© Berlin Mathematical School
The Berlin Mathematical School (BMS) is a joint graduate school of the mathematics departments at the three universities in Berlin: Freie Universität (FU), Humboldt-Universität (HU) and Technische Universität (TU). The BMS is funded by the DFG (German Research Foundation) as part of the "Excellence Initiative".
It integrates the rich Berlin mathematics research environment and broad expertise in mathematics at the three Berlin universities into an excellent environment for graduate studies in one single mathematics graduate school. It is designed to combine many of the traditional strengths of the German PhD training system with new structures modeled on successful graduate schools at US universities which BMS's initiators had themselves experienced as doctoral students and postdoctoral fellows. The program of studies at BMS is taught in English and leads from a Bachelor's degree to an oral Qualifying Exam directly to a doctoral degree in four to five years. More than 200 PhD students from around 50 countries are currently working towards their PhDs at the BMS.
The BMS PhD program consists of two phases: In three to four semesters Phase I leads from a Bachelor's degree level to an oral Qualifying Exam. The course program for Phase I covers both a broad mathematical background and the specialization required for high-level research. Phase II (four to six semesters) is dedicated to thesis research, preferably within one of the focused training programs provided by Research Training Groups (RTGs), International Max Planck Research Schools (IMPRSs), ECMath, the Collaborative Research Centers (CRCs), and the Weierstraß Institute for Applied Analysis and Stochastics (WIAS), or the Konrad-Zuse-Institute (ZIB). The BMS integrates mathematics RTGs, CRCs, and IMPRSs as certified units that provide the research environment and supervision for Phase II students. For entering straight into Phase II, applicants are expected to have a Master's degree or equivalent, or must pass the BMS qualifying exams and meet the regular admission requirements of the Berlin universities' Ph.D. programs.
The BMS offers a wide range of supervision to its students and creates outstanding conditions for study, such as the working environment at the three universities, supervision, and mentoring. Each of the three universities has a BMS area with its own lounge as a gathering point for BMS students. The One-Stop Office advises students on matters ranging from the BMS application process to visa, housing, and child-care, all the way to applying for post-doc positions. BMS professors look after students individually as mentors/advisors, helping each to find the best way through the manifold opportunities of the Berlin mathematics landscape. Women in particular find special encouragement on their mathematics career path. Currently more than 30% of BMS students are women.
Financial support is available in Phase I and Phase II through merit-based scholarships. Applications for funding need to be submitted together with the application for admission. At the moment approximately 50% of the Phase I and 25% of the Phase II students receive BMS scholarships. However, all PhD students in the BMS are financially supported for the duration of their studies. Other possible sources include the RTGs, CRCs, and ECMath and IMPRSs, TA or RA positions at the universities or research institutes.
Applications for scholarships for the 2018/19 academic year can be submitted until 1 December 2017.
The subject of the Berlin Mathematical School is Mathematics, which encompasses many fields that are traditionally termed either "pure" or "applied" mathematics.
The BMS prefers, however, not to make that distinction; instead, the teaching areas covered by the BMS are grouped into seven parts, each of which covers a quite broad, but coherent, part of mathematics. The core offering of the BMS Phase I study program consists of 16 one-semester basic courses, at least two for each of the seven teaching areas. These courses are modern introductions to research in the respective areas, stressing interdisciplinary and trans-disciplinary connections and applications, modern trends and current questions. Their purpose is to provide solid foundations in the field, geared towards ambitious students who after the BMS Phase I will head towards mathematics PhD research work.
The two Basic Courses "Analysis and geometry on manifolds" and "Riemannian geometry" give an introduction to the most important concepts of differential geometry; these are fundamental for Riemannian and symplectic geometry as well as for geometric analysis and mathematical physics. The first course provides an introduction to the basic notions of geometry and analysis on manifolds, while the second one imparts fundamental knowledge in global Riemannian geometry.
The two Basic Courses "Commutative algebra" and "Algebraic geometry" provide a rigorous introduction to the most important objects and concepts of modern algebraic geometry and number theory. The first semester focuses mainly on deepening knowledge in algebra, namely in commutative algebra, which is the basic prerequisite for algebraic geometry and number theory. The second semester then provides an introduction to the concepts of modern algebraic geometry.
The two Basic Courses "Stochastic processes I: discrete time" and "Stochastic processes II: continuous timee" give an introduction to the most important concepts of modern probability theory. These are fundamental to the theory of stochastic processes and their stochastic and statistical analysis, as well as to mathematical finance. The first course focuses mainly on stochastic processes in discrete time. The second gives a solid introduction to continuous-time stochastic processes and the basics of stochastic calculus.
The three Basic Courses in discrete mathematics, discrete optimization, and nonlinear optimization are independent. Each of them is designed to cover basic foundations of the field, in view of current research directions pursued in Berlin. The discrete combinatorics course treats basic structures and methods from the core areas of discrete mathematics, in particular enumerative combinatorics, algebraic combinatorics, and graph theory, topics which are also of great importance in nearly all other parts of mathematics. The discrete optimization course gives a solid understanding of the basic role of discrete optimization, models, methods, and consequences. The course gives a view both of the deep theoretical consequences of discrete optimization models (in terms of duality theory, geometry, and polyhedra, for instance) and of the immense practical importance of optimization tools in economic and industrial applications. Nonlinear optimization is an indispensable tool for dealing with realworld problems, e.g., for identifying system parameters and/or for optimizing the performance of a technical or economical process. In the course we consider nonlinear differentiable optimization problems in finite dimensions. In a mixture of theoretical analysis and numerics we discuss necessary and sufficient optimality conditions for unconstrained and constrained problems. We develop algorithms for the numerical solution of these problems, study their convergence properties and use MATLAB to implement some of them.
This two-semester sequence gives a graduate-level introduction to classical geometries, discrete differential geometry and mathematical visualization and algebraic topology. While noneuclidean and projective geometry are often taught at the undergraduate level at other universities, it is rare to find them at this advanced level. Discrete differential geometry is an area of special research interest in Berlin.
The two Basic Courses "Numerical methods for ODEs" and "Numerical methods for PDEs" provide a rigorous introduction to the most important strategies and concepts of modern numerical mathematics, and are independent of each other. The first course focuses mainly on numerical methods for ordinary differential equations, but also on deepening knowledge in numerical linear algebra, especially regarding iterative methods for large systems. The second semester gives an introduction to partial differential equations from fundamental theory to modern numerical concepts.
The two Basic Courses "Dynamical systems" and "Partial differential equations" provide a thorough introduction to the theory of ordinary differential equations and dynamical systems, and to that of partial differential equations.
In addition to the 16 basic courses, the BMS offers two one-semester courses that will provide students the opportunity to fill potential gaps in their general mathematical background. These courses will not be exclusively aimed at BMS students, but will be part of the master programs of the universities:
The BMS offers an English PhD program. Its purpose is to provide a broad and deep graduate education whose structure is compatible with international standards and thus attracts excellent students from around the world. It is designed to combine the traditional strengths of the German graduate education with the format of successful US graduate schools.
The BMS study program has two phases. Students with a Bachelor's degree start with Phase I. Admission to Phase II is either upon successful completion of Phase I or with a Master's degree or equivalent e.g., German Diplom.
The purpose of the three-semester Phase I study program is to provide all BMS students with an excellent and broad mathematics graduate education, and thus with a secure basis for their own thesis research work. The program of this phase consists of basic courses giving a broad view of mathematics, and first advanced courses including seminar courses, which provide in-depth background in various areas of specialization and thus prepare students for their future thesis research.
The core offering of the BMS Phase I study program consists of 16 one-semester basic courses, two or three for each of the seven teaching areas. The requirement for admission to the Qualifying Exam is the successful completion of five basic courses, including courses from at least three different BMS teaching areas, and two advanced courses: one lecture course of four hours per week (or two of two hours per week) and one seminar.
The coursework is typically completed within the first three semesters, leaving time in the fourth semester for a possible master's thesis and the BMS Qualifying Exam. The Qualifying Exam will be oral and conducted by at least two examiners from the BMS faculty. Two-thirds of the BMS Qualifying Exam is devoted to the student's intended area of research. This could cover eight semester-hours of coursework, for instance one Basic Course and one Advanced Course, but usually goes somewhat beyond standard coursework. In the case that the student is working on or has completed a master's thesis, this part of the Qualifying Exam usually covers the contents of that thesis, and can even take the form of a thesis defense. The final third of the BMS Qualifying Exam is devoted to an unrelated topic, typically the contents of a BMS Basic Course. Since the BMS Areas overlap to some extent, to ensure the desired breadth it is necessary but not sufficient that this course be from a different BMS Area. Passing the Qualifying Exam will assert that the student has reached a sufficient level of general and specialized training to begin high-level research in the chosen area of mathematics.
The Phase II study program, the research phase, has a maximum duration of six semesters. During this phase, students work on their specific thesis projects. Many of them will be integrated into one of the Berlin RTGs, CRCs or IMPRSs. In addition, students in the research phase are offered further advanced courses and special lecture series, some of them organized by the RTGs, CRCs and IMPRSs. Phase II students will also be given the opportunity to gain teaching experience as tutors for basic courses in Phase I. The final examinations will be carried out according to the regulations of the university that confers the PhD degree.
To design and monitor the study program, each student will have a member of the BMS faculty assigned to him or her as a mentor. The mentor will be independent of the thesis supervisor. The thesis supervisor will provide support in all aspects relating to the dissertation, including advice on choosing the right conferences and publishing articles. The separate mentor gives the student advice and feedback, and can help resolve problems and provides non-scientific advice.
On every second Friday during semester time, the Friday colloquia of BMS represent a common meeting point for Berlin mathematics: a colloquium with broad emanation that permits an overview of large-scale connections and insights. The conversation is about "mathematics as a whole," and mathematical breakthroughs are discussed. So far, two Field medalists presented their work. At the lunches prior to the "Sonia Kovalevskaya Colloquia" female students have a chance to discuss the career paths of successful women in mathematics.
In addition, the BMS offers annual Summer Schools, which rotate among the participating universities and have a different focus each year.
The application period for the 2018/19 academic year will start in September 2017 and end on 1 April 2018. Applicants in need of a scholarship must submit their application by 1 December 2017. After that date limited scholarships are available.
Please use our online submission form to apply for the BMS program. Note that in order to access the application form, you have to first register: This is a very simple procedure - see the login form on the main page www.math-berlin.de.
Students wishing to enter Phase I of the BMS are expected to have a bachelor degree or equivalent. For students who are further advanced, part of the Phase I course requirements may be waived. For entering Phase II, students are expected to have a master, a German "Diplom" or an equivalent degree, or to pass the BMS Qualifying Exams. It is not necessary that you have completed your degree by the time you submit your application. You need to have a degree by the time you want to start at BMS! For example, you are pursuing a master degree that will be completed in May. When you submit your application to the BMS in December, you already need to apply for Phase II! If you will have finished your Bachelor degree by October, you are welcome to apply for Phase I even though you currently hold no degree.
The academic calendar at the BMS is in accordance with its three supporting universities (FU, HU, TU):
Applications submitted by 1 December 2017 will be decided in March 2018. You will receive an e-mail notification about the admission decision by the end of March. Some of the applicants will be invited to attend the BMS Days on 19 and 20 February 2018.
Materials required to apply:
German applicants are allowed to submit their application in German! If your native language is German, your "Abitur" or "Matura" grade of at least "befriedigend" in English will serve as proof of English proficiency. If you cannot submit a copy of your "Abitur" or "Matura" or it does not show a grade for English you will have to submit a result of another English language test.
Phase I (three to four semesters) leads students from the Bachelor's degree to the Qualifying Exam. Students need to achieve an average grade of at least "good" on the German grading scale in their Phase I courses to be allowed to take the Qualifying Exam. Students must pass the Qualifying Exam with at least a grade of "good" to be allowed into Phase II. Successfully passing the Phase I confirms that the student achieved a satisfactory level on which the dissertation can be built. Students are now ready to undertake independent research. Students who are either not admitted to take the Qualifying Exam or received grade of less than "good" are given the chance to do a master. The allocation of scholarships for Phase II is based on the student's performance in Phase I and in the Qualifying Exam. Having had a Phase I scholarship does no guarantee a Phase II scholarship!
Berlin Mathematical School (BMS)
Dr. Forough Sodoudi, Managing Director
Raum MA 221
Sekr. MA 2-2
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