up from course work?

Is the sort of work you did something you would like to continue doing once you graduate? Explain.

Would you recommend your work experience to other Brown students? Explain.
The reflective essays are subject to the approval of the student's concentration adviser.
Entry to the Professional Track requires a simple application form to be completed by the student and approved by the Concentration Advisor at the time of the concentration declaration. If the student has not yet declared a concentration, the form may be approved by the Chair of the Concentration Committee. The Concentration Advisor will certify that all Professional Track students have completed the necessary internships and will grant approval for the associated reflective essays. All other requirements remain identical to those in the standard tracks in the concentrations.
Chemical and Biochemical Engineering Track:
The Chemical and Biochemical Engineering program is accredited by the Engineering Accreditation Commission of ABET, http://www.abet.org. The education objectives of the Chemical and Biochemical Engineering program are to prepare graduates: (1) to pursue productive scientific and technical careers, beginning with entrylevel engineering positions in industry, or graduate study in chemical or biochemical engineering or related fields; or to successfully pursue other careers that benefit from the analytical or quantitative skills acquired through the Brown CBE Program; (2) to effectively apply the principles of chemical and biochemical engineering, problemsolving skills, and critical and independent thinking, to a broad range of complex, multidisciplinary technological and societal problems; (3) to communicate effectively, both orally and in writing, to professionals and audiences of diverse backgrounds, and to pursue technical approaches and innovations that address the needs of society in an ethical, safe, sustainable, and environmentally responsible manner. The student outcomes of this program are the ABET (1) (7) Student Outcomes as defined by the "ABET Criteria for Accrediting Engineering Programs" (available online at http://www.abet.org/accreditationcriteriapoliciesdocuments/).
1. Core Courses:  
ENGN 0030  Introduction to Engineering  1 
or ENGN 0031  Honors Introduction to Engineering  
ENGN 0040  Dynamics and Vibrations  1 
ENGN 0410  Materials Science  1 
ENGN 0510  Electricity and Magnetism  1 
ENGN 0520  Electrical Circuits and Signals  1 
ENGN 0720  Thermodynamics  1 
ENGN 0810  Fluid Mechanics  1 
BIOL 0200  The Foundation of Living Systems  1 
CHEM 0330  Equilibrium, Rate, and Structure  1 
MATH 0190  Advanced Placement Calculus (Physics/Engineering)  1 
or MATH 0170  Advanced Placement Calculus  
MATH 0200  Intermediate Calculus (Physics/Engineering)  1 
or MATH 0180  Intermediate Calculus  
or MATH 0350  Honors Calculus  
APMA 0330  Methods of Applied Mathematics I, II  1 
or APMA 0350  Applied Ordinary Differential Equations  
APMA 0340  Methods of Applied Mathematics I, II  1 
or APMA 0360  Applied Partial Differential Equations I  
2. UpperLevel Chemical & Biochemical Engineering Curriculum  
ENGN 1110  Transport and Biotransport Processes  1 
ENGN 1120  Reaction Kinetics and Reactor Design ^{1}  1 
ENGN 1130  Chemical Engineering Thermodynamics ^{1}  1 
ENGN 1710  Heat and Mass Transfer  1 
CHEM 0350  Organic Chemistry  1 
Advanced Chemistry elective course ^{2}  
CHEM 0360  Organic Chemistry  1 
or CHEM 0400  Biophysical and Bioinorganic Chemistry  
or CHEM 0500  Inorganic Chemistry  
or CHEM 1140  Physical Chemistry: Quantum Chemistry  
Advanced Natural Sciences elective course ^{3}  1  
3. Capstone Design Course  
ENGN 1140  Chemical Process Design  1 
*In addition to program requirements above, students must take four courses in the humanities and social sciences.  
Total Credits  21 
^{1}  Note: ENGN 1120 and 1130 are only offered in alternate years. 
^{2}  An advanced chemistry course approved by concentration advisor; the following courses are preapproved for this requirement. 
^{3}  An advanced course in the natural sciences approved by the concentration advisor. For suggestions of acceptable courses that fulfill this requirement, please see the concentration advisor. 
Computer Engineering Track:
The Computer Engineering program is accredited by the Engineering Accreditation Commission of ABET, http://www.abet.org. The education objectives of the Computer Engineering program are to prepare graduates: (1) to pursue distinctive multidisciplinary scientific and technical careers beginning with either entrylevel computer engineering positions in industry or graduate study in computer engineering and related fields; (2) to participate on multidisciplinary teams that cooperate in applying problemsolving skills and critical and independent thinking to a broad range of projects that can produce the technical innovations aimed at satisfying the future needs of society. The student outcomes of this program are the ABET (1)  (7) Student Outcomes as defined by the "ABET Criteria for Accrediting Engineering Programs" (available online at http://www.abet.org/accreditationcriteriapoliciesdocuments/).
The Computer Engineering concentration shares much of the core with the other engineering programs, but is structured to include more courses in computer science, and a somewhat different emphasis in mathematics.
1. Core Courses:  
ENGN 0030  Introduction to Engineering  1 
or ENGN 0031  Honors Introduction to Engineering  
ENGN 0040  Dynamics and Vibrations  1 
ENGN 0510  Electricity and Magnetism  1 
ENGN 0520  Electrical Circuits and Signals  1 
APMA 1650  Statistical Inference I  1 
or APMA 1655  Statistical Inference I  
or CSCI 1450  Probability for Computing and Data Analysis  
MATH 0190  Advanced Placement Calculus (Physics/Engineering)  1 
or MATH 0170  Advanced Placement Calculus  
MATH 0200  Intermediate Calculus (Physics/Engineering)  1 
or MATH 0180  Intermediate Calculus  
or MATH 0350  Honors Calculus  
APMA 0330  Methods of Applied Mathematics I, II  1 
or APMA 0350  Applied Ordinary Differential Equations  
or APMA 1170  Introduction to Computational Linear Algebra  
or APMA 1710  Information Theory  
or CSCI 0220  Introduction to Discrete Structures and Probability  
or CSCI 1570  Design and Analysis of Algorithms  
or MATH 1260  Complex Analysis  
CHEM 0330  Equilibrium, Rate, and Structure ^{1}  1 
or ENGN 0410  Materials Science  
or NEUR 0010  The Brain: An Introduction to Neuroscience  
Select one of the following series (other CSCI courses subject to approval):  2  
Introduction to ObjectOriented Programming and Computer Science and Introduction to Algorithms and Data Structures  
Computer Science: An Integrated Introduction and Computer Science: An Integrated Introduction  
Accelerated Introduction to Computer Science (and one additional CSCI course subject to approval)  
2. UpperLevel Computer Engineering Curriculum:  
ENGN 1570  Linear System Analysis  1 
ENGN 1630  Digital Electronics Systems Design  1 
ENGN 1640  Design of Computing Systems  1 
MATH 0520  Linear Algebra  1 
or MATH 0540  Honors Linear Algebra  
One advanced Computer Engineering foundations course:  1  
Communication Systems  
Design and Implementation of VLSI Systems  
Image Understanding  
Analysis and Design of Electronic Circuits  
Digital Signal Processing  
One advanced Computer Science course with significant systms programming:  1  
Introduction to Computer Systems  
or CSCI 0320  Introduction to Software Engineering  
or CSCI 1230  Introduction to Computer Graphics  
or CSCI 1380  Distributed Computer Systems  
or CSCI 1670  Operating Systems  
or CSCI 1680  Computer Networks  
Select at least one Computer Engineering/Electrical Engineering course (other CE/EE courses subject to approval)  1  
Neuroengineering  
Optics  
Communication Systems  
Introduction to Semiconductors and Semiconductor Electronics  
Design and Implementation of VLSI Systems  
Image Understanding  
Analysis and Design of Electronic Circuits  
Design and Fabrication of Semiconductor Devices  
Photonics Devices and Sensors  
Biomedical Optics  
Photovoltaics Engineering  
Introduction to Power Engineering  
Design of Robotic Systems  
Control Systems Engineering  
Interfaces, Information and Automation  
Pattern Recognition and Machine Learning  
Digital Signal Processing  
Computer Vision  
Physics of Solid State Devices  
Solid State Quantum and Optoelectronics  
Advanced Computer Architecture  
Reconfigurable Computing for Machine/Deep Learning  
Scientific Programming in C++  
Low Power VLSI System Design  
Select at least one Computer Science Course (Other CSCI courses subject to approval)  1  
Introduction to Software Engineering  
Introduction to Computer Systems  
Introduction to Computer Graphics  
Database Management Systems  
User Interfaces and User Experience  
Creating Modern Web & Mobile Applications  
Distributed Computer Systems  
Artificial Intelligence  
Building Intelligent Robots  
Design and Analysis of Algorithms  
RealTime and Embedded Software  
Introduction to Computer Systems Security  
Operating Systems  
Computer Networks  
Design and Implementation of Programming Languages  
Multiprocessor Synchronization  
csciStartup  
Select up to one interdisciplinary science course ^{2}  1  
Neural Modeling Laboratory  
Computational Vision  
Properties and Processing of Electronic Materials  
Statistical Neuroscience  
3. Capstone Design ^{3}  1  
Embedded Microprocessor Design  
or ENGN 1000  Projects in Engineering Design I  
or ENGN 1001  Projects in Engineering Design II  
4. General Education Requirement: At least four approved courses must be taken in humanities and social sciences  
Total Credits  21 
^{1}  Or Biology course beyond BIOL 0200 subject to Concentration Advisor approval 
^{2}  Student should consult with concentration advisor for recommendation and approval. 
^{3}  Subject to approval by the concentration advisor, an independent study course (ENGN 1970/ENGN 1971) may be used to fulfill the Engineering Capstone Design requirement. To qualify for such approval, the independent study project must: (1) contain a significant and definable design component; (2) be based on the knowledge and skills acquired in earlier course work, (3) incorporate appropriate engineering standards; and (4) address multiple realistic constraints. 
Electrical Engineering Track:
The Electrical Engineering program is accredited by the Engineering Accreditation Commission of ABET, http://www.abet.org. The education objectives of the Electrical Engineering program are to prepare graduates: (1) to pursue distinctive multidisciplinary scientific and technical careers beginning with either entrylevel electrical engineering positions in industry or graduate study in electrical engineering and related fields; (2) to participate on multidisciplinary teams that cooperate in applying problemsolving skills and critical and independent thinking to a broad range of projects that can produce the technical innovations aimed at satisfying the future needs of society. The student outcomes of this program are the ABET (1)  (7) Student Outcomes as defined by the "ABET Criteria for Accrediting Engineering Programs" (available online at http://www.abet.org/accreditationcriteriapoliciesdocuments/ ).
1. Core Courses:  
ENGN 0030  Introduction to Engineering  1 
or ENGN 0031  Honors Introduction to Engineering  
ENGN 0040  Dynamics and Vibrations  1 
ENGN 0410  Materials Science  1 
ENGN 0510  Electricity and Magnetism  1 
ENGN 0520  Electrical Circuits and Signals  1 
ENGN 0720  Thermodynamics  1 
ENGN 0310  Mechanics of Solids and Structures  1 
or ENGN 0810  Fluid Mechanics  
or CSCI 0160  Introduction to Algorithms and Data Structures  
or CSCI 0180  Computer Science: An Integrated Introduction  
CHEM 0330  Equilibrium, Rate, and Structure  1 
MATH 0190  Advanced Placement Calculus (Physics/Engineering)  1 
or MATH 0170  Advanced Placement Calculus  
MATH 0200  Intermediate Calculus (Physics/Engineering)  1 
or MATH 0180  Intermediate Calculus  
or MATH 0350  Honors Calculus  
APMA 0330  Methods of Applied Mathematics I, II  1 
or APMA 0350  Applied Ordinary Differential Equations  
APMA 0340  Methods of Applied Mathematics I, II  1 
or APMA 0360  Applied Partial Differential Equations I  
or APMA 1650  Statistical Inference I  
or APMA 1710  Information Theory  
or MATH 0520  Linear Algebra  
or MATH 0540  Honors Linear Algebra  
CSCI 0150  Introduction to ObjectOriented Programming and Computer Science ^{2}  1 
or CSCI 0040  Introduction to Scientific Computing and Problem Solving  
or CSCI 0170  Computer Science: An Integrated Introduction  
or CSCI 0190  Accelerated Introduction to Computer Science  
or APMA 0160  Introduction to Scientific Computing  
or ENGN 1931Z  Interfaces, Information and Automation  
2. UpperLevel Electrical Engineering Curriculum  
ENGN 1570  Linear System Analysis  1 
ENGN 1620  Analysis and Design of Electronic Circuits  1 
ENGN 1630  Digital Electronics Systems Design  1 
PHYS 0790  Physics of Matter  1 
or PHYS 1410  Quantum Mechanics A  
3. Electrical Engineering Specialization  Complete at least three courses from the following groups:  3  
At least one advanced Electrical Engineering foundations course:  
Instrumentation Design  
Communication Systems  
Introduction to Semiconductors and Semiconductor Electronics  
Design and Implementation of VLSI Systems  
Image Understanding  
Design of Computing Systems  
Up to two other Electrical Engineering Courses ^{3}  
Neuroengineering  
Optics  
Embedded Microprocessor Design  
Design and Fabrication of Semiconductor Devices  
Photonics Devices and Sensors  
Biomedical Optics  
Photovoltaics Engineering  
Introduction to Power Engineering  
Design of Robotic Systems  
Control Systems Engineering  
Interfaces, Information and Automation  
Up to one interdisciplinary engineering science course:  
Neural Modeling Laboratory  
Computational Vision  
Introduction to Computer Systems ^{4}  
Advanced Engineering Mechanics  
Properties and Processing of Electronic Materials  
Statistical Neuroscience  
Quantum Mechanics B  
4. Capstone Design: At least one course from the following: ^{5}  1  
Embedded Microprocessor Design  
or ENGN 1000  Projects in Engineering Design I  
or ENGN 1001  Projects in Engineering Design II  
5. General Education Requirement: At least four approved courses must be taken in humanities and social sciences  
Total Credits  21 
^{1}  Or 1000level Applied Mathematics or Mathematics course subject to Concentration Advisor Approval 
^{2}  ENGN 1931Z may replace CSCI 0150 or meet an elective requirement, but not both. 
^{3}  Or 2000level Electrical Engineering graduate course (such as ENGN 2500, ENGN 2520, ENGN 2530, ENGN 2560, ENGN 2912K). 
^{4}  Or Computer Science course beyond CSCI 0150/CSCI 0170 subject to Concentration Advisor approval 
^{5}  Subject to approval by the concentration advisor, an independent study course (ENGN 1970/ ENGN 1971) may be used to fulfill the Engineering Capstone Design requirement. To qualify for such approval, the independent study project must: (1) contain a significant and definable design component; (2) be based on the knowledge and skills acquired in earlier course work, (3) incorporate appropriate engineering standards; and (4) address multiple realistic constraints. 
Environmental Engineering Track:
The Environmental Engineering program began in 2013. The program has not been reviewed by ABET and is not ABETaccredited. The education objectives of the Environmental Engineering program are to prepare graduates: (1) to apply in practice the knowledge obtained in school within industry, government, or private practice; (2) to work toward sustainable solutions in a wide array of technical specialties; (3) to pursue lifelong learning through continuing education and/or advanced degrees in environmental engineering. The student outcomes of this program are the (1)  (7) Student Outcomes as defined by the "ABET Criteria for Accrediting Engineering Programs" (available online at http://www.abet.org/accreditationcriteriapoliciesdocuments/).
1. Core Courses:  
ENGN 0030  Introduction to Engineering  1 
or ENGN 0031  Honors Introduction to Engineering  
ENGN 0040  Dynamics and Vibrations  1 
ENGN 0410  Materials Science  1 
ENGN 0490  Fundamentals of Environmental Engineering  1 
ENGN 0510  Electricity and Magnetism  1 
ENGN 0720  Thermodynamics  1 
ENGN 0810  Fluid Mechanics  1 
BIOL 0200  The Foundation of Living Systems  1 
CHEM 0330  Equilibrium, Rate, and Structure  1 
MATH 0190  Advanced Placement Calculus (Physics/Engineering)  1 
or MATH 0170  Advanced Placement Calculus  
MATH 0200  Intermediate Calculus (Physics/Engineering)  1 
or MATH 0180  Intermediate Calculus  
or MATH 0350  Honors Calculus  
APMA 0330  Methods of Applied Mathematics I, II  1 
or APMA 0350  Applied Ordinary Differential Equations  
APMA 0650  Essential Statistics  1 
or APMA 1650  Statistical Inference I  
2. Advance Science Courses  
GEOL 1370  Environmental Geochemistry  1 
or GEOL 1960B  Special Topics in Geological Sciences: Physical Hydrology  
BIOL 0415  Microbes in the Environment ( or an approved alternative Natural Science Course)  1 
or BIOL 0420  Principles of Ecology  
3. Environmental Engineering Specialty Options (Complete one of the following five course sequences)  5  
3a. Chemistry Specialty  
At least three of the following:  
Transport and Biotransport Processes  
Chemical Engineering Thermodynamics  
Water Supply and Treatment Systems  Technology and Sustainability  
Heat and Mass Transfer  
Advanced Fluid Mechanics  
Fuels, Energy and the Environment  
Renewable Energy Technologies  
Up to one of the following:  
Mechanics of Solids and Structures  
or ENGN 0520  Electrical Circuits and Signals  
Up to one of the following:  
Introduction to Scientific Computing and Problem Solving (or approved science elective)  
or CSCI 0150  Introduction to ObjectOriented Programming and Computer Science  
or CSCI 0170  Computer Science: An Integrated Introduction  
3b. Energy Specialty  
At least three of the following:  
Water Supply and Treatment Systems  Technology and Sustainability  
Heat and Mass Transfer  
Advanced Fluid Mechanics  
Renewable Energy Technologies  
Introduction to Power Engineering  
Photovoltaics Engineering  
Fuels, Energy and the Environment  
Up to one of the following:  
Mechanics of Solids and Structures  
or ENGN 0520  Electrical Circuits and Signals  
Up to one of the following:  
Introduction to Scientific Computing and Problem Solving  
or ENVS 1400  Sustainable Design in the Built Environment  
or ENGN 1930U  Renewable Energy Technologies  
4. Capstone Design ^{1}  1  
Projects in Engineering Design I  
or ENGN 1140  Chemical Process Design  
or ENGN 1001  Projects in Engineering Design II  
* In addition to program requirements above, students must take four courses in the humanities and social sciences.  
Total Credits  21 
^{1}  Subject to approval by the concentration advisor, an independent study course (ENGN1970/1971) may be used to fulfill the Engineering Capstone Design requirement. To qualify for such approval, the independent study project must: (1) contain a significant and definable design component; (2) be based on the knowledge and skills acquired in earlier course work, (3) incorporate appropriate engineering standards; and (4) address multiple realistic constraints. To request approval, please complete the online form available at: http://www.brown.edu/academics/engineering/undergraduatestudy 
Materials Engineering Track:
The Materials Engineering program is accredited by the Engineering Accreditation Commission of ABET, http://www.abet.org. The education objectives of the Materials Engineering program are to prepare graduates: (1) to pursue multidisciplinary scientific and technical careers beginning with entrylevel engineering positions in industry or graduate study in materials science and engineering and related fields; (2) to apply an engineering problemsolving approach combined with a broad appreciation for the liberal arts to inform and develop their understanding of current societal needs and values to achieve leadership positions in their chosen fields of endeavor. The student outcomes of this program are the (1)  (7) Student Outcomes as defined by the "ABET Criteria for Accrediting Engineering Programs" (available online at http://www.abet.org/accreditationcriteriapoliciesdocuments/).
1. Core Courses:  
ENGN 0030  Introduction to Engineering  1 
or ENGN 0031  Honors Introduction to Engineering  
ENGN 0040  Dynamics and Vibrations  1 
ENGN 0410  Materials Science  1 
ENGN 0510  Electricity and Magnetism  1 
ENGN 0520  Electrical Circuits and Signals  1 
ENGN 0720  Thermodynamics  1 
ENGN 0310  Mechanics of Solids and Structures  1 
or ENGN 0810  Fluid Mechanics  
CHEM 0330  Equilibrium, Rate, and Structure  1 
MATH 0190  Advanced Placement Calculus (Physics/Engineering)  1 
or MATH 0170  Advanced Placement Calculus  
MATH 0200  Intermediate Calculus (Physics/Engineering)  1 
or MATH 0180  Intermediate Calculus  
or MATH 0350  Honors Calculus  
APMA 0330  Methods of Applied Mathematics I, II  1 
or APMA 0350  Applied Ordinary Differential Equations  
APMA 0340  Methods of Applied Mathematics I, II  1 
or APMA 0360  Applied Partial Differential Equations I  
or MATH 0520  Linear Algebra  
or APMA 1210  Operations Research: Deterministic Models  
or APMA 1650  Statistical Inference I  
CHEM 0350  Organic Chemistry  1 
or CSCI 0040  Introduction to Scientific Computing and Problem Solving  
or CSCI 0150  Introduction to ObjectOriented Programming and Computer Science  
or CSCI 0170  Computer Science: An Integrated Introduction  
or CSCI 0190  Accelerated Introduction to Computer Science  
or ENGN 1230  Instrumentation Design  
or ENGN 1740  Computer Aided Visualization and Design  
or ENGN 1750  Advanced Mechanics of Solids  
or APMA 0160  Introduction to Scientific Computing  
2. UpperLevel Materials Engineering Curriculum  
ENGN 1410  Physical Chemistry of Solids  1 
ENGN 1420  Kinetics Processes in Materials Science and Engineering  1 
ENGN 1440  Mechanical Properties of Materials  1 
PHYS 0790  Physics of Matter  1 
or CHEM 0350  Organic Chemistry  
or CHEM 1140  Physical Chemistry: Quantum Chemistry  
Three of the following: ^{1}  3  
Properties and Processing of Electronic Materials  
Structure and Properties of Nonmetallic Materials  
Metallic Materials  
Biomaterials  
3. Capstone Design ^{2}  
ENGN 1000  Projects in Engineering Design I  1 
or ENGN 1001  Projects in Engineering Design II  
or ENGN 1930L  Biomedical Engineering Design and Innovation  
* In addition to program requirements above, students must take four courses in the humanities and social sciences.  
Total Credits  21 
^{1}  These courses are taken in either the junior or senior year. Note that ENGN 1470 is offered on a rotating basis in the fall semester of alternate years, and ENGN 1480 and ENGN 1450 are offered in the spring semester of alternate years. 
^{2}  Subject to approval by the concentration advisor, an independent study course (ENGN1970/1971) may be used to fulfill the Engineering Capstone Design requirement. To qualify for such approval, the independent study project must: (1) contain a significant and definable design component; (2) be based on the knowledge and skills acquired in earlier course work, (3) incorporate appropriate engineering standards; and (4) address multiple realistic constraints. To request approval, please complete the online form available at: http://www.brown.edu/academics/engineering/undergraduatestudy 
Mechanical Engineering Track:
The Mechanical Engineering program is accredited by the Engineering Accreditation Commission of ABET, http://www.abet.org. The education objectives of the Mechanical Engineering program are to prepare graduates: (1) to pursue scientific and technical careers beginning with either graduate study in mechanical engineering and related fields or mechanical engineering positions in industry; (2) to work on interdisciplinary teams that make use of the engineering problem solving method and a broad background in the liberal arts to address societal needs. The student outcomes of this program are the (1)  (7) Student Outcomes as defined by the "ABET Criteria for Accrediting Engineering Programs" (available online at http://www.abet.org/accreditationcriteriapoliciesdocuments/).
1. Core Courses:  
ENGN 0030  Introduction to Engineering  1 
or ENGN 0031  Honors Introduction to Engineering  
ENGN 0040  Dynamics and Vibrations  1 
ENGN 0310  Mechanics of Solids and Structures  1 
ENGN 0410  Materials Science ^{1}  1 
ENGN 0510  Electricity and Magnetism  1 
ENGN 0520  Electrical Circuits and Signals  1 
ENGN 0720  Thermodynamics  1 
ENGN 0810  Fluid Mechanics  1 
CHEM 0330  Equilibrium, Rate, and Structure  1 
MATH 0190  Advanced Placement Calculus (Physics/Engineering)  1 
or MATH 0170  Advanced Placement Calculus  
MATH 0200  Intermediate Calculus (Physics/Engineering)  1 
or MATH 0180  Intermediate Calculus  
or MATH 0350  Honors Calculus  
APMA 0330  Methods of Applied Mathematics I, II  1 
or APMA 0350  Applied Ordinary Differential Equations  
APMA 0340  Methods of Applied Mathematics I, II ^{2}  1 
or APMA 0360  Applied Partial Differential Equations I  
CSCI 0040  Introduction to Scientific Computing and Problem Solving  1 
or CSCI 0150  Introduction to ObjectOriented Programming and Computer Science  
or CSCI 0170  Computer Science: An Integrated Introduction  
or CSCI 0190  Accelerated Introduction to Computer Science  
or APMA 0160  Introduction to Scientific Computing  
or ENGN 1931Z  Interfaces, Information and Automation  
2. UpperLevel Mechanical Engineering Curriculum: Complete at least 6 courses from the following groups:  6  
Mechanical Systems: At least one course from:  
Structural Analysis  
Advanced Engineering Mechanics  
Advanced Mechanics of Solids  
Fluids/Thermal Systems: At least one course from:  
Advanced Fluid Mechanics  
Jet Engines and Aerospace Propulsion  
Heat and Mass Transfer  
Capstone: At least one course from the following must be taken in the final two semesters: ^{3}  
Projects in Engineering Design I  
or ENGN 1001  Projects in Engineering Design II  
Aircraft Design  
Industrial Design  
Design of Mechanical Assemblies  
Design of Civil Engineering Structures  
Design of Thermal Engines  
Design of Space Systems  
Design Electives: Up to two courses from:  
Instrumentation Design  
Computer Aided Visualization and Design  
Bioengineering Electives: Up to two courses from:  
Biomechanics  
Neuroengineering  
Biomaterials  
Robotic and Control Systems Electives: up to two courses from:  
Design of Robotic Systems  
Control Systems Engineering  
Engineering Analysis and Computation Electives: up to two courses from:  
Numerical Methods in Engineering  
Advanced Engineering Optimization  
Energy and Environmental Engineering Electives: up to two courses from:  
Renewable Energy Technologies  
Fuels, Energy and the Environment  
Interdisciplinary Electives: up to one course from: ^{4}  
Analysis and Design of Electronic Circuits  
or ENGN 1340  Water Supply and Treatment Systems  Technology and Sustainability  
or ENGN 1440  Mechanical Properties of Materials  
or ENGN 1470  Structure and Properties of Nonmetallic Materials  
or ENGN 1570  Linear System Analysis  
or ENGN 1931F  Introduction to Power Engineering  
or ENGN 1931X  Instrumentation for Research: A Biomaterials/Materials Project Laboratory  
or ENGN 1931Z  Interfaces, Information and Automation  
3. Upper Level, Advanced Science Course: at least one course from: ^{5}  1  
Physics of Matter  
or BIOL 0800  Principles of Physiology  
or CHEM 0350  Organic Chemistry  
or CHEM 1140  Physical Chemistry: Quantum Chemistry  
or GEOL 1450  Structural Geology  
or GEOL 1370  Environmental Geochemistry  
4. General Education Requirement: At least four approved courses must be taken in humanities and social sciences  
Total Credits  21 
^{1}  ENGN 1490 may be substituted if taken in Sophomore year. 
^{2}  Other advanced courses in mathematics or applied mathematics may be substituted with approval of the concentration advisor. 
^{3}  Subject to approval by the concentration advisor, an independent study course (ENGN 1970/ENGN 1971) may be used to fulfill the Engineering Capstone Design requirement. To qualify for such approval, the independent study project must: (1) contain a significant and definable design component; (2) be based on the knowledge and skills acquired in earlier course work, (3) incorporate appropriate engineering standards; and (4) address multiple realistic constraints. 
^{4}  ENGN 1931Z may replace CSCI 0040 or meet an elective requirement, but not both. 
^{5}  Other nonintroductory courses in physics, chemistry, neuroscience, geology, or biology may be substituted with the permission of the concentration advisor. 