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• Mathematics Minor
• Statistics Minor

Mathematical Sciences

Math Program Chart (PDF)
Actuarial Program Chart (PDF)
Department Web Site

B. Vernescu, HEAD; S. WEEKES, Associate Head
PROFESSORS: D. Berkey, P. Christopher, P. Davis, A. Heinricher, M. Humi, R. Lui, K. Lurie, U. Mosco, B. Nandram, J. Petruccelli, B. Servatius, D. Tang, B. Vernescu, H. Walker
ASSOCIATE PROFESSORS: W. Farr, J. Fehribach, C. Larsen, W. Martin, M. Sarkis, D. Vermes, S. Weekes
ASSISTANT PROFESSORS: R. Kim, H. Sayit, D. Volkov
VISITING FACULTY: S. Dai, C. Lee, J. Masamune, J. Wu, V. Yakovlev
ACADEMIC STAFF: J. Abraham, M. Blais, J. Goulet

Mission Statement

Recognizing the vital role of the mathematical sciences in today’s society, the Mathematical Sciences Department provides leading-edge programs in education, research, and professional training in applied and computational mathematics and statistics. These programs are enhanced and distinguished by project-oriented education and collaborative involvement with industry, national research centers, and the international academic community.

Program Educational Objectives

The department’s major programs provide students with preparation for effective and successful professional careers in the mathematical sciences, whether in traditional academic pursuits or in the many new career areas available in today’s technologically sophisticated, globally interdependent society. Through course work, students acquire a firm grounding in fundamental mathematics and selected areas of emphasis. Projects, which often involve interdisciplinary and industrial applications, offer further opportunities to gain mathematical depth and to develop skills in problem-solving, communication, teamwork, and self-directed learning, together with an understanding of the role of the mathematical sciences in the contemporary world.

Program Outcomes

We expect graduates to:

1. have a solid knowledge of a broad range of mathematical principles and techniques and the ability to apply them.
2. be able to read, write, and communicate mathematics inside and outside the discipline.
3. have the ability to formulate mathematical statements and prove or disprove them.
4. be able to formulate and investigate mathematical questions and conjectures.
5. understand fundamental axiom systems and essential definitions and theorems.
6. be able to formulate and analyze mathematical or statistical models.
7. have the ability to apply appropriate computational technology to analyze and solve mathematical problems.
8. be able to learn independently and as part of a team, and to demonstrate a depth of knowledge in at least one area of the mathematical sciences.

The Department of Mathematical Sciences at WPI offers:

1. the Bachelor of Science degree in Mathematical Sciences;
2. the Bachelor of Science degree in Actuarial Mathematics;
3. a Minor in Mathematics;
4. a Minor in Statistics;
5. a combined B.S./M.S. degree in Applied Mathematics, Applied Statistics, Industrial Mathematics, or Financial Mathematics.

Program Distribution Requirements for the Mathematical Sciences Major

The normal period of residency at WPI is 16 terms. In addition to the WPI requirements applicable to all students, completion of a minimum of 10 units of study is required as follows:

Requirements	Minimum Units
1. Mathematics including MQP (See notes 1-4).	7
2. Courses from other departments that are related to the student’s mathematical program. At least 2/3 unit in computer science must be included; the remaining courses are to be selected from science, engineering, computer science or management (except MG 1250) (see Note 5).	2
3. Additional courses or independent studies (except MS, PE courses, and other degree requirements) from any area.	1

Notes:

1. Must include MA 3831-3832, or their equivalents, at least one of MA 3257, MA 3457, or equivalent, and at least one of MA 3823, MA 3825, or equivalent.
2. Must include at least three of the following: MA 2073, MA 2271, MA 2273, MA 2431, MA 2631, or their equivalents.
3. At least 7/3 units must consist of MA courses at the 3000 level or above.
4. May not include both MA 2631 and MA 2621.
5. May not include both CS 3043 and CS 2022.

Program in Mathematical Sciences

Projects

Some of the most active career directions in the mathematical sciences are reflected in the MQP areas around which the department’s offerings are organized: Algebraic and Discrete Mathematics, Computational and Applied Analysis, Operations Research, and Probability and Statistics. As early as practical, and certainly no later than the sophomore year, the mathematical sciences major should begin exploring these different areas. The transition courses, MA 2073, 2271, 2273, 2431, and 2631, are specifically designed to introduce the four MQP areas while preparing the student for advanced courses and the MQP. Students should talk to faculty in the student’s area of interest to develop and select an MQP and MQP advisor.

While most students choose MQPs in one of the four areas mentioned above, it is possible to design an MQP that does not fit into any one area. In such cases, students will want to take special care to plan their programs carefully with their advisors so that sufficient background is obtained before beginning to do research. Independent studies are a good way for students to learn topics that are not taught in regularly-scheduled courses. Interested students should approach faculty with requests for independent studies.

Through the Center for Industrial Mathematics and Statistics (CIMS), students can use their mathematics and statistics training to work on real-world problems that come from sponsors in industry and finance. More information about industrial MQPs and projects can be found at CIMS web site.

In what follows, you will find for each MQP area:

• A brief description of the area including the kinds of challenges likely to be encountered by MQP students and mathematical scientists working there.
• Courses of interest.

Algebraic and Discrete Mathematics

Algebraic and discrete mathematics is recognized as an increasingly important and vital area of mathematics. Many of the fundamental ideas of discrete mathematics play an important role in formulating and solving problems in a variety of fields ranging from ecology to computer science. For instance, graph theory has been used to study competition of species in ecosystems, to schedule traffic lights at an intersection, and to synchronize parallel processors in a computer. Coding theory has been applied to problems from the private and public sectors where encoding and decoding information securely is the goal. In turn, the problems to which discrete mathematics is applied often yield new and interesting mathematical questions. The goal of a project in discrete mathematics would be to experience this interaction between theory and application. To begin, a typical project team would assess the current state of a problem and the theory that is relevant. Once this is done, the project team’s objective would be to make a contribution to solving the problem by developing new mathematical results.

In working in discrete mathematics, one may be writing algorithms, using the computer as a modeling tool, and using the computer to test conjectures. It is important that a student interested in this area have some computer proficiency. Depending on the project, an understanding of algorithm analysis and computational complexity may be helpful.

Courses of Interest

MA 2271 Graph Theory
MA 2273 Combinatorics
MA 3231 Linear Programming
MA 3233 Discrete Optimization
MA 3823 Group Theory
MA 3825 Rings and Fields
MA 4891 Topics in Mathematics (when appropriate)
CS 2301 Systems Programming for Non-Majors
CS 4120 Analysis of Algorithms
CS 4123 Theory of Computation

Computational and Applied Analysis

This area of mathematics concerns the modeling and analysis of continuous physical or biological processes that occur frequently in science and engineering. Students interested in this area should have a solid background in analysis which includes the ability to analyze ordinary and partial differential equations through both analytical and computational means.

In most circumstances, an applied mathematician does not work alone but is part of a team consisting of scientists and engineers. The mathematician’s responsibility is to formulate a mathematical model from the problem, analyze the model, and then interpret the results in light of the experimental evidence. It is, therefore, important for students to have some experience in mathematical modeling and secure a background in one branch of science or engineering through a carefully planned sequence of courses outside of the department.

With the increase in computational power, many models previously too complicated to be solvable, can now be solved numerically. It is, therefore, recommended that students acquire enough computer proficiency to take advantage of this. Computational skill is growing in importance and should be a part of every applied mathematician’s training. Students may learn these skills through various numerical analysis courses offered by the department. An MQP in this area will generally involve the modeling of a real-life problem, analyzing it, and solving it numerically.

Courses of Interest

MA 2251 Vector and Tensor Calculus for Engineers
MA 2431 Mathematical Modeling with Ordinary Differential Equations
MA 3231 Linear Programming
MA 3257 Numerical Methods for Linear and Nonlinear Systems
MA 3457 Numerical Methods for Calculus and Differential Equations
MA 3471 Advanced Ordinary Differential Equations
MA 3475 Calculus of Variations
MA 4235 Mathematical Optimization
MA 4291 Applicable Complex Variables
MA 4411 Numerical Analysis of Differential Equations
MA 4451 Boundary Value Problems
MA 4473 Partial Differential Equations

Operations Research

Operations research is an area of mathematics which seeks to solve complex problems that arise in conducting and coordinating the operations of modern industry and government. Typically, operations research looks for the best or optimal solutions to a given problem. Problems within the scope of operations research methods are as diverse as finding the lowest cost school bus routing that still satisfies racial guidelines, deciding whether to build a small plant or a large plant when demand is uncertain, or determining how best to allocate timesharing access in a computer network.

Typically, these problems are solved by creating and then analyzing a mathematical model to determine an optimal strategy for the organization to follow. Often the problem requires a statistical model, and nearly always the analysis - whether optimizing through a set of equations or simulating the behavior of a process - involves the use of a computer. Finally, operations researchers must be able to interpret and apply the results of their analyses in an appropriate manner.

In addition to a solid background in calculus, probability and statistics, and the various operations research areas, prospective operations researchers should be familiar with computer programming and managerial techniques

Courses of Interest

MA 2271 Graph Theory
MA 2273 Combinatorics
MA 3231 Linear Programming
MA 3233 Discrete Optimization
MA 3627 Applied Statistics III
MA 3631 Mathematical Statistics
MA 4235 Mathematical Optimization
MA 4237 Probabilistic Methods in Operations Research
MA 4631 Probability and Mathematical Statistics I
MA 4632 Probability and Mathematical Statistics II
OIE 2500 Management Science I: Deterministic Decision Models
OIE 3460 Simulation Modeling and Analysis
OIE 3501 Management Science II: Risk Analysis

Probability and Statistics

In many areas of endeavor, decisions must be made using information which is known only partially or has a degree of uncertainty attached to it. One of the major tasks of the statistician is to provide effective strategies for obtaining the relevant information and for making decisions based on it. Probabilists and statisticians are also deeply involved in stochastic modeling - the development and application of mathematical models of random phenomena. Applications to such areas as medicine, engineering, and finance abound.

Students interested in becoming probabilists or mathematical statisticians should consider additional study in graduate school. While graduate study is an option for students whose goals are to be applied statisticians, there are also career opportunities in business, industry, and government for holders of a Bachelor’s degree. More information about careers in statistics can be found at the American Statistical Association’s web site.

Students planning on graduate studies in this area would be well advised to consider, in addition to the courses of interest listed below, additional independent study or PQP work in probability and statistics, or some of the department’s statistics graduate offerings.

Courses of Interest

MA 2611 Applied Statistics I
MA 2612 Applied Statistics II
MA 2631 Probability
MA 3627 Applied Statistics III
MA 3631 Mathematical Statistics
MA 4237 Probabilistic Methods in Operations Research
MA 4631 Probability and Mathematical Statistics I
MA 4632 Probability and Mathematical Statistics II

Program in Actuarial Mathematics

Actuaries provide financial evaluations of risk that help professionals in the insurance and finance industries, and many in large corporations and government agencies make strategic management decisions. Fellowship in the Society of Actuaries or the Casualty Actuarial Society – achieved by passing a series of examinations – is the most widely accepted standard of professional qualification to practice as an actuary.

WPI’s program enables students to take the first steps toward preparing for these exams and introduces these majors to the fundamentals of business and economics.

Projects

Off-campus qualifying projects are regularly done in collaboration with insurance companies, and have in the past been sponsored by Aetna, Allmerica Financial, Blue Cross Blue Shield of Massachusetts, John Hancock Mutual Insurance, Premier Insurance, and Travelers Property Casualty. Visit CIMS web site.These projects give real-world experience of the actuarial field by having students involved in solving problems faced by professional actuaries. Instead of choosing a project already posed by a company/advisor team, students may instead seek out industry-sponsored projects on their own (often through internship connections) and propose them to a potential faculty advisor. Alternatively, students may choose to complete any other project in mathematics.

Program Distribution Requirements for the Actuarial Mathematics Major

The normal period of residency at WPI is 16 terms. In addition to the WPI requirements applicable to all students, completion of a minimum of 10 units of study is required as follows:

 

Requirements	Minimum Units
1. Mathematics (including MQP) (See notes 1-6).	7
2. Management (See note 7).	4/3
3. Additional courses or independent studies (except MS, PE courses, and other degree requirements) from any area (See note 8).	5/3

Notes:

1. Must include MA 3831and MA 3832, or their equivalents, at least one of MA 3257, MA 3457, or equivalent, and at least one of MA 3631, MA 4632, or equivalent.
2. Must include two of the following: MA 2073, MA 2271, MA 2273, MA 2431, MA 2631, or their equivalents.
3. Must include three of the following: MA 3211, MA 3212, MA 4213, MA 4214, or their equivalents.
4. May not include independent studies directed toward Society of Actuaries exams.
5. May not include either MA 2201 or MA 2210.
6. May not include both MA 2631 and MA 2621.
7. Must include ACC 2101 and FIN 2200 or their equivalents.
8. Must include 2/3 units of computer science.

Students interested in pursuing a degree in Actuarial Mathematics should contact Professor Abraham, the Coordinator of the Actuarial Mathematics Program, as soon as possible.

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Last modified: February 05, 2009 17:05:38