Mathematics is essential to science and engineering, and is a fascinating field in its own right. Scientific and engineering problems have often inspired new developments in mathematics, and, conversely, mathematical results have frequently had an impact on business, engineering, the sciences, and technology. At Stevens, we think that an undergraduate program in mathematics should be broad enough to prepare you for a job in industry, while giving you the background to continue your education at the graduate level, should you choose to do so.

The standard program for a concentration in mathematics includes the courses listed below, although not necessarily in exactly the order listed. If these courses do not meet your needs and goals, your program can be changed with the consent of your advisor. For example, you may wish to write a senior thesis, or you may be eligible for Advanced Placement (AP) or the honors calculus sequence. Alternatively, you may want to strengthen your grasp of fundamental concepts by taking MA 134 Discrete Mathematics. See the Department of Mathematics Web page for information on when particular courses are offered.

Mathematics B.S. Curriculum

The Bachelor of Science in Mathematics offers a broad background appropriate for students planning to pursue a job in industry, while also offering students the depth and rigor required for graduate studies in mathematics or related fields.

The curriculum satisfies the core Bachelor of Science curriculum that includes certain breadth requirements in mathematics, physics, chemistry, biology, computer science, the humanities and social sciences.  In addition to this science core, the student completes twelve upper-level mathematics courses (called technical electives).  Most of these technical courses are prescribed by the program but in some cases other courses can be substituted with the approval of the undergraduate advisor.  The program includes two general electives which can be applied toward a minor in another discipline.  A recommended study plan is shown below.  There are additional comments following the study plan regarding recommended electives and possible course substitutions.

A minor in mathematical sciences can be a valuable qualification for students concentrating in other areas. A minor consists of the courses MA 115, MA 116, MA 134, MA 221, MA 222, MA 227, MA 232, MA 234, and one other course chosen with the consent of the Department. The 300-level mathematics courses are typical choices. A student with sufficient background and the consent of the Department may substitute another course for a required course. The average grade in the nine courses must be at least 2.50 to be awarded the Minor in Mathematical Sciences.

Computational Science is an emerging field in which sophisticated computational techniques are used to build models and solve problems related to science and engineering. It complements existing theoretical and experimental approaches and may be thought of as a new mode of scientific inquiry.

At Stevens, undergraduates may study computational science through an interdisciplinary program leading to a Bachelor of Science in Computational Science degree with a specialization in an area of science or engineering. The current specializations are:

• Computational Chemistry
• Computational Mechanics
• Computational Oceanography
• Computational Physics
• Computer Vision and Computer Graphics
• Cybersecurity
• Environmental Systems

The program consists of the science curriculum core courses and technical electives. The technical electives are divided between foundation courses in mathematics and computer science, and application courses in the student's area of specialization. An important part of the program is a project or research problem to be done in the senior year. Each student must choose one of the application areas listed above prior to preparing his/her study plan. Each student's study plan reflects his/her interests and aspirations, and is made up by the student, working with a member of the Supervisory Committee. Potential students are encouraged to consult members of this committee for further information.

The following tables includes the core courses and typical foundation courses. Application area courses are discussed below. Courses need not be taken in exactly the order listed.

Computational Science Curriculum

Supervisory Committee

• Michael Bruno, Ocean Engineering
• Wayne Carr, Physics
• Quynh Dinh, Computer Science
• Robert Gilman, Mathematics
• Sophia Hassiotis, Civil Engineering
• George Kamberov, Computer Science
• Khaldoun Khashanah, Mathematics
• Yi Li, Mathematics
• Marc Mansfield, Chemistry
• Patrick Miller, Mathematics
• John Oliensis, Computer Science
• Roger Pinkham, Mathematics
• Chris Search, Physics
• Kurt Stamnes, Physics
• David Vaccari, Environmental Engineering
• Susanne Wetzel, Computer Science

Application areas correspond to the research interests of the faculty associated with the program and are subject to change. Sample selections of application courses are given below. An additional sixth application course will be chosen with the consent of the advisor. MA 441 Introduction to Mathematical Analysis and MA 442 Real Variables are strongly recommended for students considering graduate school in any field. Note that 600-level courses require special permission. For further information about an application area, consult the faculty advisor for that area.

Computational Chemistry (Professor Mansfield)
   

• CH 241 Organic Chemistry I
• CH 322 Theoretical Chemistry
• CH 421 Chemical Dynamics
• CH 498 Chemical Research I
• CH 499 Chemical Research II

Computational Mechanics (Professor Hassiotis)

• E 126 Mechanics of Solids
• CE 345 Modeling and Simulation
• CE 373 Structural Analysis
• MA 498 Senior Research Project I

    one of the following:

• CE 613 Matrix Analysis of Structures
• CE 623 Structural Dynamics
• CE 681 Introduction to Finite Element Methods

Computational Oceanography (Professor Bruno)

• E 126 Mechanics of Solids
• CE 342 Fluid Mechanics
• OE 526 Computer-Aided Naval Architecture
• OE 648 Numerical Hydrodynamics
• MA 498 Mathematical Research I

Computational Physics (Professors Stamnes and Carr)

• PEP 497 SKIL V
• PEP 498 SKIL VI
• PEP 538 Introduction to Mechanics
• PEP 542 Electromagnetism

    one of the following:

• PEP 520 Computational Physics
• PEP 575 Fundamentals of Atmospheric Radiation and Climate

Computer Vision and Computer Graphics (Professors Dinh, Kamberov, and Oliensis)

• CS 437 Interactive Computer Graphics
• CS 498 Computer Science Research I 
• CS 499 Computer Science Research II
• CS 558 Computer Vision
• CS 638 Interactive Computer Graphics II

CyberSecurity (Professors Wetzel)

• CS 335 Computational Structures
• CS 498 Computer Science Research I
• CS 499 Computer Science Research II
• CS 668 Foundations of Cryptography
• CS 693 Cryptographic Protocols

Environmental Systems (Professor Vaccari)
   

• EN 345 Modeling and Simulation
• EN 375 Environmental Systems
• EN 541 Fate and Transport of Environmental Contaminants
• MA 498 Mathematical Research I

    one of the following:

• MA 499 Mathematical Research II
• EN 571 Physiochemical Processes for Environmental Control

Admission Criteria

Adequate undergraduate preparation for admission to any master's degree or certificate program, except Financial Engineering, includes analytic geometry and calculus, elementary differential equations, one semester of linear algebra, and one semester of probability or probability and statistics. It is possible to be admitted with the requirement that you make up a deficiency in preparation. For Financial Engineering see below. Applications should include official transcripts from previous institutions and any supporting documents.

Admission to the doctoral program requires the preparation specified above. See below for a guide to how applicants will be evaluated. If your goal is a Ph.D., you should apply directly to the doctoral program and not to a master's program. In order to receive full consideration, applications to the Doctoral Program should be received by March 15 for admission in the Fall Semester, and September 15 for admission in the spring semester. Because of constraints due to course scheduling, admission for the spring semester is not always feasible and may depend on the student’s preparation. In addition financial aid is usually not available for students admitted for the spring semester. Applicants requesting financial aid should apply by February 15 and should clearly state that such aid is being requested.

This program provides a background in mathematical techniques which are useful in solving practical problems in science and engineering. You are encouraged to include courses from other departments in your program of study.

The program requires 30 credits (10 courses) of coursework. You may transfer up to one-third of this amount from outside Stevens. If you know the material in one of the required courses, you may substitute another course. In both cases, you will need the approval of a department advisor. All elective courses must be chosen with the consent of a department advisor.

Core Courses
    MA 547 Advanced Calculus I or MA 635 Real Variable I
    MA 552 Linear Algebra
    MA 611 Probability
    MA 615 Numerical Analysis I
    MA 649 Differential Equations I
    MA 681 Functions of a Complex Variable I

Typical Electives
    MA 548 Advanced Calculus II
    MA 627 Combinatorial Analysis
    MA 653 Numerical Solutions of Partial Diff. Eqs.
    CE 519 Advanced Structural Analysis
    CE 601 Theory of Elasticity
    CS 580 The Logic of Program Design
    CS 590 Introduction to Data Structures and Algorithms
    ME 674 Fluid Dynamics
    PEP 520 Computational Physics

A master’s degree in mathematics requires 30 credits of courses, including the following core courses:

Core Courses
    MA 552 Linear Algebra
    MA 605 Foundations of Algebra I
    MA 611 Probability
    MA 635 Real Variables I
    MA 651 Topology I
    MA 681 Functions of a Complex Variable I

This program focuses on analysis and optimal decision-making for complex systems involving uncertain data and risk. The program includes courses in statistics, stochastic processes, stochastic optimization, and stochastic optimal control theory. Applications to financial systems, network design and routing, telecommunication systems, medicine, actuarial mathematics, and other areas are discussed. Students are encouraged to apply the techniques they learn to problems derived from their professional work and interests.

Ten courses are required for the degree; six are core courses. Elective courses are chosen with the consent of the student's academic advisor.

Core Courses
    MA 547 Advanced Calculus or MA 635 Real Variables I
    MA 611 Probability
    MA 612 Mathematical Statistics
    MA 623 Stochastic Processes
    MA 629 Convex Analysis and Optimization
    MA 661 Stochastic Optimal Control and Dynamic Programming

Typical Electives
    MA 615 Numerical Analysis I
    MA 627 Combinatorial Analysis
    MA 632 Theory of Games
    MA 641 Time Series Analysis I
    MA 655 Optimal Control Theory
    MA 662 Stochastic Programming
    MA 720 Advanced Statistics
    CS 535 Financial Computing
    EN 780 Nonlinear Correlation and System Identification
    MGT 730 Design and Analysis of Experiments

The Mathematical Science department offers a number of graduate certificate programs. Each program consists of four courses, including one elective chosen with the consent of the departmental advisor. Most courses may be used toward a master's degree, as well as for the certificate. Admission requirements are the same as for the corresponding master's program. Requirements for the Applied Statistics certificate program are the same as those listed above for all programs, except Financial Engineering.

Applied Statistics
    MA 552 Linear Algebra
    MA 611 Probability
    MA 612 Mathematical Statistics

Typical electives:
    — CE 679 Regression and Stochastic Methods
    — MA 641 Time Series Analysis I
    — MGT 718 Multivariate Analysis
    — MGT 730 Design and Analysis of Experiments

Stochastic Systems
Choose three courses:
    MA 611 Probability
    MA 623 Stochastic Process
    MA 629 Convex Analysis and Optimization

Choose one elective:
     MA 612 Mathematical Statistics
     MA 630 Numerical Methods of Optimization
     MA 661 Stochastic Optimal Control and Dynamical Programming
     MA 662 Stochastic Programming

The primary requirement for a doctoral degree in mathematics is that you produce a dissertation containing an original and significant result in mathematics and its application. You will work under the guidance of a faculty advisor who is an expert in your area of research.

Preparation for dissertation work includes both courses in mathematical fundamentals and practice in communicating mathematics orally and in writing. The courses you take will not necessarily include everything you will need to know. As a doctoral student you will be expected to learn some mathematics on your own outside of class. Seminars afford a means to that end. They can be organized informally among students or more formally with a faculty advisor. Seminars of the latter type may be taken for academic credit. Students are encouraged to identify subjects they would like to study and to seek out faculty advisors.

Applications to the doctoral program must be prepared and sent according to the Stevens Office of Graduate Admissions regulations. Forms may be found on the Graduate Admissions Web page. Notice that the procedure is different for domestic and international applicants.

The Mathematics Department will base its evaluation of applicants on the following items:

• A personal statement, describing the student's mathematical background and interests, motivations, and goals for pursuing a Ph.D. degree. This should not exceed two pages.
• Official transcripts and diplomas. For non-English-speaking institutions, these documents must be accompanied by a certified English translation.
  Letters of recommendation: at least two; at most, four.
  GRE scores.
• TOEFL score for international students. The TOEFL score is particularly important if the student wants to be considered for a Teaching Assistantship (see the section on Teaching Assistantships).

Degree Requirements

A total of 90 credits. At least 48 must be course credits (see the Mathematics Graduate Catalog) and at least 30 must be research credits. Incoming students who have already taken graduate classes elsewhere (e.g., for a master's degree) may have a maximum of 30 credits transferred. Transfer credit will be determined by the Department’s Graduate Program Committee.

• General Exam. This is a written exam covering analysis, complex variables, and algebra. A detailed description of the subjects covered, as well as suggested references, are available from the Mathematics Department. This exam is offered twice a year, at the beginning of the fall and spring semesters. The General Exam should be taken before the student has accumulated 30 credits beyond the bachelor’s degree or within the first year of study at Stevens. One failure of the General Exam is allowed. A second failure will result in the students being dropped from the Ph.D. program.
• Ph.D. Candidacy Presentation. After the General Exam, the student will choose a thesis advisor in the area of his/her special interest. The Ph.D. Committee can provide help and advice with this important choice. In collaboration with the thesis advisor, the student will compose a plan of study in the field of interest and present this plan to the Department.
• Dissertation. The final and most important step of the Ph.D. program is writing a dissertation of publishable quality. This will embody the results of the student's original research in mathematics, and the dissertation will be presented by the student at a public defense. If the suitably appointed Dissertation Committee approves the defense, the student will be recommended to the Office of Graduate Admissions for the Ph.D. degree.

Financial Aid

The Department supports a limited number of Ph.D. students through teaching assistantships which entitle the recipients to a salary and a waiver of their tuition costs. Teaching assistants are considered for renewal each year, depending on teaching skills and progress towards graduation. Save for exceptional cases, Teaching Assistantships are normally not granted for more than five years and are usually available only for students entering in the Fall. In any case, applications should be received by the deadlines mentioned above under the heading Admission Criteria.

Students who wish to be considered for a Teaching Assistantship beginning their first year should mention this in their Personal Statement. If they already possess some teaching experience, they are encouraged to send any useful documents that address their teaching skills, such as letters of recommendation, evaluation forms, teaching awards, etc. However, no teaching experience is required for an incoming student to be considered for a Teaching Assistantship.