Applied and Computational Mathematics

The applied and computational mathematics graduate major provides students with extensive research and educational experiences in modeling, analysis, algorithms, computation and simulation for problems arising throughout mathematics, science and engineering. The ACM major offers studies leading to both the master's and doctoral degrees. The major is designed to prepare students for mathematics careers in academia, research laboratories and industry.

The faculty associated with the ACM major includes a Robert O. Lawton Distinguished Professor and the Sir James Lighthill Distinguished Professor. The faculty maintains a strong research program on a wide range of applications, algorithms and computational techniques with a significant amount of multidisciplinary research including collaborations with faculty in other FSU departments as well as universities around the world. Areas of interest include the theoretical and computational aspects of:

  • aeroacoustics
  • applied partial differential equations
  • fluid and geophysical dynamics
  • rheology of complex fluids
  • Bose-Einstein condensation
  • flow control
  • nanomaterials and nanotechnology
  • uncertainty analysis and quantification
  • digital signal and image processing
  • shape analysis
  • stochastic processes and differential equations
  • dynamical systems
  • optimization
  • differential/integral equations
  • mathematical modeling
  • high-performance and large-scale computing
  • large-scale data analysis

Students are required to have bachelor's in mathematics or closely related area, and computer programming background in a high level compiled language, such as, C++, C, Java or Fortran.

  • Expected course work: Calculus 1, 2, and 3 (multivariate calculus), ordinary differential equations, linear algebra, partial differential equations, real analysis 1 (advanced calculus), and numerical analysis.

  • Preferred course work: Mathematical modeling, complex variables, real analysis 2, statistics, optimization, and advanced numerical algorithms.

Students from engineering or science backgrounds with strong computational or application backgrounds and course work equivalent to a significant portion of the lists above are also encouraged to apply.

Students admitted with minor deficiencies in the prerequisites above may be required by the ACM director or their supervisory committee to take specific courses.

The master's (M.A./M.S.) degree in applied and computational mathematics may be earned by satisfying the requirements of either of the options below.

Course-based option

  • Pass 36 credit hours or more of approved graduate courses, at least 30 of which must be graded, with a GPA of at least 3.0. These courses may not include MAT 5971.
  • Satisfy the ACM Core Course Requirement.
  • Satisfy the ACM Mandatory Course Requirement.

Course Selection Template of ACM Master's Course Option

Year 1 Fall

  • FCM I + FCM-RS
  • MAM I
  • EPDE I

Year 1 Spring

  • FCM II
  • MAM II
  • EPDE II

Year 2 Fall

  • Mandatory 1
  • Mandatory 2
  • Elective

Year 2 Spring

  • Mandatory 3
  • Elective
  • Elective

Two mandatory courses in fall of year 2 followed by one in spring is recommended, but one followed by two is allowed.

Thesis-based option

  • Pass 30 credit hours or more of approved graded graduate courses with a GPA of at least 3.0.
  • Satisfy the ACM Core Course Requirement.
  • Satisfy the ACM Mandatory Course Requirement.
  • Satisfactorily complete 6 credit hours of MAT 5971. These are used as the two of the elective courses that may be taken S/U.
  • Form a supervisory committee chaired by a thesis advisor that includes at least 3 faculty members of the Department of Mathematics.
  • Write a master's thesis under the direction of a thesis advisor and successfully defend it at a Master's Thesis Defense Examination.

The Ph.D. degree in applied and computational mathematics (ACM) is earned by first achieving Ph.D. candidacy and then writing and successfully defending a doctoral dissertation.

Supervisory Committee

  • Appointed by the Chair of the Department of Mathematics and chaired by the Advisor. A co-chair from the Department of Mathematics is required if the Advisor is not a member of the Department of Mathematics.
  • Comprises at least 4 faculty members with Graduate Faculty Status, including the University Representative and 3 faculty members of the Department of Mathematics.
  • Supervises the coursework of the ACM student and monitors progress toward completion.
  • Conducts the Ph.D. Candidacy Examination and the Dissertation Defense Examination.

Course Requirements

  • Pass 36 credit hours of ACM Core, Mandatory, and Elective courses, at least 30 of which must be graded, with a GPA of at least 3.0.
  • Satisfy the ACM Core Course Requirement
  • Satisfy the ACM Mandatory Course Requirement
  • Register for at least 2 credit hours (1 credit hour per semester) of the Mathematics Department colloquium before defending a dissertation.
  • After achieving candidacy, register for Mathematics Department seminar courses in at least 3 semesters for a total of at least 3 credit hours. Note these are in addition to the 2 credit hours for two semesters of MAD 6939 ACM Seminar in the ACM Mandatory Course Requirement.
  • Register for at least 24 semester hours of Dissertation Research MAT 6980 before defending a dissertation.

Ph.D. Candidacy Requirements

  • Satisfy the ACM Core Course Requirement.
  • Pass the ACM Core Course Qualifying Examination.
  • Pass the Ph.D. Candidacy Examination.

Expected Progress Towards Candidacy

  • ACM students entering the major with a master's degree or suitably advanced background, should consult the ACM director to adapt the coursework to satisfy the ACM Core and Mandatory Courses Requirements.
  • ACM students are expected to satisfy the ACM Core and Mandatory Courses Requirements in the first two years of their ACM study at which time students are encouraged to apply for a Master's under the course-based option.
  • ACM Students are expected to become a Ph.D. Candidate in their third year of study.

Course Selection Template in Years 1 and 2 of ACM Ph.D. Study

Year 1 Fall

  • FCM I + FCM-RS
  • MAM I
  • EPDE I

Year 1 Spring

  • FCM II
  • MAM II
  • EPDE II

Year 2 Fall

  • Mandatory 1
  • Mandatory 2
  • Elective
  • ACM Seminar

Year 2 Spring

  • Mandatory 3
  • Elective
  • Elective
  • ACM Seminar

Two mandatory courses in fall of Year 2 followed by one in spring is recommended, but one followed by two is allowed.

Dissertation Requirements

  • Students must write a dissertation under the direction of a faculty advisor and successfully defend it at a Dissertation Defense Examination.
  • The defense must be within 5 years of admittance to candidacy. If it is not, the candidacy of the student may be reevaluated by repeating qualifying and/or candidacy examinations.

Core Course Requirements

ACM students are encouraged to attend department seminars and take courses throughout their graduate study in mathematics. These include required core courses, courses supporting admission to candidacy, courses supporting your dissertation research, and courses, both advanced and basic, intended to broaden ACM students' applied and computational mathematics expertise.

The 18 credit hour core of the ACM curriculum comprises 3 two-semester course sequences. These sequences provide a rigorous basic background and a basis upon which advanced courses and research can build.

Students must satisfy the ACM Core Course Requirement by passing, with a grade of C- or better, the FCM, MAM and EPDE sequences. MAT 5939 the FCM Recitation Seminar is recommended but not required.

Students are expected to take the core courses in the first year of their ACM studies.

Students with an advanced background may satisfy the ACM Core Course Requirement with related advanced courses as approved by the ACM director.

Sequence: FCM

  • Courses: MAD 5403/5404 Foundations of Computational Mathematics I and II

Sequence: EPDE

  • Courses: MAP 5345/5346 Elementary Partial Differential Equations I and II

Sequence: MAM

  • Courses: MAP 5165 Methods of Applied Mathematics I; MAP 5423 Complex Variables, Asymptotic Expansions and Integral Transforms (MAM II)

Mandatory Course Requirements

ACM Master's students must satisfy a 9 credit hour Mandatory Course Requirement and ACM Ph.D. students must satisfy an 11 credit hour Mandatory Course Requirement.

Both ACM master's and Ph.D. students must pass, with a grade of C- or better, any three of the group of advanced courses listed below for 9 credit hours. This list will be modified periodically to adapt to the research interests of departmental faculty and ACM students.

Additionally, two semesters of MAP 6939 ACM Seminar (1 credit hour per semester) are mandatory for ACM Ph.D. students.

Students are expected to satisfy the Mandatory Course Requirement in the second year of their ACM studies.

ACM Mandatory Courses

  • MAP 6939 ACM Seminar
  • MAP 5217 Calculus of Variations
  • MAP 5395 Finite Element Methods
  • MAP 6356 Advanced Partial Differential Equations
  • MAP 5XXX Stochastic Computing and Optimization
  • MAD 5738 Numerical Solution of Partial Differential Equations I
  • MAD 5739 Numerical Solution of Partial Differential Equations II
  • MAD 5932 Numerical Linear Algebra
  • MAD 5420 Numerical Optimization

The course requirements expected to be completed by the end of a student's second year of study in ACM include 9 credit hours of electives. These can be courses from the Mandatory Class List in addition to the three selected for the Mandatory Course Requirement or other relevant courses in the Department of Mathematics. Elective courses outside the Department of Mathematics are allowed but must be approved by the director of ACM.

Students are encouraged to discuss the selection of elective courses to be taken in their second year of ACM study with potential advisors, the ACM director and instructors of particular courses as part of their planning for their Ph.D. Candidacy Examination and choosing their areas of dissertation research.

Additionally, ACM students are encouraged to take courses throughout their graduate study to support their particular research interests and to broaden their knowledge of mathematics and related areas. Also, given the broad nature of the areas of interest for ACM students, courses associated with the biomathematics and financial mathematics programs as well as other departments, such as, statistics, scientific computing, and computer science may also be of interest and the courses offered in those departments should be consulted each semester.

Note that in addition to regular courses many advanced topics are taught intermittently as special topics courses, e.g., MAD 5932 Topics in Computational Mathematics, MAP 5932 Topics in Applied Mathematics, MAD 6408 Advanced Topics in Numerical Analysis, MAP 6437 Advanced Topics in Applied Mathematics, and seminars such as MAD 6939 Advanced Seminar in Scientific Computing. Each of these may have several sections per semester and groups of students are encouraged to make requests for such courses on topics in which they are interested.

Some Suggested Elective Courses for ACM Students

  • MAA 5616 Measure and Integration I
  • MAA 5617 Measure and Integration II
  • MAA 5406 Complex Variables I
  • MAA 5407 Complex Variables II
  • MAA 5XXX Functional Analysis
  • MAP 5107 Mathematical Modeling
  • MAP 5207 Optimization
  • MAP 5431 Introduction to Fluid Dynamics
  • MAP 5513 Wave Propagation Theory
  • MAP 5615 Monte Carlo Methods in Financial Math
  • MAP 5XXX Stochastic Analysis
  • MAP 5932 Stochastic Differential Equations
  • MAP 6416 Topics in Stochastic Calculus
  • MAD 5305 Graph Theory
  • MAD 5306 Graph Theory and Networks
  • MAD 5427 Numerical Optimal Control of Partial Differential Equations
  • MAD 5745 Spectral Methods for Partial Differential Equation
  • MAD 5757 High Order Finite Difference Methods for Computational Acoustics and Fluid Dynamics
  • MAD 5XXX Principles and Foundations of Machine Learning (New)
  • MTG 5356 Topological Data Analysis
  • STA 5106 Computational Methods in Statistics I
  • STA 5107 Computational Methods in Statistics II
  • STA 5635 Applied Machine Learning
  • STA 6468 Advanced Topics in Probability and Statistics
    • Shape and Functional Data Analysis
  • ISC 5305 Scientific Programming
  • ISC 5307 Scientific Visualization
  • ISC 5308 Computational Aspects of Data Assimilation