caltech mathematics phd

Frequently Asked Questions for Applicants

What is graduate school like at Caltech and how does the admission process work?

Graduate programs in research-intensive institutions like Caltech provide some classroom education, but the majority of the experience is centered around learning through working on an open-ended problem, with the goal of developing the ability to independently formulate and carry out a research program. Graduate students spend the majority of their time in small research groups or individually working with faculty advisors.

Admission to Caltech graduate study is highly competitive. The faculty review all the materials in the application to make a decision; they evaluate many factors including academic preparation, experience and research interests, recommendations from teachers/mentors, and they look for a match between faculty and an applicant's research interests.

Where can I find the application deadlines?

The application deadlines vary by department and range from November 21 to January 1. Please refer to our Application Deadlines document. Applications received after the posted deadline may be considered, but late applicants may be at a disadvantage in terms of being admitted and/or in the allocation of financial aid. Caltech conducts admissions once each year and applicants are considered for admission to the fall term only.

Does Caltech have rolling admissions?

Caltech admits students for the fall term only. Applications are not considered for the winter, spring and summer terms.

When can I expect to receive an admission decision?

Each academic option has a different schedule for considering applications and offers of admission will be made as the faculty make decisions on individual applications. Applicants may be notified at any time in the period between the deadline for submission and April 1. Offers are made as soon as possible so that students will have a chance to consider graduate study at Caltech together with opportunities at other institutions.

Will I be interviewed or have a chance to visit Caltech?

Most academic options host visit days in order for select applicants to learn more about the program, the campus, and community prior to making their decision. The arrangements and schedule for visit days are set by the individual options, and each option will work with selected applicants and faculty to coordinate visits. When in person visits are not feasible, online interviews may also be conducted.

Is there a separate application for financial aid?

In general, most graduate students at Caltech receive full funding for their graduate education. In fact, all doctoral students have full financial support in the form of internal or external fellowships, research assistantships, teaching assistantships, or some combination of fellowship and assistantship support. Most of the funding sources require work authorization. As a consequence, matriculation into the PhD program requires evidence of work authorization, unless special compensation can be arranged with the admitting option. In most cases financial assistance is awarded on an annual basis and is dependent upon satisfactory academic progress. A separate application for requesting financial aid is not required.

For additional questions or assistance related to financial aid, please contact the Graduate Studies Office.

Inquiries regarding loans should be directed to the Office of Financial Aid.

What type of financial support is available?

On average, more than 98% of graduate students offered admission at Caltech are offered a package of merit-based financial support that pays all tuition charges and provides them with a stipend. The only major exception is the case of students in terminal master's programs, who in many cases are self-supported or who have a financial sponsor. These students should refer to the information on financing a graduate education .

Financial support includes research and teaching assistantships, Institute fellowships, and external fellowships. Most of the funding sources require work authorization. As a consequence, matriculation into the PhD program requires evidence of work authorization, unless special compensation can be arranged with the admitting option. For additional information on the various funding sources, please refer to Financial Support .

Do I need to take the GRE exam?

The GRE tests (general and advanced subject) are not required and in most programs, scores will not be considered for admission. Some departments provide an option to submit self-reported scores, but students who choose not to submit scores as part of their application will not be at a disadvantage.

What is the minimum GPA?

Caltech does not have a minimum GPA requirement. However, most successful applicants have a US GPA of at least 3.5 on a 4.0 scale and/or are in the top 5 to 10% of their class.

Are international students required to report a GPA?

GPA's should only be reported for those schools attended within the United States. International GPA's or rankings should not be converted to the standard US grade point average.

Do I need to take an English proficiency exam (i.e., TOEFL, PTE, IELTS)?

Applicants whose first or native language is not English are asked to demonstrate English proficiency as part of the application procedure. Caltech recognizes scores from the Educational Testing Service (ETS) ( www.toefl.org ), Pearson's Test of English Academic (PTE) ( www.pearsonvue.com/pte ), and from the Cambridge Examinations and International English Language Testing System (IELTS) ( www.ielts.org ).

The following exemptions apply:

• Applicants who have studied in the US for two or more years
• Applicants with a degree from a college or university whose primary instruction is in English

Please note that regardless of any documentation of English proficiency submitted as part of the admissions process, all non-native English speakers who have not attended a school where English is the primary language of instruction will be screened prior to enrollment and may be required to take additional English as a Second Language (ESL) courses.

What is the minimum English proficiency score?

There is no minimum requirement for the English proficiency exams. However, all new students who have had limited instruction in English will participate in a one-on-one English evaluation with the ESL instructor during Orientation and may be asked to enroll in an English as a Second Language (ESL) course.

How many letters of recommendation are required?

Three letters of recommendation are required.

Does it help to submit additional letters of recommendation?

The online application currently accepts three letters maximum, so keep in mind that it's important to submit three strong letters from individuals most familiar with you.

From whom should I request letters of recommendation?

Letters should be requested from those individuals who know you best and can attest to your academic capabilities or training. While faculty members and research supervisors can provide the strongest academic recommendations, we recognize that some applicants may also have work experience that relates to their abilities and training. Keep in mind that those individuals writing recommendation letters should be able to address the following information:

• How well the applicant is known and in what capacity
• If the applicant has the intellectual capability, experimental ability, fundamental training, creativity, and motivation to be successful as a student at Caltech
• Whether the applicant would be encouraged to do doctoral research under the reference writer's supervision
• If English is not the native language, how well does the applicant read, write, and converse in English?
• How does the applicant compare to any previous students who have come to Caltech for their graduate work?

I understand that electronic recommendations are preferred, but can my referee(s) submit a paper recommendations instead?

Yes, individuals unable to submit materials electronically may send materials to:

Graduate Studies Office, Mail Code 230-87, California Institute of Technology, 1200 E. California Boulevard, Pasadena, CA 91125; or Email [email protected]

Be sure that the applicant's name is clearly indicated on any supporting documents not submitted with the application.

How will Caltech evaluate grades from spring term 2020 due to disruptions caused by COVID-19?

The Graduate Admissions Committees recognize that applicants enrolled during the spring term 2020 and beyond may pursue pass/fail or other non-standard grading options, and applicants will not be asked to notate or document these changes to the grading system on submitted transcripts.

My grades will not be posted for the most recent term prior to the application deadline. Should I wait to submit my transcripts or upload my transcripts to date?

The most recent transcripts available should be uploaded with the application form. Grade reports for additional terms are not needed for application purposes and once the application is submitted, you will not be able to submit updated transcripts. Official, sealed transcripts documenting attendance and all degrees conferred at each college or university will be required for admitted students prior to enrollment.

Do I need to submit official transcripts?

For the purpose of applying, unofficial and scanned copies of an original transcript or university generated web printouts are accepted. Please note, however, that any electronic submissions must be unofficial records from the university or college attended. Hand-typed listings of courses prepared by the applicant will not be considered. Official transcripts documenting attendance and the degree awarded at each college or university will be required for admitted students prior to enrollment.

How many copies of the transcript are required?

One copy of your transcript from each college or university attended is required.

I am interested in applying for a Master's degree, but this degree is not one of the available choices.

Very few departments admit directly for the Master of Science degree. Currently, only applicants to Aeronautics, Electrical Engineering, and Space Engineering may apply for a terminal Master's degree. All other departments admit for the PhD degree only.

I would like to apply to more than one department. Should I submit two separate applications?

Applications will not be accepted for more than one academic option per admission cycle. In reviewing your application, the admission committee of the option to which you have applied may recommend that your application be reviewed by another option. If your application is referred to another option you will not be charged any additional fees or be asked to submit a duplicate application.

How do I apply for a fee waiver?

The fee waiver request form is included as part of the online application under payment options. In order to demonstrate financial hardship, applicants requesting a fee waiver will be asked to provide earned income and expenses and explain any circumstances that impact their ability to pay the application fee. Once an application is submitted, fee waiver requests will be individually reviewed, and decisions will be sent through the online admissions system.  If a fee waiver is not granted, applicants will have the opportunity to submit additional documentation for further review demonstrating financial hardship or submit payment.

Can I make changes to the application or submit additional documents after submission?

Once the application has been submitted, you will not be able to modify supporting documents, so please proofread your materials thoroughly before submission. If there is a major error in your application, please contact the Graduate Studies Office ( [email protected] ) for instructions.

Do you have admission counselors?

Caltech does not have admissions counselors at the graduate level. Most information can be located online through the Graduate Studies Office website ( www.gradoffice.caltech.edu ) or the main Caltech homepage ( www.caltech.edu ) and searching by area of interest. The admissions staff cannot provide information on the likelihood of admission or how to prepare a successful application. Specific questions regarding current research or prerequisites should be directed to the department to which you are applying.

Computing and Mathematical Sciences

Data-driven modeling is becoming increasingly critical in diverse application domains such as machine learning, vision, control systems, biological and engineered networks, neuroscience, economics, and privacy, as well as in many areas of the physical sciences, including high energy physics, earthquake modeling, astronomy, and exploration geophysics. There is enormous potential for research on data-intensive activity of this type, which is highlighted by the emergence of new fields such as “Big Data,” “Decision Science,” and “Network Science.” However, the theoretical foundations of these subjects remain underdeveloped, limiting our understanding and development.

The mission of the CMS graduate program is to address this need by exploring and developing the fundamental mathematical, computational, and economic tools necessary to advance data-intensive science and engineering. That is, we aim to forge the algorithmic foundations necessary to move from data, to information, to action. Key to this mission is a core focus on “algorithmic thinking.” Algorithms are not just the basis for advanced technology, they are intrinsic components of diverse fields such as biology, physics, and economics. Studying the structures and mechanisms that communicate, store, and process information from this viewpoint—whether these structures are expressed in hardware and called machines, in software and called programs, in abstract notation and called mathematics, or in nature and society and called biological or social networks and markets—is crucial to pushing scientific boundaries. Simply put, it is almost impossible to do research in any scientific or engineering discipline without the ability to think algorithmically.

Because of the diversity of fields where algorithmic thinking is fundamental, there are broad differences in how algorithms are formalized, applied, and studied across areas. Over the years, these differences have been codified and the “language of algorithms” is actually quite distinct across, e.g., computer science, applied math, and electrical engineering. However, a broad view of algorithmic thinking is crucial to scientific breakthrough; and the goal of this program is to train scholars to have an interdisciplinary, cross-cutting view of algorithms.

Faculty and students in CMS are active in a broad array of research areas. Some of these include algorithms, complexity, algorithmic economics, feedback and control, inference and statistics, information systems, machine learning, networked systems, vision, optimization, quantum information, scientific computing, and uncertainty quantification.