UNDERGRADUATE STUDIES IN MATHEMATICAL SCIENCES AT BINGHAMTON

PREFACE:

This handbook is intended to be useful to undergraduate mathematics majors and to others interested in mathematics programs at Binghamton University. The information in the Handbook is a supplement to the University Bulletin, which is indispensable for all students. The Handbook does not and cannot supplant the need for all math majors to seek the advice of the faculty at all stages of their education. It may, however, help students focus more clearly on the choices and issues involved in their programs so that they can make more effective use of faculty advice.

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 DEPARTMENT:

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.

Advising

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.

Grade requirements and prerequisites

The department views the grade of D as passing, but unsatisfactory, and the grade of C- as indicating inadequate preparation for subsequent courses. Therefore:
  1. A course in which the grade of D or C- was received is not acceptable as a prerequisite. If a course is taken P/F, it may only count as a prerequisite if the instructor certifies that the student was doing at least C level work.
  2. A course cannot be used to fulfill the requirements for a major in mathematical science unless a grade higher than D has been received in it. In particular, courses taken P/F may not be counted toward a major.
  3. The department requires a GPA of 2.0 or better in courses presented to satisfy either BA or BS degree major requirements.
A student may not take for credit a course that is a prerequisite to one for which the student has already received credit unless departmental approval is obtained in advance.

DEGREE PROGRAMS:

BA degree in Mathematical Sciences: mathematics track

As students are attracted to mathematics for a variety of reasons, the requirements for the BA are relatively unspecific, allowing students to build their majors to suit their tastes. Because of the unstructured nature of this degree, it is extremely important that students seek advice and guidance from mathematical sciences faculty about designing their programs. It is best if students declare their major early so that an advisor will be assigned to them.

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:

Three additional elective MATH courses numbered above 330 must be taken (one of these may be CS 333 if it is not used in the pairing). Transfer and/or independent study credit cannot be used for more than 3 of the required courses numbered 330 and above. This allows the student to design a program suitable to his or her goals, whether they be graduate work in mathematics or some other field, professional school, a career in actuarial science, computer science, mathematics education, or business, or a liberal education with specialization in mathematics.

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.

BA degree in Mathematical Sciences: mathematics track with Computer Science minor

The Computer Science Department in the Watson School of Engineering and Applied Science offers a minor program which can be combined with a BA in mathematics to provide a strong background leading to careers in computer science. The BA in mathematics is designed to facilitate this combination by allowing two upper level (as specified in the catalog) computer science courses to be included in the degree program. Students interested in mathematics and computer science should consult with the Computer Science Department.

BA degree in Mathematical Sciences: actuarial track

An actuary uses mathematical models to solve business problems which involve risk -- that is, chance of a financial loss. Actuaries do computations related to risks, such as how much to charge policy-holders for auto, life, health insurance premiums or how much an insurance company can expect to pay in claims when financial losses occur. Actuaries are employed not only by insurance companies but also by banks, investment firms and federal and state insurance departments. Among the areas an actuary may specialize in are life insurance, casualty insurance, health insurance, pensions, and consulting. There is an expanding need for more qualified actuaries, and the competition among employers for good actuary students is keen. Salaries offered are substantial, and there is ample opportunity for advancement in the actuarial profession. In recent years, many large and small companies have actively recruited on our campus.

To obtain a BA degree in mathematics with an actuarial sciences track, a student must complete 10 courses from the Department of Mathematical Sciences and two from economics as follows:

At least three of the required mathematics courses listed above, and numbered above MATH 330, must be regular courses (not independent study) taken from the Department of Mathematical Sciences.

It is recommended that students take courses in other fields such as Economics and/or Finance as well as other math courses. Several Binghamton University courses can be used to satisfy the validation by educational experience requirements of the actuarial societies. Students interested in an actuarial track should have knowledge of computer programming equivalent to CS 100, and also take courses in economics and finance.

One possible package for this degree is:

Year     Fall               Spring

1      Math 221          Math 222
       Econ 160 or 162   Econ 160 or 162

2      Math 323          Math 447
       Math 346          Math 304          
       Econ 360 or 362   Econ 360 or 362

3      Math 448          Math 449
       Math 371 or 372   Math 330
                         

4      Math 450          Math 452
       Econ 466          Fin 322 or 324
       Fin 311
Students entering with AP credit should make appropriate adjustments in considering this package. MATH 450, MATH 452, ECON 360, ECON 362, ECON 466, FIN 311, FIN 322 and FIN 324 are not required to satisfy the requirements for the BA in Actuarial Science. It is recommended that students take Math 450 and Math 452, since they provide preparation for the third actuarial exam. ECON 466 is course approved to satisfy the requirements (vee) validated by educational experience in Applied Statistical Methods. FIN 311 and either FIN 322 or 324 are sequences approved to satisfy the vee requirements in Corporate Finance. Students should placed the courses to satisfy vee requirements as a low priority. These vee requirements can be satisfied in other ways. To get hired is very important to have passed the first two actuarial exams.

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 449 is course designed to prepare for the first actuarial examination. The calculus sequence and Math 447 are requirements for Math 449. MATH 346 covers the part of the second examination on Financial Mathematics. MATH 450 and MATH 452 cover the Society of Actuaries exam known as Models, Life Contingencies. Students wishing careers in this field are encouraged to complete the first two examination before the senior year, and have some preparation toward the third before they complete their undergraduate studies. The first two actuarial exams can be taken in any order.

The first two actuarial exams can be taken very close to campus in the Prometric Test Center in 4104 Old Vestal Rd., Vestal, NY 13850.

Further information about the actuarial program is available at http://www.math.binghamton.edu/actuary/index.html.

BS degree in Mathematical Sciences

This degree is for a truly committed student. The standard BS option provides excellent preparation for graduate work in mathematics and related fields such as statistics, computer science, operations research and business administration. An exceptionally good student may take some graduate courses while still an undergraduate, but only with departmental approval.

The requirements for the BS degree in Mathematical Sciences are the following courses:

  1. Calculus-Linear Algebra - Math 221, 222, 304, 323. (4 courses)
  2. Number Systems - Math 330. (1 course)
  3. Complex Variables & Real Analysis - Math 375, 478, 479. (3 courses)
  4. Algebra - Math 40l and 402 or 404. (2 courses)
  5. Topology - Math 461 (1 course)
  6. Five additional courses, chosen from any of the following:
At most three of these five courses may be taken outside the math department. (5 courses) Transfer and/or independent study credit cannot be used for more than 5 courses numbered above 330. Courses taken P/F may not be counted toward this major.

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.

BS degree in Mathematical Sciences; actuarial track

The BS track in actuarial sciences is designed to prepare students for an actuarial career. It is a mathematically stronger program designed for students who may wish to pursue a graduate degree in actuarial sciences. Actuaries analyze and solve complex business and social problems related to insurance and pension plans. Professional advancement results from passing a series of examinations administered by the actuarial societies and by completion of specific courses or sets of courses approved by the actuarial societies. The track in actuarial sciences provides a strong preparation for an actuarial career. To obtain a BS degree in mathematics with an actuarial sciences track, a student must complete 14 courses from the Department of Mathematical Sciences and four from the Department of Economics as follows:

Basic courses in Mathematics: Calculus, Linear Algebra, Number Systems, Ordinary Differential Equations: MATH 221, 222, 323, 304, 330, and 371 or 372.

Probability, Statistics and Actuarial Courses: MATH 346, 447, 448, 449, 450 and 452.

Advanced courses in Mathematics: MATH 478 and 479.

Courses in Micro and Macroeconomics: ECON 160, 162, 360 and 362.

MATH 449 is a preparation for the first actuarial examination. Students interested in an actuarial track should have knowledge of computer programming equivalent to CS 100, and also take courses in economics and finance.

One possible package for this degree is:
Year     Fall               Spring

1      Math 221          Math 222
       Econ 160 or 162   Econ 160 or 162

2      Math 323          Math 447
       Math 346          Math 304          
       Econ 360 or 362   Econ 360 or 362

3      Math 448          Math 449
       Math 371 or 372   Math 330
       Econ 466          Fin 311                       

4      Math 450          Math 452
       Math 478          Math 479
       Fin 322 or 324

Students entering with AP credit should make appropriate adjustments in considering this package. ECON 466, FIN 311 amd FIN 322 or 324 are not required to satisfy the requirements for the BS in Actuarial Science. But, these courses satisfy the vee requirements state by the actuarial societies.

OTHER DEPARTAMENTAL PROGRAMS:

Honors Program in Mathematics

The honors program in mathematics is designed for students who have a serious interest in advanced mathematics, particularly in research. Admission to the program is by faculty nomination, followed by a vote of the Mathematics Undergraduate Committee.

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.

Prizes

Award for Excellence in Mathematical Sciences. One or more awards each year to graduating seniors.

Guardian Life Insurance Company of America Award. Several awards each year to students who have passed the first two actuarial exam.

Clubs

Undergraduate Mathematics Club. Chartered by the Student Association. Student Chapter Of The Mathematical Association Of America.

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.

Employment and research opportunities for students

Academic Year Employment. Each semester the department hires undergraduate students to work as graders, tutors, and teaching assistants. This work is usually available only to students who have completed the calculus sequence and linear algebra, and may be available for credit rather than pay. Application forms are available in the departmental office.

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

CAREERS IN MATHEMATICS

What can you do with a BA or BS degree in mathematics? What are the employment opportunities? In this section we briefly explore some answers to these questions, ignoring the fact that some math majors will do things that may have no special relation to their mathematical education.

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.

GRADUATE STUDIES IN MATHEMATICAL SCIENCES:

If you really enjoy doing mathematics and have done well in your courses, you may want to consider continuing your study of mathematics or statistics in graduate school. Graduate degrees will be necessary if you plan on a career as a faculty member at a college or university and/or as a research mathematician, with the Ph.D. degree required for faculty positions in mathematics at universities and most four-year colleges. If your interest is in teaching at the high school level, you may want to consider programs for Masters degrees in education and mathematics such as our MAT degree. Completing graduate study will also enhance your credentials for other employment and will give you the opportunity to develop and assess your abilities and interests.

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.

FURTHER RESOURCES:

URLs
  1. http://www.ams.org/careers American Mathematical Society page on non-academic careers
  2. http://www.soa.org/ Society of Actuaries
  3. http://www.amstat.org/ American Statistical Association. Includes an extensive section on careers.
  4. http://www.maa.org/ Mathematical Association of America
  5. http://www.ams.org/employment/undergrad.html A web page of the American Mathematical Society devoted to topics of interest to undergrads
  6. http://www.informs.org/Edu/Career/booklet.html The Career Booklet of INFORMS (Institute for Operations Research and the Management Sciences)
  7. http://casact.org Casualty Actuarial Society
  8. http://www.siam.org/careers Society of Industrial and Applied Mathematics
  9. http://www.acm.org Association for Computing Machinery
  10. http://www.awm-math.org/ Association for Women in Mathematics
  11. http://www.math.buffalo.edu/mad/index.html Mathematicians of the African Diaspora
PUBLICATIONS ABOUT CAREERS

The Mathematical Sciences Department keeps copies of the materials on this list for you to read in the Department Office.

  1. Career Information in the Mathematical Sciences: A Resource Guide. The Mathematical Association of America.
  2. Mathematical Scientists at Work. The Mathematical Association of America.
  3. Careers in the Mathematical Sciences. and More Careers in the Mathematical Sciences. The Mathematical Association of America.
  4. Math Horizons. The Mathematical Association of America.
  5. Seeking Employment in the Mathematical Sciences. American Mathematical Society.
  6. Assistantships and Graduate Fellowships in the Mathematical Sciences. American Mathematical Society.
  7. The Actuarial Profession. Society of Actuaries.
  8. Actuaries at a Glance--Minorities in the Actuarial Profession. Society of Actuaries.
  9. Contingencies. The American Academy of Actuaries.
  10. Careers in Statistics. American Statistical Association.
  11. Women and Statistics. American Statistical Association.
  12. Stats. American Statistical Association.
  13. Minorities! Looking for a Challenging Career? American Statistical Association.
  14. Careers in Applied Mathematics. Society for Industrial and Applied Mathematics.
  15. Careers in Operations Research. Educational Programs in Operations Research. Operations Research Society of America.
  16. Careers that Count. Association for Women in Mathematics.
  17. Shape the Future: A Career as a Mathematics Teacher. National Council of Teachers of Mathematics.
  18. TIMS Asks: Is a Management Science Career Right for You? The Institute of Management Sciences.
  19. Computer and Related Occupations, Bulletin 2400-4. U.S. Department of Labor.