Mathematics Proficiency
Faculty
Michael Anderson, Professor, Ph.D., University of California, Berkeley: Differential geometry.
William Barcus, Professor Emeritus and Director of Mathematics Learning Center, D. Phil, University of Oxford, England: Algebraic topology.
Christopher Bishop, Professor, Ph.D., University of Chicago: Complex analysis.
Melkana Brakalova-Trevithick, Visiting Professor, Ph.D., Sofia University: Geometry and dynamical systems.
Mark de Cataldo, Assistant Professor, Ph.D., University of Norte Dame: Higher dimensional geometry.
Moira Chas, Lecturer, Ph.D., Universitat Autonoma de Barcelona: Topology and dynamical systems.
Ian Dowker, James H. Simons Instructor, Ph.D., Harvard University: Gauge theory; complex geometry.
David Ebin, Professor, Ph.D., Massachusetts Institute of Technology: Global analysis; mathematics of continuum mechanics; partial differential equations.
Janet Fenstermacher, Part-time Lecturer, M.S. in Math/Ed, Adelphi University.
Daryl Geller, Professor, Ph.D., Princeton University: Partial differential equations; harmonic analysis; several complex variables; Lie groups.
James Glimm, Distinguished Professor, Ph.D., Columbia University: Applied mathematics; numerical analysis.
Detlef Gromoll, Professor, Ph.D., University of Bonn, Germany: Differential geometry.
Phyllis Heger-Heinen, Lecturer, M.S., C.W. Post.
Suzanne Hruska, VIGRE Fellow, Ph.D., Cornell University: Dynamical systems, several complex variables.
C. Denson Hill, Professor, Ph.D., New York University: Partial differential equations; several complex variables.
Lowell Jones, Professor, Ph.D., Yale University: Topology; geometry.
Ely Kerman, Simons Instructor, Ph.D., University of California: Symplectic topology and geometry, Hamiltonian dynamical systems.
Alexander Kirillov, Jr., Assistant Professor, Ph.D., Yale University: Representation theory; low dimensional topology; mathematical physics.
Irwin Kra, Distinguished Service Professor, Ph.D., Columbia University: Complex analysis; Kleinian groups, Reimann surfaces; Teichmuller theory; applications to mathematical physics and number theory.
Matthew Kudzin, VIGRE Fellow, Ph.D., Indiana University: Cohomogeneity One manifolds of non-negative curvature and differential calculus.
Paul Kumpel, Professor, Ph.D., Brown University: Algebraic topology. Recipient of the State University Chancellor’s Award for Excellence in Teaching, 1990, and the President’s Award for Excellence in Teaching, 1990.
H. Blaine Lawson, Jr., Distinguished Professor, Ph.D., Stanford University: Differential geometry; topology; algebraic geometry.
Claude LeBrun, Professor, D. Phil, University of Oxford, England: Complex analysis; mathematical physics; differential geometry; algebraic geometry.
Mikhail Lyubich, Professor, Ph.D., Tashkent State University, former Soviet Union: Dynamical systems.
Elyse Magram, Lecturer and Coordinator of the Secondary Teacher Training Program, M.S.E., M.S., University at Stony Brook.
Bernard Maskit, Professor, Ph.D., New York University: Riemann surfaces; Kleinian groups and deformation spaces.
Mikhail Matveyev, James H. Simons Instructor, Ph.D., Michigan State University: Geometric topology of low-dimensional manifolds.
Dusa McDuff, Distinguished Professor, Ph.D., Cambridge University, England: Symplectic topology.
Araceli Medina-Bonifant, Lecturer, Ph.D., Center of Research and Advance Studies of National Polytechnical Institute (CINVESTAV-IPN), Mexico: Holomorphic dynamical systems, several complex variables, geometry complex systems.
Marie-Louise Michelsohn, Professor, Ph.D., University of Chicago: Differential geometry.
John Milnor, Distinguished Professor and Director of the Institute for Mathematical Sciences, Ph.D., Princeton University: Dynamical systems.
Yair Minsky, Associate Professor, Ph.D., Princeton University: Low-dimensional geometry and topology.
Robert Morahan, Lecturer, Ed.C., St. John's University.
Anthony Phillips, Professor, Ph.D., Princeton University: Differential topology.
Bradley Plohr, Professor, Ph.D., Princeton University: Applied mathematics; partial differential equations.
Sorin Popescu, Assistant Professor, Ph.D., University of Saarland, Germany; Algebraic geometry; computational algebraic geometry.
Julio Rebelo, Simons Instructor, Ph.D., Ecole Normale Superieure de Lyon: Dynamic systems, group actions.
Justin Sawon, Simons Instructor, Ph.D., Cambridge University, U.K.: Complex algebraic geometry, low-dimensional topology.
Rasul Shafikov, Simons Instructor, Ph.D., Indiana University: Analytical continuation of holomorphic mappings.
Santiago Simanca, Director of Computing and Lecturer, Ph.D., Massachusetts Institute of Technology: Differential geometry analysis.
Dennis Sullivan, Distinguished Professor, Ph.D., Princeton University: Dynamical systems; topology; fluid mechanics.
Scott Sutherland, Associate Professor, Ph.D., Boston University: Dynamical systems; root finding algorithms; computing.
Leon Takhtajan, Professor, Ph.D., Leningrad Branch of the Steklov Mathematical Institute, Russia: Mathematical physics.
John Terilla, VIGRE Fellow, Ph.D., University of North Carolina: Deformation theory, mathematical physics, quantum computing.
Jared Wunsch, Assistant Professor, Ph.D., Harvard University: Partial differential equations.
Saeed Zakeri, Visiting Assistant Professor, Ph.D., Stony Brook University: Dynamic systems.
Bin Zhang, Simons Instructor, Ph.D., Penn State University: Algebraic geometry, mathematical physics, representation theory.
Peter Zograf, Visiting Professor, Ph.D., Steklov Mathematical Institute, Leningrad: Riemann surfaces & complex geometry.
Affiliated Faculty
Michael Taksar, Applied Mathematics and Statistics
Teaching Assistants
Estimated number: 60
Major and Minor in
Mathematics
Department of Mathematics, College of Arts and Sciences
Chairperson: Detlef Gromoll
Director of Undergraduate Studies: Scott Sutherland
Administative Assistant: Lucille Meci
Office: Mathematics P143
Phone: (631) 632-8250
E-mail: upd@math.sunysb.edu
Web address: http://www.math.sunysb.edu
Minors of particular interest to students majoring in mathematics: applied mathematics and statistics (AMS), computer science (CSE), economics (ECO)
Mathematics is an essential element in a wide range of human activities. It is the language of the physical sciences, and as such is an indispensable tool in the formulation of the laws of nature. In the social and biological sciences, it plays an increasingly important role in modeling complicated, large-scale phenomena. In addition, mathematics has an aesthetic side: awareness of the possibility of elegance and beauty in mathematical arguments has been a significant feature of human culture throughout history. Today more mathematics is being done, and more needs to be done, than ever before.
The undergraduate course offerings in mathematics allow students to set up individualized programs of study consistent with their academic interests and career plans. Students should consider majoring in mathematics even if they do not plan to become mathematicians or teachers of mathematics. The training in abstract reasoning and problem-solving is an excellent foundation for many different careers, such as law, graduate health professions, and business. Completion of a major in mathematics points to a thinking person.
Students are encouraged to explore the various branches of pure and applied mathematics, as well as other mathematically-oriented disciplines, in order to gain both breadth of knowledge and insight into career options. Mathematics majors can use their training as the foundation for advanced professional study, leading to research and teaching in universities or research in industrial research laboratories; they can use it also in secondary school teaching. In industry, undergraduate training in mathematics is excellent preparation for the important task of liaison work between the technological arm of a company and its marketing arm. A major in mathematics is particularly appropriate for work in computer applications, operations research, and actuarial science. Double majors in mathematics and another field, such as physics, computer science, applied mathematics and statistics, or economics, are common and are encouraged.
The secondary teacher preparation option is designed for students planning a career teaching mathematics in a secondary school. This option is described in detail in the "Education and Teacher Certification" entry in the alphabetical listings of Approved Majors, Minors, and Programs.
The Department of Mathematics offers tutorial help to all undergraduate students in its 100-level courses. The Mathematics Learning Center focuses on precalculus mathematics, and the Calculus Resource Room focuses on calculus courses.
The department encourages students to seek information and advice on appropriate mathematics courses, programs, and career goals. Professors in mathematics are available as advisors in the Undergraduate Mathematics Office to help with these matters. Advising hours can be obtained by calling the Department of Mathematics.
Requirements for the Major in Mathematics (MAT)
The major in mathematics leads to the Bachelor of Science degree. Every student majoring in mathematics is expected to complete some form of a one-variable calculus sequence, which is a prerequisite for some of the courses listed below. Appropriate sequences at Stony Brook total 8 to 12 credits.
Completion of the major requires 33 to 37 credits.
- Mathematics and Mathematics-Related Courses
- One course in multivariate calculus:
MAT 203 or AMS 261 or MAT 205
and one course in linear algebra:
MAT 211 or AMS 210 - Preparation in the language and logic of mathematics: this requirement can be met by either passing MAT 200 or by passing the MAT 200 challenge examination. (Note: the writing intensive course MAT 200 is a requirement for students in the Secondary Teacher Preparation option.)
- One course in differential equations:
MAT 303 or AMS 361 or MAT 305 - One course in computer literacy:
MAT 331 or MEC 111 or CSE 114 or (for students graduating with the Secondary Teacher Preparation option) MAE 330. MAT 331 may be used both here and in requirement 7. - Two courses in algebra:
- MAT 310 and
- MAT 312 or 313 or 318
- Analysis: Students must satisfy either a or b:
- Two courses in analysis:
- MAT 319 or MAT 320 and
- MAT 322 or MAT 324 or 341 or 342
- for students graduating in the secondary teacher preparation option: MAT 319 or MAT 320
- Two courses in analysis:
- Five mathematics-related courses beyond those taken to satisfy requirements 5 and 6 (four will suffice if all of them are MAT courses), to be chosen from the following:
- MAE 301
- MAT courses numbered 310 or above except 475
- AMS courses numbered 301 or above except 361 and 475
- CSE courses numbered 301 or above except 475
- Selected upper-division courses in chemistry, economics, philosophy, and physics from a list of acceptable courses, available in the Undergraduate Mathematics Office
- MAT courses numbered 310 or above except 475
- MAE 301
- Upper-Division Writing Requirement In order to satisfy the departmental writing requirement, each student majoring in mathematics, including double majors, must submit an acceptable portfolio of three pieces of writing from upper-division MAT or MAE coursework. Students should aim for completion of the portfolio early in their next-to-last semester to allow time to resolve any difficulties. Late completion may delay graduation. Each portfolio must be submitted no later than the beginning of the final semester, and each piece in it must have been approved by a Mathematics faculty member as being mathematically correct and well written.
- Under special circumstances a student may request the director of undergraduate studies to allow substitution of an equivalent program for some or all of these requirements.
- All courses used to fulfill the requirements for the major must be taken for a letter grade and must be completed with a grade of C or higher.
- Students whose scores on the College Entrance Examination Board (CEEB) Advanced Placement Examination are documented earn credits as follows:
- 4 or 5 on BC examination: credit for MAT 131, 132 (8 credits)
- 4 or 5 on AB examination: credit for MAT 131 (4 credits)
- 3 on either examination: 3 credits applicable to graduation but not the major.
- 4 or 5 on AB examination: credit for MAT 131 (4 credits)
- 4 or 5 on BC examination: credit for MAT 131, 132 (8 credits)
- Students who learned some linear algebra or multivariate calculus before entering Stony Brook should see an advisor in the Undergraduate Mathematics Office. For a student who has had some linear algebra, it may be appropriate to skip MAT 211 and to enroll directly in MAT 310.
- Six credits of graduate MAT courses may be used in place of un-der-graduate courses in requirement A.7.
Honors Program in Mathematics
The honors program is open to junior and senior mathematics majors who have completed at least two upper-division MAT courses with grades of B or higher and who have maintained a 3.00 overall grade point average. A prospective honors major must declare to the director of undergraduate studies an intention to participate in the program sometime before registering for the senior year.
The program consists of a set of seven MAT courses, at least three of which are not used to fulfill the MAT major requirements. These courses must include: MAT 260; MAT 322 or 324; 401 or 402; a course in algebra other than MAT 310 or 318; and MAT 495. Substitution of appropriate graduate courses is permitted, and other substitutions are possible at the discretion of the undergraduate director. Conferral of honors is contingent upon:
- Completion of the set of seven courses with a grade point average of at least 3.50.
- Approval for honors by the faculty member or members who supervise MAT 495.
Mathematics Secondary Teacher Preparation Program
See the Education and Teacher Certification entry in the alphabetical listings of Approved Majors, Minors, and Programs.
Requirements for the Minor in Mathematics (MAT)
The minor in mathematics is available for those students who want their formal university records to emphasize a serious amount of upper-division work in mathematics. Although a one-variable calculus sequence is not a requirement, it is a prerequisite for some of the courses listed below. The requirements listed below do not include single variable calculus or MAT 200 Logic, Language, and Proof; these are prerequisites for some of the courses listed below.
- MAT 211 or AMS 210
- MAT 203 or AMS 261 or MAT 205
- MAT 310 or 312 or 313 or 318
- MAT 319 or 320 or 341 or 342
- Three additional MAT courses numbered 300 or higher (excluding 475)
All courses used to fulfill the requirements for the minor must be passed with a letter grade of C or higher.
Beginning Mathematics Courses
The Mathematics curriculum begins with a choice of calculus sequences, some including preparatory material from 12th-year mathematics in high school and some not. The three first-term calculus courses that assume knowledge of 12th-year mathematics are MAT 125, MAT 131, MAT 141 and AMS 151. A student may start any of these with the same background.
The three-semester sequence of one-variable calculus, MAT 125, 126, 127, is academically equivalent to the two-semester sequence MAT 131, 132. Engineering students normally take the faster-paced MAT 131, 132, or AMS 151, 161 rather than MAT 125, 126, 127 because of the many requirements they must meet. MAT 141, 142 is an enriched version of MAT 131, 132.
MAT 122 and MAT 123 combine precalculus and calculus for students who have not had 12th-year mathematics in high school. A student who completes MAT 122 will have learned some precalculus material and will have a good idea of what calculus is and how it is used. MAT 123 is designed to lead into MAT 125 or MAT 131. Students who begin with MAT 122 may follow that course with MAT 125 or MAT 131 if they take the one-credit course MAT 130 in the same semester as MAT 125 or MAT 131.
For students whose high school preparation is insufficient to begin the MAT curriculum, or to enroll in another course applicable to the D.E.C. category C requirement, Mathematical and Statistical Reasoning, there are two review courses numbered MAP 101 and 103. These courses do not carry graduation credit. MAP 103, a skills course, is for students who need further work in high school algebra and related topics before continuing with calculus or other mathematics. Some students, upon completing MAP 103, are able to pass the Mathematics Placement Examination at a level that allows them to go directly into MAT 125 or 131.
Placement
The Mathematics Department offers a placement examination which indicates the level of mathematics a student is ready to take. It tests the student’s skills at the time the test is taken; students are advised to study beforehand. The examination is given at orientation, during the first two weeks of the semester, and during Prime Time.
Currently, all incoming freshmen are required to take the placement examination. Transfer students should also take the examination under any of the following circumstances:
- If they have not met the entry skill requirement (basic mathematics competence).
- If they have not satisfied D.E.C. category C (mathematical and statistical reasoning).
- If they have been or wish to be accepted into a major in the College of Engineering and Applied Sciences.
- If they have chosen or are considering choosing a major in a department that requires mathematics.
- if they intend to take any mathematics courses at Stony Brook.
In taking the placement examination, a student chooses whether to take Parts I-II or Parts II-III. Part I deals with high school algebra, Part II with 12th-year high school mathematics, and Part III with calculus. Students who have had at least one semester of calculus should take Parts II-III; others should take Parts I-II. Students who score 7 or higher on Parts II-III will be invited to take Part IV to determine placement beyond MAT 132. The outcome of the test is one of nine levels:
| Outcome | Placement |
| Level 1 | MAP 101 |
| Level 2 | MAP 103 |
| Level 2+ & Skill 1 | MAT 118 or statistics |
 | |
| Level 3 | MAT 118, 122, 123 or statistics |
| Level 4 | MAT 125 |
| Level 5 | MAT 131 or 141 or AMS 151 |
| Level 6 | MAT 126 |
| Level 7 | MAT 132 or 142 or AMS 161 |
| Level 8 | MAT 127 or 132 or 142 or AMS 161 |
| Level 9 | Beyond 100-level calculus |
Levels 1-3 can be achieved by a sufficiently high score on Part I, and levels 4-5 can be achieved by a sufficiently high score on Parts I-II. To achieve level 6 or higher, a student must take Parts II-III, and to achieve level 8 or 9, a student must score 7 on Parts II-III, and then take Part IV. The entry skill in mathematics requirement may be satisfied by attaining a score of level 3 or higher. The general education requirement for Mathematics (D.E.C. category C) may be satisfied by attaining a score of level 6 or higher. A student who achieves a particular level is free to begin with a mathematics course corresponding to a lower level, so long as taking the course does not mean that credit is given for the same material twice.
Transfer Credit
When they enter, transfer students automatically receive credit toward graduation at Stony Brook for any courses they have already successfully completed at accredited institutions of higher education and that count there toward graduation. The number of credits transferred appears on the Stony Brook transcript with no courses or grades indicated, and the number of transferred credits is unaffected by the student’s score on the Mathematics Placement Examination. In addition, transferred mathematics courses are automatically evaluated by title for applicability to the entry skill in mathematics requirement and the D.E.C. category C requirement; this evaluation does not depend on the result of the placement examination.
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