Engineering Sciences

Professor Zhiming Kuang, Director of Undergraduate Studies

Engineering innovation has long played a critical role in enhancing social progress and bringing about an improved quality of life. Within the past 50 years, the pace and impact of innovation have increased dramatically, facilitating modern health, energy, transportation, communications, and computational infrastructures that knit together the countries of the world. At the same time, engineering innovation has enabled dramatic advances in basic science. Imaging and manufacturing structures at the nanoscales, near-lossless transmission of information, and unprecedented levels of computational power have led to fantastic new discoveries. These types of technologies, for instance, have allowed us to decode the genome, understand the formation of galaxies, and make correlations between social networks and underlying human psychology. In the 21st century, rapid and efficient access to the new innovations, necessary to tackle today's myriad challenges, has become even more imperative. Equally important is the need to educate both those who will be future engineering innovators and those who will use those innovations, deploy them, and make critical legal and political decisions about them.

Engineering has evolved over the years to not only dive deeply into specific fields, but also to seek out solutions to real-world problems by combining concepts from a broad range of scientific inquiries and innovations. For example, robotics is a highly interdisciplinary field that straddles multiple traditional engineering disciplines such as mechanical, electrical, and materials engineering and computer science. While roboticists have traditionally been trained in specific engineering disciplines, next generation roboticists must tackle large complex systems comprising multiple parts that span myriad disciplines—from the mechanical underpinnings of the physical device, to electronic control, materials properties, and high-level algorithms—all of which must work in concert to achieve broad-level objectives while adhering to numerous constraints. Alternative energy is another growing and immensely important field that requires integration of solutions across a wide range of science and engineering disciplines. Topics range from understanding the inherent properties of materials and devices that harness the sun's rays to thinking about challenges associated with large-scale production and distribution of electricity, and addressing both the societal and environmental impacts of new technologies. The Engineering Sciences concentration is ideally positioned to provide students with both the breadth and depth of study needed to excel in these and other exciting integrative areas of engineering within the liberal arts setting of Harvard.

Harvard offers two degrees in Engineering Sciences: the Bachelor of Arts (AB) and the Bachelor of Science (SB). The degree requirements differ for each of these programs: the AB program requires between 14 and 16 courses (56-64 credits) and the SB program requires 20 courses (80 credits). Students in the Engineering Sciences AB program specialize in one of five engineering tracks: biomedical sciences and engineering, electrical and computer engineering, engineering physics, environmental science and engineering, or mechanical and materials science and engineering. Students interested in an AB degree may also consider the Biomedical Engineering concentration, which is also listed in this publication. Students pursuing the SB degree in the Engineering Sciences concentration typically specialize in one of two tracks: bioengineering or environmental science and engineering. Students interested in an SB degree specializing in Electrical Engineering or Mechanical Engineering should refer directly to those concentrations, which are also listed in this publication. Students may also apply to a cross-disciplinary track within the Engineering Sciences SB program, which provides the opportunity to learn between or across traditional engineering areas.

The SB degree program requires a minimum of 20 courses (80 credits). The curriculum is structured with advanced courses building on the knowledge acquired in math, science, and introductory engineering science courses. Concentrators are encouraged to complete the common prerequisite course sequence in their first two years at Harvard. This includes Math (through 1a and 1b; plus 21a and 21b, 23a and 23b, or Applied Mathematics 21a and 21b), Physics (through Applied Physics 50a and 50b, Physical Sciences 12a and 12b, or Physics 15a and 15b), and Computer Science 50. Students are cautioned that it is more important to derive a solid understanding of these basic subjects than to complete them quickly without thorough knowledge; this material is extensively used in many subsequent courses. If in doubt, it may be wise to enroll in the Math 1 sequence rather than proceed to Math 21a or 23a with marginal preparation.

The SB and AB degree programs in Engineering Sciences share many course requirements, and there is some flexibility in moving between these programs. To get an early sample of engineering coursework, entering students are invited to enroll in Engineering Sciences 6 (Environmental Science and Engineering), Engineering Sciences 50 (Electrical Engineering), Engineering Sciences 51 (Mechanical Engineering), and Engineering Sciences 53 (Biomedical Engineering). These introductory courses have minimal prerequisites, and have been very popular with prospective engineering concentrators. Engineering Sciences 50 and 51 have extensive hands-on laboratory sections; and Engineering Sciences 6 and 50 satisfy requirements for the Program in General Education.

The Engineering Sciences program seeks to educate future leaders that have the technical background necessary to develop and critically evaluate the next wave of engineering innovations; to apply these innovations to important global and local problems; and to make informed decisions about them in a societal context.

Upon graduation, students in the Engineering Sciences AB concentration should demonstrate the following student outcomes:

  • Quantitative problem solving skills based in the fundamentals of mathematics, basic sciences, engineering sciences, and engineering design.
  • The ability to apply engineering principles to problems in a range of fields and with important societal, economic, and environmental impacts.
  • The ability to communicate technical information clearly and efficiently through written, visual, or oral presentations.

Upon graduation, students in the Engineering Sciences SB concentration should demonstrate the following student outcomes:

  • An ability to apply knowledge of mathematics, science and engineering.
  • An ability to design and conduct experiments, as well as to analyze and interpret data.
  • An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability.
  • An ability to function on multidisciplinary teams.
  • An ability to identify, formulate, and solve engineering problems.
  • An understanding of professional and ethical responsibility.
  • An ability to communicate effectively.
  • The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context.
  • A recognition of the need for, and an ability to engage in life-long learning.
  • A knowledge of contemporary issues.
  • An ability to use the techniques, skills and modern tools necessary for engineering practice.

OPTIONS
Bachelor of Arts in Engineering Sciences

  • Biomedical Sciences and Engineering
  • Electrical and Computer Engineering
  • Engineering Physics
  • Environmental Science and Engineering
  • Mechanical and Materials Science and Engineering

Bachelor of Science in Engineering Sciences

  • Bioengineering
  • Environmental Science and Engineering
  • Cross-disciplinary

REQUIREMENTS
Bachelor of Arts (AB) in Engineering Sciences: 14-16 courses (56-64 credits)

1. Required courses:

a. Mathematics (four courses): Mathematics 1a and 1b; Applied Mathematics 21a and 21b, Mathematics 21a and 21b, Mathematics 23a and 23b, or higher levels.

b. Physics (two courses): Applied Physics 50a, Physical Sciences 12a, or Physics 15a or 16; and Applied Physics 50b, Physical Sciences 12b, or Physics 15b. Appropriate advanced-level physics courses may also fulfill this requirement (please consult with SEAS advisers).

c. Computer Science (one course): Computer Science 50, 51, or 61.

2. Sophomore Forum: Sophomore year. Non-credit. Spring term.

3. General Examination: None.

4. Thesis: Required for recommendations of high honors and highest honors, and for joint concentrators.

5. Tracks:

a. Biomedical Sciences and Engineering – Mechanical Subtrack, Electrical Subtrack, and Chemical and Materials Subtrack:

i.    Required for all Subtracks (three courses):

Engineering Sciences 53 and Biomedical Engineering 110

Life Sciences 1a

ii.    Required for Mechanical Subtrack (four courses):

Engineering Sciences 120, 123, and 181

One from Engineering Sciences 52, 153, or 154

iii.    Required for Electrical Subtrack (four courses):

Biomedical Engineering 130

Engineering Sciences 150, 154, and 156

iv.    Required for Chemical and Materials Subtrack (four courses):

Engineering Sciences 123, 181, and 190 or Biomedical Engineering 191 (preferred)

Physical Sciences 1

v.    Approved Electives (two courses):

Engineering Sciences 51, 91r (one term only), 120, 123, 128, 181,190, 211, 220, 221, 228, 240

Biomedical Engineering 121, 125, 128, 130, 160, 191

Either Applied Mathematics 101 or Engineering Sciences 150

One from Engineering Sciences 52, 153, or 154

Physics 136, 140, 143a, 151, 153

One from Physical Sciences 1, Chemistry 17 or 20

Applied Mathematics 104 or 105

b. Electrical and Computer Engineering:

i.    Required (five courses):

Engineering Sciences 150, 154, and 156

Two from Computer Science 141; Engineering Sciences 151, 173, 177; Engineering Sciences 52 or 153

ii.    Approved Electives (four courses):

Engineering Sciences 51, 53, 91r (one term only), 120, 121, 123, 159, 173, 175, 177, 181, 183, 190

Computer Science 51, 141, 143, 144r, 146, 148, 175

 Applied Mathematics 104, 105, 108 (formerly Applied Mathematics 147)

Applied Physics 195

Chemistry 160

Physics 143a, 153

c. Engineering Physics – Materials, Optoelectronics, and Photonics Subtrack and Earth and Planetary Physics Subtrack:

i.    Required for all Subtracks (four courses):

Either Physics 143a or Chemistry 160

Either Engineering Sciences 181 or Physics 181

Engineering Sciences 190

 One from Applied Mathematics 104, 105, 108 (formerly Applied Mathematics 147), Engineering Sciences 111

ii.    Required for Materials, Optoelectronics, and Photonics Subtrack (three courses):

Engineering Sciences 173 and 177

Either Applied Physics 195 or Engineering Sciences 120

iii.    Required for Earth and Planetary Physics Subtrack (three courses):

One from Engineering Sciences 123, 131, 132, 162

One from Engineering Sciences 120, Earth and Planetary Sciences 161, 166, 171

One from Earth and Planetary Sciences 121, Astronomy 110, 189

iv.    Approved Electives (two courses):

Engineering Sciences 51, 53, 91r (one term only), 111, 115, 120, 123, 125, 128, 131, 132, 153, 162, 173, 175, 177

 Applied Mathematics 104, 105, 108 (formerly Applied Math 147), 120

Applied Physics 195

Astronomy 110, 189

Earth and Planetary Sciences 161, 166, 171

Physics 140, 153, 175

d. Environmental Science and Engineering

i.    Required (three courses):

Engineering Sciences 6

Chemistry: Select two from Physical Sciences 11 (recommended) or Physical Sciences 1; Physical Sciences 10 (recommended); Life Sciences 1a or Life and Physical Sciences A.

ii.    Required (three courses chosen from the following):

Engineering Sciences 109, 112, 131, 132, 133, 135, 160, 161, 162, 163, 164, 165, 166

iii.    Approved Electives (three courses chosen from the following):

Engineering Sciences 91r (one term only), 103, 109, 112, 123, 131, 132, 133, 135, 137, 160, 161, 162, 163, 164, 165, 166, 169, 181, 220, 265, 267, 268, 269

Earth and Planetary Sciences 134, 136, 186, 187, 208, 236

No more than one from Engineering Sciences 50, 51, 53, or Earth and Planetary Sciences 22

No more than one from Engineering Sciences 52, 153, 154

• No more than one from Engineering Sciences 111, 115, 121, 150, Statistics 110, Applied Math 101, 104, 105, or 108 (formerly Applied Mathematics 147)

e. Mechanical and Materials Science and Engineering

i.    Required (seven courses):

Engineering Sciences 120, 123, 125, 181, and 190

One from Applied Mathematics 104, 105, 120, Engineering Sciences 111

One from Engineering Sciences 50, 52, 151, 153, or 154

ii.    Approved Electives (two courses):

Biomedical Engineering 110

Engineering Sciences 51, 52, 53, 91r (one term only), 96, 128, 131, 132, 151, 156, 159, 162, 173, 175, 177

Applied Physics 195

Chemistry 160

Physics 143a

6. Other information:

a. Advanced Placement credit in Math 1a or 1b can be included in satisfying the requirement of 16 courses, thus potentially reducing the number of required courses to 14 or 15. Credit for additional courses such as Math 21a or 21b does not further reduce the number of required courses. Moreover, in cases when a course can satisfy both an elective and a requirement of a track, the total number of courses is not reduced. In these cases, additional electives must be taken.

b. By prior approval, other advanced undergraduate or graduate courses, as well as courses at MIT, can be used to satisfy general requirements and track requirements and electives. Electives alternative to those listed in the tracks may be counted for credit upon prior petition and approval.

c. Engineering Sciences 6, 50, 51, and 53: No more than two of these courses may count toward concentration credit. Engineering Sciences 6, 50, and 53 can only count as an engineering elective when taken during the freshman or sophomore year.

d. Pass/Fail or Sat/Unsat: None of the courses used to satisfy concentration requirements may be taken Pass/Fail or Sat/Unsat.

e. Plan of Study: Concentrators are required to file an approved departmental Plan of Study and to keep their plan up to date in subsequent years. Plan of Study forms may be obtained from the Office of Academic Programs (Pierce Hall 110) or from the School of Engineering and Applied Sciences (SEAS) website.

f. Joint concentrations: The Engineering Sciences AB program participates in joint concentrations (though the Engineering Sciences SB program does not participate in joint concentrations). The requirements for joint concentrators are the same as for sole concentrators; in addition, a joint concentrator is required to write an interdisciplinary thesis that combines the two fields. This thesis is required regardless of whether Engineering Sciences AB is the primary or allied concentration.

Bachelor of Science (SB) in Engineering Sciences: 20 courses (80 credits)

Prospective concentrators are encouraged to make early contact with concentration representatives. Students wishing to enter the concentration must obtain the appropriate Engineering Sciences SB plan of study and related instructions from the Office of Academic Programs  (Pierce Hall 110) or online at http://www.seas.harvard.edu/academics/undergraduate and review materials before meeting with an Assistant/Associate Director or the Director of Undergraduate Studies. Students should be aware that the Engineering Sciences SB degree is more demanding than typical AB degrees, requiring 20 courses (80 credits).

Students typically follow specific guidelines provided for one of two tracks: Bioengineering or Environmental Science and Engineering. Students interested in an SB degree specializing in Electrical Engineering or Mechanical Engineering should refer directly to those concentrations. Students may also apply to a cross-disciplinary track in their junior or senior years, which provides the opportunity to learn between or across traditional engineering areas.

In addition to the courses listed specifically below, other relevant and/or advanced courses may be approved by petition in the context of a particular plan of study. A petition must propound in writing a coherent and persuasive argument for the intellectual merit of the proposal in question.

1. Required courses: 

    1. Mathematics/Probability and Statistics/Applied Mathematics (four courses):
      1. Mathematics 1a and b; and Applied Mathematics 21a and 21b, Mathematics 21a and 21b, or Mathematics 23a and 23b. (Note: Students who start in Mathematics 1a will not be required to satisfy either the probability and statistics requirement or the applied math requirement. Students who start in Mathematics 1b must take a course that satisfies the probability and statistics requirement. Students who start in Mathematics 21a, 23a, or Applied Mathematics 21a must complete the courses in both probability and statistics and applied mathematics.)
      2. Probability and Statistics (one course): At least one of Applied Mathematics 101, Engineering Sciences 150, or Statistics 110 (if starting in Mathematics 1b, 21a or 23a, or Applied Mathematics 21a). Please note that ES 150 is preferred for students pursuing the Electrical Subtrack of the Bioengineering Track.
      3. Applied Mathematics (one course): At least one of Applied Mathematics 104, 105, 106, or 107 (if starting in Mathematics 21a or 23a or Applied Mathematics 21a).
    2. Physics (two courses): Applied Physics 50a, Physical Sciences 12a, Physics 15a or 16; Applied Physics 50b, Physical Sciences 12b, or Physics 15b. Appropriate advanced-level physics courses may also fulfill this requirement (please consult with SEAS advisers).
    3. Computer Science (one course): Computer Science 50, 51, or 61.
    4. Engineering design (two courses): Engineering Sciences 96 (or 227 for Bioengineering track) and Engineering Sciences 100hf (see item 4 below).
    5. Note: Students entering Harvard with secondary school preparation that places them beyond the level of any of the required courses listed above may substitute appropriate advanced level courses. However, all SB programs must include a minimum of 20 approved courses and meet the overall ABET guidelines. Given the number and complexity of the requirements, students interested in pursuing engineering should consult with the Director of Undergraduate Studies about their plans of study as early as possible.


2. Sophomore Forum: Sophomore year. Non-credit. Spring term.

3. Tutorial: Required. Engineering Sciences 100hf.

4. Thesis: Required. An individual engineering design project is an essential element of every SB program and is undertaken, ordinarily, during the senior year as part of Engineering Sciences 100hf. Faculty-supervised reading and research is an important aspect of this requirement. 

5. General Examination: None.

6. Tracks

a. Bioengineering – Mechanical Subtrack, Electrical Subtrack, and Chemical and Materials Subtrack

i. Required for all Subtracks (five courses)

▪ Engineering Sciences 53, Biomedical Engineering 110

▪ Engineering Electives (three courses): Three courses from the list in item 7 (any area), with at least two at the 100 or 200 level.

ii. Required for Mechanical Subtrack

▪ Biology and/or Chemistry (two courses): Two of the following: Life Sciences 1a or Life and Physical Sciences A, Life Sciences 1b, Physical Sciences 1, Physical Sciences 10, Physical Sciences 11, and, by approval, other relevant introductory courses in biology or chemistry (please consult with SEAS advisers).

▪ Mechanical core (four courses): Engineering Sciences 120, 123, 181, and Engineering Sciences 190 or Biomedical Engineering 191 (preferred).

iii. Required for Electrical Subtrack

▪ Biology and/or Chemistry (two courses): Two of the following: Life Sciences 1a or Life and Physical Sciences A, Life Sciences 1b, Physical Sciences 1, Physical Sciences 10, Physical Sciences 11, and, by approval, other relevant introductory courses in biology or chemistry (please consult with SEAS advisers).

▪ Electrical core (four courses): Biomedical Engineering 130, Engineering Sciences 154, and 156; and an additional electrical engineering course (ES 52 strongly recommended).

iv. Required for Chemical and Materials Subtrack

▪ Biology and/or Chemistry (one course): Life Sciences 1a or Life and Physical Sciences A, Life Sciences 1b, Physical Sciences 1, Physical Sciences 10, Physical Sciences 11, and, by approval, other relevant introductory courses in biology or chemistry (please consult with SEAS advisers).

▪ Organic Chemistry (one course): Chemistry 17 or 20.

Chemical & Materials core (four courses): Engineering Sciences 123, Biomedical Engineering 121 or 125, Engineering Sciences 181 or 112, and Engineering Sciences 190 or Biomedical Engineering 191 (preferred).

  1. b. Environmental Science and Engineering
    1. Engineering electives (one course): At least one course from the list in item 7 (any area).
    2. Engineering breadth (three courses): One upper-level (>100) course from each of the following depth areas (see item 7 below):
      1. Mechanics and Materials
      2. Electrical
      3. Engineering Physics and Chemistry
    3. Environmental Science and Engineering core (five courses):
      1. Engineering Sciences 6
      2. Select four from Engineering Sciences 103, 109, 112, 123, 131, 132, 133, 135, 160, 161, 162, 163, 164, 165, 166, 169
    4. Chemistry (two courses): Two from: Physical Sciences 11 (preferred) or Physical Sciences 1; Life Sciences 1a or Life and Physical Sciences A; Physical Sciences 10. Students should be aware that many upper-level courses in the Environmental Science and Engineering track have Physical Sciences 1 or 11 as a pre-requisite.

c. Cross-disciplinary

▪ Biology and/or Chemistry (two courses): Two of the following: Life Sciences 1a or Life and Physical Sciences A; Life Sciences 1b, Physical Sciences 1 or 11; Physical Sciences 10; and, by approval, other relevant introductory courses in biology or chemistry (please consult with SEAS advisers).

▪ Engineering depth (three courses):  At least three courses from one area of engineering sciences (see item 7 below).

▪ Engineering breadth (three courses): At least three courses from three other areas of engineering sciences (see item 7 below).

▪ Engineering electives (three courses): At least three courses in engineering sciences or relevant related fields with engineering topics (see items 7 below).

7. Engineering Sciences courses organized by area:

a. Biomedical: Engineering Sciences 53, 211, 221, 227, 228, Biomedical Engineering 110, 121, 125, 128, 130, 160, 191

b. Computer: Computer Science 51, 61, 141, 143, 146, 148, 175

c. Electrical: Engineering Sciences 50, 52, 151, 153, 154, 155, 156, 158, 159, 173, 175, 177, Computer Science 141, 146, 148

d. Engineering Physics and Chemistry: Engineering Sciences 135, 173, 181, 190

e. Environmental: Engineering Sciences 6, 103, 109, 112, 123, 131, 132, 133, 135, 160, 161, 162, 163, 164, 165, 166, 169

f. Mechanics and Materials: Engineering Sciences 51, 120, 123, 125, 128, 181, 183, 190

8. Note: Students may count other advanced-level engineering courses after consultation with the SEAS advisers.

9. Other Information:

a. Engineering Sciences 6, 50, 51, and 53: No more than two of these courses may count towards concentration credit. Engineering Sciences 6, 50, and 53 can only count as an engineering elective when taken during the freshman or sophomore year.

b. Pass/Fail or Sat/Unsat: None of the courses used to satisfy the concentration requirements may be taken Pass/Fail or Sat/Unsat.

c. Plan of Study: Students entering the concentration must file an Engineering Sciences SB plan of study and present an intellectually coherent plan in consultation with an Assistant/Associate Director or the Director of Undergraduate Studies. Subsequent modifications to the plan must be reviewed by the faculty adviser and a relevant Assistant/Associate Director of Undergraduate Studies. All SB programs must meet the overall ABET program guidelines with 12 courses in engineering topics.

d. Cross-Disciplinary Track Requirements: Admission to the cross-disciplinary track is by application. To apply to the track, students must have at least a 3.5 College grade point average at the time of application. Applications can be submitted no earlier than the end of sophomore year, and no later than the fifth Monday of the student's seventh semester.

e. Additional Terms: Concentrators who wish to remain beyond the end of the second term of their senior year to complete the SB requirements must be approved to do so by the Undergraduate Engineering Committee. A written petition is required and should always be submitted as early as possible and under discussion with the Assistant/Associate Director of Undergraduate Studies or Director of Undergraduate Studies. Petitions can be submitted no later than January 15 between the student’s fifth and sixth terms (i.e., middle of junior year), or August 15 between the student’s fifth and sixth terms if the student’s fifth term is the spring. Under no circumstances will the Committee grant a student permission for more than two additional terms. Petitions are only granted in exceptional cases, and only to meet specific SB degree requirements. More information can be found on the SEAS website.

f. Joint Concentrations. The Engineering Sciences SB program does not participate in joint concentrations.

ADVISING

Students interested in concentrating in Engineering Sciences should discuss their plans with the Director of Undergraduate Studies, the Assistant/Associate Director of Undergraduate Studies, or the Undergraduate Academic Programs Administrator. Each undergraduate who elects to concentrate in Engineering Sciences is assigned a faculty adviser depending on the student's track. The faculty adviser might also be a member of the Undergraduate Engineering Committee, whose members have the responsibility for reviewing departmental Plans of Study. If students do not request a change in adviser, they have the same adviser until they graduate. Each student is reassigned to another faculty member while the original faculty adviser is on leave. It is expected that students will discuss their Plans of Study and progress with their Director of Undergraduate Studies or Assistant/Associate Director of Undergraduate Studies at the beginning of each term. Students may also seek advice from their faculty adviser, the Director of Undergraduate Studies, the Assistant/Associate Director of Undergraduate Studies, or the Academic Programs Administrator at any time.

HOW TO FIND OUT MORE

Further information is available from the Director of Undergraduate Studies in Engineering Sciences, Prof. Zhiming Kuang (es-dus@seas.harvard.edu), the Director of Undergraduate Studies in Environmental Science and Engineering, Prof. Frank Keutsch (keutsch@seas.harvard.edu), or the relevant Assistant/Associate Director of Undergraduate Studies: for Mechanical and Materials Science and Engineering and Electrical and Computer Engineering, Dr. Christopher Lombardo (lombardo@seas.harvard.edu); for Bioengineering, Dr. Linsey Moyer (lmoyer@seas.harvard.edu); for Environmental Science and Engineering, Dr. Patrick Ulrich (pulrich@seas.harvard.edu). Students can also contact the SEAS Undergraduate Academic Programs Administrator, Kathy Lovell (klovell@seas.harvard.edu).

ENROLLMENT STATISTICS
Number of Concentrators as of December

  • Concentrators 2008 2009 2010 2011 2012 2013 2014 2015 2016
    Engineering Sciences 110 145 148 165 147 111 98 99 112
    Engineering Sciences + another field 2 1 5 4 6 2 4 3 1
    Another field + Engineering Sciences 1 1 0 0 0 3 3 5 8