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Mathematics and Statistics

Mathematics and Statistics | Courses | Faculty

1622 Lederle GRC Towers

Degrees: Bachelor of Science
Bachelor of Arts

Contact: Farshid Hajir
Office: 1118 Lederle GRC Towers
Phone: (413) 545-6015

Head of Department: Professor George Avrunin. Associate Head: Professor Robert Gardner; Administrative Coordinator: Lecturer Arline Norkin. Professors Buonaccorsi, Cattani, Cook, Eisenberg, Ellis, Hsieh, Katsoulakis, Kusner, Meeks, Mirkovic, Nahmod, Norman, Pedit, Turkington, Whitaker, Young; Associate Professors Braden, W. Chen, Conlon, Gunnells, Hajir, Kevrekidis, Markman, Rey-Bellet, Rudvalis, Sommers, Staudenmayer, Sullivan, Weston, Wong; Assistant Professors Q. Chen, Johnston, Kim, Liu, Oblomkov, Tevelev, Wang, Zhang; Visiting Assistant Professors Broshi, Dalakov, Espinola-Rocha, Hacking, Han, Savelyev, Urzna, Wang.
The Field

Mathematics is the language of the sciences, providing a bridge between experimental observation and scientific theory. Modern mathematics encompasses a wide variety of fields, from the formulation of mathematical models of complicated physical and biological systems to the study of abstract objects.

As our technology improves, it becomes more reliant on powerful mathematics, while simultaneously driving mathematics forward. Modern algebra is closely connected to theoretical physics; number theory is increasingly applied to computer and communications security; geometry and analysis are applied to many problems of science and engineering; and ordinary, partial, and stochastic differential equations are central to many branches of engineering research. Contemporary applications of sophisticated mathematics include aircraft design, properties of materials, weather prediction, understanding the spread of disease, oil well simulation, image processing, communication, economics, genomics and many others. In addition, mathematics is increasingly applied in other fields such as biology, medicine, ecology, and sociology.

The last decade has seen an explosion in the quantity and variety of data available about virtually everything including pictures, stock prices, purchase patterns, medical information, and voting behavior. However, many agree with the characterization of our time as “drowning in information and starving for knowledge.” This challenge is the essential problem of the field of statistics: seeking understanding and knowledge through the study of data. Statistics has historically played a key role in medical research, and more generally in experimental science, by quantifying the interaction between various “causes” and “effects.” However, many new and exciting applications of statistics are emerging, such as deciphering the human genome, analyzing and facilitating Internet traffic, and the “mining” of very large collections of data to discern patterns and relationships. Statistics in inherently an interdisciplinary field allowing the practitioner to learn from and contribute to a wide variety of different areas.

Students interested in majoring or minoring in mathematics should contact Professor Peter Norman, tel. (413) 545-2282, Lederle Graduate Research Tower 1521E.


The Major

The requirements for a degree provide the student with maximum flexibility in designing an overall course of study to meet his or her scientific, educational, and career goals. The beginning courses emphasize computational skills, problem solving, and the understanding of basic concepts. As students progress, they must solve problems that are less and less routine and more abstract or intricate. Some upper-level courses emphasize proofs and the understanding of abstract structures, while others emphasize advanced computational methods or the formulation and analysis of mathematical or statistical models of reality. A number of the courses involve the use of computers in a fundamental manner in the development of the material covered.

Specific requirements for a major in mathematics are given in 1-6 below. All courses used to satisfy these requirements must be completed with a passing grade, but not with a “P.” A cumulative quality point average of 2.000 is required in all Mathematics and Statistics courses taken.

1. Differential and integral calculus: MATH 131 and 132
2. Multivariable calculus and linear algebra: MATH 233 and 235
3. Introduction to abstract mathematics: MATH 300 or COMPSCI 250 (may be waived by the Chief Undergraduate Adviser for exceptionally well-prepared students)
4. Computer programming: COMPSCI 121 or equivalent
5. Writing in mathematics: MATH 370
6. Completion of the requirements of one of the concentrations detailed below (Applied Mathematics, General, Individual, Mathematical Computing, Pure Mathematics, Statistics or Teaching). At most four of the courses used to satisfy the concentration requirements may be taken outside the Department of Mathematics and Statistics. The chief undergraduate Adviser must approve all such courses taken outside the department. These grades earned in the courses that satisfy the concentration requirement must average C or higher.

Note: STATISTC 501 may not be applied to requirements if it is taken after STATISTC 515 or STATISTC 516.

The Concentrations

Applied Mathematics Concentration prepares the student for a career as a mathematician in government or industry. Requirements:

Advanced calculus: MATH 425
Differential equations: MATH 331
Linear algebra for applied mathematics: MATH 545
Introduction to scientific computing: MATH 551
At least one of the following courses: MATH 456, MATH 532, MATH 534, MATH 552
At least three additional courses numbered 400 or higher. With the approval of the chief undergraduate adviser, these may be appropriate courses outside the department.

General Concentration provides the student with broad training in abstract mathematics, statistics, and computing. Requirements:

Algebra: MATH 411 or 511 and one of Math 412, 471, 512, 545
Statistics: STATISTC 515 and 516
Analysis: MATH 425 and 523
Scientific Computing: MATH 551 and 552

Individually designed concentration permits students, in consultation with their academic adviser, to design their own concentration so as to explore thoroughly a theme in mathematics or statistics or to investigate connections between mathematics and/or statistics and another field, such as biology or economics. An individual concentration must include eight courses numbered 400 or above, of at least three credits each. At least four of these eight courses must be in mathematics or statistics. In consultation with their academic adviser, students propose a plan for the eight courses to be used to fulfill the requirements of the individual concentration. No later than the end of the semester in which students are taking MATH 300 or during the second semester of the students’ sophomore year, whichever comes first, students will: prepare the plan in writing, secure approval of the plan by their adviser, and submit the written plan for approval to the chief undergraduate adviser. No later than the end of the junior year, students review the plan with their academic adviser. If any changes are proposed to the original plan, students will: prepare a revised plan in writing, secure approval of the revised plan by their adviser, and then submit the revised plan for approval to the chief undergraduate adviser.

Teaching Concentration provides the student with the knowledge of mathematics and statistics required by the Commonwealth as an 8-12 teacher of mathematics. Requirements:

Abstract Algebra: MATH 411
Mathematical Modeling: MATH 456
Discrete/finite mathematics: MATH 112, 119 or 455
Geometry: MATH 461 and 462
Probability and Statistics: STATISTC 501 followed by STATISTC 515
Use of technology: MATH 236, 503 or 551

Mathematical Computing Concentration prepares the student for careers that require both knowledge of advanced mathematics and extensive knowledge of computer programming. Requirements:

Computer programming: CMPSCI 250 or MATH 455
Two courses that focus on programming (CMPSCI 287 and CMPSCI 311) or on theory (CMPSCI 401 and MATH 513/CMPSCI 575)
Three courses chosen from the following:
CMPSCI 401
MATH 411 or MATH 511
MATH 412 or MATH 512
MATH 471
MATH 513/CMPSCI 575
MATH 551
MATH 552
STATISTC 515
STATISTC 516
At least two additional courses numbered 400 or higher. With the approval of the chief undergraduate adviser, these may be appropriate courses outside the department.

Pure Mathematics Concentration prepares the student for graduate study in mathematics. Requirements:

Algebra: MATH 411 or MATH 511
Complex variables: MATH 421
Advanced multivariate calculus: MATH 425
Analysis: MATH 523
At least one of the following courses:
MATH 412
MATH 512
MATH 563
At least one “applied mathematics”course either chosen from the following list or another course with sufficent applied mathematical content approved by the chief undergraduate adviser:
MATH 331
MATH 456
MATH 532
MATH 534
MATH 551
MATH 552
STATISTC 516
At least two additional courses numbered 400 or higher. With the approval of the chief undergraduate adviser, these may be appropriate courses outside the department.

Statistics Concentration prepares the student for a career as an applied statistician or for graduate study in statistics. Requirements:

Advanced multivariate calculus: MATH 425
Algebra: MATH 545 or MATH 411 or MATH 511
Introduction to statistics: STATISTC 515 and STATISTC 516
At least one of the following courses:
STATISTC 505
STATISTC 506
STATISTC 511
At least three additional courses numbered 400 or higher. With the approval of the chief undergraduate adviser, these may be appropriate courses outside the department.

Honors Program

The department also offers a program of study in mathematics leading to higher honors at graduation (i.e., magna cum laude or summa cum laude) at graduation. Prospective honors students are strongly advised to take MATH 300 as early as possible, as well as the honors sections which are offered throughout the calculus courses. In their senior year, honors students may register for a two-semester Capstone sequence, MATH 499C (fall) and MATH 499D (spring). For more information, consult the Chief Undergraduate Adviser, tel. (413) 545-2282, Lederle GRT 1521E.

Mathematics Information Leaflet

Each year the department publishes, for its majors and other interested students, a Mathematics Information Leaflet which contains more detailed information on the requirements, suggested electives for students with various career interests, and other information of particular interest to mathematics majors. Copies of this leaflet, as well as answers to further questions about the undergraduate program, can be obtained from Professor Norman, the Chief Undergraduate Mathematics Adviser, in Room 1521E, Lederle GRC Towers, tel. (413) 545-2282.

Career Opportunities

Abundant opportunities exist for individuals with the highly developed mathematical and statistical skills and problem-solving ability that the major provides. High-technology industrial firms avidly seek such individuals, especially those with knowledge of computers, statistics, and applied areas such as differential equations and numerical analysis.

Employment opportunities for mathematicians in business, industry, and government are many and varied. The habits of careful, analytic thought instilled by training in mathematics are valuable for both managerial and scientific careers. Mathematics majors with courses in computer science and statistics compete favorably with majors in computer science or engineering for positions in computer-related industries. For those students interested in teaching, there are many opportunities in the primary and secondary schools due to the severe shortage of qualified mathematics and science teachers.

Students with an undergraduate major in mathematics often go on to graduate study in disparate fields such as computer science, philosophy, operations research, and econometrics, or to professional schools in law or business.

Students with a solid grasp of statistical thinking and computational skills are highly valued in several core employment areas such as the pharmaceutical industry, insurance companies, governmental agencies and laboratories, and financial institutions. Furthermore, the range of employers showing interest in statistically trained candidates keeps pace with the growing breadth of statistical applications. Defense contractors, credit card companies, biotechnology firms, online retailers, data mining and statistical consulting firms, and educational testing organizations are among the many recent employers of statisticians. With the ever-growing supply of so many varieties of data, this trend will continue.

For information on career opportunities contact the Chief Undergraduate Adviser, tel. (413) 545-2282, Lederle GRT 1521E.

The Minor

Requirements

Specific requirements for a minor in Mathematics are given in 1-4 below. All courses used to satisfy these requirements must be completed with a passing grade, but not with a P. A GPA of 2.000 is required in all Mathematics and Statistics courses taken.

1. Calculus: MATH 131-132 or MATH 135-136 and MATH 233 or equivalent.
2. Computer Science: proficiency in a computer programming language. May be satisfied by CMPSCI 121, CMPSCI 187, E&C-ENG 242, or equivalent.
3. Linear Algebra: MATH 235.
4. Upper-Division Courses: four upper-division courses, of at least three credits each. At least two of these four courses must be taken in the department. At most one of the four courses may be in a field other than mathematics and statistics. Any course taken in another department must be approved by Professor Norman, the Chief Undergraduate Adviser.

Mathematics and Statistics | Courses | Faculty