In the past half century there has been a noticeable increase in the importance of mathematics to our society. The need for trained mathematicians at all levels is on the rise as the use of computers and automation has spread to almost all sectors of our economy. Solutions of many technological and engineering problems on which our survival quite literally depends will involve a high level of mathematical thought. Today, someone entering business or government will be expected to know far more mathematics than was expected of the college graduate of ten years ago. This is especially true of professionals working in the biological and social sciences, as well as of those working in finance and business management.
There are many different areas of business where mathematical training is essential. Actuarial work, production management, and business forecasting are but a few. A major in mathematics, focusing on statistics, augmented by a minor in computer science and by courses in accounting, economics, general business, finance, or industrial engineering, for example, would provide a solid basis for a business career.
A mathematics major who wishes to prepare for a career in a government agency, such as the National Security Agency or the Department of Defense, or in a technically-related or service-oriented industry would do well to focus on statistics and applied mathematics and to complete a minor in computer science.
There is a demand for qualified mathematics teachers in the nation's secondary schools.
Advanced work in mathematics and/or statistics should make for more attractive employment opportunities. Most Ph.D.s find employment in academic positions, while those holding Master's degrees usually take positions in government or industry.
Finally, it should be noted that a significant number of students with an undergraduate major in mathematics go on to graduate or professional degrees in fields other than mathematics. Recent majors have pursued graduate work in business, law, computer science, operations research, philosophy, biostatistics, medicine and oceanography.
Further information or advice regarding careers in mathematics and the mathematical sciences, including graduate work in mathematics and/or statistics, can be obtained from the Chief Undergraduate Advisor and from the Career Services Office and from the following sites:
It is essential that all mathematics majors learn some probability and statistics, become acquainted with computers, and study other fields where mathematics plays a significant role.
Students interested in actuarial science, business, computer programming and data processing, graduate study in mathematics (both pure and applied), industrial work, probability and statistics, or teaching may find the following course suggestions useful.
Actuarial ScienceActuaries are business executives who use mathematical skills to define, analyze, and solve complex business and social problems arising in the insurance and pension fields. They create and manage programs to reduce the financial impact of expected and unexpected events such as illness, accidents, unemployment, or premature death. Actuaries must understand the entire operation of the insurance and pension fields because their evaluations often influence company policies and practices. The actuary has a good command of applied mathematics and statistics, financial markets, tax and insurance law, regulatory requirements, accounting, etc.
Professional status is attained through fellowship in one of the actuarial societies. Fellowship is earned, and most of the theoretical training is provided, by passing a series of rigorous examinations sponsored by the societies.
Mathematics majors considering the actuarial field should include courses in finance, economics, computing, operations research, and communication skills in their program.
BusinessThe student who is considering a career in the business world may find that focusing on statistics and electing some of the following courses will be helpful:
| Course | Title | ||
| Math 331 | Ordinary Differential Equations | ||
| Math 425 | Advanced Multivariable Calculus | ||
| Math 455 | Introduction to Discrete Structures | ||
| Math 456 | Mathematical Modeling | ||
| Math 551 | Numerical Analysis I | ||
| Math 552 | Numerical Analysis II | ||
| MIE 379 | Operations Research I | ||
| MIE 380 | Operations Research II | ||
| MIE 422 | Statistical Quality Control | ||
| Acctg 221 | Introduction to Accounting I | ||
| Acctg 222 | Introduction to Accounting II | ||
| Acctg 321 | Financial Reporting I | ||
| Acctg 331 | Cost Accounting | ||
| FOMgt 347 | Production Management I | ||
| FOMgt 353 | Introduction to Management Science | ||
| FOMgt 354 | Topics in Management Science | ||
| CompSci 187 | Programming with Data Structures | ||
| CompSci 201 | Assembly Language Programming | ||
| CompSci 250 | Introduction to Computation | ||
| Econ 103 | Introduction to Microeconomics | ||
| Econ 104 | Introduction to Macroeconomics | ||
Application programmers are professional programmers who tailor existing algorithms to fit the specific needs of their employer. The student contemplating a career as an application programmer will find the following courses especially useful:
| Course | Title | ||
| CompSci 121 | Introduction to Problem Solving with Computers | ||
| CompSci 187 | Programming with Data Structures | ||
| CompSci 201 | Assembly Language Programming | ||
| CompSci 250 | Introduction to Computation | ||
| CompSci 287 | The Structure and Interpretation of Computer Programs | ||
| CompSci 320 | Programming Methodology | ||
| CompSci 377 | Operating Systems | ||
| CompSci 445 | Information Systems | ||
| CompSci 520 | Software Engineering | ||
| Math 236 | Linear Algebra with Programming | ||
| Math 432 | Ordinary Diffential Equations | ||
| Math 455 | Introduction to Discrete Structures | ||
| Math 534 | Introduction to Partial Differential Equations | ||
| Math 551 | Numerical Analysis I | ||
| Math 552 | Numerical Analysis II | ||
| Stat 511 | Multivariate Statistical Methods | ||
| Stat 515 | Introduction to Statistics I | ||
| Stat 516 | Introduction to Statistics II | ||
| ECE 221 | Introduction to Digital and Compputer Systems | ||
| ECE 660 | Interactive Computer Graphics | ||
| MIE 379 | Operations Research I | ||
| MIE 380 | Operations Research II | ||
| Acctg 513 | COBOL and Date Base Design | ||
Courses in economics and management (accounting, finance, etc.), such as those listed under business are also useful.
Systems programmers normally do graduate work in computer science. They should plan on thorough coverage of the material in above. Successful completion of a major in mathematics and a minor in computer science is good preparation for a graduate program in Computer Science.
Graduate Study in MathematicsA terminal Master's degree can lead to a wide variety of nonacademic positions if the degree program is oriented toward applications, or a teaching position at the high school or community college level. Most new Ph.D.'s in mathematics find employment in academic institutions, while some take positions in government, business, or industry.
There are about 1500 colleges and universities in the United States, most of which seek people with a Ph.D. to fill faculty positions involving varied mixtures of teaching and research responsibility. This job market has been tight in recent years, but is showing improvement due to a nationwide wave of faculty retirements coupled with growth in the traditional college-age population. Those who go into graduate programs intending to teach at the college level need to acquire the broadest possible foundation in both theoretical and applied subjects, along with experience in communicating mathematics, in order to compete successfully in this market.
The growth of microelectronics, computers, and other information-age technologies, along with financial services, has produced a strong demand in the nonacademic world for mathematically trained persons who are willing to apply their skills to technical problems. Employers are still reluctant to hire mathematicians whose interests are purely theoretical. But for those who have prepared themselves well, having gained a broad background not only in mathematics but also in some allied fields, many opportunities are now available.
Graduate Study: Pure MathematicsFor a student planning to do graduate work in pure mathematics, the following courses are recommended: Math 411-412 (Introduction to Abstract Algebra) or Math 511-512 (Abstract Algebra). Math 421 (Complex Variables), Math 425 (Advanced Multivariate Calculus), Math 523 (Introduction to Modern Analysis), Math 532 (Topics in Ordinary Differential Equations), Math 534 (Introduction to Partial Differential Equation), Math 545 (Linear Algebra for Applied Mathematics), and Math 563 (Introduction to Differential Geometry).
| Course | Title | ||
| Math 411/511H | Abstract Algebra I | ||
| Math 412/512H | Abstract Algebra II | ||
| Math 421 | Complex Variables | ||
| Math 425 | Advanced Multivariable Calculus | ||
| Math 523H | Introduction to Modern Analysis | ||
| Math 532H | Topics in Ordinary Differential Equations | ||
| Math 534H | Introduction to Partial Differential Equations | ||
| Math 545 | Linear Algebra for Applied Mathematics | ||
| Math 563H | Introduction to Differential Geometry | ||
Talented students should also consider participating in the Mathematics Honors Program and/or enrolling in beginning graduate level courses such as Math 611 (Algebra I), Math 671 (Topology I), or Math 621 (Complex Analysis). A qualified undergraduate may register for a graduate course in mathematics, subject to the permission of the instructor of the course, the Graduate Program Director, and the student's advisor.
Since many graduate schools require some reading knowledge in a foreign language, it is suggested that this proficiency be acquired as part of the undergraduate program. The recommended languages for mathematics majors are French, German, and possibly Russian.
Graduate Study: Applied MathematicsWith the current surge in technological development, there are a large variety of mathematical problems originating not only in the traditional areas of physics and engineering (e.g., fluids and other materials, remote sensing, meteorology, aerospace) but also in such diverse fields as computer science (e.g., security of data, data compression), biology (e.g., biofluid dynamics, genetics), ecology (e.g., competition among species) and finance (e.g., options pricing). The problems are of substantial mathematical interest and often are amenable only to numerical solution on large-scale computers. There is great satisfaction to be derived from the solution of a practical problem and much philosophical gratification in seeing mathematics interact with the ``real world''. Students interested in applied mathematics should develop strength in applied analysis, scientific computing and related areas:
| Course | Title | ||
| Math 331 | Ordinary Differential Equations | ||
| Math 411 | Abstract Algebra I | ||
| Math 412 | Abstract Algebra II | ||
| Math 421 | Complex Variables | ||
| Math 425 | Advanced Multivariable Calculus | ||
| Math 523H | Introduction to Modern Analysis | ||
| Math 532H | Topics in Ordinary Differential Equations | ||
| Math 534H | Introduction to Partial Differential Equations | ||
| Math 545 | Linear Algebra for Applied Mathematics | ||
| Math 551 | Numerical Analysis I | ||
| Math 552 | Numerical Analysis II | ||
| Stat 515 | Introduction to Statistics I | ||
| Stat 516 | Introduction to Statistics II | ||
Talented students interested in applied mathematics should also consider participating in the Mathematics Honors Program or enrolling in beginning graduate level courses such as Math 651 (Numerical Analysis I), Math 697P (Mathematical Methods in Engineering I) Stat 607 (Mathematical Statistics I) or Math 621 (Complex Analysis).
Since applied mathematicians, either in idustry or in the academic world, will work on problems formulated outside of mathematics and deal with people who are not mathematicians, it is important that they learn something of the fields from which the applications arise. Students can prepare for this by taking courses in engineering, physics, biology, etc. and by developing their communication skills. Other subjects useful for applied mathematics are listed in industrial work and probability and statistics.
Industrial WorkMathematicians in this category are frequently associated with a mathematical consultant group that is part of a large industrial firm. Because of the computer revolution, it is strongly recommended that students desiring this type of employment receive a solid background in computer programming. Students who combine applied mathematics courses with courses in computer programming, numerical analysis, computational modeling, differential equations, statistics, and probability frequently obtain stimulating positions.
General areas of possible industrial employment include planetary exploration (NASA and contractors), high-technology industries (many located in Massachusetts), missile guidance systems (U.S. military contractors), energy conversion, and operations research. Since the specific work a person does will vary a great deal from one industry to another, the student should try to obtain a general understanding of basic science, engineering, and computing in addition to an understanding of those branches of mathematics applicable to physical problems. Courses in applied mathematics, as well as those listed below, will help the student reach this goal.
| Course | Title | ||
| Physics 261 | General Physics III | ||
| Physics 283 | Physics III | ||
| Chem 111 | General Chemistry for Science and Engineering Majors | ||
| ECE 211 | Circuit Analysis I | ||
| ECE 212 | Circuit Analysis II | ||
| MIE 379 | Operations Research I | ||
| MIE 380 | Operations Research II | ||
| MIE 230 | Thermodynamics I | ||
| MIE 330 | Thermodynamics II | ||
| CompSci 121 | Introduction to Problem Solving with Computers | ||
| CompSci 187 | Programming with Data Structures | ||
| CompSci 287 | The Structure and Interpretation of Computer Programs | ||
| CompSci 320 | Intro. Software Engineering | ||
| CompSci 377 | Operating Systems | ||
Statistics is now used in business, industry, government, and virtually every field of science. Consequently, some training in statistics, probability, and computing is likely to enhance considerably your job opportunities after graduation, especially in insurance and actuarial work, in the pharmaceutical industry, in other businesses, and in government. A master's degree in statistics offers good employment opportunities. In addition to taking basic courses in statistics (e.g. Stat 515, Stat 516, etc.), students interested in probability and statistics should make sure that their background in calculus (including advanced multivariate calculus) and linear algebra is strong, since these are the most important mathematical tools in statistics. These courses will also be indispensable for students going on to graduate school in mathematics or statistics.
Secondary School TeachingMathematics majors wishing to obtain the intermediate equivalent of the Massachusetts certification to teach mathematics at the middle or high school level must include in their program courses that satisfy the Commonwealth's Standard I requirements on subject matter knowledge; must complete the School of Education's Secondary Teacher Education Programl; and must achieve a passing score on both sections of the Massachusetts Educator's Certification Test (MECT).
Any student who is interested in becoming a middle or high school mathematics teacher should contact the Secondary Teacher Education Program. The program includes student-teaching which requires a full semester during which regular courses cannot be taken. Consequently, students interested in teaching should plan to get most of their requirements out of the way before their student-teaching, and they should take note of the fact that they will have one less semester to satisfy Departmental, College, and University requirements.
The Commonwealth's Standard I Subject Matter Knowledge for mathematics states: "The effective teacher of mathematics has completed the college's or university's requirements for a major in mathematics, or the equivalent, by demonstrating knowledge of: mathematics, including: algebra, geometry, analytical geometry, trigonometry, calculus, number theory, probability and statistics, and the history of mathematics; how to use computers in mathematics; modes of inquiry and methods of research in mathematics; relationships between mathematics and other fields of knowledge."
The teaching concentration is designed to help the student fulfil these requirements. Specifically, the following courses can be used to satisfy the Commonwealth requirements:
Completion of the School of Education's Secondary Teacher Education Program for Prospective Middle and High School Teachers of Mathematics requires the following courses: Students may enroll in (1)-(3) prior to applying to STEP; to enroll in (4)-(7) the student must already be in STEP.
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