Ph.D. in Mathematical Sciences

The Ph.D. in Mathematical Sciences is a doctoral program that offers two tracks: Applied Mathematics and Applied Statistics and Probability. Students are admitted to one of these tracks and must fulfill the requirements for the doctor of philosophy as specified in the catalog.

Degree Requirements

Students entering with a bachelor's degree must complete 36 credits of coursework, while those entering with a master's degree in mathematical sciences or equivalent must complete 12 credits of advanced 700-level coursework. 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. To graduate, students must have an approved dissertation and are expected to attain an overall GPA of at least 3.0.

Course Requirements

• For students with a Master's degree in Mathematical Sciences or equivalent:
  • 12 credits of 700-level courses
  • Dissertation: MATH 790A (Doct Dissertation & Res) and MATH 792B (Pre Doctoral Research)
  • Seminar: MATH 791 (Graduate Seminar)
• For students with a Bachelor's degree in Mathematical Sciences or equivalent:
  • 36 credits of 600 and 700-level courses
  • Dissertation: MATH 790A (Doct Dissertation & Res) and MATH 792B (Pre Doctoral Research)
  • Seminar: MATH 791 (Graduate Seminar)

Typical Schedule of Courses

A typical schedule of courses for the first two semesters in Applied Mathematics and Applied Probability and Statistics is provided.

Applied Mathematics

• 1st Semester:
  • MATH 599: Teaching in Mathematics (3 credits)
  • MATH 613: Advanced Applied Mathematics I: Modeling (3 credits)
  • MATH 631: Linear Algebra (3 credits)
  • MATH 645: Analysis I (3 credits)
  • MATH 651: Methods of Applied Mathematics I (3 credits)
• 2nd Semester:
  • MATH 614: Numerical Methods I (3 credits)
  • MATH 656: Complex Variables I (3 credits)
  • MATH 689: Advanced Applied Mathematics II: Ordinary Differential Equations (3 credits)
  • MATH 745: Analysis II (3 credits)

Applied Probability and Statistics

• 1st Semester:
  • MATH 599: Teaching in Mathematics (3 credits)
  • MATH 631: Linear Algebra (3 credits)
  • MATH 644: Regression Analysis Methods (3 credits)
  • MATH 645: Analysis I (3 credits)
  • MATH 662: Probability Distributions (3 credits)
• 2nd Semester:
  • MATH 665: Statistical Inference (3 credits)
  • MATH 699: Design and Analysis of Experiments (3 credits)
  • MATH 745: Analysis II (3 credits)
  • MATH 768: Probability Theory (3 credits)

Advanced Courses

There are advanced courses available in various topics, including:

• Partial differential equations
• Ordinary differential equations and dynamical systems
• Optimization
• Numerical methods
• Computational electromagnetics
• Computational fluid dynamics
• Computational neuroscience
• Financial mathematics
• Integral equations
• Materials science
• Probability and statistics

Deadlines

• The required coursework for the Ph.D. program and the major part of the qualifying exams must be completed successfully by the end of the second year in the program.
• The dissertation proposal must be defended successfully by the end of the third year in the Ph.D. program.
• The dissertation must be defended successfully by the end of the sixth year in the Ph.D. program.

Selection of Dissertation Advisor

Students select a dissertation topic and advisor in the second year of the program. In cases where more than one advisor is directing the dissertation, the primary advisor must be on the core departmental faculty.

Qualifying Examination

The qualifying examination consists of a preliminary examination in three parts and an oral examination. The preliminary examination has different components for the Applied Mathematics and Applied Probability and Statistics tracks.

Applied Mathematics Track

• 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.

Applied Probability and Statistics Track

• 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.

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, 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.

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.

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Overview:

New Jersey Institute of Technology (NJIT) is a public research university located in Newark, New Jersey. It is known for its strong focus on science, technology, engineering, and mathematics (STEM) fields. NJIT is consistently ranked among the top schools for return on investment.

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The provided context highlights the positive experiences of NJIT students. Students have access to various resources and opportunities, including research experiences, internships, and career fairs. The university emphasizes the importance of student involvement and provides a supportive environment for students to pursue their academic and professional goals.

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Key Reasons to Study There:

• Strong focus on STEM fields
• High return on investment
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