# Department of Mathematics and Statistics

#### Faculty

*Distinguished Professor
* Charles A. Micchelli, Ph.D.

Stanford University

*Distinguished Teaching Professor*

Edward S.Thomas Jr., Ph.D.

University of California, Riverside

*Distinguished Service Professor Emeritus*

Timothy L. Lance, Ph.D.

Princeton University

*Professors Emeriti
* Louis Brickman, Ph.D.

University of Pennsylvania

Lindsay N. Childs, Ph.D. (Collins Fellow)

Cornell University

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

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

Richard O’Neil, Ph.D.

University of Chicago

Edward C. Turner, Ph.D.

University of California, Los Angeles

Donald R. Wilken, Ph.D. (O'Leary Fellow)

Tulane University

*Professors
* Richard Z. Goldstein, Ph.D.

University of Pennsylvania

Cristian Lenart, Ph.D.

University of Cambridge

R. Michael Range, Ph.D.

University of California, Los Angeles

Michael I. Stessin, Ph.D.

Moscow State University

Kehe Zhu, Ph.D. (Department Chair)

State University of New York at Buffalo

*Associate Professors Emeriti
* Guy D. Allaud, Ph.D.

University of Wisconsin

Herbert I. Brown, Ph.D.

Rutgers University

William F. Hammond, Ph.D.

Johns Hopkins 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*

Boris Goldfarb, Ph.D.

Cornell University

Martin V. Hildebrand, Ph.D.

Harvard University

Antun Milas, Ph.D.

Rutgers 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

Alexandre Tchernev, Ph.D.

Purdue University

Rongwei Yang, Ph.D.

State University of New York at Stony Brook

*Assistant Professors*

Ivana Alexandrova, Ph.D.

University of California, Berkeley

Joshua Isralowitz, Ph.D.

State University of New York at Buffalo

Marco Varisco, Ph.D.

University of Münster

Jing Zhang, Ph.D.

Washington University

*Adjuncts (estimated): 7
Teaching Assistants (estimated): 30*

The Mathematics Department provides a broad offering of courses from which a 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**

Careers in mathematics typically require study beyond the undergraduate level. Examples include careers in the insurance industry (as an actuary), in the pharmaceutical industry (as a statistician), in the financial industry (as an analyst) or in education (as a mathematics teacher or professor). However, a student with an undergraduate degree in mathematics has an excellent fundamental preparation for careers in many fields. Many areas of business require high-level quantitative and analytical problem-solving skills, and a major in mathematics exercises those skills at a high level. A degree with a major in mathematics signifies that the graduate is well prepared to handle the mathematical demands of positions in a wide range of fields. The Mathematical Association of America (www.maa.org/careers) has a number of resources on careers in or related to mathematics.

The Department has several options or concentrations that focus on particular career tracks. The Department offers a major in Actuarial and Mathematical Sciences for students interested in pursuing a career as an actuary. The undergraduate major includes coursework that constitutes substantial preparation for the four preliminary examinations set by the Society of Actuaries and the Casualty Actuary Society that are required for professional advancement in the field.

For a career as a statistician, a student can choose within the mathematics major a concentration in statistics and probability that, along with appropriate courses in analysis and algebra, is excellent preparation for a graduate degree in statistics or biostatistics.

The combined Mathematics/Master of Business Administration program merges a major in mathematics with an M.B.A. to provide strong preparation for a career in business or finance.

A major in mathematics followed by a master's degree in education or in mathematics with appropriate courses in education provides the prerequisites for a career as a secondary school mathematics teacher. A mathematics major followed by graduate work at the doctoral level provides suitable preparation for a career as a college or university professor.

In addition to these career options, a major in mathematics and a major or minor in a social or natural science or business are good preparation for graduate work in quantitative or mathematical areas of the other (or a related) discipline. Some examples include economics, physics, atmospheric science, biology, marketing, geography and planning, engineering, cryptography, sociology, demography, management, nanotechnology, epidemiology, biophysics, education, and finance. Mathematics majors have also gone on to law school and to medical school.

**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 sciences 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.

#### Mathematics Major

Students majoring in mathematics may choose to complete the requirements for either the B.A. or B.S. degree. With either degree option, a student may apply for admission to the honors program.

Since advanced courses in mathematics typically have long chains of prerequisites, students considering a major in mathematics or actuarial sciences are encouraged to visit the department office (ES 110) as early as possible for informal advice. Information is also available on the Mathematics Department’s website http://math.albany.edu.

To complete a mathematics major comfortably in four years, the calculus sequence and A MAT 220 or a suitable 300 level course (A MAT 326, 308 or 362) should be completed by the end of the sophomore year.

### Degree Requirements for the Major in Mathematics

**General Program B.A.:** The purpose of the B.A. program is to provide the student a broad view of mathematics and statistics. The B.A. degree requires 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 four areas. The areas, and appropriate courses within each area, are:

The purpose of the B.A. program is to provide the student a broad view of mathematics and statistics. The B.A. degree requires 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 four areas. The areas, and appropriate courses within each area, are:

- Algebra: A MAT 326, 327, 424
- Analysis: A MAT 311, 312, 314, 409, 412, 413, 414
- Geometry/topology: A MAT 331, 342, 432, 441, 442
- Probability/statistics: A MAT 308, 362 or 367*, 363, 467, 464

Equivalent courses with a Z suffix may be substituted for these courses. Other courses may be substituted with Departmental approval.

* Only one of A MAT 362 and 367 may be applied toward any major or minor in mathematics or a minor in 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 five sequence options:

- A MAT 326 and 327
- Either (a) both A MAT 314 and 315 or (b) any two of 312, 412, 413, 414
- Any two of A MAT 331, 342, 432, 441, 442
- Any two of A MAT 308, 362 or 367*, 363, 369, 464, 467, 468
- A MAT 312 and A MAT 424 (A MAT 312 cannot be part of two sequence options.)

* Only one of A MAT 362 and 367 may be applied toward any major or minor in mathematics or a minor in statistics.

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 I CSI 101, 201, 203, 204, 205, 310; and
- a minor in atmospheric science, biology, business, chemistry, computer science, economics, electronics, geology, informatics, or physics.

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

#### Career Tracts

With suitable advisement, students can design programs that will best meet their particular interests and career goals. To guide students in their planning, a number of options are presented here.

**1. Secondary School Teaching
**Students planning to become mathematics teachers at the secondary level in New York State normally need to obtain a master's degree in mathematics or education to attain a professional level of certification. For undergraduate preparation, students are urged to include the following courses in their programs:

- A MAT 312 (analysis), 326 and 327 (algebra), 331 or 432 (geometry), 362 (probability), 308 or 363 (statistics), and 452 (history)
- Six credits of computer science or of one science
- One year of a language

Also recommended is E TAP 201 (Exploring Teaching as a Profession)

A grade point average of 3.0 or higher overall and in mathematics is normally required for admittance to master's programs. Seniors interested in pursuing a master's degree should contact advisers in the Pathways into Education (PIE) Center.

**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 or statistics should try to include in their programs a core of advanced undergraduate courses chosen from at least three of the following four areas:

*Algebra:*A MAT 327, 424*Analysis:*A MAT 413, 414*Geometry/Topology*: A MAT 342, 441, 442*Probability/Statistics*: A MAT 467, 468

For additional advanced study, students have two choices. One option is to pursue an independent study project leading to an undergraduate thesis, either (preferably) within or (optionally) independent of the honors program. This option can provide an opportunity for the student to pursue research in mathematics. Students considering an undergraduate research/thesis should meet with the Director of Advisement or the Director of Undergraduate Studies during the junior year to begin planning this option.

Another option is to take graduate courses. Qualified undergraduate mathematics students may be admitted to the Department’s 500 level graduate courses in algebra, real analysis, complex analysis, topology, and other areas. (Students admitted to the combined bachelor's/master's program may take graduate courses for graduate credit — see below.)

**3. Statistics**

Statistics is a widely applied area of mathematics and the demand for statisticians is high. A concentration in statistics may begin with either of two sequences: A MAT 308, 362, or A MAT 362, 363. (The former sequence can be started after completion of Calculus II.) Either sequence can be followed by courses in applied statistics (A MAT 369, 465), applied probability (A MAT 464) and mathematical statistics (A MAT 467, 468). Students who plan to pursue the further study of statistics at the graduate level are advised to take A MAT 312 (Basic Analysis) and A MAT 424 (Advanced Linear Algebra). Statistics in practice usually involves heavy use of the computer, so students should include I CSI 201 and additional computer science in their programs.

**4. Applied Mathematics**

Although it is common to classify mathematics as either “pure” or “applied,” the division is often arbitrary. In recent years some extremely abstract mathematics has turned out to be useful in areas outside mathematics. Students preparing for a career in applied mathematics area 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.

Here are some mathematical areas 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, 374*Applied analysis*: A MAT 311, 314, 315, 409, 412, 416*Numerical Methods*: A MAT 301, 313, 401*Probability/Statistics*: A MAT 308, 362, 363, 369, 464, 465

**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 or a mathematics-related discipline.

At the lower division level, the Department offers Honors Calculus I (A MAT 118), II (A MAT 119), and III (an honors section of A MAT 214). A strong student may begin in whichever of these courses is appropriate based on the student’s previous coursework in calculus.

A student may be admitted formally to the Department’s 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.

The requirements for graduation with honors in mathematics include:

- Required courses: A MAT 413, 414, 424, and 9 additional credits from among A MAT 327, 416, 420, 425, 432, 441, 442, 464, 467, 468, 510A, 513A, 520A, 520B, 540A, 557A, 557B, and independent study, Senior Seminar or thesis (maximum of 3 credits).
- An acceptable honors thesis presented in a public venue.
- 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.

#### Actuarial and Mathematical Sciences Major

Actuaries are professionals who manage risk for insurance companies, pension plans and other financial institutions, and government and business. To attain professional standing as an actuary requires successful completion of a sequence of examinations offered by the Society of Actuaries and the Casualty Actuarial Society. The actuarial major is designed to prepare students for employment in the actuarial field by offering coursework related to 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 actuarial exams described immediately below are interdisciplinary, testing material from several courses. Some of the courses listed as preparation for an exam are relevant to only a few questions on that exam, so students may reasonably take an exam before taking all the courses listed as relevant.

Exam P (probability). Students need A MAT 112, 113, 214, 362. A MAT 467 may also be useful, but for at most a few questions.

Exam FM (financial mathematics). Students need A MAT 301 (which in turn requires calculus). A ECO 110 and 111 may also prove useful.

Exam M (actuarial models). Students need A MAT 403 and topics from A MAT 464 for the life contingencies segment of the two-part Exam M.

Exam C (construction and evaluation of actuarial models). Several required courses are relevant, including A MAT 362, 363, 464, 465, and 467.

The Society of Actuaries grants VEE (validation by educational experience) credit in the indicated area to students completing the following listed courses with a grade of B- or better.

Applied Statistical Methods: A MAT 465 (or 565). Or students can take (i) both A ECO 621 and 720, or (ii) both A MAT 558 and 664 (which are equivalent to H STA 558 and 664).

Economics: A ECO 110 and 111. Or students can take both A ECO 300 and 301.

Corporate Finance: both B FIN 300 and A ECO 466.

Students completing the B.S. program in actuarial science will have studied virtually all the material tested on Exam P, Exam FM and the life contingencies segment of Exam M. Students will also have studied about half the material tested on Exam C. Students who complete a B.S. in actuarial science will have taken courses carrying VEE credit in the three required areas: applied statistical methods, corporate finance, and economics.

Students who enter as freshman with AP credit for Calculus I and II (calculus BC) should be able to prepare for the financial economics segment of Exam M and for the topics of Exam C not covered by required courses. Doing so requires additional advanced courses in statistics, business and economics. Completing such courses and graduating within four years requires advanced planning.

Actuarial majors without AP credit in calculus are encouraged (but not required) to take A MAT 118 and 119, the honors versions of A MAT 112 and 113 . Students who do not take A MAT 118 and 119 are encouraged to take A MAT 312 during their junior year.

#### 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), 362, 363, 403, 464, 465 (or 565), and 467 (or 554)
- 6 credits: chosen from I 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 following is the recommended schedule of mathematics courses for students entering without AP credit in calculus:

Year | Fall | Spring |

Fresh. | 112 or 118 | 113 or 119 |

Soph. | 214 | 220 & 301 |

Junior | 362 & 469 (& 312) |
363(Z) & 464 |

Senior | 465 & 467 | 403 & 469 |

Note: A MAT 469, which may be repeated for credit, is an optional one-credit course that drills students on problems from one of the preliminary actuarial exams (either P, FM or M).

Students are advised to take A ECO 110 and 111 as freshmen, and in any event, not 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.

#### Honors Program in Actuarial and Mathematical Sciences

A student may be admitted formally to the Department’s honors program in actuarial science at any time after the sophomore year. However, any student who is interested in the program should see the Director of the Actuarial Science Program as early as possible for informal advisement concerning the honors thesis. 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

The requirements for graduation with honors include:

- Required courses: A MAT 468 together with the other required courses of the Actuarial Science major.
- An acceptable honors thesis presented in a public venue.
- 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.

#### 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, and residence requirements. The main benefit of the combined program is that up to 12 graduate credits in mathematics may be applied simultaneously to both the undergraduate degree program and the M.A. program.

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. A cumulative grade point average of 3.20 or higher and three supportive letters of recommendation from faculty are required for consideration.

#### Combined Mathematics and Master of Business Administration

In this program students are able to obtain a B.S. degree in mathematics and a M.B.A. degree in a total of five years (instead of six years). Students with a B.S. in mathematics with supporting computing courses are particularly well prepared to pursue the M.B.A. concentration in Information Technology Management, and students with a B.S. in mathematics and a business minor that includes accounting courses are particularly well prepared to pursue the M.B.A. concentration in Information Assurance.

For the combined program, students must complete 90 credits during the first three years that includes all requirements for the mathematics major (36 credits for the B.A., 42 for the B.S.), a minor (18 credits), and the general education program (30 credits). (Certain sets of undergraduate courses can waive the M.B.A. courses B FIN 515 or B ACC 518 and allow room for up to 6 credits of general education courses in the senior year. For details, consult the School of Business.) Since the B.A. degree requires 90 credits of Liberal Arts and Sciences courses, compared with 60 credits for the B.S. degree, students who choose an undergraduate minor in business will need to follow the B.S. program in mathematics. In the fourth and fifth year students follow the M.B.A. program in the School of Business. The first 30 credits of the 60 credit M.B.A. program complete the undergraduate degree. Application should be made during the second semester of the junior year to the director of the M.B.A. program, School of Business. Students considering the Combined Math-M.B.A. program should consult with the School of Business before the beginning of their junior year.

**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 The Department of Computer Science in the College of Computing and Information.