College of Arts & Sciences

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 I 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 advisers in the Pathways in Education Center in the School of Education.

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 I 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.

Students completing the BS program in actuarial science will have studied virtually all the material tested on actuarial exam P (probability), exam FM (financial mathematics) and the life contingencies segment of exam M (actuarial models). Students will also have studied about half the material tested on exam C (construction and evaluation of actuarial models). Students who complete a BS in actuarial science will have taken courses carrying VEE (validation by educational experience) credit in the three required areas: applied statistical methods, corporate finance and economics.

Requirements for the B.S. in actuarial science were revised in 2002 to reflect extensive changes (jointly made by the Society of Actuaries and the Casualty Actuarial Society) in the actuarial examinations. The new graduation requirements reflect the new examinations� greater emphasis on applied probability, stochastic modeling, economics, and finance.

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. Students may reasonably take an exam before taking all the courses listed as relevant.

Exam P (probability). Students need A Mat 112, 113, 214, 367, 368 (but only the continuous probability in A Mat 368). 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 110M may also prove useful.

Exam M (actuarial models). Students need A Mat 403A 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 367, 368, 464, 465 and 467.

The Society of Actuaries grants VEE credit in the indicated area to students completing the listed courses with a grade of B- or better.

Applied Statistical Methods: A Math 465 (or 565).

Or students can take
(i) both Eco 621 and 720, or
(ii) both Mat 558 and 664 (which are equivalent to HSTA 558 and 664).

Economics: A Eco 110M and 111M.

Or students can take both A Eco 300 and 301.

Corporate Finance: both B Fin 300 and A Eco 466.

Students who enter as freshmen with credit for AP calculus AB and 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 advance planning.

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.

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

Year       Fall                  Spring
Fresh.   112 or 118        113 or 119
Soph.    214                   220 & 301
Junior    367(Z) & 469   368 & 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 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), 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 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 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 3.2 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.