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Courses

SEAS offers undergraduate and graduate courses in Computer Science. SEAS faculty also offer several Freshman Seminars. Many additional courses of interest to concentrators can be found in the Applied Mathematics, Engineering Sciences, Mathematics, Physics, and Statistics sections of the my.harvard course catalog.

The SEAS 4 year course plan contains the most up to date plan for courses to be offered in the near future. You can filter the “catalog” entry to CS to see only Computer Science courses. The following courses are guaranteed to be offered at least once per year: CS 20, CS 50, CS 51, CS 61, CS 120, CS 121, CS 124, CS 181, CS 182.

The Sample schedules and plans page contains some examples of plans of study that satisfy the CS concentration requirements.

Placement

Most students start with CS 50 or CS 32, even if they have had an AP course in Computer Science. These course are designed to accommodate both students who are starting from scratch and students with prior programming experience. However, some students have sufficient programming background to skip CS 50 and start with CS 51 or CS 61. See the CS 50 FAQs for more advice, or consult the Directors of Undergraduate Studies.

Students should consult with the Mathematics Department, Chemistry Department, and Physics Department for advice about appropriate placement in courses in those departments.

CS 20, Discrete Mathematics for Computer Science, teaches the mathematics needed for later computer science courses that is not covered in the calculus and linear algebra sequence in Mathematics and Applied Mathematics. Some students may already have the background covered in the course or may wish to self-study the material, in which case they may be able to “place out” of taking CS 20. The mechanism for doing so will be posted in early fall. The CS 121 page on Background and Prerequisites is a good source for figuring out if you need to take CS 20 before taking courses such as CS 120, CS 121, and CS 124.

Which courses count for what? (2021 requirements)

Students following the 2020 concentration requirements should read that description instead.

The official information is in listed in our requirements page but we summarize here which courses count for fulfilling various requirements. The list below is not exhaustive, and if there is any conflict between this list and the handbook, the handbook information is the correct one. We generally allow a student to replace a course with a more advanced course of the same type, though you should ask us for authorization in advance for each such case.

Harvard extension school courses do not count for CS concentration courses. Harvard summer courses could potentially count if they are equivalent to courses that are counted in the concentration (e.g., summer versions of CS 50 or Stat 110 or other math classes). Courses taken at other universities do not count towards the concentration, unless part of an official study abroad program, or you are a transfer student. (If you are a transfer student, come talk to us and we will decide which courses to count on a case-by-case basis).

No more than two of the courses used to satisfy CS requirements may be taken PA/FL or SUS. Of the tag requirements, courses taken PA/FL or SUS can be used only for the Programming 1 and Advanced Computer Science tags. For instance, if taken PA/FL, CS 124 would not satisfy the Formal Reasoning or Algorithms tags.

  • Mathematical preparation: The Linear Algebra requirement can be fulfilled by one of Math 22a/23a/25a/55a/21b or AM 22a. The statistics/probability requirement can be fulfilled by STAT 110. Depending on math placement, students may need to take one or more out of Math Ma, Mb, 1a, or 1b as preparation for these courses. For students that place into the Math 21 or above series, we recommend they take a linear algebra course in first-year fall. Hence we recommend taking Math 22a, AM 22a or Math 21b over taking Math 21a in the first-year fall.

  • Programming requirement: A standard way to fulfill the programming 1 and 2 requirement is to take either CS 50 or CS 32 as a first programming course, and then take either CS 51 or CS 61 as a second programming course. However, depending on your background and interests, there can be other ways to fulfill it by either skipping CS 50 / 32, or taking an alternative course to CS 51 / 61 (see also placement above).

  • Formal reasoning requirement: Common combinations for fulfilling the formal reasoning requirement include CS 20 + CS 121 + CS 124 and CS 20 + CS 120 + CS 124. However, there are many other approaches. Some students may be able to skip CS 20 (see placement above), leaving room for other courses such as CS 136, CS 152, and CS 183 that also satisfy the formal reasoning requirement. We recommend all concentrators take CS 124 (algorithms), but it is only required for the honors track.

  • Computer science core courses: The full list of CS core courses is listed in the tags table, which includes all courses with CS numbers, as well as several courses from other concentrations/departments.

    • Summer courses: Summer courses that receive college credit and are the equivalent of courses that are offered during the term are treated equally. In particular, provided you get college credit for it, CSCI S-20 counts as equivalent to CS 20, CSCI S-109A counts as equivalent to CS 109A, and CSCI S-50 (Summer 2020 & 2021) or CSCI S-111 counts as equivalent to CS 50. Students may also take a Summer CS 91r, which would count as CS 91r.

    • Other courses: Some MIT course 6 courses can be used as CS core courses: consult the DUSes before enrolling. Please visit our cross-registration page for directions on cross-registration. Some study abroad courses count, though you should always check with the DUSes in advance. Courses and requirements change, and you should not assume that a course will count even if you know it did so in the past. Note: Harvard CS does not ordinarily allow concentration credit for MIT courses that are equivalent to one of our annual core courses (CS 20, 50, 51, 61, 120, 121, 124, 181, and 182).

  • Tags: The following table contains information about which courses satisfy the following tags: programming 1, programming 2, formal reasoning, discrete mathematics, computational limitations, algorithms, intermediate algorithms, systems, computation and the world, artificial intelligence, advanced computer science.

  • Secondary: The requirements for a CS secondary are rather light (only four courses) but these have to be Harvard CS courses numbered 100 and higher, or at most two of CS 20, 32 or 50, 51, & 61. You cannot count non-CS Harvard courses, MIT courses, or study abroad courses. See this web page for more information. If you are a transfer student, contact the CS DUSes for information on whether courses from the previous institution can count.

Table of course substitutions for CS concentration

The following table summarizes some course substitutions that are allowed. It also includes the answers to some commonly asked questions about which courses satisfy certain requirements. If a course appears here as a valid substitution then you can use it in your plan of study instead of the original course. July 2021: Please note that we are still determining how some of these courses will be tagged. However, when you use a substitution, you should add a note saying so to the plan of study and mention it in your email to cs-dus submitting the plan of study. Courses change, and so can the allowed substitutions. If you have any question about a course that’s not listed here (or one that is) you can check with the DUSes. These substitutions are only valid for the computer science concentration. These substitutions are not valid for a secondary in CS, for which the requirements are listed here.

Course Can be used in place of
Math 23b,23c, 25b, 55b, 110, 112, 113, 114, 115, 116, AM 105, 108, and 111 Math 21a: Multivariate Calculus
Math 22b (Fall 2019 and after) Math 21a: Multivariate Calculus
Math 23a, 25a, 55a,121,122, AM 120, 121 Math 21b: Linear algebra
Math 22a (Fall 2019 and after) Math 21b: Linear algebra
AM 22a: Solving and Optimizing Math 21b: Linear algebra
STAT 185: Introduction to Dimension Reduction Math 21b: Linear algebra
STAT 210: Probability Theory and Statistical Inference I STAT 110: Probability
STAT 220: Bayesian Data Analysis STAT 110: Probability
STAT 111: Introduction to Statistical Inference STAT 110: Probability
Math 154 Probability Theory STAT 110: Probability
ES 150: Introduction to Probability with Engineering Applications STAT 110: Probability
STAT S-110 (Summer course: intro to probability) STAT 110: Probability
ENSC S-138: (Summer course: intro to probability) STAT 110: Probability
CSCI S-20 (Summer course: intro to discrete math) (Currently Summer 2020 only) CS 20: Discrete Mathematics for Computer Science
CSCI S-50 (Summer course: intro to programming) (Currently Summer 2020 only) CS 50: Introduction to Computer Science
CSCI S-111 (Summer course intro to programming) CS 50: Introduction to Computer Science
MIT 6.849: Computational Geometry Tech elective
CS 1xx, 2xx Tech elective, can satisfy breadth if penultimate digit 3-8
CS 20: Discrete Mathematics Tech elective (no breadth)
CS 91r: Supervised Reading and Research Tech elective (one semester only)
CS 96: System Design Projects Tech elective (no breadth)
STAT 110: Probability Can be used as tech elective (not breadth) if not used to satisfy probability requirement.
AM 106: Applied Algebra Tech elective (no breadth): as of fall 2018 cannot be used as second theory course
AM 120: Applied linear algebra and big data Tech elective (no breadth)
AM 121: Introduction to Optimization: Models and Methods Tech elective (no breadth)
AM 216: Inverse Problems in Science and Engineering Tech elective (no breadth)
AM 231 (ES 201): Decision Theory Tech elective (no breadth)
STAT 195: Statistical Machine Learning Tech elective
APCOMP 221 Critical Thinking in Data Science Tech elective (no breadth) - equivalent to a CS 20x course
ES 170: Engineering Quantum Mechanics Tech elective (no breadth)
SCI-6478 / ES 256: Informal robotics Tech elective (no breadth)
MIT 6.338j: Parallel Computing and Scientific Machine Learning Tech elective
MIT 6.809: Interactive Music Systems Tech elective (no breadth)
MIT 8.370: Quantum Computation Tech elective (no breadth)
MIT 6.857: Computer and Network Security Tech elective (no breadth)
MIT 6.875: Cryptography and Cryptanalysis Tech elective (no breadth)
PHYS 160 Tech elective (no breadth)
STAT 121a/b , AC 209a/b CS 109a/b: Introduction to Data Science
CSCI S-109A (Summer course: intro to data science) CS 109a: Introduction to Data Science I
CS 221: Computational Complexity CS 121: Introduction to Theoretical Computer Science
AM 107: Graph Theory and Combinatorics Tech elective (no breadth), also second theory course
CS 229r courses: theory advanced topics Sometimes satisfy second theory course requirement but check with DUS as topics vary from term to term
MIT 6.841 / 18.405: Advanced Complexity Theory CS 221: Computational Complexity
MIT 6.854: Advanced Algorithms CS 224: Advanced Algorithms
PHY123, ES153: Laboratory Electronics CS 14x
CS 51: Abstraction and design in computation / CS 61: Systems Programming and Machine Organization One of CS51/61 can satisfy breadth if student took CS50+51+61
MIT 6.172: Performance Engineering of Software Systems CS 16x
MIT 6.858: Comp Systems Security CS 26x
MIT 6.170: Software Studio CS 17x
MIT 6.837: Computer Graphics CS 17x
ES 143: Computer Vision CS 17x
AM 207: Stochastic Methods for Data Analysis, Inference and Optimization CS 28x
Study abroad courses Case by case basis, check with DUS
MIT 6.006: Introduction to Algorithms Can not be used for concentration requirements
AM 101: Statistical Inference for Scientists and Engineers Can not be used for concentration requirements
Math 157: Mathematics in the World Can not be used for concentration requirements
DPI 663: Tech and Innovation in Government Can not be used for concentration requirements
ES 21: The innovator's practice Can not be used for concentration requirements
CS 1: Great Ideas in Computer Science Can not be used for concentration requirements
CS courses with "n" suffix (for example CS90nar and CS90nbr) Can not be used for concentration requirements
MIT 6.042: Mathematics for Computer Science As of Spring 2021, cannot be used for concentration requirements (CS 20 equivalent)
MIT 6.00: Introduction to Computer Science and Programming As of Spring 2021, cannot be used for concentration requirements (CS 50 equivalent)
MIT 6.031: Software Construction As of Spring 2021, cannot be used for concentration requirements (CS 51 equivalent)
MIT 6.004: Computation Structures As of Spring 2021, cannot be used for concentration requirements (CS 61 equivalent)
MIT 6.045: Automata, Computability, and Complexity Theory As of Spring 2021, cannot be used for concentration requirements (CS 121 equivalent)
MIT 6.840: Introduction to the Theory of Computation As of Spring 2021, cannot be used for concentration requirements (CS 121 equivalent)
MIT 6.046: Algorithms As of Spring 2021, cannot be used for concentration requirements (CS 124 equivalent)
MIT 6.036: Introduction to Machine Learning As of Spring 2021, cannot be used for concentration requirements (CS 181 equivalent)
MIT 6.034: Artifical Intelligence As of Spring 2021, cannot be used for concentration requirements (CS 182 equivalent)
MIT 18.600 (18.440) Probability and random variables As of Spring 2021, cannot be used for concentration requirements (STAT 110 equivalent)
MIT 6.033: Computer Systems Engineering As of Spring 2021, cannot be used for concentration requirements (CS 16x equivalent)

If you have questions about what courses (at Harvard, MIT, or elsewhere) count for concentration credit, feel free to contact the DUSes.