2026-2027 Course Catalog

Source: https://catalog.illinois.edu/graduate/las/applied-mathematics-ms/ Parent: https://catalog.illinois.edu/graduate/

for the Master of Science in Applied Mathematics

The MS in Applied Mathematics program is intended for students wishing to pursue a career in applied mathematics. It is also suitable as preparation for a PhD program in Applied Mathematics. It is rare for students to enter the PhD program at the University of Illinois Urbana-Champaign after finishing this degree. Students may choose one of three tracks: Optimization and Algorithms, Applications to the Sciences, or Computational Science and Engineering. This degree program requires 32 credit hours and can normally be completed in 18 months. A master's thesis is optional. Applications are accepted for Fall semester. Financial aid is generally not available.

for the Master of Science in Applied Mathematics

Students pursuing the M.S. in Applied Mathematics have the opportunity to customize the their studies the following ways:

Through the Computational Science and Engineering Concentration.
By completing the coursework for the option in Optimization and Algorithms;
By completing the coursework for the option in Applications to the Sciences;
By completing the coursework for the option in Computational Science and Engineering.

For additional details and requirements refer to the Department of Mathematics Graduate Guide and the Graduate College Handbook.

Thesis Option

Course List

 | Code | Title | Hours |

| --- | --- | --- | | For all options: | | | | Coursework to total 32 hours in MATH or ASRM (in consultation with advisor). | | | | MATH 599 | Thesis Research | 4 | | Choose one of these three (3) options: | | | | Optimization and Algorithms Option | | | | Courses from at least three (3) of the following areas: Optimization, Control Theory and Coding Theory, Combinatorics and Graph Theory, Algorithms and Theory of Computation, Statistics (including core courses listed below) | | 20 | | Select four (4) of the following: | | 12-16 | | MATH 412 | Graph Theory | | | MATH 413 | Intro to Combinatorics | | | MATH/CS 450 | Numerical Analysis | | | MATH/CS 473 | Algorithms | | | ASRM 450/STAT 420 | Methods of Applied Statistics | | | MATH 482 | Linear Programming | | | MATH 484 | Nonlinear Programming | | | Applications to the the Sciences Option | | | | Select three (3) of the following: | | 9-16 | | MATH 489 | Dynamics & Differential Eqns | | | MATH 550 | Dynamical Systems I | | | MATH 553 | Partial Differential Equations | | | MATH 558 | Methods of Applied Mathematics | | | Credit hours in a department other than Mathematics, providing substantive applications of differential equations and applied mathematics. | | 8 | | Computational Science and Engineering Option | | | | MATH 550 | Dynamical Systems I | 4 | | or MATH 553 | Partial Differential Equations | | | Choose one (1) advanced course in Algebra or Analysis: | | 3-4 | | MATH 418 | Intro to Abstract Algebra II | | | MATH 448 | Complex Variables | | | MATH 540 | Real Analysis | | | MATH 542 | Complex Variables I | | | 12 hours from CSE courses (at least 4 in MATH, 4 not in MATH) | | 12 | | Total Hours | | 32 |

Other Requirements

Course List

 | Code | Title | Hours |

| --- | --- | --- | | MATH 405, MATH 415, MATH 444, and MATH 499 cannot be counted toward this graduate degree. | | | | Minimum hours required within the unit: | | 20 | | Minimum 500-level hours required overall: | | 12 (8 in Mathematics) | | Minimum GPA: | | 3.0 | | Total Hours (graduate study) | | 32 |

Non-Thesis Option

Course List

 | Code | Title | Hours |

| --- | --- | --- | | For all options: | | | | Coursework to total 32 hours in MATH or ASRM (in consultation with advisor). | | | | Choose one of these three (3) options: | | | | Optimization and Algorithms Option | | | | Courses from at least three (3) of the following areas: Optimization, Control Theory and Coding Theory, Combinatorics and Graph Theory, Algorithms and Theory of Computation, Statistics (including core courses listed below) | | 20 | | Select four (4) of the following: | | 12-16 | | MATH 412 | Graph Theory | | | MATH 413 | Intro to Combinatorics | | | MATH/CS 450 | Numerical Analysis | | | MATH/CS 473 | Algorithms | | | ASRM 450/STAT 420 | Methods of Applied Statistics | | | MATH 482 | Linear Programming | | | MATH 484 | Nonlinear Programming | | | Applications to the the Sciences Option | | | | Select three (3) of the following: | | 9-16 | | MATH 489 | Dynamics & Differential Eqns | | | MATH 550 | Dynamical Systems I | | | MATH 553 | Partial Differential Equations | | | MATH 558 | Methods of Applied Mathematics | | | Credit hours in a department other than Mathematics, providing substantive applications of differential equations and applied mathematics. | | 8 | | Computational Science and Engineering Option | | | | MATH 550 | Dynamical Systems I | 4 | | or MATH 553 | Partial Differential Equations | | | Choose one (1) advanced course in Algebra or Analysis: | | 3-4 | | MATH 418 | Intro to Abstract Algebra II | | | MATH 448 | Complex Variables | | | MATH 540 | Real Analysis | | | MATH 542 | Complex Variables I | | | 12 hours from CSE courses (at least 4 in MATH, 4 not in MATH) | | 12 | | Total Hours | | 32 |

Other Requirements

Course List

 | Code | Title | Hours |

for the Master of Science in Applied Mathematics

Optimization and Algorithms Track

Students will be able to explain and apply mathematical techniques from at least four of the seven core subjects of graph theory, combinatorics, numerical analysis, algorithms, applied statistics, linear programming, nonlinear programming.
Students will be able to apply mathematical concepts to solve problems in at least three of the following areas: optimization, control theory and coding theory, combinatorics/graph theory, algorithms/theory of computation, statistics.
For thesis track: Students will be able to effectively communicate extended arguments about the applications of mathematics in written form.

Applications to the Sciences Track

Students will be able to explain central definitions and theorems of differential equations and dynamical systems.
Students will be able to explain and apply mathematical modeling techniques that use differential equations and dynamical systems.
Students will be able to explain the application of mathematics to problem solving in one or more of the sciences.
For thesis track: Students will be able to effectively communicate extended arguments about the applications of mathematics in written form.

Computational Science and Engineering (CSE) Track

Students will be able to explain central definitions and theorems of differential equations and dynamical systems.
Students will be able to explain central definitions and theorems of at least one of the core subjects of abstract algebra or real/complex analysis.
Students will be able to use computational techniques to address mathematical problems in the sciences.
For thesis track: Students will be able to effectively communicate extended arguments about the applications of mathematics in written form.

for the Master of Science in Applied Mathematics

Graduate Degree Programs in Mathematics

for the Master of Science in Applied Mathematics

Mathematics Department

Department Chair: Vera Hur\ Director of Graduate Studies: Jared Bronski\ Mathematics Department faculty\ Mathematics faculty research\ 273 Altgeld Hall, 1409 West Green Street, Urbana, IL 61801\ (217) 333-5749\ math-grad@illinois.edu

College of Liberal Arts & Sciences

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Admissions

Mathematics Admissions & Requirements\ Graduate College Admissions & Requirements