Master of Science in Applied Mathematics
The Master of Science in Applied Mathematics program at Illinois Tech is a modern graduate program tailored to serve students based on their academic background and future career goals. For students who wish to pursue a doctoral degree in the mathematical sciences, it provides a strong academic foundation that prepares the student for the challenge of Ph.D. coursework and research. For students who wish to pursue careers in industry, Illinois Tech trains students in state-of-the-art advanced mathematical techniques and models that are appealing to future employers. These options are possible due to the remarkably flexible structure of the program that allows students to craft their own coursework to meet their career goals by choosing one of the three options of study:
- Coursework only option
- Completing an industry-based project
- Writing an M.S. thesis
In addition, students can choose a specialization from a wide range of contemporary areas of applied mathematics:
- Computational Statistics for Data Science
- Discrete Computation and Optimization
- Industrial Mathematics
- Quantitative Risk Management
- Stochastic Computation
Students satisfying the requirements of a specialization will have the specialization recognized on official transcripts.
Admission Requirements
The program normally requires a bachelor’s degree in mathematics or applied mathematics. Candidates whose degree is in another field (for example, computer science, physics, or engineering) and whose background in mathematics is strong are also eligible for admission and are encouraged to apply. Applicants should have a bachelor’s degree from an accredited university with a minimum cumulative GPA of 3.0/4.0. A combined verbal and quantitative GRE examination score of at least 304 and an analytic writing score of at least 2.5 are required. TOEFL scores (if required) should be a minimum of 80/550 (internet-based/paper-based test scores). A professional statement of goals/objectives (two pages) and a curriculum vitae must be submitted. Two letters of recommendation are required. Students must remove deficiencies in essential undergraduate courses that are prerequisites for the degree program, in addition to fulfilling all other degree requirements. Typically, admitted students score at least 156 on the quantitative portion of the GRE; however, meeting the minimum or typical GPA and test score requirements does not guarantee admission.
The Director of Graduate Studies serves as temporary academic adviser for newly admitted graduate students in the master of science programs until an appropriate faculty member is selected as the adviser. Students are responsible for following all departmental procedures, as well as the general requirements of the Graduate College.
Curriculum
Students may transfer up to two classes from a graduate program at another accredited university if the student has not used the classes to satisfy the requirements for a degree at the previous university.
General Program Requirements
- All students will follow the requirements for core courses as given below.
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All students will choose one of the following three options:
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Coursework Only Option. Students must pass the comprehensive exam, consisting of two exams corresponding to the courses MATH 500, MATH 540, MATH 553, MATH 563, and MATH 577, which must be passed at a master's level or above.
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Master's Project Option. Perform an industrial project for three to five credit hours taken as MATH 594. A project may focus on the applications of existing methodologies or mathematical modeling of a real-life phenomenon, possibly from outside mathematics, including industry sponsored group projects. This option also requires MATH 522 and the completion of a formal specialization.
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M.S. Thesis Option. M.S. Thesis for five to eight credit hours taken as MATH 591. A thesis should go into substantial depth on a topic or problem from a methodological or mathematical perspective and make a contribution towards the advancement of mathematical understanding of the problem under study.
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All students will take the colloquium course MATH 593 (zero credit hours) at least one semester.
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All students will take their remaining credit hours from the elective courses listed below or other courses with the approval of the academic adviser.
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Students will maintain a GPA of at least 3.0 in their coursework.
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Students in the coursework only option or thesis option may complete one of the listed specializations, but are not required to do so.
Master of Science in Applied Mathematics (Coursework Only Option)
| Minimum Degree Credits | 32 |
| Maximum 400-Level Credit | 9 |
| Minimum MATH Credit | 25 |
| Code | Title | Credit Hours |
|---|---|---|
| Core Courses | (9) 1 | |
| MATH 577 | Computational Mathematics I | 3 |
| Select a minimum of six credit hours from the following: | 6 | |
| Applied Analysis I | 3 | |
or MATH 400 | Real Analysis | |
| Probability 2 | 3 | |
or MATH 475 | Probability | |
| Discrete Applied Mathematics I | 3 | |
or MATH 454 | Graph Theory and Applications | |
| Mathematical Statistics 3 | 3 | |
or MATH 476 | Statistics | |
| Additional Requirements | (0) | |
| MATH 593 | Seminar in Applied Mathematics | 0 |
| Elective Courses | (23) | |
| Select 23 credit hours 4 | 23 | |
| Total Credit Hours | 32 | |
- 1
Students in the coursework only option must pass the comprehensive exam, consisting of two exams corresponding to the courses MATH 500, MATH 540, MATH 553, MATH 563, and MATH 577, which must be passed at a master's level or above.
- 2
MATH 540 or MATH 475 is required for students pursuing specializations in Stochastic Computation, Computational Statistics for Data Science, or Quantitative Risk Management.
- 3
MATH 563 is required for students pursuing a specialization in Computational Statistics for Data Science.
- 4
The remaining courses in each student’s program are selected in consultation with, and approval of, the Director of Graduate Studies. Students pursuing a specialization should choose approved courses specific to their specialization. See the Specializations tab on this page for more details.
Master of Science in Applied Mathematics (Master's Project Option)
| Minimum Degree Credits | 32 |
| Maximum 400-Level Credit | 9 |
| Minimum MATH Credit | 25 |
| Code | Title | Credit Hours |
|---|---|---|
| Core Courses | (9) | |
| MATH 522 | Mathematical Modeling | 3 |
| MATH 577 | Computational Mathematics I | 3 |
| Select a minimum of three credit hours from the following: | 3 | |
| Applied Analysis I | 3 | |
or MATH 400 | Real Analysis | |
| Probability 1 | 3 | |
or MATH 475 | Probability | |
| Discrete Applied Mathematics I | 3 | |
or MATH 454 | Graph Theory and Applications | |
| Mathematical Statistics 2 | 3 | |
or MATH 476 | Statistics | |
| Additional Requirements | (0) | |
| MATH 593 | Seminar in Applied Mathematics | 0 |
| Specialization Courses | (9-15) | |
| Select 9-15 credit hours from an approved specialization 3, 5 | 9-15 | |
| Master's Project | (3-5) | |
| MATH 594 | Professional Master's Project 5 | 3-5 |
| or MATH 597 | Reading and Special Projects | |
| Elective Courses | (3-11) | |
| Select 3-11 credit hours 4, 5 | 3-11 | |
- 1
MATH 540 or MATH 475 is required for students pursuing specializations in Industrial Mathematics, Stochastic Computation, Computational Statistics for Data Science, or Quantitative Risk Management.
- 2
MATH 563 is required for students pursuing a specialization in Computational Statistics for Data Science.
- 3
Students should choose approved courses specific to their specialization. See the Specializations tab on this page for more details.
- 4
The remaining courses in each student’s program are selected in consultation with, and approval of, the Director of Graduate Studies.
- 5
- Variable credit hours should sum up to a minimum 23 credit hours so that students fulfill a minimum 32 credits together with 9 credits of Core Courses.
Master of Science in Applied Mathematics (Thesis Option)
| Minimum Degree Credits | 32 |
| Maximum 400-Level Credit | 9 |
| Minimum MATH Credit | 25 |
| Code | Title | Credit Hours |
|---|---|---|
| Core Courses | (9) | |
| MATH 577 | Computational Mathematics I | 3 |
| Select six credit hours from the following: | 6 | |
| Applied Analysis I | 3 | |
or MATH 400 | Real Analysis | |
| Probability 1 | 3 | |
or MATH 475 | Probability | |
| Discrete Applied Mathematics I | 3 | |
or MATH 454 | Graph Theory and Applications | |
| Mathematical Statistics 2 | 3 | |
or MATH 476 | Statistics | |
| Additional Requirements | (0) | |
| MATH 593 | Seminar in Applied Mathematics | 0 |
| Elective Courses | (15-18) | |
| Select 15-18 credit hours 3, 4 | 15-18 | |
| Thesis Research | (5-8) | |
| MATH 591 | Research and Thesis M.S. 4 | 5-8 |
- 1
MATH 540 or MATH 475 is required for students pursuing specializations in Stochastic Computation, Computational Statistics for Data Science, or Quantitative Risk Management.
- 2
MATH 563 is required for students pursuing a specialization in Computational Statistics for Data Science.
- 3
The remaining courses in each student’s program are selected in consultation with, and approval of, the Director of Graduate Studies. Students pursuing a specialization should choose approved courses specific to their specialization. See the Specializations tab on this page for more details.
- 4
- Variable credit hours should sum up to a minimum 23 credit hours so that students fulfill a minimum 32 credits together with 9 credits of Core Courses.
Comprehensive Examination
The comprehensive examination requirement is fulfilled by either (a) passing written tests in two of the five core areas of study at the master of science level; or (b) performing an industrial project (three to five credit hours of MATH 594 ), satisfying the requirements for one specialization, and taking MATH 522; or (c) a master's thesis (five to eight credit hours of MATH 591) under the supervision of a faculty member.
Specializations
Computational Statistics for Data Science
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | (9) | |
| MATH 540 | Probability 1 | 3 |
| or MATH 475 | Probability | |
| MATH 563 | Mathematical Statistics 1 | 3 |
| MATH 564 | Regression | 3 |
| Elective Courses | (0) 2 | |
| Bioinformatics | 3 | |
| Online Social Network Analysis | 3 | |
| Probabilistic Graphical Models | 3 | |
| Machine Learning | 3 | |
| Natural Language Processing | 3 | |
| Machine and Deep Learning | 3 | |
| Design and Analysis of Experiments | 3 | |
| Optimization I | 3 | |
| Stochastic Processes | 3 | |
or MATH 481 | Introduction to Stochastic Processes | |
| Introduction to Time Series | 3 | |
or MATH 446 | Introduction to Time Series | |
| Algebraic and Geometric Methods in Statistics | 3 | |
| Monte Carlo Methods | 3 | |
| Advanced Design of Experiments | 3 | |
or MATH 483 | Design and Analysis of Experiments | |
| Statistical Learning | 3 | |
| Bayesian Computational Statistics | 3 | |
| Computational Mathematics II | 3 | |
| Meshfree Methods | 3 | |
| Computational Physics | 3 | |
- 1
MATH 540, MATH 475, and MATH 563 may be used to satisfy both the core degree requirements and specialization requirements.
- 2
Students may also select core course options that were not used to satisfy the core course requirement.
Discrete Computation and Optimization
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | (9) | |
| Select nine credit hours from the following: | 9 | |
| Applied and Computational Algebra | 3 | |
| Optimization I | 3 | |
| Discrete Applied Mathematics I | 3 | |
| Modern Methods in Discrete Applied Mathematics | 3 | |
| Statistical Learning | 3 | |
| Elective Courses | (0) 2 | |
| Design and Analysis of Algorithms | 3 | |
| Game Theory: Algorithms and Applications | 3 | |
| Online Social Network Analysis | 3 | |
| Probabilistic Graphical Models | 3 | |
| Machine Learning | 3 | |
| Coding for Reliable Communications | 3 | |
| Computer Vision and Image Processing | 3 | |
| Applied Algebra | 3 | |
| Graph Theory and Applications 1 | 3 | |
| Stochastic Processes | 3 | |
or MATH 481 | Introduction to Stochastic Processes | |
| Introduction to Time Series | 3 | |
or MATH 446 | Introduction to Time Series | |
| Algebraic and Geometric Methods in Statistics | 3 | |
| Mathematical Statistics | 3 | |
or MATH 564 | Regression | |
| Monte Carlo Methods | 3 | |
| Advanced Design of Experiments | 3 | |
or MATH 483 | Design and Analysis of Experiments | |
| Bayesian Computational Statistics | 3 | |
- 1
MATH 454 may not be taken if the student has already completed MATH 553.
- 2
Students may also select core course options that were not used to satisfy the core course requirement.
Industrial Mathematics
Note: The master's project track is required to pursue this specialization.
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | (15) | |
| MATH 540 | Probability 1 | 3 |
| or MATH 475 | Probability | |
| MATH 522 | Mathematical Modeling 1 | 3 |
| SCI 511 | Project Management | 3 |
| or SCI 522 | Public Engagement for Scientists | |
| MATH 523 | Case Studies and Project Design in Applied Mathematics | 6 |
| or MATH 592 | Internship in Applied Mathematics | |
| Elective Courses | (0) 2 | |
| Design and Analysis of Algorithms | 3 | |
| Game Theory: Algorithms and Applications | 3 | |
| Online Social Network Analysis | 3 | |
| Probabilistic Graphical Models | 3 | |
| Machine Learning | 3 | |
| Applied Algebra | 3 | |
| Graph Theory and Applications 2 | 3 | |
| Stochastic Processes | 3 | |
or MATH 481 | Introduction to Stochastic Processes | |
| Introduction to Time Series | 3 | |
or MATH 446 | Introduction to Time Series | |
| Algebraic and Geometric Methods in Statistics | 3 | |
| Mathematical Statistics | 3 | |
or MATH 564 | Regression | |
| Monte Carlo Methods | 3 | |
| Advanced Design of Experiments | 3 | |
or MATH 483 | Design and Analysis of Experiments | |
| Bayesian Computational Statistics | 3 | |
- 1
MATH 540, MATH 475, and MATH 522 may be used to satisfy both the core degree requirements and specialization requirements.
- 2
Students may also select core course options that were not used to satisfy the core course requirement.
Quantitative Risk Management
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | (12) | |
| MATH 540 | Probability 1 | 3 |
| or MATH 475 | Probability | |
| MATH 542 | Stochastic Processes | 3 |
| or MATH 543 | Stochastic Analysis | |
| MATH 588 | Advanced Quantitative Risk Management | 3 |
| MATH 565 | Monte Carlo Methods | 3 |
| or MATH 582 | Mathematical Finance II | |
| or MATH 584 | Mathematical Methods for Algorithmic Trading | |
| or MATH 587 | Theory and Practice of Modeling Risk and Credit Derivatives | |
| Elective Courses | (0) 2 | |
| Stochastic Analysis | 3 | |
| Stochastic Dynamics | 3 | |
or MATH 545 | Stochastic Partial Differential Equations | |
| Introduction to Time Series | 3 | |
or MATH 566 | Multivariate Analysis | |
| Mathematical Statistics | 3 | |
or MATH 564 | Regression | |
| Statistical Learning | 3 | |
| Bayesian Computational Statistics | 3 | |
| Computational Mathematics II | 3 | |
| Finite Element Method | 3 | |
or MATH 589 | Numerical Methods for Partial Differential Equations | |
or MATH 590 | Meshfree Methods | |
| Theory and Practice of Fixed Income Modeling | 3 | |
- 1
MATH 540 or MATH 475 may be used to satisfy both the core degree requirements and specialization requirements.
- 2
Students may also select core course options that were not used to satisfy the core course requirement.
Stochastic Computation
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | (12) | |
| MATH 540 | Probability 1 | 3 |
| or MATH 475 | Probability | |
| Select nine credit hours from the following: | 9 | |
| Stochastic Processes | 3 | |
or MATH 543 | Stochastic Analysis | |
| Stochastic Dynamics | 3 | |
| Stochastic Partial Differential Equations | 3 | |
| Monte Carlo Methods | 3 | |
| Bayesian Computational Statistics | 3 | |
| Elective Courses | (0) 2 | |
| Topics in Computer Science (Advanced Scientific Computing) | 3 | |
| Mathematical Modeling | 3 | |
| Applied and Computational Algebra | 3 | |
| Introduction to Time Series | 3 | |
| Statistical Learning | 3 | |
| Reliable Mathematical Software | 0 | |
| Computational Mathematics II | 3 | |
| Numerical Methods for Partial Differential Equations | 3 | |
