Degrees Offered:

• Master of Science in Applied Mathematics
• Master of Science in Applied Statistics
• Doctor of Philosophy in Mathematical Sciences

The Master of Science in Applied Mathematics, with its areas of specialization in analysis, applied mathematics, computational methods, and mathematical biology is designed to serve the needs of students who may be interested in pursuing a doctoral degree in the mathematical, physical, or biological sciences. The program also strengthens the quantitative and analytical skills of students with a baccalaureate degree who are planning to work in industry, commerce, or education, as well as practicing engineers and others already employed in industry and commerce.

Admission Requirements:
It is expected that students applying for admission will have an undergraduate education in mathematics, the physical or biological sciences, or engineering. For additional information, see the Admissions section of this catalog. An undergraduate GPA of at least 2.8 on a 4.0 scale or equivalent is normally required.  GRE scores are required for those students applying for financial support, or if the most recent degree was earned at a school outside the United States. Applications are considered on a case-by-case basis.

Bridge Program: Students with a baccalaureate degree in an area different from mathematics may be admitted and required by the department to take an individually-designed program of courses that may include undergraduate courses before proceeding to the graduate curriculum. Such courses do not count towards a graduate degree.

Degree Requirements:
The Master of Science in Applied Mathematics requires 30 credits: 15 credits in core courses, 15 credits in an area of specialization, of which six credits are required and nine credits are electives. Students must successfully complete at least 24 of these credits at the 600-level or higher, and no more than six credits at the 500-level will be counted towards the degree. Specific course requirements depend on the area of specialization. A master's thesis or a master's project is optional. (Advisor's permission is required)

Seminar: In addition to the minimum 30 degree credits required, all students who receive departmental or research-based awards must enroll every semester in Math 791 Graduate Seminar.

Core:
15 credits:

Required Courses in Areas of Specialization:
6 credits:
Analysis:

Electives are chosen in consultation with a Departmental Graduate Advisor and consist of advanced courses in mathematics and advanced courses from biology, physics, computer science, and engineering, for example. Courses offered by appropriate departments at NJIT, UMDNJ, and Rutgers-Newark can be used as electives within the limits of the NJIT transfer policy. All elective courses must be approved by the graduate advisor.

The Master of Science in Applied Statistics program will serve the needs of students with a baccalaureate degree who are planning to work in industry, commerce, or education, as well as practicing engineers and others already employed in industry and commerce. The program also strengthens the analytical and quantitative skills of graduate students who may be interested in pursuing a doctoral degree in Applied Probability and Statistics, since it equips them with basic training in the foundations of statistics in preparation for further advanced studies and research.

Admission Requirements:
Applicants must have a degree from an accredited institution with at least 12 credits in mathematics, including calculus. Students who do not meet these requirements may be admitted if they satisfy the university's requirements for admission. An undergraduate GPA of at least 2.8 on a 4.0 scale or equivalent is normally required.  GRE scores are required for those students applying for financial support, or if the most recent degree was earned at a school outside the United States. Applications are considered on a case-by-case basis.

Bridge Program: Students who do not satisfy the credit requirement in mathematics will be required to take a bridge program of six credits in appropriate mathematics courses. Such courses do not count towards a graduate degree.

Degree Requirements:
The Master of Science in Applied Statistics requires 30 credits: 21 credits in core courses and 9 credits of elective courses. Students must successfully complete at least 24 of these credits at the 600-level or higher, and no more than six credits at the 500-level will be counted towards the degree. A master's thesis or a master's project is optional.

Seminar: In addition to the minimum 30 degree credits required, all students who receive departmental or research-based awards must enroll every semester in Math 791 Graduate Seminar.

Core:
21 credits:

Electives are chosen in consultation with a departmental graduate advisor and consist of advanced courses in mathematics and statistics and advanced courses from engineering, computer science, and biology that have a significant statistics content. Students are encouraged to choose courses in application areas. Courses offered by appropriate departments at NJIT, UMDNJ, and Rutgers University-Newark can be used as electives within the limits of the NJIT transfer policy. All elective courses must be approved by the graduate advisor.

• Applied Mathematics
• Applied Probability and Statistics
• Pure Mathematics

The doctoral program reflects the research interests of the faculty and is focused on the development and use of mathematical tools for solving modern scientific, technological and industrial problems, and advancing the research knowledge and methodology in various fields of specialization.

The Applied Mathematics track emphasizes the applications of mathematical methods to the physical and biological sciences and engineering, including acoustics, electromagnetics, fluid dynamics, materials science, biology, and medicine. Mathematical modeling, asymptotic analysis, and scientific computing are emphasized. Students are expected to develop a broad range of capabilities both in mathematics and in an area of application.

The Applied Probability and Statistics track emphasizes directed instruction and independent research in areas that are specializations of the faculty. Current research interest areas of the faculty include applied probability, nonparametric statistics, and statistical reliability theory and applications.

The Pure Mathematics track offers research opportunities in many fields of specialization, including representation theory, number theory, low-dimensional topology, Riemann surfaces and Kleinian groups, geometric group theory, and 4-manifolds.

Admission Requirements:
Admission to the program is based on a review of the applicant's credentials and interests as expressed in academic transcripts, GRE scores, letters of recommendation, statement of interests, and TOEFL scores (for students whose native language is not English). Applicants with strong academic records whose abilities and interests complement the research of the faculty are sought. In general, applicants should have a bachelor's or master's degree in mathematics, an engineering discipline, or a branch of the natural sciences. Students choosing the Applied Mathematics track or the Applied Probability and Statistics track must fulfill the admissions requirements specified in the Admissions section of this catalog.

Students interested in either the Applied Mathematics track or the Applied Probability and Statistics track should apply to NJIT. Students interested in the Pure Mathematics track should apply to Rutgers-Newark.

Degree Requirements:

Applied Mathematics Track (NJIT)

Students choosing the applied mathematics track must fulfill the requirements for the doctor of philosophy as specified in this catalog. Specific courses of study are planned in consultation with a faculty advisor and are subject to approval. In general, students are encouraged to take courses both in mathematics and in areas of application.

Seminar: In addition to the minimum degree credits required, all doctoral students must enroll each semester in Math 791 Graduate Seminar.

Courses: A typical schedule of courses for the first four semesters in Applied Mathematics consists of the following:

Semester I

• Mathematical Fluid Dynamics I and Mathematical Fluid Dynamics II (Math 715 , Math 716)
• Mathematical Biology (Math 637 , Math 672 , Math 673)
• Wave Propagation (Math 722)
• Asymptotic Methods II (Math 771)
• Mathematical Modeling II (Math 639)
• Partial Differential Equations (Math 675)
• Inverse Problems and Global Optimization (Math 717)

Also, there are special topics courses in:

• computational electromagnetics
• computational fluid dynamics
• computational neuroscience
• financial mathematics
• integral equations
• materials science
• microwave processing of materials
• courses in probability and statistics

Qualifying Examination: The qualifying examination for the applied mathematics track consists of three components: Analysis, Linear Algebra - Numerical Methods, and Applied Mathematics. Students must achieve a grade of A in each component to pass the qualifying examination. Components may be passed at different times. However, a student may attempt each component at most twice and must pass all three components by the end of the second year in the program. Typically, two opportunities to take each component are provided each year: Analysis and Linear Algebra - Numerical Methods (August and January), Applied Mathematics (January and May).

The following courses will be useful in helping the students to prepare for the qualifying examinations : Math 645, Math 656, and Math 745 for Analysis; Math 614 and Math 631 for Linear Algebra Numerical Methods; and Math 613, Math 689, and Math 690 for Applied Mathematics. It should be noted that taking the above courses is not mandatory but students are strongly encouraged to take them before attempting the qualifying examinations. The scope of the qualifying examinations is not limited to the specific list of topics covered in these courses, but these topics are indicative of the overall scope of these examinations.

Dissertation Committee: The dissertation committee is an important resource for the doctoral student in the conduct of research for their dissertation. Within six months of passing the qualifying examination a dissertation committee must be formed according to the regulations specified in this catalog.

Dissertation Proposal: Doctoral students must prepare a research proposal for approval by their dissertation committee. The student must offer an oral defense of this proposal before the dissertation committee and obtain its approval within one year of passing the qualifying examination. The committee determines if the proposal has an appropriate objective, if there is a reasonable plan to reach that objective, and if the student possesses the knowledge and skills needed to carry out the plan. The dissertation proposal can only be approved by unanimous consent of the committee members.

Dissertation Defense: A public oral defense of the dissertation before the dissertation committee is required. All members of the committee must be present for the defense. Success of the defense is determined by a majority vote of the dissertation committee.

Applied Probability and Statistics Track (NJIT)

Students choosing the applied probability and statistics track must fulfill the requirements for the doctor of philosophy as specified in this catalog. Specific courses of study are planned in consultation with a faculty graduate advisor and are subject to approval. In general, students are encouraged to take courses both in mathematics and in areas of application.

Seminar: In addition to the minimum degree credits required, all doctoral students must enroll each semester Math 791 Graduate Seminar

Courses: A typical schedule of courses for the first four semesters in Applied Probability and Statistics consists of the following:

Semester I

Semester IV

• Time Series Analysis - II ( Math 647 )
• Stochastic processes with applications ( Math 691 )
• Statistical reliability theory and applications ( Math 761 )
• Large sample theory and inference ( Math 786 )

Also, there are special topics courses ( Math 707 ), in:

• Categorical data analysis,
• Financial mathematics.
• Generalized linear models,
• Markov chain Monte Carlo methods,

Qualifying Examination: The qualifying examination for the applied probability and statistics track consists of three components: Analysis, Linear Algebra, and Statistics. Students must achieve a grade of A in each component to pass the qualifying examination. Components may be passed at different times. However, a student may attempt each component at most twice and must pass all three components by the end of the second year in the program. Typically, two opportunities to take each component are provided each year: Real Analysis and Probability, Linear Algebra, Distribution Theory and Statistical Inference (August and January); Topics in Statistics (January and May).

The following courses will be useful in helping the students to prepare for the qualifying examinations : Math 645, Math 668, and Math 745 for Real Analysis and Probability; Math 631, Math 662, and Math 762 for Linear Algebra, Distribution Theory and Statistical Inference; Math 644, Math 699, and Math 707 (Linear Models) for Topics in Statistics. The scope of the "Topics in Statistics" examination may include additional advanced courses in statistics that the students may have taken. It should be noted that taking the above courses are not mandatory but students are strongly encouraged to take them before attempting the qualifying examinations. The scope of the qualifying examinations is not limited to the specific list of topics covered in these courses, but these topics are indicative of the overall scope of these examinations.

Dissertation Committee: The dissertation committee is an important resource for the doctoral student in the conduct of research for their dissertation. Within six months of passing the qualifying examination a dissertation committee must be formed according to the regulations specified in this catalog.

Dissertation Proposal: Doctoral students must prepare a research proposal for approval by their dissertation committee. The student must offer an oral defense of this proposal before the dissertation committee and obtain its approval within one year of passing the qualifying examination. The committee determines if the proposal has an appropriate objective, if there is a reasonable plan to reach that objective, and if the student possesses the knowledge and skills needed to carry out the plan. The dissertation proposal can only be approved by unanimous consent of the committee members.

Dissertation Defense: A public oral defense of the dissertation before the dissertation committee is required. All members of the committee must be present for the defense. Success of the defense is determined by a majority vote of the dissertation committee.


Pure Mathematics Track (Rutgers-Newark)

Students interested in the Pure Mathematics track should contact the Department of Mathematics and Computer Science at Rutgers-Newark.