WHAT IS MATHEMATICS

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.

CAREER OPPORTUNITIES IN

MATHEMATICS

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 careers in fields such as management, engineering, banking, insurance, government service, the military, and geology.

An excellent source for information about careers in the mathematical sciences is the Mathematical Association of America (MAA). The pamphlets "Careers in the Mathematical Sciences" and “More Careers in the Mathematical Sciences,” provide an indication of the variety of careers available to persons with interest and preparation in the mathematical sciences. Copies may be obtained from the Department of Mathematics Undergraduate Office in LeConte College 413. The following websites are excellent sources of career information in mathematics, applied mathematics and actuarial science:

www.maa.org/students/career.html

www.ams.org/careers/home.html

www.beanactuary.com

www.siam.org/careers/

The following is a partial list of employers who were recruiting math majors on campus during recent years:

Anderson Consulting

Bell South

Blue Cross/Blue Shield of South Carolina

Central Intelligence Agency

Colonial Life

Computer Services Corporation (CSC)

Computer Task Group

Duke Power Company

Educational Data Center

Electronic Data Systems (EDS)

First Federal of Charleston

Fleet

Liberty Life Insurance

Microsoft Corporation

National Security Agency

Naval Air Systems Command

Naval Surface Weapons Center

National Cash Register (NCR)

Provident Life and Accident Insurance Co.

Resource Bancshares Resource Group (RBMG)

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

United States Office of Comptroller of the Currency

Westinghouse

Xerox

The electronic version of this brochure includes hyperlinks to employment information at many of the above corporations and agencies. The URL is www.math.sc.edu/undergrad/ugradbrochure.html.

Additional career information can be found on the Careers link on the Mathematics Department’s homepage (http://www.math.sc.edu/careers.html). The US Department of Labor, Bureau of Labor Statistics, maintains an Occupation Outlook Handbook at http://www.bls.gov/oco/. This is an excellent source of general information about almost any career.

Job prospects depend on one's educational background and personal interest. A mathematics major is encouraged to take several courses in a field that uses or is closely related to mathematics. Popular examples include education, statistics, biology or other physical science, business, finance, and computer science. A double major in mathematics and computer science, or mathematics and statistics, is particularly attractive to employers. The actuarial emphasis combines a major in mathematics with a strong background in statistics and risk management (insurance). This program is particularly suited for students interested in becoming an actuary.

MATHEMATICS AT USC

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 number of computer-equipped classrooms and open computer labs. A large collection of mathematical and statistical software is installed on these computers for use in courses and research.

DEGREE PROGRAMS

The Department of Mathematics offers the Bachelor of Science degree in Mathematics. The major is completed with 128 semester hours of overall coursework. Mathematics majors may select from one of five emphases:

· 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).

· Mathematics Education – Leads to a bachelor’s degree in mathematics, with a 12-semester hour education component. Certification is obtained upon completion of the Master of Teaching degree program in Secondary Education. In addition to the core courses, the program requires courses in number theory and geometry and one mathematics elective.

· 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, statistics, or one of the physical sciences.

· 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. Depending on the specific collection of courses selected, a cognate and/or minor can be obtained in Statistics and/or Risk Management and Insurance.

· Intensive Mathematics – Requires completion of one of the above emphases plus an additional 12 semester hours of upper-division mathematics courses approved by the academic advisor.

In addition to the major requirements, each student is required to complete a minor (18 hours of courses related to a common topic) or a cognate (12 hours of integrated courses from a single department) in a discipline related to, but distinct from the major. Note that the Actuarial and Education emphases automatically include a cognate and/or minor.

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. Students interested in pursuing this option should contact the Graduate Director during the first two years of undergraduate studies.

ADVISING

When you enroll as a mathematics major, the Director of Undergraduate Studies will initially advise you. Mr. Robert Murphy will be your advisor until you have completed calculus (Math 241 or Math 250). A permanent advisor will be assigned to you as you begin to take upper division mathematics courses. Your advisor will assist you in formulating your program of study and preparing for the beginning of your career (or further education). While the advisor’s role is to provide guidance, the student has final responsibility for staying fully informed on University deadlines and relevant academic policies.

It is essential that you meet with your advisor each semester 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. Your academic advisor will post sign-up sheets for academic advisement appointments during each semester’s advisement period. To increase your likelihood of getting the courses you want and need, please be certain to be advised during the regular advisement period..

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.

At the beginning of your last year before graduation, when you have earned 95 credit hours, you should ask your advisor to complete a Major Program Card. This involves listing all major and cognate courses that you intend to take to fulfill the degree requirements. Then, call the Assistant Dean’s Office at (777-2505, PSC 109) to request a "Senior Records Check". The purpose of this check is to identify all unfulfilled graduation requirements while you still have time to complete them without delaying your graduation.

AWARDS AND SCHOLARSHIPS

The Department of Mathematics and College of Arts and Sciences recognize continuing and graduating students at the end of each academic year. The current list of awards and scholarships, with brief descriptions, is shown below. The Undergraduate Advisory Council solicits applications from interested students each spring; the awards are announced and presented at Undergraduate Awards Day.

Outstanding Undergraduate Student in Mathematics Education

… presented yearly to an outstanding undergraduate student in mathematics education who has exhibited excellence in the mathematics program.

Outstanding Undergraduate Student in Mathematics

… presented yearly to an outstanding undergraduate student who has exhibited excellence in the mathematics program.

College of Arts and Sciences Rising Senior Award

… awarded annually by the College of Arts and Sciences to a rising senior mathematics major who has demonstrated excellence in mathematics and has a cumulative GPA of at least 3.50.

James Bruce Coleman Mathematics Scholarship

… awarded annually by the Department of Mathematics to an outstanding mathematics major from South Carolina. The scholarship was established in 1992 by Joseph Harold Burckhalter (Class of 1934), in memory of the late James Bruce Coleman, who was a professor of mathematics and head of the department from 1915—1942.

Thomas Markham Mathematics Scholarship

… awarded annually to an outstanding mathematics major who also has significant extracurricular mathematical activities. The scholarship was established in 1999 in honor of Professor Emeritus Thomas Markham, who was a professor of mathematics from 1968—1999 and undergraduate director 1996—1999.

Cary K. Smith, Jr., Mathematics Scholarship

… awarded annually by the Department of Mathematics to an outstanding undergraduate mathematics major who has demonstrated excellence in mathematics and leadership. The scholarship was established in 1998 in memory of Cary Kincaid Smith, Jr., an Honors graduate of USC who died while performing his duties as a pilot in the U.S. Marine Corps.

Wyman L. Williams Scholarship

… awarded to an undergraduate mathematics major at the University of South Carolina. Can be renewed for not more than 3 additional years of undergraduate study. Wyman L. Williams came to the University in 1919 as a freshman, joined the Mathematics Department faculty in 1924 and retired in 1970 as Distinguished Professor Emeritus. The Wyman L. Williams Mathematics Scholarship Fund was established in 1975.

Jeong S. Yang Award for Excellence in Undergraduate Mathematics

… awarded yearly to outstanding undergraduate mathematics majors at the University of South Carolina selected from students who have earned at least 100 credit hours and have completed at least 4 of the 5 core mathematics courses required for the major with a GPA of at least 3.70 in all upper-division mathematics courses. The award was established by the Department of Mathematics in memory of the late Professor Jeong S. Yang, undergraduate director 1984—1995.

Pi Mu Epsilon Award

… presented annually to an outstanding member of Pi Mu Epsilon based on performance in mathematics courses and service to the department. The Undergraduate Advisory Council, in conjunction with the Pi Mu Epsilon advisor, selects the recipient.

Victor W. Laurier Undergraduate Research Scholarship

… provides monetary support for an undergraduate student interested in being involved with mathematical research during the summer. This is a competitive award based on proposals submitted by all interested students. The selection is based on a written proposal.

Phone: 777-6183

A GUIDE FOR UNDERGRADUATE MAJORS

MATHEMATICS