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

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

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

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.

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.