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
John
T. Therrien, M.A.
University at Albany
Associate
Professors
Hara
Charalambous, Ph.D.
University of Illinois, Urbana-Champaign
Boris
Goldfarb, Ph.D.
Cornell University
William
F. Hammond, Ph.D.
Johns Hopkins University
Martin
Victor Hildebrand, Ph.D.
Harvard University
Cristian
Lenart, Ph.D.
University of Cambridge
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
Antun
Milas, Ph.D.
Rutgers University
Alexandre
Tchernev, Ph.D.
Purdue University
Rongwei
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
101, 201, 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.
Secondary School Teaching:
Students
planning to become mathematics teachers at the secondary level and
would like to pursue the Teacher Certification Program after
graduation need to fulfill the following requirements:
36 credits in mathematics as follows: A Mat 112, 113, 214, 220,
311 or 312, 326, 327, 331, 342, 367, 368.
6 credits in one science,
one year of a language.
use of graphing Calculator.
GPA 3.0 or higher overall and in mathematics
A
suggested schedule of courses in mathematics is:
Year
Fall Spring
Fresh.
112 or 118 113 or 119
Soph.
214 220 & 367(Z)
Junior
326 & 368 327
Senior
311 or 312 & 342 331
Students
are also encouraged to take Etap 201 in their Junior year. Seniors
should contact advisors in the Academy for Initial Teacher
Preparation of the Department of Educational Theory and Practice.
3.
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.
4.
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
5.
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 201, 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 exam while in college are likely to secure employment
in the field, and some students have secured actuarial employment
before taking or passing any exams. The B.S. program in actuarial
science exposes students to virtually all the material on the Course
1, 2, 3 exams and to most of the content of the Course 4 exam.
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 whose first enrollment at the University at Albany was prior
to September 2002 are responsible for fulfilling the requirements of
the catalogue in effect when they first enrolled. Such students are
encouraged to make approved course substitutions so that the courses
they take are relevant to current actuarial exams.
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.
Actuarial
majors are encouraged (but not required) to take A Mat 118 and 119,
the honors versions of A Mat 112, 113. Students who do not take A Mat
118 and 119 are encouraged to take A Mat 312 during their junior
year.
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 110 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 110); Macroeconomics (A Eco 111); 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, 403, 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.
Year
Fall Spring
Fresh.
A 112 or 118 113 or 119
Soph.
214 220 & 367(Z)
Junior
301 & 368(Z) 464
Senior
465 & 467 403 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 110 and 111 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), 403, 464,
465, and 467.
6
credits: chosen from A Csi 201, 203, 204, 205, and 310.
6
credits: B Acc 211, B Fin 300.
15
credits in economics: A Eco 110, 111, 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
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.