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:

Plan of Study Grid
Semester ITerm Credits
MATH 599 Teaching in Mathematics 3
MATH 613 Advanced Applied Mathematics I: Modeling 1 3
MATH 631 Linear Algebra 2 3
MATH 645 Analysis I 3 3
MATH 651 Methods of Applied Mathematics I 1 3
 Term Credits15
Semester II
MATH 614 Numerical Methods I 2 3
MATH 656 Complex Variables I 3 3
MATH 689 Advanced Applied Mathematics II: Ordinary Differential Equations 3
MATH 745 Analysis II 3 3
 Term Credits12
Semester III
MATH 671 Asymptotic Methods I 3
MATH 676 Advanced Ordinary Differential Equations 3
MATH 690 Advanced Applied Mathematics III: Partial Differential Equations 3
MATH 712 Numerical Methods II 3
 Term Credits12
Semester IV
MATH 707 Advanced Applied Mathematics IV: Special Topics (Advanced Applied Mathematics IV) 3
MATH 713 Advanced Scientific Computing: Multi-Dimensional Finite-Difference Schemes and Spectral Methods 3
MATH 756 Complex Variables II 3
Course from Natural Sciences or Engineering relevant to student's interests. 3
 Term Credits12
 Total Credits51
1

Helps to prepare for applied mathematics preliminary examination.

2

Helps to prepare for linear algebra-numerical methods preliminary examination.

3

Helps to prepare for analysis preliminary examination.

In addition to these courses, there are advanced courses in:

Mathematical Fluid Dynamics I and Mathematical Fluid Dynamics II
MATH 715Mathematical Fluid Dynamics I3
MATH 716Mathematical Fluid Dynamics II3
Mathematical Biology
MATH 637Foundations of Mathematical Biology3
MATH 672Biomathematics I: Biological Waves and Oscillations3
MATH 673Biomathematics II: Pattern Formation in Biological Systems3
Wave Propagation
MATH 722Wave Propagation3
Asymptotic Methods II
MATH 771Asymptotic Methods II3
Mathematical Modeling II
MATH 639Mathematical Modeling II3
Partial Differential Equations
MATH 675Partial Differential Equations3
Inverse Problems and Global Optimization
MATH 717Inverse Problems and Global Optimization3

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.

Topics for the oral examination are:

  1. Applied Mathematics, based on the courses MATH 689 Advanced Applied Mathematics II: Ordinary Differential Equations and MATH 690 Advanced Applied Mathematics III: Partial Differential Equations
  2. choice of two out of the following three:
    1. Ordinary Differential Equations, based on MATH 676 Advanced Ordinary Differential Equations
    2. Asymptotic Methods, based on MATH 671 Asymptotic Methods I
    3. Numerical Methods, based on MATH 614 Numerical Methods I and MATH 712 Numerical Methods II

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:

Plan of Study Grid
Semester ITerm Credits
MATH 599 Teaching in Mathematics 3
MATH 631 Linear Algebra 3
MATH 644 Regression Analysis Methods 1 3
MATH 645 Analysis I 2 3
MATH 662 Probability Distributions 1 3
 Term Credits15
Semester II
MATH 665 Statistical Inference 2 3
MATH 699 Design and Analysis of Experiments 3 3
MATH 745 Analysis II 2 3
MATH 768 Probability Theory 3 3
 Term Credits12
Semester III
MATH 659 Survival Analysis 3
MATH 691 Stochastic Processes with Applications 3
MATH 707 Advanced Applied Mathematics IV: Special Topics 3
Course in statistics/mathematics/engineering/computing sciences relevant to student's interest 3
 Term Credits12
Semester IV
MATH 664 Methods for Statistical Consulting 3
MATH 698 Sampling Theory 3
Two Courses in statistics/mathematics/engineering/computer science relevant to student's interest 6
 Term Credits12
 Total Credits51
1

Helps to prepare for probability distributions and regression analysis methods preliminary examination.

2

Helps to prepare for real analysis and statistical inference preliminary examination.

3

Helps to prepare for probability theory and design and analysis of experiments preliminary examination.

In addition to these courses, there are advanced courses in:

Time Series Analysis
MATH 646Time Series Analysis3
Clinical Trials Design and Analysis
MATH 654Clinical Trials Design and Analysis3
Statistical Reliability Theory and Applications
MATH 761Statistical Reliability Theory and Applications3
Large Sample Theory and Inference
MATH 786Large Sample Theory and Inference3
Non-Parametric Statistics
MATH 787Non-Parametric Statistics3

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.

Topics for the oral examination are:

  1. Stochastic Processes, based on MATH 691 Stochastic Processes with Applications
  2. Survival Analysis, based on MATH 659 Survival Analysis
  3. Generalized Linear Models, based on MATH 707 Advanced Applied Mathematics IV: Special Topics.

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.