Computer Science

Professor Stephen Chong, Co-Director of Undergraduate Studies

Professor Steven J. Gortler, Co-Director of Undergraduate Studies (fall)

Professor Boaz Barak, Co-Director of Undergraduate Studies (spring)

Computer science is a dynamic, versatile field, full of open problems and opportunities for creative invention. The concentration in computer science is designed to teach students skills they will use immediately and ideas they will exploit in the future in ways unimaginable today. Because information technology affects every aspect of society, graduates with computer science degrees have open to them an enormous variety of careers—engineering, teaching, medicine, law, basic science, entertainment, management, and countless others.

Computer scientists must know basic mathematics, the lingua franca of all the quantitative sciences; they must understand the abstract models that describe universal computational phenomena; and they must know how computers are designed, programmed, and used. Concentration requirements are intended to ensure balanced programs with emphasis on subjects that will endure through rapid technological change. At the same time, the requirements are flexible and permit students to choose courses that reflect their individual interests.

Students are advised to obtain the needed mathematical background early in their careers. Computer Science 50 serves as the introductory course in computer science; ideally prospective concentrators will take this course freshman year, but it is quite possible to take Computer Science 50 during the sophomore year and still complete the honors-eligible program. The Computer Science concentration is administered by the Paulson School of Engineering and Applied Sciences, and it is particularly easy to move into Computer Science from the other SEAS concentrations—Applied Mathematics and areas of Engineering.

The Computer Science concentration has the following learning objectives. Our graduates should be able to:

  1. Design and code correct solutions to problems.
  2. Design a system, identifying trade-offs on dimensions such as performance, usability, robustness, security, and durability.
  3. Design an algorithm to solve a problem. Reason about the algorithm's properties—correctness, specifications, time complexity—informally at least, and formally as much as possible.
  4. Starting from an informal, English language description of a problem, give a fully formal description of it, and prove something about the behavior of the system.
  5. Compose a large data set from networked sources, draw some inferences about it, and convey those conclusions effectively to others visually and verbally.
  6. Give a 1-hour talk to a novice about how computers work, from the hardware to a user-visible application.
  7. Explain how a solution designed for a specific domain can be applied to another domain.
  8. Explain the appropriateness of alternative system designs to the social context in which the system would be used.
  9. When presented with a technical solution to a problem, formulate a set of questions that probe the solution for its soundness.
  10. Conduct an "experiment" to study an algorithm or system, ideally one designed by someone else.
  11. Pick up and work with new environments (languages, APIs, OS-es, simulators, etc.) independently and efficiently.
  12. After listening to a CS colloquium talk, objectively analyze and critique the work.
  13. Apply computational approaches in the natural sciences, the social sciences, and the humanities.
  14. Decompose a large problem into a collection of manageable, interrelated tasks.

In addition to these technical objectives, we identified five softer objectives. We hope our graduates will be able to:

  1. Present ideas clearly and forcefully, both orally and in writing.
  2. Solve problems cooperatively and in an ethically principled way.
  3. Apply their strengths to areas of known weakness and discomfort.
  4. Work productively, responsibly, and effectively within a group.
  5. Adapt to changes in the technological landscape.

REQUIREMENTS

There are four types of concentrations in Computer Science: Basic concentration, Honors Concentration, Joint Concentration, and the Mind, Brain, Behavior track of the Computer Science concentration.

The number of credits required for each degree depends on the student’s mathematics placement. The ranges given here depend on whether the student starts mathematics at the Mathematics 1a, Mathematics 1b, or Mathematics 21a level. (With good planning it is also possible to earn a Computer Science degree starting with Mathematics Ma.) For example, a basic concentration requires 48 credits (12 courses), of which Mathematics 1a and/or Mathematics 1b can be waived, depending on placement, to reduce the number to 44 or 40 credits (11 or 10 courses). No student may reduce concentration requirements by omitting other courses: any required course not taken must be replaced by a similar course at a more advanced level.

The four concentration options share a common requirement structure, which is part “Required” and part “Elective.”

Required

  • Basic mathematics
  • Basic software
  • Theory

Elective

  • The breadth requirement
  • Other electives

Basic Requirements: 10-12 courses (40-48 credits)

  1. Required courses:
    1. Basic mathematics (2-4 courses): 
        1. Mathematics 1a and Mathematics 1b, if needed as preparation.
        2. Multivariable calculus: Mathematics 21a, Applied Mathematics 21a, Mathematics 23b, Mathematics 25b, or Mathematics 55b.
        3. Linear algebra: Mathematics 21b, Applied Mathematics 21b, Mathematics 23a, Mathematics 25a, or Mathematics 55a.

          In order to limit to 12 the maximum number of courses required for a basic concentration, a student who takes all three of Computer Science 20 and Mathematics 1a and Mathematics 1b is not required to take Mathematics 21a (or equivalent). (Mathematics 21b or its equivalent is required, but does not have 21a as a prerequisite.)

          Students usually take two courses with the same number in the natural sequence, but any combination is permitted, as long as it includes both a multivariable calculus and a linear algebra course. For example, it would be appropriate to take Mathematics 23a and Mathematics 21a, but it would not be appropriate to take Mathematics 21a and Applied Mathematics 21a. Students who feel they have background equivalent to Mathematics 21a and/or Mathematics 21b prior to matriculation may, with prior consultation, substitute more advanced analysis and/or algebra courses, respectively.
    2. Basic software (2 courses): Two out of the following three courses: Computer Science 50, Computer Science 51, and Computer Science 61. Since Computer Science 50 is a prerequisite for both Computer Science 51 and Computer Science 61, students who skip Computer Science 50 must take both Computer Science 51 and Computer Science 61. Students who take Computer Science 50 need take only one or the other. 
    3. Theory (2 courses): Either Computer Science 121 or Computer Science 125, plus any one additional theory course, including Computer Science courses numbered in the 120s and 220s. Applied Mathematics 106, and Applied Mathematics 107. Students may not receive credit for both Computer Science 125 and either Computer Science 121 or Computer Science 124. 
    4. Technical electives (4 courses): Courses may be drawn from the following list:
       
      • Computer Science courses numbered greater than 50 (including 91r). A student who takes all three of Computer Science 50, Computer Science 51, and Computer Science 61 may count either Computer Science 51 or Computer Science 61 as a technical elective.
      • Statistics 110
      • Mathematics 154
      • Applied Mathematics 106, 107, 120, and 121
      • Engineering Sciences 50 or Engineering Sciences 52
      • Many—but not all—MIT “Course 6” courses can be used as technical electives. Consult the DUS before enrolling.

        Breadth Requirement:
         In order to ensure breadth in the program two of the four technical electives must be Computer Science courses from different course groupings, identified by the penultimate digit of the course number. For example, Computer Science 61 and Computer Science 165 have penultimate digit “6.” Physics 123 or Engineering Sciences 153 counts as a Computer Science hardware (penultimate digit 4) course.
         
          • 3: Economics and Computation
          • 4: Hardware and Networks
          • 5: Programming Languages
          • 6: Systems
          • 7: Graphics, Visualization, and User Interfaces
          • 8: Artificial Intelligence
             

        Note that theory courses (penultimate digit 2) do not count toward the breadth requirement.

        Computer Science courses with penultimate digit 0, 1, 2, and 9 are valid technical electives if not used to satisfy other concentration requirements, but do not contribute to the breadth requirement. However, no Computer Science course numbered less than 20 may be used in a concentration program, and Computer Science 20 only in honors programs.

  2. Tutorial: Optional. Available as Computer Science 91r.  This course is repeatable, but may be taken at most twice for academic credit, and only one semester of Computer Science 91r may be counted toward concentration requirements. Students wishing to enroll in Computer Science 91r must file a project proposal to be signed by the student and the faculty supervisor and approved by the Director of Undergraduate Studies.
  3. Thesis: None.
  4. General Examination: None.
  5. Other information:
    1. Approved courses: With the approval of the Director of Undergraduate Studies, courses other than those listed above may be used to satisfy requirements. Statistics 121 will be treated as equivalent to Computer Science 109. To satisfy any of the requirements 1A, 1B, or 1C, a substituted course must be in the same area of mathematics or computer science but more advanced than the stipulated course. Students must secure advance approval for course substitutions by filing a Plan of Study to be approved by the Director of Undergraduate Studies. The Plan of Study form and a description of the process to submit the form can be found here.
    2. Pass/Fail and Sat/Unsat: None of the courses used to satisfy concentration requirements may be taken Pass/Fail. While Computer Science 50 will count for concentration credit if it is taken for a grade of SAT, students intending to concentrate in computer science should take the course for a letter grade.
    3. Credit for prior work: Except for Math 1ab, there is no reduction in concentration requirements for prior work. As noted in 1(B) above, students who skip CS50 must take both CS51 and CS61. Rarely, students wish, on the basis of prior experience, to skip CS51 or CS61 or courses such as Math 21a or Math 21b. They may be allowed to do so, with the prior approval of the Director of Undergraduate Studies, if they substitute a more advanced course of the same kind: for example, CS152 in place of CS51, CS161 in place of CS61, Math 112 or Applied Math 105 in place of Math 21a, and Math 121 or Applied Math 120 in place of Math 21b.
    4. Plans of study: Concentrators must file a Plan of Study showing how they intend to satisfy these degree requirements, and keep their plan of study up to date until their program is complete. If the plan is acceptable, the student will be notified that it has been approved. To petition for an exception to any rule, the student should file a new plan of study and notify the Director of Undergraduate Studies of the rationale for any exceptional conditions. Approval of a plan of study is the student’s guarantee that a given set of courses will satisfy degree requirements. The Plan of Study form and a description of the process to submit the form can be found here.

Requirements for Honors Eligibility: 12-14 courses (48-56 credits)

  1. Required courses:
    1. Basic mathematics (2-4 courses): Same as Basic Requirements. Note: for the Honors requirements, students who start with Mathematics 1a may not replace Mathematics 21a with Computer Science 20. 
    2. Basic software (2 courses): Same as Basic Requirements.
    3. Theory (2 courses): Same as Basic Requirements.
    4. Technical electives (6 courses): Courses may be drawn from the following list:
       
      • Computer Science courses numbered greater than 50 (including 91r). Note that a student who takes all three of Computer Science 50, Computer Science 51, and Computer Science 61 may count either Computer Science 51 or Computer Science 61 as a technical elective.
      • Statistics 110
      • Mathematics 154
      • Applied Mathematics 106, 107, 120, and 121
      • Engineering Sciences 50 or Engineering Sciences 52
      • Many—but not all—MIT “Course 6” courses can be used as technical electives. Consult the DUS before enrolling.
         
      Breadth Requirement

      In order to ensure breadth in the program, three of the six technical electives must be Computer Science courses from different course groupings identified by the penultimate digit of the course number. For example, Computer Science 61 and Computer Science 165 both have penultimate digit “6.” Physics 123 or Engineering Sciences 153 counts as a Computer Science hardware (penultimate digit 4) course.
       
      • 3: Economics and Computation
      • 4: Hardware and Networks
      • 5: Programming Languages
      • 6: Systems
      • 7: Graphics, Visualization, and User Interfaces
      • 8: Artificial Intelligence


      Note that theory courses (penultimate digit 2) do not count toward the breadth requirement.

      Computer Science courses with penultimate digit 0, 1, and 2 are valid technical electives, but do not contribute to the breadth requirement. However, no Computer Science course numbered less than 20 may be used in a concentration program, and Computer Science 20 only in honors programs.

  2. Tutorial: Same as Basic Requirements.
  3. Thesis: Optional but encouraged. See honors requirements. Students writing theses are often enrolled in Computer Science 91r. This course is repeatable, but may be taken at most twice for academic credit, and only one semester of Computer Science 91r may be counted toward concentration requirements. Students wishing to enroll in Computer Science 91r must file a project proposal to be signed by the student and the faculty supervisor and approved by the Director of Undergraduate Studies.
  4. General Examination: None.
  5. Other information:
    1. Approved courses. Same as Basic Requirements.
    2. Pass/Fail and Sat/Unsat: Same as Basic Requirements
    3. Credit for prior work: Same as Basic Requirements.
    4. Plans of Study: Same as Basic Requirements
       

Requirements for Joint Concentrations: 36-44 credits for CS field (9-11 courses for CS field)

Joint concentrations with certain other fields are possible. This option is intended for students who have interests in the intersection of two fields, not simply in the two fields independently; for example, a combined concentration in computer science and linguistics might be appropriate for a student with a special interest in computational linguistics. Course requirements are the same as for the Requirements for Honors Eligibility, except that only three technical electives are required. These three technical electives must satisfy the breadth requirement as stated in 1D, with the further provision that one semester of Computer Science 91r may be used to satisfy the breadth requirement for joint concentrations. Such courses may also be double-counted towards the requirements of the other field. Joint concentrations are not “double majors.” Joint concentrators should be interested in the overlap between two fields, not simply in both. A thesis in the intersection of the fields is required for joint concentrators, read by both concentrations. The student is typically awarded the minimum honors recommended by the two concentrations separately. These requirements, including the thesis requirement, are the same whether Computer Science is the primary field or the allied field of the joint concentration. Students interested in combined programs should consult the Director of Undergraduate Studies at an early date and should work carefully with both concentrations to ensure all deadlines and requirements of both concentrations are met. Students with separate interests in more than one field should consider a secondary rather than a joint concentration, or simply using some of their electives to study one of the fields.

The Mind, Brain, and Behavior Program

Students interested in addressing questions of neuroscience and cognition from the perspective of computer science may pursue a special program of study affiliated with the University-wide Mind, Brain, and Behavior Initiative, that allows them to participate in a variety of related activities. (Similar programs are available through the Anthropology, History and Science, Human Evolutionary Biology, Linguistics, Neurobiology, Philosophy, and Psychology concentrations.) Requirements for this honors-only program are based on those of the computer science Requirements for Honors Eligibility, except that:

  • Statistics 110 or Computer Science 124 replaces the second theory course. Statistics 110 is an option for the theory requirement only in the MBB track.
  • In item 1d, the six courses comprise:
        • MCB 80,
        • one approved biology or psychology course,
        • an approved MBB junior tutorial,
        • Computer Science 181 or 182,
        • and two courses from different course groupings, identified by the penultimate digit of the course number  (3, 4, 5, 6, 7). Group 8 is not an option for the breadth requirement in MBB programs, but Computer Science 91r may also be used to satisfy the breadth requirement. (SLS 20 is not an approved course for the Computer Science MBB track.)
  • In item 3, a computationally-oriented thesis on a Mind, Brain, and Behavior-related topic is required. Students pursuing thesis research may want to enroll in Computer Science 91r under item 1d.

Students pursuing the Mind, Brain, and Behavior track are assigned an adviser in the field and are expected to participate in the University-wide Mind, Brain, and Behavior research milieu, including a non-credit senior year seminar for Mind, Brain, and Behavior thesis writers. To participate in the MBB track, students must both complete the Computer Science concentration Plan of Study and register at the beginning of every academic year on the MBB website. Interested students should contact the Computer Science liaison to the MBB program, Professor Stuart Shieber (shieber@seas.harvard.edu).

ADVISING

Students interested in concentrating in Computer Science are urged to consult the Director of Undergraduate Studies early and often for advice on placement in courses and selection among courses. The Director of Undergraduate Studies is happy to talk with freshmen and sophomores about their Plans of Study and to answer questions. When a student enters the concentration mid-way through the sophomore year, the Director of Undergraduate Studies assigns a professor to serve as the student’s faculty adviser. Every effort is made to match the student’s special interests to the expertise of the adviser. Students should consult their advisers regularly, certainly at the beginning of each term. When a faculty adviser is on leave, the student is temporarily reassigned to a new adviser. Students desiring a change of adviser for any reason should contact the Director of Undergraduate Studies. The Director of Undergraduate Studies is also available to discuss problems or questions of any kind with students in the concentration.

HOW TO FIND OUT MORE

Students interested in computer science are invited to join the mailing list for the Computer Science Newsletter, which carries announcements of new courses, colloquia, job and internship opportunities, and a variety of get-togethers for the Harvard computer science community. Information about the newsletter and other community resources can be found on the Computer Science website.

For further information, students should consult the Director of Undergraduate Studies, (cs-dus@seas.harvard.edu). 

ENROLLMENT STATISTICS
Number of Concentrators as of December

Concentrators 2008 2009 2010 2011 2012 2013 2014 2015 2016
Computer Science 86 86 99 143 198 253 263 306 363
Computer Science + another field 4 7 10 13  17 22 32 42 47
Another field + Computer Science 4 8 10 15  7 18 21 24 25