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Mathematics
Administered By: Department of Mathematical Sciences
mathematics
2
p1 * Students specializing in Applied Mathematics or Computational Mathematics may take Math 545 Introductory Mathematical Analysis and Math 546 Advanced Calculus, instead of Math 645 and 3 credits of elective.
p2 ** Math 661 and Math 663 cannot both be used toward degree credits at NJIT. The requirements of Math 661 may, in individual cases, be substituted by Math 663, at the discretion of the Graduate Advisor.
5
s1 * Joint appointment with Department of Biomedical Engineering
s2 ** Joint appointment with the Department of Information Systems
s3 *** Joint appointment with the Federated Department of Biological Sciences
s4 **** Joint appointment with the Department of Electrical and Computer Engineering
s5 ***** Joint appointment with School of Mangement
2

Administration
6
Chair lukej
Acting Chair bechtold
Associate Chair, Undergraduate Studies michalop
Director, Graduate Studies lcumming
Director, Statistics Program dhar
Departmental Coordinator michie

Administration
Chair Jonathan H. Luke
Acting Chair John K. Bechtold
Associate Chair, Undergraduate Studies Zoi-heleni Michalopoulou
Director, Graduate Studies Linda J. Cummings
Director, Statistics Program Sunil K. Dhar
Departmental Coordinator Eileen M. Michie

Faculty
8
Distinguished Professors grkrie,miura[s1]
Professors bose,ahluwali,blackmor,deek[s2],farzan[s3],lukej,bechtold,kondic,bhattach,perez,booty,misieg,milojevi,andrushk,dhar,wychoi,michalop[s4]
Associate Professors aw224,bukiet,cct21,muratov,horntrop,russell[s3],horacio,kappraff,loh,golowasc[s3],lcumming,lieb,rmoore,peterp,plastock,dios,goodman,jiang,sundars,matveev,yyoung,boubendi
Assistant Professors diekman,dbunker[s3,shahriar,wguo,rsverdlo[s5]
Senior University Lecturers Ratnaswa,Rappapor,sjkim
Lecturers klimekd,hayesj,hunter,zaleski,profsr31,sieminsk,pnatar,rkelly, mohebbi
Post Doctoral Fellows ahong,gchaves,skm21

Faculty
Distinguished Professors Gregory A. Kriegsmann, Robert M. Miura*
Professors Amitabha K. Bose, Daljit S. Ahluwalia, Denis L. Blackmore, Fadi Deek** , Farzan Nadim*** , Jonathan H. Luke, John K. Bechtold, Lou Kondic, Manish Bhattacharjee, Manuel Perez, Michael R. Booty, Michael S. Siegel, Petronije Milojevic, Roman I. Andrushkiw, Sunil K. Dhar, Wooyoung Choi, Zoi-heleni Michalopoulou****
Associate Professors Antai Wang, Bruce G. Bukiet, Catalin C. Turc, Cyrill B. Muratov, David J. Horntrop, Gareth J. Russell*** , Horacio G. Rotstein, Jay M. Kappraff, Ji M. Loh, Jorge P. Golowasch*** , Linda J. Cummings, Murray I. Lieb, Richard O. Moore, Peter G. Petropoulos, Roy A. Plastock, Rose Dios, Roy H. Goodman, Shidong Jiang, Sundarraman Subramanian, Victor V. Matveev, Yuan-nan Young, Yassine Boubendir
Assistant Professors Casey O. Diekman, Daniel E. Bunker*** , Shahriar Afkhami, Wenge Guo, Ronald Sverdlove*****
Senior University Lecturers Jeyakumaran Ratnaswamy, Karen D. Rappaport, Seonja Kim
Lecturers Diana P. Klimek, Jimmy L. Hayes, John Hunter, Joseph Zaleski, Ken Horwitz, Katarzyna M. Sieminska, Padma Natarajan, Rudy Kelly, Soroosh Mohebbi Forushani
Post Doctoral Fellows Andrew E. Hong, Gabriel D. Chaves, Sashi K. Marella
*  Joint appointment with Department of Biomedical Engineering
**  Joint appointment with the Department of Information Systems
***  Joint appointment with the Federated Department of Biological Sciences
****  Joint appointment with the Department of Electrical and Computer Engineering
*****  Joint appointment with School of Mangement
 
5
Master of Science in Applied Mathematics 7
 
Master of Science in Applied Mathematics

This program is intended for students with a strong interest in Applied Mathematics. Applied Mathematics is the application of classical and modern mathematical techniques to the solution of practical problems in the physical and biological sciences and engineering. The applied mathematician develops and analyzes mathematical models of physical and biological phenomena and engineering systems, interprets solutions to mathematical problems and uses the results to identify relationships, patterns, and the effects of altering one or more variables or modeling assumptions. Many of the courses in the program illustrate how mathematics can be used to predict the behavior of physical, biological, and engineering systems.

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:

math613,math631,math645[p1],math656,math689
  Math 613Advanced Applied Mathematics I: Modeling (3 credits)
  Math 631Linear Algebra (3 credits)
 * Math 645Analysis I (3 credits)
  Math 656Complex Variables I (3 credits)
  Math 689Advanced Applied Mathematics II: Ordinary Differential Equations (3 credits)
Project, Thesis (optional): math700,math701
  Math 700Master's Project (3 credits)
  Math 701Master's Thesis (6 credits)

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

math745,math756
  Math 745Analysis II (3 credits)
  Math 756Complex Variables II (3 credits)
Applied Mathematics: math614,math690
  Math 614Numerical Methods I (3 credits)
  Math 690Advanced Applied Mathematics III: Partial Differential Equations (3 credits)
Computational Mathematics: math614,math712
  Math 614Numerical Methods I (3 credits)
  Math 712Numerical Methods II (3 credits)
Mathematical Biology: math635,math637
  Math 635 Analytical Computational Neuroscience (3 credits)
  Math 637Foundations of Mathematical Biology (3 credits)
Elective:
9 credits selected with approval of graduate advisor.

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.

Students specializing in Applied Mathematics or Computational Mathematics may take Math 545 Introductory Mathematical Analysis and Math 546 Advanced Calculus, instead of Math 645 and 3 credits of elective.

Master of Science in Applied Statistics 3
 
Master of Science in Applied Statistics

The objective of the Master of Science in Applied Statistics is to prepare students for a wide range of professional activities as practicing statisticians in both academia and industry. A statistician develops and analyzes models of data-driven situations where uncertainty of the outcomes plays a major role, identifies statistical relationships among observable variables, forecasts probable future outcomes, and draws inferences about background parameters that impact the phenomenon of interest. Thus the program is designed to provide students with the comprehensive knowledge and technical skills that are needed for the planning, execution, and analysis of statistical studies. These statistical studies are increasingly used as advisory instruments for policy decisions in the corporate and other sectors of the economy.

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:

{math611|math630},math644,math661[p2],math662,math664,math665,math699
 Math 611Numerical Methods for Computation (3 credits) or
 Math 630Linear Algebra and Applications (3 credits)
  Math 644Regression Analysis Methods (3 credits)
 ** Math 661Applied Statistics (3 credits)
  Math 662Probability Distributions (3 credits)
  Math 664Methods for Statistical Consulting (3 credits)
  Math 665Statistical Inference (3 credits)
  Math 699Design and Analysis of Experiments (3 credits)
Project, Thesis (optional): math700,math701
  Math 700Master's Project (3 credits)
  Math 701Master's Thesis (6 credits)
Elective:
9 credits selected with approval of graduate advisor.

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.

Math 661 and Math 663 cannot both be used toward degree credits at NJIT. The requirements of Math 661 may, in individual cases, be substituted by Math 663, at the discretion of the Graduate Advisor.

Master of Science in BioStatistics 3
 
Master of Science in BioStatistics

The Master of Science program in Biostatistics will provide advanced graduate education and training to students interested in applying statistical methods to the health sciences in general and clinical studies in particular. It will focus on training students in quantitative methods that will prepare them for careers in the health, life sciences, and pharmaceutical areas. Graduates, upon satisfactory completion of the degree program, are expected to have acquired appropriate skills in data analysis and computing that are typically required in their profession. This program will address the growing demand for trained biostatisticians in these fields, especially in New Jersey.

Admission Requirements:
Applicants must have a baccalauareate degree in Statistics, Mathematics, Sciences, or Engineering, with at least 12 credits in mathematics, including calculus and at least one upper division course in statistics. Applicants with other baccalaureate degrees will also be considered and may be subject to a suitable bridge program. An undergraduate GPA of at least 3.0 on a 4.0 scale or equivalent is required.

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

Degree Requirements:
A minimum of 30 credits is required for the degree. Bridge courses, if any, will not count toward degree credits. The graduate curriculum consists of seven core courses in background statistical theory and biostatistics, as described in the curriculum below. The remaining courses are electives, chosen in consultation with a departmental graduate advisor and consist of topics courses in statistics, biostatistics, epidemiology and biology that have significant statistics content or/and applications thereof. Students will be 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. A masters project is optional, and is in addition to the minimum 30 approved credits, required for the degree.

Core:

math644,math654,math659,math662,math663[p2],math665,math699
  Math 644Regression Analysis Methods (3 credits)
  Math 654Clinical Trials Design and Analysis (3 credits)
  Math 659Survival Analysis (3 credits)
  Math 662Probability Distributions (3 credits)
 ** Math 663Introduction to Biostatistics (3-0-3)
  Math 665Statistical Inference (3 credits)
  Math 699Design and Analysis of Experiments (3 credits)
Electives:

At least three from the following illustrative list:

math664,math691,math698,math707,math763,math786,math787,{UMDNJ;UMDNJ Courses},{PHCO-0502J;Introduction to Epidemiology;3 credits}
  Math 664Methods for Statistical Consulting (3 credits)
  Math 691Stochastic Processes with Applications (3 credits)
  Math 698Sampling Theory (3 credits)
  Math 707Advanced Applied Mathematics IV: Special Topics (3 credits)
  Math 763Generalized Linear Models (3 credits)
  Math 786Large Sample Theory and Inference (3 credits )
  Math 787Non-Parametric Statistics (3 credits )
  UMDNJ (UMDNJ Courses) 
  PHCO-0502J (Introduction to Epidemiology) (3 credits) 
Electives are chosen in consultation with a departmental graduate advisor. Subject to such approval, 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.

Math 661 and Math 663 cannot both be used toward degree credits at NJIT. The requirements of Math 663 may, in individual cases, be substituted by Math 661, at the discretion of the Graduate Advisor.

Master of Science in Mathematical and Computational Finance 33 credits 4
 
Master of Science in Mathematical and Computational Finance (33 credits)

In the past several decades the field of Mathematical and Computational Finance has developed into a well established discipline of great importance within the financial, investment and banking industries and increasingly in regulatory agencies. Practitioners of this field combine high-level analytical, computational and modeling skills with a thorough understanding of financial markets and instruments to assess value and risk. These assessments are needed to structure solutions to financial problems, to manage risk and to identify and exploit financial opportunities. As the financial industry is highly concentrated around the New York City area, practitioners of Mathematical and Computational Finance are in high demand locally.

The M.S. in Mathematical and Computational Finance delivers the theoretical knowledge, the practical methods and the essential skills needed for students to begin or enhance careers as quantitative analysts in the financial industry. Students graduating from this program will possess a broad knowledge of financial and capital markets including understanding of systemic risks, the ability to develop quantitative models of financial markets and instruments and the analytical, statistical and computational capabilities to analyze those models to obtain practical information of value in the financial industry. Due to the evolving nature of financial markets and institutions, practitioners in this field must be ready to learn new ideas and methods across a broad range of disciplines including mathematics, statistics, computational science, finance, and economics. The program aims to provide the multidisciplinary foundations preparing quantitative analysts for this life-long development of skills and understanding and for responsible participation in the financial system.

Admission Requirements:
Applicants must have earned an undergraduate degree with an overall GPA of 2.8 (on a 4.0 scale) and are expected to have fulfilled the following program prerequisites:

  • undergraduate finance (FIN 315 or equivalent),
  • practical computer programming skills in C/C++,
  • two semesters of calculus-based undergraduate courses in probability or statistics,
  • undergraduate calculus and multivariate calculus (Math 111, Math 112 and Math 213 or equivalent),
  • undergraduate differential equations (Math 222 or equivalent),
  • undergraduate linear algebra (Math 337 or equivalent),
  • experience with partial differential equations as models such as is typical in undergraduate courses in electromagnetism, heat transfer, fluid dynamics, elasticity and quantum mechanics.

A GPA of at least 3.0 (on a 4.0 scale) is expected in the courses fulfilling these prerequisites. GRE  or GMAT 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. Required courses for the program are generally offered in the evenings and part-time study is possible.

Bridge Program: Students with a baccalaureate degree not fully covering the prerequisites listed above 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 Mathematical and Computational Finance requires 33 credits: 27 credits in core courses, 3 credits in an approved elective, and 3 credits in a project course.

SEMESTER I

fin641,math605,math611,math646
  Fin 641Derivatives Markets (3 credits)
  Math 605Stochastic Calculus (3 credits)
  Math 611Numerical Methods for Computation (3 credits)
  Math 646Time Series Analysis (3 credits)
SEMESTER II math604,math606,math608,{cs666|math666}
  Math 604Mathematical Finance (3-0-3)
  Math 606Term Structure Models (3-0-3)
  Math 608Partial Differential Equations for Finance (3 credits)
 CS 666Simulation for Finance (3 credits) or
 Math 666Simulation for Finance (3 credits)
SEMESTER III math607,{Elective;Approved Elective},math609
  Math 607Credit Risk Models (3-0-3)
  Elective (Approved Elective) 
  Math 609Projects in Mathematical and Computational Finance (3-0-3)
For students having already successfully completed the equivalent of a course required for the program, more advanced courses can substituted with departmental approval.

Electives must be selected with the approval of the Program Director/Advisor; potential electives include:

em602,fin624,fin626,fin650,math644,math647,math662,math665,math668,math691,math699,math712
  EM 602Management Science (3 credits)
  Fin 624Corporate Finance II (3 credits)
  Fin 626Financial Investment Institutions (3 credits)
  Fin 650Investment Analysis and Portfolio Theory (3 credits)
  Math 644Regression Analysis Methods (3 credits)
  Math 647Time Series Analysis II (3 credits)
  Math 662Probability Distributions (3 credits)
  Math 665Statistical Inference (3 credits)
  Math 668Probability Theory (3 credits)
  Math 691Stochastic Processes with Applications (3 credits)
  Math 699Design and Analysis of Experiments (3 credits)
  Math 712Numerical Methods II (3 credits)
Doctor of Philosophy in Mathematical Sciences 9
 
Doctor of Philosophy in Mathematical Sciences

The Doctor of Philosophy in Mathematical Sciences is offered in collaboration with the Department of Mathematics and Computer Science at Rutgers University-Newark. The doctoral program in Mathematical Sciences is designed to prepare students for a wide range of professional activities in science and engineering. Prospective students must choose one of the following tracks:

  • 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, non-parametric 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

math599,math613,math631,math645,math651
  Math 599Teaching in Mathematics (3 credits)
  Math 613Advanced Applied Mathematics I: Modeling (3 credits)
  Math 631Linear Algebra (3 credits)
  Math 645Analysis I (3 credits)
  Math 651Methods of Applied Mathematics I (3 credits)

Semester II
math614,math656,math689,math745
  Math 614Numerical Methods I (3 credits)
  Math 656Complex Variables I (3 credits)
  Math 689Advanced Applied Mathematics II: Ordinary Differential Equations (3 credits)
  Math 745Analysis II (3 credits)
Semester III math671,math676,math690,math712
  Math 671Asymptotic Methods I (3 credits)
  Math 676Advanced Ordinary Differential Equations (3 credits)
  Math 690Advanced Applied Mathematics III: Partial Differential Equations (3 credits)
  Math 712Numerical Methods II (3 credits)
Semester IV math707,math713,math756,{Elective;Course from Natural Sciences or Engineering relevant to student's Interests.}
  Math 707Advanced Applied Mathematics IV: Special Topics (3 credits)
  Math 713Advanced Scientific Computing: Multi-Dimensional Finite-Difference Schemes and Spectral Methods (3 credits)
  Math 756Complex Variables II (3 credits)
  Elective (Course from Natural Sciences or Engineering relevant to student's Interests.) 
In addition to these courses, there are advanced courses in:

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 a preliminary examination in three parts and an oral examination. The three components of the preliminary examination are: Applied Mathematics, Analysis, and Linear Algebra-Numerical Methods. Students must achieve a grade of A in each component to pass the preliminary examination and proceed to the oral examination. Components may be passed at different times. However, a student may attempt each component at most twice and must pass all three components before taking the oral examination. The qualifying examination must be passed by the end of the second year in the program. Typically, two opportunities to take each component are provided each year: Applied Mathematics (January and May), Analysis and Linear Algebra-Numerical Methods (May and August). The oral examination is usually offered in January and May. The following courses will be useful in helping students to prepare for the preliminary examinations: Math 613 and Math 651 for Applied Mathematics; Math 645, Math 656, and Math 745 for Analysis; Math 614 and Math 631 for Linear Algebra-Numerical Methods. Topics for the oral examination are Applied Mathematics, based on the courses Math 689 and Math 690, choice of two out of the following three: Ordinary Differential Equations, based on Math 676; Asymptotic Methods, based on Math 671; Numerical Methods, based on Math 614 and Math 712.

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 the examinations.

Dissertation Committee: The dissertation committee is an important resource for the doctoral student in the conduct of research for their dissertation. According to the regulations specified in this catalog, doctoral students are required to have a dissertation advisor selected, a dissertation committee formed, and research proposal approved within one year of passage of the qualifying examination.

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 in 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

math599,math631,math644,math645,math662
  Math 599Teaching in Mathematics (3 credits)
  Math 631Linear Algebra (3 credits)
  Math 644Regression Analysis Methods (3 credits)
  Math 645Analysis I (3 credits)
  Math 662Probability Distributions (3 credits)
Semester II math665,math699,math745,math768
  Math 665Statistical Inference (3 credits)
  Math 699Design and Analysis of Experiments (3 credits)
  Math 745Analysis II (3 credits)
  Math 768Probability Theory (3 credits)
Semester III math659,math691,math707,{Elective;Course in statistics/mathematics/engineering/computing sciences relevant to student's interest.}
  Math 659Survival Analysis (3 credits)
  Math 691Stochastic Processes with Applications (3 credits)
  Math 707Advanced Applied Mathematics IV: Special Topics (3 credits)
  Elective (Course in statistics/mathematics/engineering/computing sciences relevant to student's interest.) 
Semester IV math664,math698,{Electives;Two Courses in statistics/mathematics/engineering/computer science relevant to student's interest.}
  Math 664Methods for Statistical Consulting (3 credits)
  Math 698Sampling Theory (3 credits)
  Electives (Two Courses in statistics/mathematics/engineering/computer science relevant to student's interest.) 
In addition to these courses, there are advanced courses in:
  • Time Series Analysis ( Math 646)
  • Clinical Trials Design and Analysis (Math 654)
  • Statistical Reliability Theory and Applications (Math 761)
  • Large Sample Theory and Inference (Math 786)
  • Non-Parametric Statistics (Math 787)

Qualifying Examination: The qualifying examination for the applied probability and statistics track consists of a preliminary examination in three parts and an oral examination. The three components of the preliminary examination are: Probability Distributions and Regression Analysis Methods, Real Analysis and Statistical Inference, Probability Theory and Design and Analysis of Experiments. Students must achieve a grade of A in each component to pass the preliminary examination and proceed to the oral examination. Components may be passed at different times. However, a student may attempt each component at most twice and must pass all three components before taking the oral examination. The qualifying examination must be passed by the end of the second year in the program. Typically, two opportunities to take each component are provided each year: Probability Distributions and Regression Analysis Methods (January and May), Real Analysis and Statistical Inference and Probability Theory and Design and Analysis of Experiments (May and August). The oral examination is usually offered in January and May.

The following courses will be useful in helping students to prepare for the preliminary examinations: Math 644 and Math 662 for Probability Distributions and Regression Analysis Methods; Math 645, Math 665, and Math 745 for Real Analysis and Statistical Inference; Math 699 and Math 768 for Probability Theory and Design and Analysis of Experiments. Topics for the oral examination are Stochastic Processes, based on Math 691; Survival Analysis, based on Math 659; Generalized Linear Models, based on Math 707.

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 the examinations.

Dissertation Committee: The dissertation committee is an important resource for the doctoral student in the conduct of research for their dissertation. According to the regulations specified in this catalog, doctoral students are required to have a dissertation advisor selected, a dissertation committee formed, and a research proposal approved within one year of passage of the qualifying examination.

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.



*  Students specializing in Applied Mathematics or Computational Mathematics may take Math 545 Introductory Mathematical Analysis and Math 546 Advanced Calculus, instead of Math 645 and 3 credits of elective.
**  Math 661 and Math 663 cannot both be used toward degree credits at NJIT. The requirements of Math 661 may, in individual cases, be substituted by Math 663, at the discretion of the Graduate Advisor.
 


Catalog and curricula information approved by the relevant academic department.