harvard math phd requirements

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Application Requirements

We look forward to learning about you through your application.

Here you'll find a detailed explanation of each admission application requirement. Most of the information here applies to both first-year and transfer applicants, and requirements are the same for domestic and international applicants.  

Don't forget to reference our Application Tips for guidance on filling out the Common Application.

Application

We accept the Common Application  and the Coalition Application by Scoir . Both are treated equally by the Admissions Committee. Complete and submit your materials as soon as possible to ensure full and timely consideration of your application. Your portions of the application are due by the application deadlines (November 1 for Restrictive Early Action and January 1 for Regular Decision); high school counselors are given an additional week to submit materials on your behalf. 

If you use the Common Application , you must submit your application before your supporting materials (Secondary School Report, Teacher Recommendations, etc.) can be released to a college. Until you submit your own application sections, no part of your application will be transmitted to the Harvard Admissions Office.

If you use the Coalition Application , remember you must submit the separate Harvard supplement in addition to the application by the application deadline for your application to be considered complete. 

Submitting Your Application

Receiving confirmation of your application.

After you submit your application, we will send an email confirmation with a PIN to access the Applicant Portal. We begin sending these daily application confirmation emails in mid-September each year. Most applicant receive their confirmation email the day after they submit their application online. Applications sent in the mail will take up to two weeks to process.

If you have not received your confirmation email, please check your spam/junk folder for messages from [email protected] or [email protected]. 

If have searched your inbox and still cannot find your confirmation email, we encourage you to check the application system you used and ensure you clicked "Submit" and not just "Save".

If you still cannot locate your application confirmation email, please contact us . Choose the category “Admissions” and then the subject “Applicant Questions (if you've already submitted your application)” in the drop-down menu, or call 617-495-1551.

Paying the application fee or requesting a fee waiver

You may pay your application fee online with a credit card via the Common Application or Coalition Application, Powered by Scoir websites.

You may also send a check or money order to Harvard College Admissions, 86 Brattle Street, Cambridge, MA 02138. Please include the applicant’s name with the payment.

Fee waivers: We are committed to making the application process accessible for all students. If the admissions application fee presents a hardship for you or your family and you plan on applying for financial aid, the fee will be waived. Please follow these instructions to request your fee waiver . Requesting a fee waiver will not disadvantage your application in any way.

Completing the Harvard supplement questions

Complete the Harvard Questions with the Common Application or Coalition Application, Powered by Scoir*. This includes the following five required short-answer questions, each with a 200 word limit. 

• Harvard has long recognized the importance of enrolling a diverse student body. How will the life experiences that shape who you are today enable you to contribute to Harvard?
• Briefly describe an intellectual experience that was important to you. 
• Briefly describe any of your extracurricular activities, employment experience, travel, or family responsibilities that have shaped who you are.
• How do you hope to use your Harvard education in the future?
• Top 3 things your roommates might like to know about you. 

*Please note that the Harvard supplement is separate for the Coalition Application, so you must submit both the application AND supplement for your application to be considered complete. 

Additional application questions

What if i am homeschooled.

Each applicant to Harvard College is considered with great care and homeschooled applicants are treated the same as all other applicants. There is no special process, but all relevant information about your educational and personal background is welcome. In addition to the application, all applicants are required to submit a transcript (which can be created by the family member or agency overseeing your schooling), and recommendations. If the application fee presents a hardship for your family,  simply request a fee waiver .

Hear from Harvard students who were homeschooled, in the Harvard Gazette article ‘ Homeschooled en route to Harvard .’

What if I need to make updates to my application after I submit it?

Do not resend your application in order to make updates. If you need to update your identification or contact information, or send updates, additional information, or corrections, please do so via the  Applicant Portal .

Misrepresentation of Credentials

Be completely accurate in your application materials. If we discover a misrepresentation during the admissions process, you will be denied admission. If you have already been admitted, your offer will typically be withdrawn. If you have already registered, your admission will normally be revoked, and we will require you to leave the College. Harvard rescinds degrees if misrepresentations in application materials are discovered.

The determination that an application is inaccurate or contains misrepresentations rests solely with the Admissions Office and will be resolved outside the student disciplinary process.

School Reports and Teacher Recommendations

Secondary school report.

The secondary school report is a required form that is submitted by your school counselor or another school leader. This form gives an overview of the student's academic record. It includes the applicant's academic transcript(s), a letter of recommendation, and a school profile (if available). If a counselor is unable to submit a letter of recommendation for the applicant, another teacher or school leader may submit an additional recommendation letter. 

Midyear School Report

When you apply, your school counselor will often send your transcript with few or no senior year course grades included. That is why the midyear school report is required - to allow us to review your performance in the first half of your senior year coursework .  The midyear school report must be completed by your school counselor or other school official. Please request that the midyear school report is completed and returned to our office as soon as possible. 

Midyear School Report FAQs

What if i'm applying restrictive early action and i don't have my midyear grades yet.

Restrictive Early Action applicants are not required to submit the midyear report by the November 1 deadline. If you applied Restrictive Early Action and are deferred to Regular Decision, please submit the midyear report and transcript in February, or as soon as your midyear grades are available.

I'm an international student and my academic year is different. Do I still need to submit the midyear report?

If you study the IB curriculum or the A-level curriculum, then we expect that your school will send predicted grades, based on your current classroom work and the results of any internal or mock exams you have taken up to that point. If your school does not issue official or predicted midyear grades for your final year of school, then you do not need to submit the midyear report form, although the item may remain on your checklist.

What if I have already graduated from high school?

If you have already graduated from high school, you should ignore the midyear report requirement (though the item may remain on your Checklist in the Applicant Portal) and simply ask your school to send a final school report if you have not already done so.

Teacher Evaluations

Ask two teachers in different academic subjects who know you well to complete the Teacher Recommendation forms (which includes an evaluation form and a letter of recommendation). If you wish to submit additional letters of recommendation, you can do so after you submit your application. In your application confirmation email, there will be a personalized link to send to your recommenders.

What courses should I take to prepare for applying to Harvard?

There is no “one size fits all” rule about which curriculum to study during secondary school years. Students should challenge themselves by taking courses deemed appropriate by their teachers and counselors. But some students believe that “more is always better” when it comes to AP, IB or other advanced courses.

While some students prosper academically and personally by taking large numbers of such courses, others benefit from a more balanced approach that allows them additional time for extracurricular and personal development. Even the best students can be negatively affected by taking too many courses at once, and might benefit instead from writing, reading or research projects on subjects of great interest to them.

To learn more, read our Guide to Preparing for College. To avoid the “burnout” often seen among secondary school students, please refer to our article, Time Out or Burn Out for the Next Generation .

Is there a specific math requirement?

Applicants to Harvard should excel in a challenging high school math sequence corresponding to their educational interests and aspirations. We recommend that applicants take four years of math courses in high school. Ideally, these math courses will focus on conceptual understanding, promote higher-order thinking, and encourage students to use mathematical reasoning to critically examine the world. Examples include rigorous and relevant courses in computer science, statistics and its subfields, mathematical modeling, calculus, and other advanced math subjects.

Students’ math records are viewed holistically, and no specific course is required. Specifically, calculus is not a requirement for admission to Harvard. We understand that applicants do not have the same opportunities and course offerings in their high schools. Moreover, many programs of study at Harvard do not require knowledge of calculus. We encourage applicants to take the courses that are available to them and aligned with their interests and goals.

Students intending to study engineering, computer science, physics, mathematics, statistics or other fields where calculus is needed may benefit from taking calculus in high school. However, students at Harvard can still pursue such fields by starting with one of our introductory calculus classes that has no high school calculus prerequisite. On balance, we encourage all students to master foundational mathematical material instead of rushing through any of the more advanced courses.

Final School Report and Transcripts

All admitted students who choose to enroll are required to send a Final School Report and transcript as soon as their final grades become available – no later than July 1. The Final School Report and transcript should be completed and sent by a school counselor or other school official through Parchment/Docufide or Scrip-Safe International, if your school has access to these submission options.

IB students should send their final results as soon as they are released in mid-July. We will expect to see final A levels results by mid-August.

Standardized Test Scores

Harvard College will require the submission of standardized test scores from applicants for admission as part of the comprehensive application process that takes a whole-student approach.

The College will accept the SAT or ACT to meet the standardized testing requirement. In exceptional cases when those tests are not accessible, one of the following can meet the requirement:   

• AP exam results
• IB Actual or Predicted Scores   
• GCSE/A-Level Actual or Predicted Results   
• National Leaving Exams Results or Predictions

Standardized Testing FAQs

Can i self-report my test scores.

Yes. Applicants may provide self-reported SAT and ACT test scores (including Subject Tests, Advanced Placement, IB, etc.). Admitted students who decide to enroll at Harvard College will be required to submit official test scores.

How do I send my test scores?

You are free to use the College Board Score Choice option or the similar option offered by the ACT. Our official codes are 3434 for the College Board SAT Reasoning Tests and 1840 for the ACT if you are submitting official test scores as part of your application.

• How to send your SAT scores
• How to send your ACT scores

Are there test score "cutoffs"?

There are no score cutoffs, and we do not admit “by the numbers.” For the ACT, we will evaluate your highest composite score and any other scores you choose to share with us. We take into account your educational background when reviewing your scores.

How should I prepare for standardized tests?

Our admissions committee understands that opportunities to prepare for standardized tests vary greatly for students of different socioeconomic backgrounds. You may find it helpful to utilize free-test prep from Khan Academy or join a free SAT bootcamp on Schoolhouse.world . The ACT provides sample tests to practice.  Such free programs could help students from under-resourced schools by providing the academic tools that will serve them well on standardized tests and also in college. Students can also do well by studying widely and deeply  on their own with the help of family, school, or community organizations.

What do standardized tests and grades indicate about academic preparation for college?

SAT and ACT tests are better predictors of Harvard grades than high school grades. However, admission officers understand that not all students attend well-resourced schools throughout their lives, and that those who come from modest economic backgrounds or first-generation college families may have had fewer opportunities to prepare for standardized tests.

High school grades in a rigorous academic program can also be helpful in assessing readiness for college courses, but the thousands of secondary schools around the country and the world employ various high school curricula and a wide range of grading systems - and some have no grades at all. Other students have been homeschooled or prepared for college by taking part in multiple schooling opportunities both in person and electronic.

Given the wide variation in how students prepare for Harvard – as well as the fact that most applicants and admitted students have outstanding academic records – it is difficult for high school grades to differentiate individual applications. That does not mean that high school grades are unimportant. Students who come to Harvard have done well day to day in their high school studies, providing a crucial foundation for academic success in college, including a 97% - 98% graduation rate.

Each application to Harvard is read with great care, keeping in mind that talent is everywhere, but opportunity and access are not.

How will Harvard evaluate the new digital SAT?

The College Board's shift to a digital delivery of the SAT will not impact the way in which Harvard reviews test scores within applications. Please  visit the College Board FAQs  for more information.  

Supplemental Materials

Our standard application materials typically give us ample information for making admission decisions. However, we recognize you may have truly exceptional talents or achievements you wish to share, and we want you to have every opportunity to best represent yourself.

At the discretion of the Admissions Committee, supplementary materials—such as music recordings, artwork, or selected samples of academic work—may be evaluated by faculty. These materials are entirely optional.

Material Types

How to submit documents and articles.

Scholarly articles, research, creative writing or other documents of which you are the primary author should be submitted in the Upload Materials section of the Applicant Portal . This is the most efficient and direct method of submitting these materials, because they will be added directly to your official application. All submissions should include a list of any individuals with whom you collaborated in the production of the work. If appropriate, please identify your research sponsor, mentor, and/or laboratory or research group leader and provide a short description of your particular contribution to the work.

How to submit media (video, audio, or images)

You may submit optional supplementary media materials (e.g. videos, audio recordings, or images) electronically via Slideroom . Details for submissions in art, dance or choreography, musical performance or composition, will be found on the Slideroom website. There is a small submission fee, but if this fee causes you economic hardship, you may request a fee waiver at the point of submission. You may also contact us to request a fee waiver.

If you encounter technical difficulties on Slideroom, you may submit a document via your portal with YouTube video links. Our team may follow up to request a Slideroom submission at a later time. 

Should I submit other academic materials?

Harvard accepts other standardized tests or other academic credentials if you choose to submit them. In any admissions process, additional information can be helpful. For example, Advanced Placement, International Baccalaureate, A-levels, national leaving examinations, national or international contests, early high school assessment scores such as the PSAT or pre-ACT, or courses taken outside your school during the school year or summer are just some examples of information that could be submitted. Subject Tests and the essay portion of the SAT have been terminated, except in certain special circumstances. Harvard admission officers review all materials that an applicant submits, so if you’ve already taken Subject Tests or the essay portion of the SAT, you may still submit them along with your other application materials.

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Applied Mathematics

Undergraduate Program

The Applied Mathematics concentration consists of a broad undergraduate education in the mathematical sciences, especially in those subjects that have proved vital to an understanding of problems arising in other disciplines, and in some specific area where mathematical methods have been substantively applied. For concentrators, a core learning objective is building and demonstrating foundational knowledge in computation, probability, discrete, and continuous mathematics through the successful completion of the foundation and breadth courses. Students are also eligible to apply for an A.B./S.M. degree program.

Harvard School of Engineering offers a Doctor of Philosophy (Ph.D.) degree in Applied Mathematics. Doctoral students may earn the masters degree en route to the Ph.D. Students are drawn to Applied Mathematics by the flexibility it offers in learning about how to apply mathematical ideas to problems drawn from different fields, while remaining anchored to empirical data that drive these questions. Research and educational activities have particularly close links to Harvard’s efforts in Mathematics, Economics, Computer Science, and Statistics. Graduates go on to a range of careers in industry, academics, to professional schools in business, law, medicine, among others. All Ph.D.s are awarded through the Harvard Graduate School of Arts and Sciences.

Applied Mathematics

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Applied Mathematics is an area of study within the Harvard John A. Paulson School of Engineering and Applied Sciences. Prospective students apply through Harvard Griffin GSAS; in the online application, select  “Engineering and Applied Sciences” as your program choice and select “PhD Applied Math” in the Area of Study menu.

Applied Mathematics at the Harvard John A. Paulson School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities

Working individually and as part of teams collaborating across the University and beyond, you will partner with faculty to quantitatively describe, predict, design and control phenomena in a range of fields. Projects current and past students have worked on include collaborations with mechanical engineers to uncover some of the fundamental properties of artificial muscle fibers for soft robotics and developing new ways to simulate tens of thousands of bubbles in foamy flows for industrial applications such as food and drug production.

Graduates of the program have gone on to a range of careers in industry in organizations like the Kingdom of Morocco, Meta, and Bloomberg. Others have secured faculty positions at Dartmouth, Imperial College in London, and UCLA.

Standardized Tests

GRE General:  Not accepted

APPLICATION DEADLINE

Questions about the program.

Applied Mathematics

Applied Mathematics at Harvard School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities.

Working individually and as part of teams collaborating across the University and beyond, faculty and students in Applied Mathematics seek to quantitatively describe, predict, design and control phenomena in a range of fields. This involves the study of relations between models and observations, while examining the mathematical foundations and limitations of these models and techniques.

Research and educational activities have particularly close links to Harvard's efforts in  Mathematics ,  Economics ,  Computer Science , and  Statistics . 

Applied Math Programs

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The Applied Math/Economics (AM/Ec) "marriage" is a rational one. Mathematical modeling is used extensively in economics, and the foundation of economic theory is formed on a mathematical basis.

The Applied Math/Economics requirements include five Economics classes:

• ECON 1010A or ECON 1011A (preferably ECON 1011A)
• One of ECON 1126, STAT 186, or STAT 111
• Two economics classes from this list (if you would like more information on which courses historically counted, please email [email protected] )

Ordinarily, Applied Math / Economics does not give concentration credit for the less mathematical classes ECON 1010B or ECON 1123.

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Winners of 2024 harvard student prizes.

On May 6, 2024, the department celebrated the achievements of our undergraduate and graduate students with awards presentation:

Jack T. Sanderson Memorial Prize in Physics for graduating seniors with the highest GPA among concentration courses

• Mincheol Park     

Carol Davis Prize Awarded to a Physics concentrator in recognition of their efforts to build a more inclusive and welcoming environment in the Physics Department.

• Mincheol Park, " for his work as an exceptional Course Assistant who goes above and beyond to support his peers. And, his work as the Chair of Chilloquium, a series of weekly moderated conversations between students and experienced career physicists, to expand the networks of our Physics community."
• Emma Weller ,  "for her exceptional dedication to SPS and the Physics community. Emma is a diligent and consistent member of the SPS Events and Panels team who does not hesitate to get involved and show her community spirit. Countless students have benefited from poundages of pumpkins tossed out the window and gallons of LN ice-cream served."  
• Victoria Zhang  and  Qijia Zhou ,  "for their work as the Co-Presidents of the Society of Physics students to bring the community together through various fun and creative programs, while sharing their love of physics with the greater Harvard community. Thanks to their efforts, the Harvard chapter of SPS was awarded the Distinguished Chapter of the Year award for 2022-2023."  

White Prize Awarded annually to Teaching Fellows who have demonstrated excellence in teaching introductory courses in Physics. 

• Caelan Brooks 
• Miles Butler 
• Chandrika Chandrashekar  
• Dominic Chang – not sure if attending 
• Diyaselis Delgado Lopez 
• Aurelien Dersy 
• Elise Koskelo 
• Joyce Kwan 
• Madelyn Leembruggen 
• Moriah Lim 
• Noah Miller 
• Anmol Raina 
• Barbara Skrzypek 
• Ophelia Sommer 
• Shivesh Sood 
• Noah Toyonaga 
• Arthur Tsang 
• Gemma Zhang   

Merit Fellowship Winners Each year, the department chooses an outstanding experimentalist and theorist for nomination for a Merit Fellowship. The nominees must have passed their qualifying exams and have an approved dissertation prospectus. The winners of the Merit Fellowship are chosen by the Graduate School of Arts and Sciences from among all nominations from all departments, and the award allows students to focus their time on research and or writing. This year two Physics students were awarded a Merit Fellowship.

• Maine Christos
• Patrick Ledwith  

Gertrude and Maurice Goldhaber Prize Awarded annually to the outstanding theoretical and experimental graduate students who have passed their qualifying oral examinations in the preceding year.

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