About the Program
The Department of Mathematics offers both a PhD program in Mathematics and Applied Mathematics.
Students are admitted for specific degree programs: the PhD in Mathematics or PhD in Applied Mathematics. Requirements for the Mathematics and Applied Mathematics PhDs differ only in minor respects, and no distinction is made between the two in day-to-day matters. Graduate students typically take 5-6 years to complete the doctorate.
Continuing students wishing to transfer from one program to another should consult the graduate advisor in 910 Evans Hall. Transfers between the two PhD programs are fairly routine, but must be done prior to taking the qualifying examination. It is a formal policy of the department that an applicant to the PhD program who has previous graduate work in mathematics must present very strong evidence of capability for mathematical research.
Students seeking to transfer to the department's PhD programs from other campus programs, including the Group in Logic and the Methodology of Science, must formally apply and should consult the Vice Chair for Graduate Studies.
Admissions
Admission to the University
Applying for Graduate Admission
Thank you for considering UC Berkeley for graduate study! UC Berkeley offers more than 120 graduate programs representing the breadth and depth of interdisciplinary scholarship. A complete list of graduate academic departments, degrees offered, and application deadlines can be found on the Graduate Division website.
Prospective students must submit an online application to be considered for admission, in addition to any supplemental materials specific to the program for which they are applying. The online application can be found on the Graduate Division website.
Admission Requirements
The minimum graduate admission requirements are:
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A bachelor’s degree or recognized equivalent from an accredited institution;
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A satisfactory scholastic average, usually a minimum grade-point average (GPA) of 3.0 (B) on a 4.0 scale; and
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Enough undergraduate training to do graduate work in your chosen field.
For a list of requirements to complete your graduate application, please see the Graduate Division’s Admissions Requirements page. It is also important to check with the program or department of interest, as they may have additional requirements specific to their program of study and degree. Department contact information can be found here.
Where to apply?
Visit the Berkeley Graduate Division application page.
Admission to the Program
Undergraduate students also often take one or more of the following introductory Mathematics graduate courses:
| Code | Title | Units |
|---|---|---|
| MATH 202A | Introduction to Topology and Analysis | 4 |
| MATH 202B | Introduction to Topology and Analysis | 4 |
| MATH 214 | Differential Topology | 4 |
| MATH 225A | Metamathematics | 4 |
| MATH 225B | Metamathematics | 4 |
| MATH 228A | Numerical Solution of Differential Equations | 4 |
| MATH 228B | Numerical Solution of Differential Equations | 4 |
| MATH 250A | Groups, Rings, and Fields | 4 |
| MATH 250B | Commutative Algebra | 4 |
The Math Department admits new graduate students to the fall semester only. The Graduate Division's Online Application will be available in early September at: http://grad.berkeley.edu/admissions/index.shtml. Please read the information on Graduate Division requirements and information required to complete the application.
Copies of official or unofficial transcripts may be uploaded to your application. Please do not mail original transcripts for the review process.
We require three letters of recommendation, which should be submitted online. Please do not mail letters of recommendation for the review process.
For more information, please review the department's graduate admissions webpage at: https://math.berkeley.edu/programs/graduate/admissions. We also recommend reviewing our admissions FAQs page at: https://math.berkeley.edu/programs/graduate/faqs.
Doctoral Degree Requirements
Curriculum
Prerequisites
The Department of Mathematics offers two PhD degrees, one in Mathematics and one in Applied Mathematics. Applicants for admission to either PhD program are expected to have preparation comparable to the undergraduate major at Berkeley in Mathematics or in Applied Mathematics. These majors consist of two full years of lower division work (covering calculus, linear algebra, differential equations, and multivariable calculus), followed by eight one-semester courses including real analysis, complex analysis, abstract algebra, and linear algebra. These eight courses may include some mathematically based courses in other departments, like physics, engineering, computer science, or economics.
Applicants for admission are considered by the department's Graduate Admissions and M.O.C. Committees. The number of students that can be admitted each year is determined by the Graduate Division and by departmental resources. In making admissions decisions, the committee conducts a comprehensive review of applicants considering broader community impacts, academic performance in mathematics courses, level of mathematical preparation, letters of recommendation, and GRE scores.
Degree Requirements
In outline, to qualify for the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.
- During the first year in the PhD program:
- take at least four courses, two or more of which are graduate courses in mathematics;
- and pass the six-hour written preliminary examination covering primarily undergraduate material. (The exam is given just before the beginning of each semester, and the student must pass it within their first three semesters.)
- Pass a three-hour, oral qualifying examination emphasizing, but not exclusively restricted to, the area of specialization. The qualifying examination must be attempted within two years of entering the program.
- Complete a seminar offered by the Math department, giving a talk of at least one hour duration. Research presentations held at Mathematical Sciences Research Institute (MSRI), or Lawrence Berkeley National Lab (LBNL) are also acceptable. A Math Department faculty member must be present at the talk and sign the seminar form confirming.
- Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee.
- Meet the University residence requirement of two years or four semesters.
The detailed regulations of the PhD program are as follows:
Course Requirements
Students must take and pass at least four 4-unit courses during the first year of the Ph.D. program; at least two courses per semester. At minimum, two of these courses must be graduate courses (200-level) offered by the Department of Mathematics. Two upper division (100-level) undergraduate courses offered by the Department of Mathematics may also be used toward this requirement. Exceptions may also be considered and must be reviewed by the Head Graduate Advisor for approval.
Preliminary Examination
The preliminary examination consists of six hours of written work given over a two-day period. Most of the examination covers material, mainly in analysis and algebra, and helps to identify gaps in preparation. The preliminary examination is offered twice a year—during the week before classes start in both the fall and spring semesters. A student may repeat the examination twice. A student who does not pass the preliminary examination within 13 months of the date of entry into the PhD program will not be permitted to remain in the program past the third semester. In exceptional cases, a fourth try may be granted upon appeal to committee omega.
Qualifying Examination
To arrange for the qualifying examination, a student must first settle on an area of concentration, and a prospective dissertation supervisor, someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective supervisor, the student forms an examination committee of four members. Committee members must be members of Berkeley's Academic Senate and the Chair must be a faculty member in the Mathematics Department. The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval it is to be circulated to all faculty members of the appropriate sections. The qualifying examination must cover material falling in at least three subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be seen on the Qualifying Examination page on the department website.
The student must attempt the qualifying examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program.
For a student to pass the qualifying examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student, if asked. The student must obtain an official dissertation supervisor within one semester after passing the qualifying examination or leave the PhD program. For more detailed rules and advice concerning the qualifying examination, consult the graduate advisor in 910 Evans Hall.
Master's Degree Requirements
Eligibility
At this time, the MA in Mathematics is a simultaneous degree program only offered to students currently enrolled in a doctoral program at UC Berkeley. The doctoral student must be in good standing in their program and have a faculty adviser in the Mathematics Department who is supportive of the addition of the MA in Mathematics and agrees to supervise the MA work. Current doctoral students must apply during the regular admissions cycle for consideration for fall admission. The degree must be completed prior to or in tandem with the PhD degree. Interested students must inquire with the Mathematics Graduate Student Affairs Officer.
Unit Requirements
Plan I requires at least 20 semester units of upper division and graduate courses and a thesis. At least 8 of these units must be in graduate courses (200 series). These 8 units are normally taken in the Department of Mathematics at Berkeley. In special cases, upon recommendation of the Graduate Adviser and approval of the Dean of the Graduate Division, some of the 8 graduate units may be taken in other departments.
Plan II requires at least 24 semester units of upper division and graduate courses, followed by a comprehensive final examination, the MA examination. At least 12 of these units must be in graduate courses (200 series). These 12 units are normally taken in the Department of Mathematics at Berkeley. In special cases, upon recommendation of the graduate advisor and approval of the dean of the Graduate Division, some of the 12 graduate units may be taken in other departments. All courses fulfilling the above unit requirements must have significant mathematical content. In general, MA students are encouraged to take some courses outside the Department of Mathematics. In many jobs, at least some acquaintance with statistics and computer science is essential; and, for some students, courses in such fields as engineering, biological or physical sciences, or economics are highly desirable.
A breadth requirement consisting of at least one course in each of three fields must be met by all students. Fields include algebra, analysis, geometry, foundations, history of mathematics, numerical analysis, probability and statistics, computer science, and various other fields of applied mathematics. The last category specifically covers courses in a variety of departments, and the graduate adviser may allow more than one such course to count toward the breadth requirement. A depth requirement consisting of a coherent program of three courses all in one of the above fields, at least two of these courses being at the graduate level, must be met. Students interested in a field of applied mathematics are encouraged to take some of these courses outside the department.
Curriculum
| Code | Title | Units |
|---|---|---|
| Courses Required | ||
| Breadth Requirement: | ||
| Select one courses in three fields from the following: | ||
algebra; analysis, geometry, foundations, history of mathematics, numerical analysis, probability and statistics, computer science, applied mathematics | ||
| Depth Requirement: | ||
| Select a coherent program of three courses all in one field from the following: | ||
algebra; analysis, geometry, foundations, history of mathematics, numerical analysis, probability and statistics, computer science, applied mathematics | ||
- Advancement to Candidacy
- Thesis (Plan I)
- Capstone/Comprehensive Exam (Plan II)
- Capstone/Master's Project (Plan II)
Contact Information
Graduate Student Affairs Officer - Academic Advising
Clay Calder
910 Evans Hall
Phone: 510-642-0665
Graduate Student Affairs Officer - Funding & Employment
Christian Natividad
914 Evans Hall