This handbook is available online, possibly with updates from the printed version, from the Math Department web page: www.math.binghamton.edu.
Mathematics belongs both to the liberal arts and to the sciences. It is the language of the physical sciences (and, to some extent, of the biological and social sciences), and it is also studied for its own challenge and beauty. Current mathematical research spans a vast array of fields, from immediately applicable areas such as cryptography and optimization to beautiful problems in geometry and logic whose applications may not appear for many years.
The Mathematical Sciences Department has undergraduate programs leading to BA and BS degrees. The BA degree has two tracks: a general track and an Actuarial Sciences track. The requirements for the BA are relatively unspecific, allowing students to build their majors to suit their tastes. The Actuarial Sciences track within the BA program provides strong preparation for an actuarial career. The BA program also facilitates the pursuit of a minor in Computer Science. The BS program is more demanding, and provides excellent preparation for graduate work in mathematics and related fields such as statistics, computer science, operations research and business administration. All of these programs are described in more detail below. The various degree possibilities within the department accomodate students with a wide variety of interests and ambitions. In addition, many math majors have a second major in another department.
The department also has a full range of graduate programs (MA, PhD, and MAT) and a research faculty. Thus, even the most talented student will find appropriate guidance and preparation for graduate school.
Students who declare a mathematics major are assigned a departmental advisor, who works closely with the student to prepare an appropriate course of study. It is important that any student planning to major in Mathematical Sciences declare this major and obtain an advisor at the earliest possible opportunity. It cannot be emphasized too strongly that there is no substitute for the quality of the advice a student gets from a knowledgeable faculty member. This document is designed to answer some frequently asked questions and to help in the advising process. Specific requirements are detailed in the catalog from the year in which a student begins at Binghamton University.
Transfer students should quickly establish precisely which Mathematical Sciences courses they will receive major credit for so that they can properly plan to meet all remaining requirements in their semesters at SUNY-Binghamton.
Deviations from the current requirements are made only in rare cases under extenuating circumstances. These must be approved in advance by the Department if at all possible.
The requirements are MATH 221 (Calculus I), 222 (Calc II), 323 (Calc III), 304 (Linear Algebra), and 330 (Number Systems). Students must also take a pairing of two related courses from the following list:
Listed below are several sample core curricula which satisfy the requirements from the BA but have different emphases. These are minimal programs and should be strengthened with electives from inside the department. These are meant to be suggestions and/or recommendations, not requirements. Each student should take this advice and tailor it to his/her needs. Where choice is indicated it should, of course, be made to satisfy the required pairing described previously. Students entering with AP credit should make appropriate adjustments in considering these sample curricula.
Note that many courses are not offered every semester, or even every year. Students should check the course schedules online when planning their curriculum.
It is strongly recommended that students take MATH 330 (Number Systems) as early as possible. This course covers fundamental methods and ideas of higher mathematics, and provides important preparation for later courses.
Required Courses
Year Fall Spring
1 221 222
2 323, 330 304
1. Pure math
Year Fall Spring
3 401, 478 479 or 402
4 46l 375
2. Computer science
Year Fall Spring
3 358 or 404 357
314
4 381 386 or 471
371 335
3. Science and engineering
Year Fall Spring
3 371 471
401 or 404
4 478, 447 375 or 357
4. Math. education
Year Fall Spring
3 two of: 448 or 386
381,447, 465
4 two of: 375 or 386 or 402
401, 407, 478
5. Social sciences
Year Fall Spring
3 447 448
404
4 371 or 478 357
Note: A person who follows this program and takes ECON 160, 162, 360,
362,464, 466, plus three other 400 level ECON courses has fulfilled the
requirements for the B.S. degree in Economics with a double major in Economics and
Mathematics.
The Department of Mathematical Sciences offers an actuarial track for the BA degree in Mathematics. This program provides a strong preparation for an actuarial career. To obtain a BA degree in Actuarial Sciences a student must complete the following 12 mathematics and economics courses:
Year Fall Spring
1 Math 221 Math 222
Econ 160 or162 Econ 160 or 162
2 Math 323 Math 304
Econ 360 or362 Econ 360 or 362
3 Math 447 Math 448
Math 371 Math 324
one of Math 357, 358, 386 or 471
4 Math 449 Math 450
Econ 442 one of Math 357, 358, 386 or 471
All the courses above (except Econ 442) are required to satisfy the
requirements for the BA in Actuarial Sciences. It is recommended that
students take Econ 442 as well as other math courses.Professional certification as an actuary results from passing a series of examinations administered by the actuarial societies. Several courses in Binghamton University cover all the material required in the first two actuarial examinations. MATH 324 is course designed to prepare for the first actuarial examination. The calculus sequence and Math 447 are requirements for Math 324. MATH 449 covers the part of the second examination on the Theory of Interest. Courses in the Department of Economics can be used to prepare for the parts in economics and finance of the second actuarial exam. MATH 450 covers part of the material in the third actuarial exam. Students wishing careers in this field are encouraged to complete the first examination before the junior year, complete the second examination around graduation, and have some preparation toward the third before they complete their undergraduate studies. At the very least, students pursuing this career should pass the first actuarial exam within a few months of graduation.
The first two actuarial exams are given on this campus. The University itself has nothing to do with the preparation of the exam questions, it is merely an agent of the Society of Actuaries, administering the exams for the convenience of the SUNY-Binghamton students.
Further information about the actuarial program is available at http://www.math.binghamton.edu/stat/actuary.html.
The requirements for the BS degree in Mathematical Sciences are the following courses:
It is strongly recommended that students take Math 330 (Number Systems) as early as possible. This course covers fundamental methods and ideas of higher mathematics, and provides important preparation for later courses.
One possible package for this degree is:
Fall Spring
Year 1 Math 221 Math 222
Math 304
Year 2 Math 323 Math 371
Math 330 Math 375
Year 3 Math 478 Math 479
Math 401 Math 402 or 404
Math 480
Year 4 Math 461 Math 407 or 335
Math 447 or 358 Math 448 or 357
Math 381 Math 386
Students entering with AP credit should make appropriate adjustments in
considering this package.
One requirement for the honors program is strong and broad coursework in mathematics. The student must complete, by graduation, with a grade-point average of at least B, the following: MATH 375; 401; 402 or 404; 478 and 479; and 461, or 447 and 448. Courses on the same subjects at the same or higher level may be substituted upon approval of the Mathematics Undergraduate Committee.
The additional requirements for the honors program are individually designed by the student, in consultation with a faculty sponsor. A proposal for this extra work must be presented to the mathematics undergraduate committee during the student's junior year, with the support of the faculty sponsor. Such a proposal typically involves extra coursework at the graduate level and/or independent research leading to a thesis. If independent study is required in the proposal, the student may register for MATH 498 under the direction of the faculty sponsor.
In cases of unusual merit, the undergraduate committee may award honors to a student who is judged to have met the above standards, even though no program sponsored by a faculty member was submitted.
The mathematics undergraduate committee has final authority for accepting a student into the honors program (based on the merits of the proposal) and for granting graduation with honors (based on the student's success in fulfilling the goals of the honors proposal).
More details, including sample proposals, are available from the Department of Mathematical Sciences.
Guardian Life Insurance Company of America Award. Several awards each year to students who have passed the first actuarial exam.
Though these are different organizations, there is a considerable overlap in membership, and some of their activities are jointly sponsored. Activities include talks on interesting and/or popular mathematical topics, one meeting per semester (at pre-registration time) on advisement, participation in regional undergraduate mathematics meetings, etc. The two groups have a web page at http://www.math.binghamton.edu/dept/math_club/index.html.
Actuarial Association. Provides information about summer internships and regular employment opportunities in the actuarial field. Some club meetings involve presentations from people currently employed in the field.
Summer Research Opportunities. Each summer there are a number of "mathematical research for undergraduate students" programs around the country. These programs typically do not charge tuition, and provide a stipend. The Colleges and Universities hosting these programs vary from year to year. Many such programs are sponsored by the National Science Foundation: a list of such programs is available at http://www.nsf.gov/home/crssprgm/reu/reu98dms.htm. Interested students should also look for information about these programs on the departmental bulletin boards and at meetings of the Undergraduate Math Club and the Student Chapter of the MAA.
Summer Actuarial Internships Doing an internship during the summer is the best way to know whether you really like the Actuarial profession. In some companies, you do not need to have passed any exams. Summer positions provide students with valuable experience and excellent summer income. You can arrange interviews for summer internships through the Career Development Center of Binghamton University. In this center you also can get information about careers, graduate schools, internships, or employers. For a small fee, you can get a very complete information on the interviews on campus for summer internships
Another section of this handbook deals with going to graduate school in the mathematical sciences, especially for those who aim for a Ph.D. in mathematics.
In general, employers hire math majors because of their knowledge of quantitative methods, skills and experience with symbolic reasoning and manipulation, and ability to analyze complex phenomena. An individual employer is likely to have particular requirements or demands, such as a knowledge of statistics. Industrial employers may expect you to have a basic knowledge of relevant subjects; e.g. a chemical company may hire only people who have taken a year or more of college chemistry. Many companies are interested in double majors between mathematics and another field (chemistry, biology, economics, etc). The ability to solve quantitative problems and work efficiently with mathematical models in one of these other fields is prized.
You can expect that any employment will involve the use of computers, at least amounting to the use of ready-made software. You can also expect that any employment will require the ability to speak and write in a clear, well-organized and cogent manner. Good communications skills are essential.
Most jobs will involve the use or development of mathematical models, the mathematical description of real-life phenomena. You will find some work with models in many math courses, including calculus, linear algebra, mathematical methods in science, probability and statistics, operations research, graph theory, combinatorics, etc. Experience with models can also be gained in physics and other science courses, and in some social sciences, especially economics.
The position of actuarial assistant probably attracts more of our graduates than any other single job. Employers usually require entry-level actuarial assistants to have passed at least the first actuarial exam. The financial sciences industry, banks, brokerages, and insurance companies, hire math majors. Any business with problems of resource management, inventory control, or scheduling of operations can use mathematically trained people. The health care industry, including drug manufacturers, needs statisticians. There is mathematical work in companies, organizations, and government agencies concerned with environmental issues, from water resource management to wildlife protection. And math teachers are always needed in secondary schools.
Some jobs will require advanced education -- possibly a master's degree, in mathematics, statistics, operations research, or computer science, or in other fields, such as business management, economics, or some aspect of the biological sciences. Some employers will support employees who pursue advanced education on a part-time basis.
Think ahead. Get advice and information from the faculty. Get to know the Career Development Center and what it has to offer; its resources and services are invaluable.
A list of sources of information about mathematical careers appears in the references at the end of this handbook.
In an earlier section of this handbook and in the catalog you will find suggestions about courses to take if you are planning on going to graduate school. You should certainly include the sequences in Real Analysis (478-479) and Algebra (401-402), if you are planning for graduate study in mathematics. If you are planning for study in statistics you should include Real Analysis (478-479), Probability and Statistics (447-448) and Advanced Linear Algebra (404). Seminar in Algebra (480) is a valuable ``gateway'' course to graduate school, introducing the style of learning and study you can expect. This course also fulfills the University's ``O'' requirement. In addition to courses, a summer research experience program (discussed earlier in ``employment and research opportunites'') is an excellent way to get a taste of the graduate school experience, and is looked on well by prospective graduate schools.
It is also advisable for you, and for any mathematics major, in fact, to get to know some faculty member(s) reasonably well. This will be helpful in connection with letters of recommendation. Also, it will give you faculty you can talk with about graduate schools and your plans for applying.
You would be well advised to get started early on the application process. By very early in your senior year, or before, you should obtain information and application forms from the schools you are considering and learn of the deadlines and requirements for the particular schools. Since many schools require applicants to have taken the aptitude parts of the Graduate Record Examination (GRE) and some the specialized or subject part, you should plan on taking at least the aptitude parts. The GRE's are usually given in October and December. Taking them in October would generally be advisable. The deadline for applying for the October exam occurs during the preceding summer.
Most graduate students in mathematics are able to support themselves modestly on financial assistance in the form of stipends for Teaching Assistantships, Fellowships, etc. Applications for graduate study will usually have a place to indicate that you are applying for financial assistance, as most applicants do. The application deadline may be earlier for those applying for financial assistance.
It has been customary in recent years for the Undergraduate Mathematics Club and the MAA Student Chapter to sponsor an event in the early Fall, sometimes entitled, "Is There Life After Majoring in Mathematics?" At this time there is a discussion about graduate schools and the application process. Some information about specific graduate schools and information and application forms for the GRE's can be obtained from the Career Development Center. Application forms for the GRE's can also be obtained in the Academic Advising Office. Don't hesitate to ask questions and seek advice.
The Mathematical Sciences Department keeps copies of the materials on this list for you to read in the Department Office.