A GUIDE FOR UNDERGRADUATE MAJORS

IN

MATHEMATICS

2001-2002

Did you ever notice those little whirlpools, or vortices, that are swept downstream from the piers of a bridge, or that spin off the end of your oar when you are rowing a boat? That same thing happens in the slipstream of a car or an airplane, or in the wind blowing past a tall building. In some instances it may be a small effect, but at higher velocities they may affect the drag on a car or an airfoil, and in extreme cases the resonance produced may be large enough to bring down bridges or the cooling towers of a power station. In studying the case of a wind tunnel or any other situations, a scale model has to be built and modified every time changes are desired.

Here is where the mathematics comes in; we build a mathematical model. The only real construction that goes on here is in our minds. By formulating the mathematical equations that govern the process, we can attempt to solve them mathematically to obtain a description of what will happen in the real world. This is not always an easy process. Often the models have to be so complicated to take into account all the factors involved that solving them explicitly is impossible. However, sophisticated mathematical techniques can be used to generate approximate solutions on high-speed computers. The mathematics allows us to build the model, to go as far as we can with theoretical means to solve it, to organize it in a suitable form for computer processing, and to analyze the results. Frequently, the results obtained provide new insights into the mechanisms involved, thereby enabling the mathematical model to be improved.

The process is called computer simulation. It is used extensively in the design of automobiles and airplanes, in energy resource discovery and recovery, and to understand complex industrial processes such as chemical reactions or the reactions that occur inside a nuclear reactor. This is mathematics at work. Remember that the computer only does what it is told to do (very quickly, of course), and so highly trained mathematical scientists, teamed with specialists from other areas, are essential to the success of such ventures. Industry is increasingly turning to mathematical modeling and computer simulation as the primary tools in its research and development operations, particularly since the advent of the supercomputer.

Does all of mathematics require the use of a computer? Not at all, but the process of discovery in any area of mathematics is similar to that in modeling and simulation. The problem is formulated in mathematical terms, modeled, analyzed, perhaps only partially resolved, modified, analyzed again, and so on, until a solution is obtained. And all of science is so inherently mathematical that expertise in mathematics is essential nowadays in virtually every branch of science and engineering, and even in business administration and the social sciences. Mathematics is indeed the language of science, the universal means of expression, the source of communication between diverse disciplines.

In today's world of rapidly expanding technology, there are many career opportunities for the well-qualified mathematician. Business, government, and industry have strong needs for mathematicians in areas such as operations research, optimization, numerical analysis, computer programming, systems analysis, communications, statistics, and information and actuarial science. Whether it be in operations research, systems analysis, computer software and hardware development, modeling and simulation, numerical analysis, development and test of algorithms, cryptology, or teaching, some familiarity with computers and the mathematics of computation is usually essential. The mathematics degree, at the baccalaureate, masters, or doctoral level, provides the grounding in analytical thinking and the scientific skills necessary to function in today's interdisciplinary environment. The Bachelor of Science degree is a sound preparation for graduate study in mathematics or any of the mathematical sciences, but also for advanced degrees in business administration and some of the quantitative social sciences. A bachelor's degree in mathematics can also provide entry to jobs in management, engineering, and geology, among others.

The pamphlets "Careers in the Mathematical Sciences" and "More Careers in the Mathematical Sciences," published by the Mathematical Association of America, provide an indication of a variety of careers available to persons with interest and preparation in the mathematical sciences. Copies may be obtained from the Mathematics Main office, LeConte 413. The following websites are excellent sources of career information in mathematics, applied mathematics and actuarial science:

Anderson Consulting

Bell South

CIA

Computer Task Group

Duke Power Company

Educational Data Center

Electronic Data Systems (EDS)

First Federal of Charleston

Liberty Life Insurance

Microsoft Corporation

National Security Agency

Naval Air Systems Command

Naval Surface Weapons Center

National Cash Register

Provident Life and Accident Insurance Co.

Smith Data Processing

South Carolina Department of Education

Spring Industries

State Farm Insurance

Texas Instruments

United States Air Force

United States Bureau of Labor Statistics

United States Bureau of the Census

United States Coast Guard

United States Department of Energy

United States General Accounting Office

Westinghouse

Xerox

Job prospects depend on one's training. A mathematics major is urged to take several courses in a field that uses or is closely related to mathematics such as computer science, statistics, engineering, operations research, a physical science, or business. A double major in mathematics and computer science, or mathematics and statistics, is particularly desirable.

The University of South Carolina is fast evolving into one of the premier mathematics research centers in the Southeast. The distinguished faculty has attracted national and international recognition through the quality of its research program. The Department has particular strengths in mathematical analysis, discrete mathematics, linear algebra, differential geometry, commutative algebra, logic, number theory, topology, and numerical analysis. It is thus uniquely poised to provide undergraduate and graduate students with the broad background in pure and applied mathematics necessary to perform in today's high-tech environment, whether in an industrial, business, governmental, or academic setting. The Department also maintains a strong commitment to excellence in teaching and proudly counts a number of award-winning teachers among its ranks.

Department computing facilities are excellent. In addition to various University mainframe and workstation computers available via the campus network and in numerous satellite PC laboratories, the Department houses a separate computing laboratory with Pentium PC and Unix workstations. Installed on these platforms are several statistical and mathematical software packages to support coursework and research.

The Department of Mathematics offers the Bachelor of Science degree in Mathematics. The major is completed with 128 semester hours of overall coursework. Each student is required to complete 12 hours of integrated courses in a discipline related to, but distinct from the major discipline. Mathematics majors may select from one of five tracks:

• General Mathematics – Requires 24 semester hours of mathematics courses beyond calculus (comprising the required core of 15 semester hours and nine semester hours of mathematics electives).

• Applied Mathematics – Offers specialization in applied or computational mathematics. A one semester hour computational lab is added to the 15 semester hour core and nine hours of mathematics electives required in such disciplines as numerical analysis, optimization, and partial differential equations. Applied mathematics majors are encouraged to select a cognate or minor in computer science or statistics.

• Actuarial Mathematics – Offers a program of study designed to prepare students for the actuarial profession in the insurance and financial securities industries. In addition to the required mathematics courses, this track requires a minimum of 24 credit hours in Business Administration and Statistics. The program also includes an option for a minor in Risk Management and Insurance. Students in this track are also encouraged to choose appropriate electives from the social sciences and humanities.

• Teacher Preparation – Leads to a bachelor’s degree in mathematics, with a 12 semester hour education component, and is followed by the Master of Teaching Degree Program in Secondary Education. In addition to the core courses, the program also requires a course in number theory and geometry.

• Intensive Mathematics – Requires 36 semester hours of advanced mathematics courses beyond calculus.

The department also offers a five year program of study leading to a Bachelor of Science degree and a Master of Science degree in Mathematics. The program is designated to permit an outstanding student to obtain both a bachelor’s degree and a master’s degree in mathematics in five years. Detailed degree requirements are described in DEGREE REQUIREMENTS.

It is essential that you meet with your advisor each semester during the regularly scheduled advisement period so that you can plan your course of studies for the following semester. The advisement process must be completed before the student can register for the next semester. Please don't leave this until the last minute. Sign up sheets for academic advisement appointments will be posted by the academic advisor during each semester's advisement period.

When you have earned 95 credit hours, you will be sent a letter asking you to go to the office of the Assistant Dean, PSC Room 108, for a "Senior Records Check." The purpose of this check is to insure that you are aware of any unfulfilled graduation requirements. Before you report to the Office of the Assistant Dean, however, you must secure a Major Program Card from your advisor listing all major and cognate courses to be used to fulfill the degree requirements.

Problems do arise, of course, and we encourage you to discuss them with your advisor at any time, whether they are academic or personal in nature. When you have a special problem that is beyond your advisor's authority (such as variations on requirements or special cognates), or when your advisor is not available and you need assistance, see the Director of Undergraduate Studies.

Dr. Gerald T. Cowley, Assistant Dean

PSC 108 (Phone 7-2505)

Dr. Manfred Stoll, Chairman

LeConte 409 (Phone 7-4225)

Dr. George Johnson, Assistant Chairman

LeConte 417 (Phone 7-5313)

Dr. Anton Schep , Director of Graduate Studies

LeConte 411 (Phone 7-4226)

Dr. Douglas Meade, Undergraduate Director

LeConte 300E (Phone 7-6183)

Students interested in the Master of Arts in Teaching (MAT) degree may obtain information from Dr. Anton Schep, Director of Graduate Studies.

For an outline of the General Education Requirements see the listing for the College of Science and Mathematics in the Undergraduate Studies Bulletin or the College of Science and Mathematics Guidelines for advisement.

The following pre-major courses may fulfill some of the General Education requirements.

1. STAT 511 (or MATH 511) and STAT 512
2. Either STAT 509 or STAT 515 and either STAT 516 or CSCE 146

There are five program options offered in Mathematics, each leading to a Bachelor of Science degree.

1. Math 520, 526 or 544, 546, 554, 574
2. At least one course selected from MATH 534, 550, 552
3. 6 hours in MATH numbered above 500, selected in consultation with the advisor

1. Statistics (6 – 12 hours): STAT 512, 513 and 0 – 6 hours from STAT 510, 520 (=MGSC 520)
2. Business Administration (12 – 18 hours): ACCT 222, ECON 224, FINA 363 (=ECON 363) FINA 341 or 444, and 0 – 6 hours from FINA 342, 346, 443, 444, 445, MGSC 392, 393, 520 (=STAT 520), 594 ECON 420, 594, BADM 499. For the Minor in Risk Management & Insurance (18 hours), of the additional 6 hours, an additional three hours must be chosen from FINA 342, 443, 444, or 445.

3. Computing (7 – 8 hours): CSCE 145, plus one elective from CSCE 146, MGSC 390, STAT 517

Any major above, plus an additional 4 courses in MATH numbered above 500 and selected in consultation with the Advisor.

A grade of C or better is required in each major course and in each of MATH 141, 142, 241. A student may enroll in each major course and in each of MATH 141, 142, 241 a maximum of two times. (Enrolled in a course is interpreted to mean that a grade, including W, has been recorded). The student may repeat a maximum of three mathematics courses (receiving a grade of W is not to be considered a repeat).

The cognate consists of 12 hours of upper-division courses selected in consultation with, and approved by, your advisor. A mathematics major may satisfy this requirement by selecting 12 credit hours of cognate eligible courses offered by the College of Science and Mathematics or Department of Computer Science and Engineering. Cognates elected from other disciplines should be supportive(*) of the major and must be in one field selected with and approved by the student’s academic advisor. All exceptions must be approved in advance by the Undergraduate Director.

Here is a list of eligible courses in other disciplines within the College of Science and Mathematics and the Department of Computer Science and Engineering from which you may select a cognate to supplement your mathematics major. There are many other possibilities involving coursework in other Colleges.

Astronomy: All courses numbered 311 and above

Biology: All courses numbered 300 through 600 levels

Chemistry: All courses except 101, 102, 105, 106, 111, 112, 118

CSCE: All courses numbered 213 and above except 500 and 508

Geology : All courses numbered 300 and above

Marine Science: All courses numbered 311 and above

Physics: All courses numbered 212 and above

Statistics: All courses numbered 500 and above. Only one of STAT 509 and 515 may be used for cognate credit.

You may replace the cognate with a minor if you so desire. The minor consists of eighteen hours of coursework instead of the twelve needed for the cognate. The minor is also more structured. All courses in the minor must be passed with grades of C or better. Students who are planning to minor in a subject area need to go to the Dean’s office and fill out the appropriate forms to declare the minor. Otherwise the minor will not show up on the transcript.

Three minors that should be very appealing to mathematics majors are as follows:

1. Prerequisite Courses: CSCE 145, 146; MATH 141, and 142.
2. Required Courses: (Not available at time of printing. Check the College Brochure or with the Department of Computer Science and Engineering.)

Six 500 level STAT courses approved by the Undergraduate Director of Statistics. Only one of STAT 509 and STAT 515 may be counted.

ACCT 222, ECON 224, FINA 363[=ECON 363], plus

1. FINA 341 or 444,
2. 3 credit hours chosen from FINA 342, 443, 444, or 445,
3. 3 credit hours chosen from FINA 342, 346, 443, 444, 445, MGSC 392, 393, 520 [=STAT 520], 594, ECON 420, 594, or BADM 499.

Instead of selecting a cognate (12 hours) or a minor (18 hours), you may wish to select a double major, which requires an additional 24 hours or more in a second discipline. Such a program, which must be approved by the Dean, can be easily accommodated within the 128-hour degree requirement if you make the decision reasonably early, say in your second year. The double major in Mathematics and Computer Science should be particularly attractive to many students.

Requirements for the baccalaureate degree in the College of Science and Mathematics include at least 128 hours in academic subjects. Students in the College of Science and Mathematics may elect acceptable courses offered in other colleges of the University. Elective credits for participation in the University chorus, orchestra, or band may be counted up to a maximum of 4 credits.

This program of study is designed to permit an outstanding mathematics student to obtain both a bachelor's degree, as described in A above, and a master's degree in mathematics in five years, while at the same time receiving undergraduate and graduate assistant support during the last two years.

(i) To be considered for the program, the student must have earned at least 103 hours by the start of his senior year, and must have completed one of the preparatory undergraduate sequences MATH 546-547 or MATH 554-555. This is easily accomplished if the student has received undergraduate credit through advanced placement examinations, or enrolls for one or more summer sessions.

(ii) During their senior year, the student takes the basic graduate sequence, MATH 700-701 (or 706) or MATH 703-704 corresponding to the undergraduate sequence they have already taken, for graduate credit. In addition, the student will complete the other preparatory undergraduate course sequence. The remaining 9 hours in the fall semester of the senior year will consist of additional undergraduate or graduate courses. This will leave the student 10 hours short of his bachelors degree, which will be completed in the spring semester.

(iii) For the spring semester of the senior year, the student is conditionally admitted into the graduate program. Final acceptance into the program will be contingent upon receipt of the bachelor's degree at the end of spring semester. To be considered for ad-mission, except for the lacking the bachelor's degree, the student must meet all other requirements for admission to the graduate program.

The prospective student will normally be considered for admission into the program during the fall semester of their senior year on the recommendation of their undergraduate advisor. It is expected that the prospective student will have attained a 3.5 overall GPA, a 3.5 on all mathematics courses taken, and will have taken the GRE examination by the end of October of their senior year.

By November 1, the prospective student must submit an application with all supporting material to the Graduate School for admission into the M.S. program in mathematics for the following spring semester. A decision on admission into the graduate program will be made prior to the start of the spring semester. Prior to registration for the fall semester, the student must also secure the required signatures on the "Senior Privilege" form (GS19) available from the Graduate School to register for 700 level courses.

Upon admission to the program, the student will be eligible for financial assistance from the department as follows: During the fall semester of the senior year, the student will receive consideration for employment as an undergraduate assistant for 10 hours per week, and during the spring semester of the senior year, the student will receive consideration for a quarter time graduate assistantship. In the fifth year and the first and second summer of graduate study, the student will be eligible for a halftime graduate teaching assistantship.