harvard math phd qualifying exam

To apply for admissions and financial aid, or for additional information on admissions requirements for the Ph.D. program in pure mathematics, please go to the appropriate Harvard Kenneth C. Griffin Graduate School of Arts and Sciences website listed below. All other inquiries may be directed to the Graduate Program Administrator of the Mathematics Department.

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Graduate Program Administrator

The Department values diversity among its members, is committed to building a diverse intellectual community, and strongly encourages applications from women and minorities.

Preparing the Application The statement of purpose for graduate applications is carefully weighted by the admissions committee. The applicant’s statement should convince the committee that they are able to communicate effectively and with a deep understanding of mathematics. It is not intended to be a biographical sketch or a reflection on one’s decision to enter the field.

Three letters of recommendation are required. Letter writers should be faculty or others qualified to evaluate the applicant’s potential for graduate study in mathematics. The letters must be submitted online and by the application deadline.

Applicants should include any research papers, publications, and other original works they would like to have evaluated by the admissions committee.

The department requests that applicants submit GRE Mathematics Subject Test scores if practical. Applicants should check on the ETS website for test dates in their area to ensure the scores will be submitted before the application deadline. An official score report should be sent to Harvard Kenneth C. Griffin Graduate School of Arts and Sciences using code 3451.

While the admissions committee reviews all applications submitted before the deadline, missing math subject test scores provide one less data point available to evaluate the application. Depending on the strength of the application, the missing subject test scores may put the application at a disadvantage.

Applicants who are non-native English speakers and who do not hold an undergraduate degree from an institution at which English is the primary language of instruction must submit scores from the Internet Based Test (IBT) of the Test of English as a Foreign Language (TOEFL) or the International English Language Testing System (IELTS) Academic test.

Harvard Griffin GSAS requires applicants to upload an electronic copy of undergraduate transcripts. Hard copies of official transcripts are not required at the time of application.

Ph.D. Program in Pure Mathematics The department does not grant a terminal Master’s degree, but the Master’s can be obtained “on the way” to the Ph.D. by fulfilling certain course and language exam requirements.

In general, there is no transfer status application to the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences or to the Department of Mathematics. No formal credit is given for an MSc or MA earned elsewhere. All applicants are considered to be applying as first-year graduate students. The only difference Master’s study may make is to better prepare students for the Qualifying Exam.

All graduate students are admitted to begin their studies in the fall term. The department plans on an entering class of about twelve students. Since the admissions committee receives a few hundred applications, the competition is keen.

Funding Graduate Study Applicants are urged to apply for all funding available to them. If no outside funding is available to the applicant, financial aid in the form of scholarships, research assistantships, and teaching fellowships is available. In general, students who do not have outside support will get scholarship support in their first year, but students are required to act as a teaching fellow for one-half course (i.e. for a one-term course) in their second through fifth years.

The department strongly recommends applicants to seek out and apply for all sources of financing available to them for graduate study. Recommended sources for funding US graduate students are NSF Graduate Fellowships and NDSEG Fellowships . Applicants from the UK are urged to also apply for the Kennedy fellowships and applicants from UK, New Zealand, Canada and Australia for Knox fellowships . International students may apply for the Fullbright IIE or any home country fellowships available for study abroad.

Harvard John A. Paulson School of Engineering and Applied Sciences The Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) offers programs for both the Master’s degree and the Ph.D. degree in Applied Mathematics. Please visit the SEAS website for more information on degrees in applied mathematics at www.seas.harvard.edu

The Qualifying Exam

The qualifying exam is designed to measure the breadth of students’ knowledge in mathematics. While some students are able to pass the qualifying exam in one try, passing the exam early is mainly an indication that a student has attended an undergraduate university with a broad undergraduate program in mathematics. It is not a good predictor of the quality of the eventual PhD dissertation.

Students are required to take the qualifying examination at the beginning in the first term. The exam may prove a useful diagnostic in helping to identify areas in which a student’s knowledge is weak. There is no stigma attached to taking the exam several times, but students are expected to pass the examination by the second year in residence in order to begin more specialized study leading to research work.

The department runs tutorials and offers several introductory graduate courses (e.g. Math 212a, 213a, 230a, 231a, and 232a) to help students acquire the necessary broad basic background in mathematics to pass the exam.

The exam consists of three, three-hour papers held on consecutive afternoons. Each paper has six questions, one each on the subjects: Algebra, Algebraic Geometry, Algebraic Topology, Differential Geometry, Real Analysis and Complex Analysis. Each question carries 10 points. In order to pass each subject, students must obtain at least 20 of the 30 points in that subject. Students are considered to have passed the qualifying exam when they have passed in all six subjects (120 of 180 points) in one sitting, or they have passed at least four subjects in one sitting and obtained an A or A- grade in the basic graduate courses corresponding to the subject(s) not passed. Students are expected take the recommended course(s) at the first opportunity.

Once students have passed the qualifying exam, they no longer need to take math courses for a letter grade and may elect to receive the grade (EXC) excused. Students should inform the instructor at the beginning of the term if they elect to take (EXC) as a grade.

Oral Qualifying Examination in Applied Mathematics

This document sets forth guidelines for the structure of the qualifying examination for students in Applied Mathematics, supplementing the description of the exam in the ​ Policies of the Committee on Higher Degrees ​ .​ It is intended for students preparing for the exam as well as for members of the student’s examination committee.  Students should make themselves familiar with both this document and the school-wide policies  for the exam.

The purpose of the qualifying examination is to:

verify the adequacy of the student's ability and preparation to perform doctoral-level research

assess the student’s ability to synthesize technical knowledge already acquired

determine a student’s depth and breadth of scholarship in a chosen area of application

determine the student’s capacity for originality, synthesis and critical examination; intensity of intellectual curiosity; and clarity of communication.

Preparation

The student, in consultation with his or her advisor, selects an area of application in which the student has done some research and taken appropriate courses and on which the examination is to be based.

No later than two weeks before the examination, the student must deliver to the committee members a short report outlining the research project to be presented, highlighting the background and motivation for the project, the content and results of the project itself, and a brief survey of related work. No specific format is required for the report, although as a guideline it should be between six and ten pages in length. (The page length guideline is not an absolute requirement, but a recommendation.)

The scope of the research project presented during the exam is not meant to represent mature, publishable research. It is acceptable to present negative or partial results. The intention is not to provide evidence that the student has already done PhD level research, but merely that he or she has the capability to do so. The student is expected to have a full knowledge of the technical material and background for the chosen topic. Both students and advisors should keep these scope issues in mind when selecting research projects and subfields.

The exam typically has two components: First, presentation the research project that the student has undertaken within his or her area of application. During the presentation, the committee will ask questions to probe the depth of the student's understanding of the project and related work. If the project has produced preliminary results they can be included in the presentation, however ​conclusive​ ​results are neither expected nor required​. Second, an oral examination of the student's technical expertise and breadth of knowledge within the application area.

As specified in the ​Policies of the CHD​ document, the qualifying examination must be taken by the end of May of the student’s second year of graduate study. No exceptions are made to this deadline without a prior written petition to the CHD.

It is the student’s responsibility to schedule the exam for 2-hour time block when all of the committee members are available. Once a date and time has been agreed upon, the student must contact the Office of Academic Programs by emailing ​[email protected]​ for official scheduling.

Criteria for Passing the Qualifying Examination

The outcome is based on the exam committee's determination of the student's ability and preparation for undertaking research in his or her chosen application area. Aspects include:

Did the student demonstrate adequate technical depth?

Was the quality of the presentation clear, in terms of oral delivery, visual materials, and answers to questions?

Was the motivation for the chosen research project adequate?

Did the student present a detailed and thorough discussion of prior work?

Did the student demonstrate a breadth of knowledge in his or her chosen area, beyond the specific research project presented during the exam?

All committee members must be satisfied that the student has met these criteria in order to pass the exam. Apart from the presentation and discussion during the examination itself, the committee may use other means at its disposal to determine the outcome of the examination, including a review of the student's full record.

As stated in ​Policies of the CHD​, the qualifying committee may declare the student to have passed​ the exam (perhaps with stipulation of further requirements), to have ​failed​ the exam, or may declare the result to be ​inconclusive.​ Typical stipulations include completion of additional coursework, a further oral presentation, or submission of a satisfactory paper for publication by a certain date. In the case of an inconclusive outcome, the committee will specify a future date range (typically between 3 and 6 months, taking term boundaries into account) during which the student may schedule a second examination, the result of which must be conclusive (pass/fail).

[August 2018]

In Applied Mathematics

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PhD Qualifying Exams

Current Requirement: To qualify for the Ph.D. in Mathematics, students must pass two examinations: one in algebra and one in real analysis. 

Requirement for students starting in Autumn 2023 and later:  To qualify for the Ph.D. in Mathematics, students must choose and pass examinations in two of the following four areas: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics. 

The exams each consist of two parts. Students are given three hours for each part.

Topics Covered on the Exams:

Algebra Syllabus

Applied Mathematics Syllabus

 Geometry and Topology Syllabus

Real Analysis Syllabus

Past and Practice Qualifying Exams

Timeline for Completion:

Current Requirement: Students must pass both qualifying exams by the autumn of their second year. Ordinarily first-year students take courses in algebra and real analysis throughout the year to prepare them for the exams. The exams are then taken at the beginning of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn. 

Because some students have already taken graduate courses as undergraduates, incoming graduate students are allowed to take either or both of the exams in the autumn. If they pass either or both of the exams, they thereby fulfill the requirement in those subjects. However, they are in no way penalized for failing either of the exams.

Requirement for students starting in Autumn 2023 and later: Students must choose and pass two out of the four qualifying exams by the autumn of their second year. Students take courses in algebra, real analysis, geometry and topology, and applied math in the autumn and winter quarters of their first year to prepare them for the exams. The exams are taken during the first week of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn. 

Because some students have already taken graduate courses as undergraduates, incoming graduate students are allowed to take any of the exams in the autumn. If they pass any of the exams, they thereby fulfill the requirement in those subjects. However, they are in no way penalized for failing any of the exams.

Exam Schedule

Unless otherwise noted, the exams will be held each year according to the following schedule:

Autumn Quarter:  The exams are held during the week prior to the first week of the quarter. Spring Quarter:  The exams are held during the first week of the quarter.

The exams are held over two three-hour blocks. The morning block is 9:30am-12:30pm and the afternoon block is 2:00-5:00pm.

For the start date of the current or future years’ quarters please see the  Academic Calendar

Upcoming Exam Dates

Spring 2024.

The exams will be held on the following dates: 

Monday, April 1st: Analysis, Room 384H

Wednesday, April 3rd: Algebra, Room 384I

Thursday, April 4th: Geometry & Topology, Room 384I

Friday, April 5th: Applied Math, Room 384I

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Harvard Griffin GSAS strives to provide students with timely, accurate, and clear information. If you need help understanding a specific policy, please contact the office that administers that policy.

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Questions about these requirements? See the contact info at the bottom of the page. 

The First Two Years

The first year is a time to get to know Harvard, the faculty, and fellow students. This is a time to get a sense of what sort of mathematics is done here, at what level, in what style, and by whom. By the end of the first year, it should be possible for the student to have some idea of the area that is most interesting to them and with whom they might work.

While preparing for the qualifying examination or immediately after taking it, the student should enroll in more advanced courses with the idea of choosing a field of specialization. Most students choose a dissertation advisor during their second year or earlier. It is not usually a good idea to wait longer than two years before doing so. One method of choosing a professor with whom to work is to spend a term reading under the direction of two or more faculty members simultaneously on a tentative basis. Faculty members vary a great deal in the way that they go about dissertation supervision; one’s needs in that direction should be taken into account. 

The director of graduate studies and the department chair are available for consultation about choosing an advisor or to help with resolving other issues that might arise.

The Qualifying Examination

The examination is given twice each year: at the beginning of the fall and spring terms. Students are required to take the qualifying examinations (quals) in the fall term of the first year. The qualifying exam consists of three three-hour papers held on consecutive afternoons. 

The department offers a basic sequence of mathematics courses for the first two years in residence, which covers much of the qualifying exam syllabus. A qualifying examination syllabus and samples of prior exams and solutions are available on the department’s website .

A student may take the qualifying examination any number of times beginning in the first term. Students are expected to pass the examination by the end of the second year in residence in order to begin real mathematical research.

It is extremely rare for a student not to pass the qualifying examination by the third year. 

The department does not have a prescribed set of course requirements, but the University requires a minimum of two years of academic residence for the PhD degree.

Please see Enrolling in Courses  for relevant processes. 

The Minor Thesis

For the minor thesis, students choose a topic outside their area of expertise and, working independently, learn it well and produce a written exposition of the subject. The exposition is due within three weeks—or four, if the student is teaching. The minor thesis must be completed before the start of the third year in residence.

The topic is selected in consultation with the student's chosen faculty member other than the student’s PhD dissertation advisor. The topic should not be in the area of the student’s PhD dissertation. (For example, a student working in number theory might do a minor thesis in analysis or geometry). At the end of the allowed time, the student will submit to the faculty member a written account of the subject and be prepared to answer questions on the topic.

The minor thesis is complementary to the qualifying exam. In the course of mathematical research, the student will inevitably encounter areas in which they are ignorant. The minor thesis is an exercise in confronting gaps of knowledge and learning what is necessary efficiently.

Language Requirement

Mathematics is an international subject in which the principal languages are English, French, German, and Russian. For the PhD, every student is required to acquire an ability to read mathematics in one of these three foreign languages. The student’s competence is demonstrated by passing a two-hour written examination. Usually, the student is asked to translate into English a page of text from a mathematics book or journal. Students may, if they wish, use a dictionary. If another language is specifically appropriate to the student’s PhD program, the student may request approval from the director of graduate studies to substitute that language. If a student has studied undergraduate mathematics in a language other than English, the student may request to have the language requirement waived.

The language requirement should be fulfilled by the end of the second year.

All graduate students are required to gain at least two terms of classroom experience in teaching. Teaching may be a source of support for some students. Students without outside support are usually required to teach once in each of years two through five.

Teaching fellows ordinarily prepare and teach their own sections of undergraduate calculus. Participation in course-wide meetings, examination writing, grading, and holding office hours are also part of the duties, but routine homework grading is done by a course assistant. There are a few upper-level tutorial seminars taught by experienced teaching fellows.

All students must complete Mathematics 300: Teaching Undergraduate Mathematics and an apprenticeship program run by the department in a term before they start teaching. Students usually complete the course in their first term and the apprenticeship during their first year.

The Master of Arts (AM) degree is not a prerequisite for the PhD degree but may be obtained by students on their way to a PhD. The formal requirements for the continuing AM degree are a minimum academic residence of one year and eight four-credit courses in mathematics at the 100 or 200 level, with at least four at the 200 level, and candidates must pass the language examination.

Applicants are accepted into the PhD program only; the department does not offer a terminal AM degree in mathematics.

The Remaining Years

The doctor of philosophy (PhD) is awarded to students who have demonstrated their mastery of the basic techniques of mathematics and their ability to do independent research. The former is tested in the qualifying examination, the latter in the dissertation. The dissertation, however, is the more important of the two.

The University requires a minimum of two years’ academic residence (sixteen four-credit courses). On the other hand, the PhD usually takes four to five years.

The Dissertation

The PhD dissertation is an original treatment of a suitable subject leading to new results, usually written under the guidance of a faculty member. Many of the more advanced courses and seminars are designed to lead the student to areas of current research.

Traditionally, dissertation defenses are held in March and April for a May degree. Degrees are conferred three times during the year—in November, March, and May, but most students finish for the May degree. The University Commencement is held once in May.

Dissertation presentations are scheduled some weeks prior to the University dissertation submission deadline date. A final draft of the dissertation must be placed in the Birkhoff Library two weeks prior to the advisor’s dissertation report to the faculty. The student should consult their advisor regarding the selection of the required second and third readers to form the dissertation committee. The student’s advisor presents the dissertation to the faculty during the departmental meetings that coincide with the timetable of the University.

Once the faculty members agree the dissertation can move forward, the student may proceed with their oral defense. The oral defense will be in the style of a seminar with a public presentation of about 50 minutes with 10 minutes for questions. The student’s dissertation committee members will attend the defense and formally approve the dissertation.

When the dissertation is accepted, the student can submit the dissertation to the registrar. The final manuscript must conform to the requirements described online in the Harvard Griffin GSAS policies. 

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The qualifying exams.

The purpose of the Qualifying Examinations is to help the student and the Department determine whether or not the student should continue in the Ph.D. program at Yale. These exams are meant to answer whether the student has mastered the basic material in the various fields to qualify as a member of the profession, and whether the student have the ability and preliminary knowledge to carry out a research. 

Passing the Qualifying Exams is one of the basic Ph.D. requirements of the math department, and among the first that students encounter. Each one is a 4-hour written exam. The exams are offered at the end of each semester (though they may be offered at other times by request) and the student is required to pass, at high enough score, all three by the end of the second year. So normally there are 4 chances to take the exams. As there is no limit to the number of times one can take the exam, students are strongly encouraged to take the exam as soon as they feel that they can pass it.  

The exams cover three topics: Algebra, Analysis and Algebraic Topology. The exams in Algebra and Analysis cover many subtopics that are learned in different courses (as can be seen below in the syllabi of the exams), whereas the exam in Algebraic Topology is given in the fall semester as the final exam of the related course, Math 544 (as such, the most updated syllabus of the exam is always the syllabus of the course, find it here  and here ). Thus, the students are encouraged to take the course in their first year and take the exam as the final exam. Past exams are available upon request from the Department  Registrar. 

• Syllabus for the Analysis Qualifying Exam
• Syllabus for the Algebra Qualifying Exam
• Syllabus for the Algebraic Topology Qualifying Exam

Though the exams in Algebra and Analysis are not linked to a specific course, there are several courses that cover some of the advanced topics in the qualifying exams. As such, even though that these courses are not mandatory, they are highly recommended for students that have not taken similar courses.  The list of classes relevant for Algebra can be found in the syllabus. The courses suggestion in Analysis are:  Measure Theory and Integration (Math 320/520a – Fall semester), Intermediate Complex Analysis (Math 315/515b – Spring semester) and Introduction to Functional Analysis (Math 325/525b – Spring semester).

Mathematics

Undergraduate Program

Mathematics is the science of order, and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations. The concentration in Mathematics is designed to acquaint the student with the most important general concepts underlying the three branches of modern mathematics. Concentration in mathematics will provide an adequate basis for further study in either pure or applied mathematics. Students are also eligible to apply for an A.B./A.M. degree program.

The graduate Mathematics Program at Harvard is designed for students who hope to become research mathematicians and show definite promise in this direction. Once the student has demonstrated a command of basic mathematical concepts by passing the qualifying examination, the emphasis is on getting to the frontiers of some field by independent reading, advanced courses, and seminars. The Cambridge area is one of the most active centers of mathematics in the world. Harvard, Brandeis, and Northeastern Universities and the Massachusetts Institute of Technology have an especially close association in mathematics, and the Harvard University Center of Mathematical Sciences and Applications hosts conferences, seminars, and workshops.

The first milestone in the Mathematics PhD program are the qualifying exams. Exams are offered in Fall (before the academic year begins) and in Spring. PhD students must pass at least one exam before the start of their 4th quarter. All exams must be completed before the start of the student's 7th quarter. Failure to meet these deadlines is cause for dismissal from the program. Carefully read the Guidelines for Graduate Qualifying Exams document.

Exam requirements are different depending on which program a student is in. Please refer to the UCSD catalog for specific requirements:  https://www.ucsd.edu/catalog/curric/MATH-gr.html .

During any examination period the student may take as many exams as he or she chooses. The qualifying exams are written and graded by the faculty who teach the courses. The scores are brought before the Qualifying Exam Appeals Committee (QEAC) and the grades are discussed. The final decision as to whether the student has failed or passed (and at what level) is made by QEAC. This decision is based upon exam performance, and performance in exam cognate coursework, though the QEAC is free to consider additional circumstances in rendering its decision. After the QEAC meeting, the PhD staff advisor will inform students when/how they can find out their results.

Students can request to see their exams after grading in order to find out what they did well/poorly on. Students who wish to see their exam for purpose of contesting the grading should be advised that there will be a very strong burden of proof needed to sustain a grade appeal on a graduate exam because of the nature of the exam writing and grading process. Such an appeal is most likely not going change the exam result.

Qualifying Exam Requirements, Old and New

The Department of Mathematics has undertaken a reform of our Qualifying Exams. This brief note explains the old/current system, the new system, and how the changes are being phased in. These requirements apply to PhD students in Mathematics ; Statistics and CSME PhD students have separate requirements administered by the faculty.

Qualifying Exam Courses and Areas

There are 7 qualifying exams administered each Spring and Fall. Each corresponds to a three-quarter graduate course. They are organized into three Areas.

Old/Current Requirements

For PhD students who entered our program in Fall 2023 or earlier, the following are the current requirements to complete the qualifying exams.

• Each exam is assigned one of four grades: PhD Pass, Provisional PhD Pass (also known as PhD- Pass), Masters Pass, and Fail. The grade cutoffs are determined by the instructors who create/grade the exams; those cutoffs are not released to students.
• At least one exam must have a PhD Pass.
• At least one additional exam must have a Provisional PhD Pass or better.
• At least one additional exam must have a Masters Pass or better.
• Students must pass at least one exam from Area 1 , and at least one exam from Area 2 .
• Students must have two exams, each with a Provisional PhD Pass or better, from two different Areas .
• Students must pass at least one exam with a Provisional PhD Pass or better before the start of their 4th quarter .
• Students must complete all the qualifying exams before the start of their 7th quarter

New Requirements

For students who enter our program in Fall 2024 or later, the following are the requirements to complete the qualifying exams.

• PhD Area Pass indicates readiness to begin research in that area. This grade is equivalent to PhD Pass in the current system.
• PhD General Pass indicates sufficient familiarity with the subject to begin research in a different area. This standard is lower than Provisional PhD Pass, and higher than Masters Pass .
• Masters Pass is only relevant for Masters students. A Masters Pass no longer counts towards completion of qualifying exams for PhD students.
• At least one exam must have a PhD Area Pass.
• At least two additional exams must have a PhD General Pass or better.
• Students must complete qualifying exams from at least two different Areas .
• Students must pass at least one exam before the start of their 4th quarter .
• Students must complete all the qualifying exams before the start of their 7th quarter .

Principal Differences

The new system has more flexibility: students no longer have to take quals from both Areas 1 and 2, simply from 2 distinct Areas among 1, 2, and 3. The standards for completion are simplified. Although Masters Pass is no longer a sufficient standard for PhD students, the PhD General Pass standard is lower than the old Provisional PhD Pass standard, and more consistent with the intent of the exams: to prepare students for focused research in one main area.

Phasing In Period

Any current PhD students (who entered in Fall 2023 or earlier) still progressing towards completing the qualifying exams may satisfy either the current or the new requirements . To be precise:

• Each Spring and Fall (in fact starting this past Fall 2023), qual instructors will select cutoffs corresponding to all five possible grades:

PhD Pass = PhD Area Pass > Provisional PhD Pass > PhD General Pass > Masters Pass > Fail

• At each qual session, each PhD student’s file will be evaluated using both the current and the new requirements. It will be judged complete if it satisfies the current requirements or if it satisfies the new requirements.

Caveat : students who entered in Fall 2022 or earlier already have qualifying exams graded only using the old cutoffs. Qualifying exams from Spring 2023 or earlier will not be regraded to compute PhD General Pass cutoffs.

Other Aspects of Qualifying Exam Reforms

In addition to the logistical changes described above:

• Faculty will be undertaking the creation of standardized syllabi for all seven qualifying exams, to be available to PhD students upon entry. This is a process that will take the faculty significant time and energy to complete, and is planned to be available starting in Fall 2024 .
• In the meantime, qualifying exam course instructors will give detailed syllabi in each course (as always, per Academic Senate regulations), and content cutoffs for the exams will be communicated to students by the Graduate Advisor in advance of the qualifying exams. The same content cutoffs will apply to both Spring and Fall qualifying exams, as has been standard.
• There will be closer coordination of mentoring efforts by course advisors and the Vice Chair for Graduate Affairs. All advisors for first-year PhD students will formulate plans for course enrollment for the full year, as well as plans for which qualifying exams to take in Spring 2024 . Advisors should meet again with their advisees before the beginnings of Winter and Spring quarters, and possibly make adjustments at those times.
• Preliminary full year course and qualifying exam plans should be submitted by the advisors to the Graduate Vice Chair by the end of Week 1 of the Fall quarter.

Sample Qualifying Exams

Algebra (Math 200A/B/C): SP04 ,  SP05 ,  SP06 ,  FA06 ,  SP07 ,  FA07 ,  SP08 ,  FA08 ,  SP09 ,  FA09 ,  FA10 ,  SP11 , FA11 ,  SP12 ,  SP13 ,  FA13 ,​​​​ SP14 ,  FA14 ,  SP15 ,  SP16 ,  SP17 ,  FA17 ,  SP18 , FA18 ,  SP19 ,  FA19 ,  SP20,    FA20 ,  SP21 , FA21 , SP22 , FA22 , SP23 , FA23

Applied Algebra (Math 202A/B/C): SP04 ,  FA04 ,  SP05 ,  SP06 ,  SP08 ,  FA06 ,  SP07 ,  FA07 ,  FA11 ,  SP11 ,  SP13 ,  SP15 ,  SP17  ,  FA17 ,  SP18 ,  FA18 ,  SP19 ,  SP20 ,  FA20 ,  SP21 , FA21 , SP22 , FA22 , SP23A , SP23B , FA23A , FA23B , FA23C

Complex Analysis (Math 220A/B/C): SP04 ,  SP05 ,  FA05 ,  SP06 ,  FA06 ,  SP07 ,  FA07 ,  SP08 ,  FA08 ,  SP09 ,  FA09 ,  FA10 ,  FA11 ,  FA15 ,  SP11 ,  SP12 ,  SP13 ,  FA13 ,  SP15 ,  FA16 ,  SP17 ,  FA17 ,  SP18 ,  SP19 ,  FA19 ,  SP20 ,  FA20 ,  SP21 , FA21 , SP22 , FA22 , SP23 , FA23

Numerical Analysis (Math 270A/B/C): SP99 ,  SP00 ,  FA00 ,  SP01 ,  FA01 ,  SP02 ,  FA02 ,  SP03 ,  FA03 ,  SP04 ,  FA04 ,  SP05 ,  FA06 ,  SP06 ,  FA07 ,  SP07 ,  SP08 ,  FA08 ,  SP09 ,  FA09 ,  FA10 ,  SP11 ,  SP13 ,  FA15 ,  SP17 ,  FA17 ,  SP18 ,  SP20 ,  FA20 ,  SP21 , FA21 , SP22 , FA22 , SP23 , FA23

Real Analysis (Math 240A/B/C): SP04 ,  FA04 ,  FA05 ,  SP06 ,  FA06 ,  SP07 ,  FA07 ,  SP08 ,  SP09 ,  FA09 ,  FA10 ,  FA11 ,  SP11 ,  SP13 ,  SP15 ,  FA16 ,  SP16 ,  SP17 ,  FA17 ,  SP18 ,  FA18 ,  SP20 ,  FA20 ,  SP21 , FA21 , SP22 , FA22 , SP23 , FA23

Statistics (Math 281A/B): SP99 ,  FA99 ,  SP00 ,  FA00 ,  SP01 ,  SP02 ,  FA02 ,  SP03 ,  FA03 ,  SP04 ,  SP05 ,  SP06 ,  SP07 ,  SP08 ,  SP09 ,  FA10 ,  SP11 ,  SP13 ,  FA15 ,  SP17 ,  FA17 ,  SP18 ,  SP18 Formulas ,  SP19 Part A ,  SP19 Part BC ,  FA19 (Part A) ,  FA19 (Part BC) ,  SP20 ,  FA20 ,  SP21 , FA21 , SP22 , FA22 , SP23AB , SP23C , FA23AB , FA23C

Topology (Math 290A/B/C): SP00 ,  SP01 ,  SP02 ,  FA02 ,  FA03 ,  SP04 ,  FA04 ,  SP05 ,  SP06 ,  SP07 ,  FA06 ,  FA07 ,  SP08 ,  FA08 ,  FA09 ,  SP10 ,  FA10 ,  SP11 ,  SP13 ,  FA15 ,  SP17 ,  FA17 ,  SP18 ,  FA18 ,  FA19 ,  SP20 ,  FA20 ,  SP21 , FA21 , SP22 , FA22 , SP23 , FA23

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Placement Exams 

Harvard College placement exam results help incoming students select the classes that will be most appropriate for them to begin their course of study and achieve their academic goals.  All fields of study are open to all students at Harvard; your placement exams will help you know where to get started.

Background video of aerial view of Harvard University and other b roll video of the inside of campus buidlings

Announcements

Language placement exams begin on March 5, 2024 for current students.

Congratulations to the incoming Class of 2028! Information on your summer placement exams will be available at the end of April.

Have a Question?

Experiencing technical issues, frequently asked questions.

Scores from the online placement exams will appear on your Placement and Test Scores Report, available under Documents in my.Harvard. Results are generally available within 24 hours of submitting an exam (with the exception of the Writing exam.) The report will not be available to incoming students in the summer until mid-July.

The Placement and Test Scores Report is designed to help students and advisors select the most appropriate courses based on their previous academic experiences. It is particularly useful for incoming first year students.

The Report contains three main sections:

• Test Scores from exams taken pre-matriculation
• Harvard placement exams results
• Course recommendations

Pre-matriculation Test Scores

Scores listed in this section include any AP and IB (HL only), SAT, and ACT exams that have been taken before a student arrives at Harvard. While students may have submitted the results for these exams as part of their admissions application, students will need to resend official final reports to the Registrar’s Office. Information about sending these scores can be found on the Registrar’s website.

Harvard Placement Exam Results

Students who take exams in Math, Writing, Life Sciences (Chemistry and Biology), and Languages (French, German, Italian, and Spanish) will see their results listed in this section.

“Harvard Placement” exams refer to exams administered through the online Questionmark system while “Harvard Department” exams refer to exams administered by individual departments (e.g. all other Language exams).

Course Recommendations

Course recommendations are based on the results of any exam listed in the pre-matriculation or placement exams. Here are some general thoughts that may be helpful when reviewing this section:

• The course recommendations are meant to help students identify which courses may be most appropriate based on their prior academic experience.
• Students are advised to follow the recommendations in the Placement Report.
• Students should discuss their recommendations with their academic adviser and with advisers in the relevant department.

If you get disconnected or accidentally close the exam browser, simply return to this online tool and you will be able to click the “Resume” exam button (as long as your exam has not expired, and you still have time remaining). If your exam time has expired, click the “Request Reset” button and submit your reason for the exam restart so that administrators may review your request within two business days and then confirm your exam status via email.  Once the exam time has expired any resets will be from the start of the exam.   

Students with a documented disability may be eligible for accommodations on the placement exams. To request accommodations for placement exams, please contact the Disability Access Office . If you already receive an accommodation for courses you must contact your DAO advisor to request an accommodation for the placement exams. Placement exams should not be taken before accommodations are approved and in place.

You are expected to take the Writing and Math exams during the scheduled time period. If it is unavoidable you may take the Math exam as soon as you are able. In exceptional circumstances, students with unavoidable conflicts may take the Writing exam during a make-up period. To petition to take the Writing exam during the make-up period, please visit the  Online Placement Exams Registration  (OPER) application.

For questions about the Writing Exam, please visit the Writing Program website or email [email protected] .

All incoming first-year students are required to complete the Writing and Math exams, regardless of scores on any other exam. All first-year students interested in studying the sciences are strongly encouraged to take the Life Sciences (Chemistry and Biology) placement exam. A Language and Culture AP score of a 5 or an IB Language (HL only) score of a 7 may be used to fulfill the Foreign Language Requirement. Course recommendations are based on the result of the language placement exam.

No, you may only take a language placement exam once for the purpose of fulfilling the language requirement. Qualifying students who are invited to take a Live Verification Exam (LVE) after completing the placement exam must schedule the LVE at that time. A passing score on the LVE is necessary to fulfill the language requirement and must be taken within the same period as the original exam.

Yes, if you receive a 600 or higher on a Harvard College language exam you may be eligible to fulfill the language requirement.  A Live Verification Exam (LVE) is also required. Students with a qualifying score will be notified by email to sign-up for a time to complete a proctored LVE. The LVE must be completed within the same period as the original exam; it cannot be taken at a later date or during a future exam period. You are not eligible to take a language placement exam for the purposes of fulfilling the language requirement if you have already begun studying that language at Harvard College. This applies to exams in French, German, Italian, and Spanish.

Students may not take a language placement exam in order to fulfill the requirement in a language they have already studied at Harvard.

Departmental language placement exams in all other languages also provide both the opportunity to test out of the language requirement and to receive a course recommendation. The LVE does not apply to those language exams.

If you are a Harvard Graduate Student you may take a language placement exam and you must register through the  Online Placement Exams Registration (OPER) application during an exam period. Exam periods are offered each Fall (October/November), Spring (March/April) and over the Summer. To access an exam during an exam period, first click the “Register” button for an exam. You will then receive an email confirming your registration that includes helpful exam information, and a “Start” exam button will then appear in your list of Current Exams. When you are ready to begin an exam,  click the exam’s “Start” button. 

To obtain your course recommendation email the FAS Registrar’s Office with the subject line “Graduate student DPT results” at [email protected] . Please allow one day to process the results of the exam.

If you would like to request to take a language exam that is currently not offered to determine whether your knowledge is sufficient such that you have fulfilled the language requirement, please contact [email protected] .