Mathematics 1 The Graduate Division will admit students for a second doctoral degree Mathematics only if they meet the following guidelines: 1. Applicants with doctoral degrees may be admitted for an additional The Department of Mathematics offers both a PhD program in doctoral degree only if that degree program is in a general area of Mathematics and Applied Mathematics. knowledge distinctly different from the field in which they earned their Students are admitted for specific degree programs: the PhD in original degree. For example, a physics PhD could be admitted to a Mathematics or PhD in Applied Mathematics. Requirements for the doctoral degree program in music or history; however, a student with Mathematics and Applied Mathematics PhDs differ only in minor a doctoral degree in mathematics would not be permitted to add a respects, and no distinction is made between the two in day-to-day PhD in statistics. matters. Graduate students typically take 5-6 years to complete the 2. Applicants who hold the PhD degree may be admitted to a doctorate. professional doctorate or professional master’s degree program if there is no duplication of training involved. Continuing students wishing to transfer from one program to another should consult the graduate advisor in 910 Evans Hall. Transfers Applicants may apply only to one single degree program or one between the two PhD programs are fairly routine, but must be done prior concurrent degree program per admission cycle. 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 Required Documents for Applications in mathematics must present very strong evidence of capability for 1. Transcripts: Applicants may upload unofficial transcripts with your mathematical research. application for the departmental initial review. If the applicant is admitted, then official transcripts of all college-level work will be Students seeking to transfer to the department's PhD programs required. Official transcripts must be in sealed envelopes as issued from other campus programs, including the Group in Logic and the by the school(s) attended. If you have attended Berkeley, upload Methodology of Science, must formally apply and should consult the Vice your unofficial transcript with your application for the departmental Chair for Graduate Studies. initial review. If you are admitted, an official transcript with evidence Admission to the University of degree conferral will not be required. 2. Letters of recommendation: Applicants may request online letters Minimum Requirements for Admission of recommendation through the online application system. Hard The following minimum requirements apply to all graduate programs and copies of recommendation letters must be sent directly to the will be verified by the Graduate Division: program, not the Graduate Division. 3. Evidence of English language proficiency: All applicants who have 1. A bachelor’s degree or recognized equivalent from an accredited completed a basic degree from a country or political entity in which institution; the official language is not English are required to submit official 2. A grade point average of B or better (3.0); evidence of English language proficiency. This applies to institutions 3. If the applicant has completed a basic degree from a country from Bangladesh, Burma, Nepal, India, Pakistan, Latin America, or political entity (e.g., Quebec) where English is not the official the Middle East, the People’s Republic of China, Taiwan, Japan, language, adequate proficiency in English to do graduate work, as Korea, Southeast Asia, most European countries, and Quebec evidenced by a TOEFL score of at least 90 on the iBT test, 570 on (Canada). However, applicants who, at the time of application, have the paper-and-pencil test, or an IELTS Band score of at least 7 on a already completed at least one year of full-time academic course 9-point scale (note that individual programs may set higher levels for work with grades of B or better at a US university may submit an any of these); and official transcript from the US university to fulfill this requirement. The following courses will not fulfill this requirement: 4. Sufficient undergraduate training to do graduate work in the given field. • courses in English as a Second Language, Applicants Who Already Hold a Graduate Degree • courses conducted in a language other than English, The Graduate Council views academic degrees not as vocational training • courses that will be completed after the application is submitted, certificates, but as evidence of broad training in research methods, and independent study, and articulation of learning. Therefore, applicants who already have academic graduate degrees should be able to pursue new • courses of a non-academic nature. subject matter at an advanced level without the need to enroll in a related or similar graduate program. If applicants have previously been denied admission to Berkeley on the Programs may consider students for an additional academic master’s or basis of their English language proficiency, they must submit new test professional master’s degree only if the additional degree is in a distinctly scores that meet the current minimum from one of the standardized tests. different field. Official TOEFL score reports must be sent directly from Educational Test Services (ETS). The institution code for Berkeley is 4833. Official Applicants admitted to a doctoral program that requires a master’s degree IELTS score reports must be sent electronically from the testing center to to be earned at Berkeley as a prerequisite (even though the applicant University of California, Berkeley, Graduate Division, Sproul Hall, Rm 318 already has a master’s degree from another institution in the same or MC 5900, Berkeley, CA 94720. TOEFL and IELTS score reports are only a closely allied field of study) will be permitted to undertake the second valid for two years. master’s degree, despite the overlap in field. 2 Mathematics Where to Apply level of mathematical preparation, letters of recommendation, and GRE scores. Visit the Berkeley Graduate Division application page (http:// grad.berkeley.edu/admissions/apply/). Degree Requirements Admission to the Program In outline, to qualify for the PhD in either Mathematics or Applied Undergraduate students also often take one or more of the following Mathematics, the candidate must meet the following requirements. introductory Mathematics graduate courses: 1. During the first year in the PhD program: a. take at least four courses, two or more of which are graduate MATH 202A Introduction to Topology and Analysis 4 courses in mathematics; MATH 202B Introduction to Topology and Analysis 4 b. and pass the six-hour written preliminary examination covering MATH 214 Differentiable Manifolds 4 primarily undergraduate material. (The exam is given just before MATH 225A Metamathematics 4 the beginning of each semester, and the student must pass it MATH 225B Metamathematics 4 within their first three semesters.) MATH 228A Numerical Solution of Differential Equations 4 2. Pass a three-hour, oral qualifying examination emphasizing, but not MATH 228B Numerical Solution of Differential Equations 4 exclusively restricted to, the area of specialization. The qualifying MATH 250A Groups, Rings, and Fields 4 examination must be attempted within two years of entering the program. MATH 250B Commutative Algebra 4 3. Complete a seminar offered by the Math department, giving a The Math Department admits new graduate students to the fall semester talk of at least one hour duration. Research presentations held at only. The Graduate Division's Online Application will be available in early Mathematical Sciences Research Institute (MSRI), or Lawrence September at: http://grad.berkeley.edu/admissions/index.shtml (http:// Berkeley National Lab (LBNL) are also acceptable. A Math grad.berkeley.edu/admissions/index.shtml/). Please read the information Department faculty member must be present at the talk and sign the on Graduate Division requirements and information required to complete seminar form confirming. the application. 4. Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee. Copies of official or unofficial transcripts may be uploaded to your 5. Meet the University residence requirement of two years or four application. Please do not mail original transcripts for the review process. semesters. We require three letters of recommendation, which should be submitted The detailed regulations of the PhD program are as follows: online. Please do not mail letters of recommendation for the review process. Course Requirements During the first year in the PhD program, the student must enroll in at For more information, please review the department's graduate least four courses. At least two of these must be graduate courses in admissions webpage at: https://math.berkeley.edu/programs/graduate/ mathematics. Exceptions can be granted by the student's graduate admissions (https://math.berkeley.edu/programs/graduate/admissions/). adviser. We also recommend reviewing our admissions FAQs page at: https:// math.berkeley.edu/programs/graduate/faqs (https://math.berkeley.edu/ Preliminary Examination programs/graduate/faqs/). The preliminary examination consists of six hours of written work given over a two-day period. Most of the examination covers material, mainly Curriculum in analysis and algebra,