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University at Albany Undergraduate Bulletin - 2004-2005

Department of Mathematics & Statistics


Faculty

Distinguished Teaching Professor

Edward S. Thomas Jr., Ph.D.
University of California, Riverside


Distinguished Service Professor

Timothy L. Lance, Ph.D.
Princeton University


Distinguished Research Professor

Charles A. Micchelli, Ph.D.
Stanford University


Professors Emeritae/i

Louis Brickman, Ph.D.
University of Pennsylvania

Vincent Cowling, Ph.D.
Rice University

Edward D. Davis, Ph.D.
University of Chicago

Nathaniel A. Friedman, Ph.D.
Brown University

Benton N. Jamison, Ph.D.
University of California, Berkeley

Joe W. Jenkins, Ph.D.
University of Illinois

Melvin L. Katz, Ph.D.
University of California, Berkeley

Violet H. Larney, Ph.D.
University of Wisconsin

Thomas H. MacGregor, Ph.D.
University of Pennsylvania

George E. Martin, Ph.D.
University of Michigan

Hajimu Ogawa, Ph.D.
University of California, Berkeley


Professors

Lindsay N. Childs, Ph.D.
Cornell University

Richard Z. Goldstein, Ph.D.
University of Pennsylvania

Boris Korenblum, Sc.D.
Moscow State University

Timothy L. Lance, Ph.D.
Princeton University

Charles Micchelli, Ph.D.
Stanford University

Richard C. O'Neil, Ph.D.
University of Chicago

R. Michael Range, Ph.D.
University of California, Los Angeles

Michael I. Stessin, Ph.D.
Moscow State University

Howard H. Stratton, Ph.D.
University of California, Riverside

Edward C. Turner, Ph.D.
University of California, Los Angeles

Donald R. Wilken, Ph.D.
Tulane University

Kehe Zhu, Ph.D.
State University of New York at Buffalo


Associate Professors Emeritae/i

Guy D. Allaud, Ph.D.
University of Wisconsin

Herbert I. Brown, Ph.D.
Rutgers University

Lloyd L. Lininger, Ph.D.
University of Iowa

Robert Luippold, M.A.
University of Buffalo

Ricardo Nirenberg, Ph.D.
New York University

Erich Nussbaum, Ph.D.
University of Virginia

John T. Therrien, M.A.
University at Albany


Associate Professors

Hara Charalambous, Ph.D.
University of Illinois, Urbana-Champaign

William F. Hammond, Ph.D.
Johns Hopkins University

Martin Victor Hildebrand, Ph.D.
Harvard University

Steven Plotnick, Ph.D.
University of Michigan

Karin B. Reinhold-Larsson, Ph.D.
Ohio State University

Carlos C. Rodriguez, Ph.D.
Columbia University

Malcolm J. Sherman, Ph.D.
University of California, Berkeley

Anupam Srivastav, Ph.D.
University of Illinois, Urbana-Champaign

Mark Steinberger, Ph.D.
University of Chicago


Assistant Professors

Boris Goldfarb, Ph.D.
Cornell University

Cristian Lenart, Ph.D.
University of Cambridge

Jennifer Taback, Ph.D.
University of Chicago

Alexandre Tchernev, Ph.D.
Purdue University

Roungwei Yang, Ph.D.
SUNY Stony Brook


Adjuncts (estimated): 0
Teaching Assistants (estimated): 30


The department provides a broad offering of courses from which each student can make a selection designed to satisfy any of a large variety of objectives. In addition to including the standard courses in pure and applied mathematics, our course offerings are unusually strong in statistics and actuarial mathematics. The department offers two majors: the major in mathematics and the major in actuarial and mathematical sciences. A third major, the major in computer science and applied mathematics, is offered jointly with the computer science department.


Careers

The objective of the department is to serve the needs of students aspiring to careers that require mathematical background: physical, biological, social, and management sciences; statistics, actuarial work, computer science, applied mathematics; secondary school teaching; graduate work; college and university teaching; and research in mathematics. In most cases, training beyond the bachelor’s degree is desirable and can often be obtained after the graduate has secured employment. The department also welcomes students who wish to study mathematics as part of a traditional liberal arts education.


Placement and Proficiency Credit

The University awards up to 8 credits and advanced placement in its sequences of calculus courses based on performance on the advanced placement calculus examinations administered by the College Board. Details concerning the decisions on credit and placement are available from the Admissions Office.


Admission

Students may not declare a major in either mathematics or actuarial and mathematical science until they have completed at least one of A Mat 113, 119, or 214 with a grade of A, B, C, or S. Transfer credits and grades may be used to satisfy the requirement.


The Mathematics Major

Students majoring in mathematics may choose to complete the requirements for either the B.A. or B.S. degree. Under any of the four program-degree combinations, a student may apply for admission to the honors program.

Students considering a major in mathematics or actuarial minor are encouraged to visit the department office (ES-110) for advice. Information is also available at the web site http://math.albany.edu.


Degree Requirements for the Major in Mathematics

General Program B.A.: A minimum of 36 credits from the Department of Mathematics and Statistics in courses numbered above 110, including A Mat 214, 220, and a 3-credit course numbered above 300 in each of these four areas: algebra, analysis, geometry/topology, and probability/statistics.

General Program B.S.:

A minimum of 36 credits from the Department of Mathematics and Statistics in courses numbered above 110, including A Mat 214, 220, and two of the following four options: (1) A Mat 326 and 327, (2) either (a) both A Mat 314 and 315 or (b) any two of 312, 412, 413, or 414, (3) any two of A Mat 342, 441, or 442, (4) any two of A Mat 367, 368, 369, 464, 465, 467, 468. With departmental approval, other 400-level or 500-level courses may be substituted for the courses listed above. In addition, each student must complete: 6 credits in computer science from A Csi 101N, 201N, 203, 204, 205, 310; and a minor in atmospheric science, biology, business, chemistry, computer science, economics, electronics, geology, or physics.

NOTE:  The Statistics minor is not open to students with a major in mathematics.

General Program
Students, with suitable advisement, can design programs that will best meet their particular interests and career goals. Note, however, that those who plan to do graduate work in any mathematical field-pure or applied-should obtain as strong an undergraduate background as possible in the basic areas of mathematics: algebra, analysis, and geometry/topology. In particular, they should make every effort to include A Mat 413 and 414 (Advanced Calculus) in their programs.

To guide students in their planning, a number of options, some of a general nature and others to meet specific career objectives, are presented here.

  1. Liberal Arts (B.A.)
    Some professional careers and many jobs require a mathematical background characterized more by breadth than by concentration in any particular area of the mathematical sciences. The purpose of the B.A. program is to assure that the student acquires a broad view of mathematics and statistics. Each B.A. major is required to complete a 3-credit course numbered above 300 in each of these areas: algebra, analysis, geometry/topology, and probability/statistics. The following lists those courses that can be taken to fulfill that requirement:

    Algebra: A Mat 326, 326Z, 327, 327Z, 424

    Analysis: A Mat 311, 312, 312Z, 314, 409, 412, 412Z, 413, 413Z, 414

    Geometry/Topology: A Mat 331, 331Z, 342, 342Z, 432, 432Z, 441, 442

    Probability/Statistics: A Mat 367, 367Z, 368, 369, 464, 465, 465Z, 467, 468

    Students are urged to explore in greater depth, preferably at the 400 level. Since students will have different goals, it is impossible to provide useful sample programs. Students are encouraged to devise their own plans in consultation with their advisers. However, if a student is to graduate on time, the calculus sequence and linear algebra should be completed during the freshmen and sophomore years.

  2. Graduate School Preparation
    The department offers excellent opportunities for students who plan to go on to graduate work in mathematics and statistics as well as other areas such as computer science, the natural sciences, and the social and behavioral sciences.

    Students whose goal is to obtain a graduate degree in mathematics should include in their programs as many of the following core courses as possible in each of the designated areas:

    Algebra: A Mat 326, 327, 424

    Analysis: A Mat 413, 414

    Geometry/Topology: A Mat 342

    Probability/Statistics: A Mat 467, 468

    Those hoping to do graduate work should also consider entering the honors program.

  3. Applied Mathematics
    Although it is common to classify mathematics as either “pure” or “applied,” the division is often arbitrary. Some extremely abstract mathematics in recent years has turned out to be useful in areas outside mathematics. Students preparing for a career in applied mathematics would be well advised to acquire as strong a background as possible in the pure mathematical areas of analysis, algebra, and geometry/topology. On the other hand, students concentrating in pure mathematics should have some understanding of how to apply mathematical methods to other disciplines.

    Listed here are the mathematical subjects that are more commonly applied to problems in other fields along with the corresponding courses in which methodology or applications are treated.

    Applied algebra: A Mat 326, 372

    Applied analysis: A Mat 311, 314, 315, 409, 412, 416

    Numerical Methods: A Mat 313, 401

    Probability/Statistics: A Mat 367, 368, 369, 464, 465

  4. Statistics
    Statistics is a widely applied branch of mathematics and the demand for statisticians is high. Preparation for a career or for advanced study in statistics should include one of the following two combinations of courses: (1) probability (A Mat 367 or 367Z, 464) and statistics (A Mat 368 or 368Z, 369 or 369Z, 465 or 465Z), or (2) probability (A Mat 367 or 367Z, 464) and statistics (A Mat 467, 468). Sequence (2) is recommended as the more advanced and thorough treatment. A Mat 424 (advanced linear algebra) is highly recommended. Also useful are A Mat 401, 409, 413 or 413Z, and 414. Because computing is a close adjunct to statistics, students are strongly advised to include A Csi 201N, 205, and 310 as a minimal introduction.


Honors Program

The honors program is designed for the talented and committed student of mathematics. Successful completion of the program is excellent preparation for graduate work in mathematics.

Students entering the University with strong mathematical backgrounds should consider taking Honors Calculus, A Mat 118 and 119, in place of the standard Calculus, A Mat 112 and 113.

A student may be admitted formally to the honors program at any time after the sophomore year, and then will be formally advised by the Director of the Honors Program. However, any student who is interested in the program should see the Director of the Honors Program as early as possible for informal advisement.

To be admitted, the applicant must have an academic average in all University courses of at least 3.30, and an academic average in all mathematics courses of at least 3.40. Specific course requirements are: A Mat 413 or 413Z, 414, 424, and 9 additional credits from among A Mat 327 or 327Z, 416, 420, 425, 432 or 432Z, 441, 442, 464, 467, 468, 510A, 513A, 520A, 520B, 540A, 557A, 557B, and independent study (maximum of 3 credits).

To be recommended for graduation with honors, the candidate must write an acceptable honors thesis and also maintain an academic average of at least 3.30 in all University courses and at least 3.40 in all mathematics courses numbered 400 or above.


The Actuarial Major

The actuarial major is designed to prepare students for employment in the actuarial field and as preparation for the preliminary actuarial examinations. Past experience suggests that students who pass even one actuarial examination while in college are likely to receive multiple employment offers. Many students have secured employment in the actuarial field before taking or passing any actuarial examinations. The B.S. program in actuarial science exposes students to virtually all the material on the Course 1, 2, 3, and 4 actuarial examinations.

The B.S. in actuarial science was revised in 2002 to reflect recent revisions (jointly made by the Society of Actuaries and by the Casualty Actuarial Society) of the actuarial examinations. The new actuarial major reflects the new examinations’ greater emphasis on applied probability, stochastic modeling, economics, and finance.

Actuarial majors who first enrolled at the University at Albany prior to September 2002 may choose to fulfill the requirements of the catalogue in effect at the time of their first enrollment. Or they may decide to fulfill the requirements of the new program. A third option is to modify the old program by making course substitutions - with the written approval of their adviser.

The actuarial exams are interdisciplinary, testing material from several courses. Some of the courses listed below as preparation for an exam are relevant to only a few questions on that exam. Students may reasonably decide to take an exam before taking all the courses listed as relevant.

Course 1 Exam: Mathematical Foundations of Actuarial Science.

Students need A Mat 112, 113, 214, 367, and 368 (continuous probability) before attempting this exam. A Mat 467 and A Eco 110M will also be useful, but only for a few questions.

Course 2 Exam: Interest Theory, Economics, and Finance.

Topics: Interest Theory (A Mat 301/A Eco 351); Microeconomics (A Eco 110M); Macroeconomics (A Eco 111M); Finance (A Eco 466); Interest Theory/Finance (A Mat 301, A Eco 466); Finance/Economics (A Mat 301, A Eco 466).

B Fin 300 may also be useful for the last two topics.

Course 3 Exam: Actuarial models.

Requires A Mat 301, 403A, 464, and 465 (which in turn requires 368).

Course 4 Exam: Actuarial Modeling.

Requires A Mat 464, 465, plus some self-study on topics not normally covered in these course.

Students are encouraged to adhere to the following schedule for required mathematics course.

YearFallSpring
Fresh.112 or 118113 or 119
Soph.214220 & 367(Z)
Junior301 & 368(Z)464
Senior     465 & 467     403A and 469 (optional)
Notes: (1) A 469 is an optional one-credit course that drills students on problems from the Course 1 actuarial exam. (2) Actuarial students are encouraged (but not required) to take the honors versions, A Mat 118 and 119 of A Mat 112 and 113.

Students are advised to take A Eco 110M and 111M as freshmen, and in any event, no later than their sophomore year. By doing so, students will not need to take more than one upper division economics course during any single semester.

Most actuarial students will take A Mat 367Z or 368Z (instead of A Mat 367 or 368) in order to meet the University’s upper division writing requirement.


Degree Requirements for the Major in Actuarial and Mathematical Sciences

General Program B.S. A combined major and minor sequence consisting of 63 credits as follows:

36 credits in mathematics: A Mat 112 (or 118), 113 (or 119), 214, 220, 301 (or A Eco 351), 367 (or 367Z), 368 (or 368Z), 403A, 464, 465, and 467.

6 credits: chosen from A Csi 201N, 203, 204, 205, and 310.

6 credits: B Acc 211, B Fin 300.

15 credits in economics: A Eco 110M, 111M, 300, 301, and 466. Note: Actuarial majors automatically fulfill the requirement for a minor in economics (since A Mat 301 is equivalent to A Eco 351).

The requirements for graduation with honors for actuarial majors are included under the heading Honors Program.


Combined B.A./M.A. and B.S./M.A. Programs

The combined B.A./M.A. and B.S./M.A. programs in mathematics provide an opportunity for students of recognized academic ability and educational maturity to fulfill integrated requirements of undergraduate and master’s degree programs from the beginning of their junior year. A carefully designed program can permit a student to earn the B.A or B.S. and the M.A. degrees within nine semesters.

The combined programs require a minimum of 138 credits, of which at least 30 must be graduate credits. In qualifying for the B.A. or B.S., students must meet all University and college requirements, including the requirements of the undergraduate major described previously, the minimum 90- or 60-credit liberal arts and sciences requirement, general education requirements, and residence requirements. In qualifying for the M.A., students must meet all University and college requirements as outlined in the Graduate Bulletin, including completion of a minimum of 30 graduate credits and any other conditions such as a research seminar, thesis, comprehensive examination, professional experience, and residence requirements. Up to 12 graduate credits may be applied simultaneously to both the B.A. and M.A. programs or to both the B.S. and M.A. programs.

Students are considered as undergraduates until completion of 120 graduation credits and satisfactory completion of all B.A. or B.S. requirements. Upon meeting B.A. or B.S. requirements, students are automatically considered as graduate students.

Students may apply to the graduate committee of the department for admission to either combined program in mathematics at the beginning of their junior year or after the successful completion of 56 credits, but no later than the accumulation of 100 credits. A cumulative grade point average of 3.2 or higher and three supportive letters of recommendation from faculty are required for consideration.


Combined Mathematics and Master of Business Administration Program:

In this program a student is able to obtain a B.S. degree in mathematics and a M.B.A. degree in a total of five years by taking a coordinated program in mathematics and business administration during the senior year. Application should be made during the second semester of the junior year to the director of the M.B.A. program, School of Business.


Related Program: Interdisciplinary Major in Computer Science and Applied Mathematics:

This major prepares a student to handle mathematically oriented computer applications in engineering and business. Details of the program are listed under Computer Science.


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