Graduate Department of Scientific Computing

College of Arts and Sciences

Website: https://sc.fsu.edu

Chair: Beerli; Professors: Beerli, Erlebacher, Lemmon, Meyer-Baese, Plewa, Shanbhag, Speer, Wang; Associate Professors: Huang, Quaife; Assistant Professors: Chipilski, Dexter, Zavala Romero; Professor Emeritus: Gunzburger, Navon, Peterson; Courtesy Faculty: Algee-Hewitt, Barbu, Chi, Crock, Duke, Ke, Linn, Mascagni, Mashayekhi, Moore, Petersen, Pinker-Domenig, Ridley, Tahmassebi, Ye

Program Overview

Over the last few decades, computations have joined theory and experimentation to form the three pillars of scientific discovery and technological design. Many of the critical problems facing society can only be solved by teams of individuals from a variety of disciplines. Integral to these teams are computational scientists, who provide the simulation, optimization, and visualization algorithms used to solve problems on computers. The main activity of scientific computing is the development of computational tools that have applicability over a range of scientific disciplines.

The Department of Scientific Computing houses faculty interested in the invention, analysis, implementation, and application of computational algorithms to problems arising in several new and traditional disciplines. Examples include biology, chemical engineering, chemistry, computer science, fire dynamics, geology and geophysics, material science, mathematics, mechanical engineering, medicine, physics and astrophysics. An increasing number of algorithms involve machine learning and data science. Faculty and graduate students are supported in their research by several federal, state, laboratory, and commercial organizations. Further breadth and depth are added to the research and educational missions of the department through faculty from other departments at Florida State University and individuals from several national laboratories who interact closely with our faculty. These faculty members ensure that the department is ideally positioned to offer innovative degree programs that impart a synergy between the mathematical and applications-driven aspects of scientific computing, thus providing the student with extensive interdisciplinary training.

Students are trained and to conduct research in a truly interdisciplinary environment. The graduate programs offered by the Department of Scientific Computing are designed to provide broad training in the core methods of computational science across disciplines, followed by in-depth specialization in areas of particular interest to students. Even within specializations, the focus remains on interdisciplinary approaches to solving science and engineering problems.

The Department of Scientific Computing offers degree programs leading to the Master of Science (M.S.) and Doctor of Philosophy (Ph.D) in Computational Science and to a Master's degree in Data Science. Please refer to the Department of Scientific Computing Website at https://sc.fsu.edu/ for the latest information about these programs, including new courses. The degree in Computational Science further subdivides into various specialized degree programs, including Atmospheric Science, Fire Dynamics, and Geophysical Fluid Dynamics.

The Geophysical Fluid Dynamics (GFD) Degree Program is based in the Department of Scientific Computing and leads to a doctoral degree in Computational Sciences with a specialization in either GFD or Fire Dynamics (FD). It is an interdisciplinary field of study whose primary goal is an improvement in our fundamental understanding of fluid flows that occur naturally, including such diverse topics as climate and paleoclimate, ocean and atmospheric processes, hydrology and karst dynamics, air-sea interaction, wild and fire dynamics, double-diffusive processes, and hurricane dynamics with strong links to the Applied Mathematics Program. The approach to this understanding is through quantitative analysis of observational data, laboratory experimentation, and theoretical, mathematical, and numerical modeling. A geophysical fluid dynamicist must have a firm grasp of the fundamental principles of classical physics, knowledge of the techniques of applied mathematics, and an interest in the natural sciences. The course of study leading to a degree in Computational Sciences with a specialization in GFD or FD is flexible, suitable for students with a range of backgrounds, and rewarding as the student gains an overview of the geophysical sciences not available from a program of study in a single discipline.

Facilities associated with the GFD and FD majors are situated in the Geophysical Fluid Dynamics Institute (https://gfdi.fsu.edu).

Computational Resources

The Department of Scientific Computing oversees a diverse computing infrastructure in support of research and education. Computing resources include clusters and computational servers, a bioinformatics server, and more. To best accommodate research, education, and application development, the department maintains a heterogeneous desktop and workstation environment, as well as a state-of-the-art computer classroom. In addition, the department's Computational Intelligence Laboratory provides high-powered visualization and computational resources to the FSU community for research, analysis of large data collections, and research in machine learning and education.

Admission Requirements

Note: Please review all University and college-wide degree requirements summarized in the “College of Arts and Sciences” chapter of this Graduate Bulletin.

Major in Computational Science

Students considering graduate work in computational science should exhibit a strong desire to develop, analyze, implement, and apply computational algorithms. Typically, incoming students will hold a bachelor's degree in mathematics, computer science, statistics, computational science, or a science or engineering discipline, and will be knowledgeable of at least one object-oriented programming language.

Applications for admission to the graduate programs in Computational Science are submitted to the Graduate School at Florida State University. An application form for admission that includes an official transcript from each college attended, a transcript of Graduate Record Examinations (GRE) scores, and the application fee, should be sent to the Office of Admissions, A2500 University Center, Florida State University, Tallahassee, FL 32306-2400.

The department also requests: 1) a letter of intent that explains the basis for the applicant's pursuit of the degree and their experience and commitment to the field of computational science, 2) a curriculum vitae, and 3) three letters of recommendation from individuals with knowledge of the applicant's education or professional background. Instructions can be found at https://sc.fsu.edu/graduate/application. A student seeking admission to the program should have taken the aptitude test of the Graduate Record Examinations (GRE) within the last three years with a minimum percentile placement of 50 and 70 in the verbal and analytical sections, respectively. Foreign nationals whose native language is not English must meet Florida State University's minimum TOEFL examination requirement.

The student should also refer to the Department of Scientific Computing Website at https://sc.fsu.edu/education or contact the Associate Chair for Graduate Studies for any revisions to the requirements listed above since the publication of this document.

Specialization Fire Dynamics

Students apply to the Geophysical Dynamics program through the Department of Scientific Computing or through the Geophysical Fluid Dynamics Institute. Students are accepted into the program on the basis of their academic record, their Graduate Record Examinations (GRE), Test of English as a Foreign Language (TOEFL) score (for international students), and their letters of recommendation. To be admitted, students must have achieved a “B” average (a 3.0 average on a 4.0 scale for all upper division work) of their baccalaureate degree (or any graduate degree work they may have taken) and earned a GRE score at the 50th percentile or better on the verbal section and on the quantitative section. Students expecting to receive financial assistance will need a significantly higher GRE score. Foreign nationals are expected to have a score of 80 or better on the Internet based TOEFL, 6.5 on the IELTS examination or 77 on the MELAB examination.

Specialization in Geophysical Fluid Dynamics

Students apply to the Geophysical Dynamics program through the Department of Scientific Computing or through the Geophysical Fluid Dynamics Institute. Students are accepted into the program on the basis of their academic record in science and mathematics, their Graduate Record Examinations (GRE), Test of English as a Foreign Language (TOEFL) score (for international students), and their letters of recommendation. To be admitted, students must have achieved a “B” average in the science and mathematics portions of their baccalaureate degree work (or any graduate degree work they may have taken) and earned a GRE score at the 50th percentile or better on the verbal section and on the quantitative section. Students expecting to receive financial assistance (see below) will need a significantly higher GRE score. Foreign nationals are expected to have a score of 80 or better on the Internet-based TOEFL, 6.5 on the IELTS examination, or 77 on the MELAB examination.

Master's Degree

The MS degrees in Computational Science and Data Science are intended for students who wish to terminate their graduate studies with the M.S. degree but whose primary career goal is to be a part of a research team in a non-academic environment. It is also appropriate for students seeking a Ph. D. in Computational Science but also wants to obtain an M.S. degree.

These degrees require a total of thirty semester hours. Required for the M.S. in Computational Science are ISC 5305 and ISC 5315 (totaling seven semester hours), a minimum of nine hours from remaining computational science courses with an ISC prefix, a minimum of six hours from approved courses from other departments, and a minimum of two hours of seminars. The remaining six semester hours must be satisfied through additional approved course work, thesis hours, seminars, etc. Furthermore, a student must write and defend a thesis or project if the thesis or project option is selected.

Detailed, up-to-date information about the M.S. degree in Computational Science can be found in the Graduate Handbook available on the Department of Scientific Computing website at https://sc.fsu.edu/graduate/handbook. More details about the M.S. in Data Science can be found in the Data Science program chapter of this Graduate Bulletin.

Doctoral Degree

Major in Computational Science

The doctoral degree is awarded in recognition of the student's broad knowledge of computational science and the student's ability to conduct original, independent research in computational science. To complete the requirements for a doctoral degree, the student must 1) complete the requisite course work, 2) satisfactorily complete preliminary examinations for admission to candidacy, 3) choose a major professor and supervisory committee, 4) submit and defend a dissertation prospectus to their supervisory committee, and 5) complete independent research in computational science culminating in a written dissertation which must be successfully defended to their supervisory committee.

The doctoral degree in Computational Science has several tracks that allow students to specialize in a specific applied science or engineering discipline. All tracks require the same number of total semester hours and the same core courses. To obtain a specialization in a particular area a student must take a minimum of nine semester hours (approved by their supervisory committee) in the area. Current areas of specialization include: atmospheric science, biochemistry, biological science, fire dynamics, materials science, fluid dynamics, geophysical fluid dynamics, and physics.

Detailed, up to date information about the Ph.D. degree in Computational Science can be found in the Graduate Handbook available on the Department of Scientific Computing website.

Specialization in Geophysical Fluid Dynamics

The interdepartmental graduate program of study leads to the Doctor of Philosophy (Ph.D.) degree; currently there is no Master's degree offered. The program is administered by the Geophysical Fluid Dynamics Institute and has its own separate degree requirements. It differs from the regular departmental offerings in the Earth sciences mainly through its interdisciplinary approach and emphasis on the fundamentals of mathematics, physics, and fluid dynamics, with less focus on descriptive material from any one discipline.

Specialization in Fire Dynamics

The interdepartmental graduate program of study leads to the Doctor of Philosophy (Ph.D.) degree; currently, there is no master's degree offered. The program is administered by the Geophysical Fluid Dynamics Institute and has its own separate degree requirements. It differs from the regular departmental offerings in the Earth sciences mainly by its interdisciplinary approach and emphasis on the fundamentals of mathematics, physics, and fluid dynamics, with less focus on descriptive material from any one discipline.

Coursework

Required courses across the three majors are ISC 5305 and ISC 5315. The remaining required courses depend on each of the three majors in the department: Computational Science, Fire Dynamics, and Geophysical Fluid Dynamics.

Major in Computational Science

In addition to the two required courses, students are required to take ISC 5316 and ISC 5318, a minimum of nine semester hours from remaining computational science courses with the prefix ISC, a minimum of nine semester hours among approved courses from other departments, a minimum of six seminar semester hours, and a minimum of 24 semester hours of dissertation. Additional semester hours can be chosen from other courses, seminars, dissertation credit, etc., approved by the student's supervisory committee to meet the total number of 62 semester hours and to satisfy the University's minimum course requirement.

Specialization in Geophysical Fluid Dynamics

The program of study for students is individually tailored to meet their particular needs and interests. The formal requirements are few and include completion of coursework from several different departments with a grade of “B” or better, participation in a seminar at least two times, mastery of modern computer techniques, particularly numerical analysis and the two Common Core Courses: Scientific Programming (ISC 5305) and Applied Computational Science-1 (ISC 5315). The remainder of the curriculum is chosen by the advisory committee in consultation with the student based on the student's program of study. There is no foreign language requirement. The remainder of the curriculum is usually chosen from among courses offered by several departments. Typically, students, in consultation with their advisory committee, will choose courses from Engineering, Geological Sciences, Mathematics, Meteorology, Oceanography, Physics, Scientific Computing, and Statistics. The courses in each discipline are listed at https://sc.fsu.edu/graduate/phd/gfd.

GFD 6925 Geophysical Fluid Dynamics Colloquium (1). (S/U grade only).

Major in Fire Dynamics

The program of study for students is individually tailored to meet their particular needs and interests. The formal requirements are few and include completion of coursework from several different departments with a grade of “B” or better, participation in a seminar at least two times, mastery of modern computer techniques, particularly numerical analysis and the two Common Core Courses: Scientific Programming (ISC 5305) and Applied Computational Science-1 (ISC 5315) is the common core for all students. The remainder of the curriculum is chosen by the advisory committee in consultation with the student based on the student's program of study. There is no foreign language requirement. The remainder of the curriculum is generally chosen from among courses offered by several departments. Typically, students, in consultation with their advisory committee, will select courses from Engineering, Geological Sciences, Mathematics, Meteorology, Oceanography, Physics, Scientific Computing, and Statistics.

In addition to the two required courses, students will take the fire dynamics core courses and an additional 12 credit hours from elective courses. The core courses in FD are as follows:

GFD 6935 Fire Dynamics Seminar (1–2), and a Field School beginning in Spring 2022.

Major Professor and Supervisory Committee

The major professor and supervisory committee play a crucial role in guiding the student's training by approving a program of study, approving the student's prospectus, and certifying that the student can conduct original and independent research and communicate the results orally and in writing. As early as possible, a student should identify an area of research interest and obtain an informal agreement with a Department of Scientific Computing faculty member to serve as their major advisor. The student and advisor should subsequently establish the student's supervisory committee. In concert with the interdisciplinary nature of the Ph.D. degree program, students may have co-major advisors.

Prospectus

After the student has successfully completed the preliminary examinations and has been admitted to candidacy, the student is required, within a year, to submit to the supervisory committee a written summary of the proposed research that will comprise their dissertation. The prospectus must be successfully defended to the student's supervisory committee.

Dissertation

After completion of the original research proposed in the prospectus, the student must write a dissertation document that must comply with all current University standards for style. The dissertation must be successfully defended to the student's supervisory committee.

Definition of Prefixes

CAP—Computer Applications

GFD—Geophysical Fluid Dynamics

IDS— Interdisciplinary Studies

ISC—Interdisciplinary Sciences

MAD—Mathematics: Discrete

MAP—Mathematics Applied

Graduate Courses

Note: Each of the courses listed below includes the prerequisites according to their FSU course number.

CAP 5771. Data Mining (3). Prerequisite: ISC 3222 or ISC 3313 or ISC 4304C or COP 3330 or COP 4530 or instructor permission. This course enables students to study concepts and techniques of data mining, including characterization and comparison, association rules mining, classification and prediction, cluster analysis, and mining complex types of data. Students also examine applications and trends in data mining.

GFD 5936r. Advanced Topics in Fire Dynamics—Research Seminar (1). (S/U grade only). Prerequisites: General knowledge of natural and environmental sciences; the ability to perform relatively simple mathematical formulations of natural phenomena; and enrollment in a relevant program. This seminar course exposes students to fire dynamics research through a variety of methods. Specific research topics of fire dynamics will be addressed by group discussion of ongoing student research, faculty research, and outside speakers. May be repeated to a maximum of four credit hours.

GFD 6905r. Directed Individual Study (3). (S/U grade only). May be repeated to a maximum of nine credit hours. May be repeated within the same term.

GFD 6915r. Supervised Research (1–5). (S/U grade only). May be repeated to a maximum of five credit hours. May be repeated within the same term.

GFD 6925. Geophysical Fluid Dynamics Colloquium (1). (S/U grade only).

GFD 6935r. Seminar (1–2). May be repeated to a maximum of two credit hours. May be repeated within the same term.

GFD 6980r. Dissertation (1–12). (S/U grade only). A student may not enroll for GFD 6980r before passing the preliminary (comprehensive) examination. Students must establish their ability to handle modern computer techniques applicable to their research.

GFD 8964r. Doctoral Preliminary Examination (0). (P/F grade only.) Maybe be repeated within the same term.

GFD 8985r. Dissertation Defense (0). (P/F grade only.) Maybe be repeated within the same term.

IDS 5945. Data Science Internships (0–3). This course facilitates the transition from the academic world to the workplace in the data science industry. It allows students to familiarize themselves with issues that they will encounter in the workplace and to apply the knowledge acquired in academic courses in a real-world setting. May be repeated to a maximum of six credit hours.

ISC 5225. Molecular Dynamics: Algorithms and Applications (3). Prerequisites: ISC 5305; MAC 2311, 2312. This course provides a comprehensive introduction to molecular dynamics simulation algorithms and their corresponding applications in molecular science.

ISC 5226. Numerical Methods for Earth and Environmental Sciences (3). Prerequisites: ISC 5305; MAC 2311, 2312. Application of numerical methods to the solution of scientific problems for earth and environmental sciences.

ISC 5227. Survey of Numerical Partial Differential Equations (3). Prerequisite: ISC 5305. This course provides an overview of the most common methods used for numerical partial differential equations. These include techniques such as finite differences, finite volumes, finite elements, discontinuous Galerkin, boundary integral methods, and pseudo-spectral methods.

ISC 5228. Monte Carlo Methods (3). Prerequisites: ISC 5305; MAC 2311, 2312. This course provides an introduction to probabilistic modeling and Monte Carlo methods (MCMs) suitable for graduate students in science, technology, and engineering. It provides an introduction to discrete event simulation, MCMs and their probabilistic foundations, and the application of MCMs to various fields. In particular, Markov chain MCMs are introduced, as are the application of MCMs to problems in linear algebra and the solution of partial differential equations.

ISC 5237. Uncertainty Analysis in Computational Science (3). Prerequisite ISC 5226 or instructor permission. This course includes lectures and computer labs for understanding various uncertainty sources in computational science. Methods are taught for quantifying the uncertainties and their propagation through mathematical and computational modeling. Students learn how to communicate the uncertainty qualification to colleagues and decision makers. They also discuss how to reduce predictive uncertainty to improve the scientific understanding of complex systems.

ISC 5238C. Scientific Computing for Integral Equation Methods (3). Prerequisites: MAD 3703 and MAP 4341; ISC 4232; or instructor permission. This course covers key algorithms that are required when solving integral equations.

ISC 5247C. Geometric Morphometrics: An Introduction to Modern Methods of Applied Shape Analysis (3). Prerequisite: STA 2122, STA 2171, or equivalent. In this course, students learn about the mathematical, statistical, computational, and practical aspects of the quantitative analysis of shape. This course provides the basic background that allows those who need to use such techniques to address research questions in their own work the means to effectively do so. It also provides students coming from a more computational or quantitative background the knowledge and understanding of the methods and problems of the field so that they might contribute to the development of new and/or improved methods of shape analysis.

ISC 5249C. Computational Forensics: An Introduction to Objective, Quantitative Tools, and Methods for Forensic Science (3). Prerequisites: STA 2122, STA 2171, or equivalent, or instructor permission. In this course, students investigate some of the methods and protocols of Computational Forensics with an emphasis on the analysis and interpretation of physical evidence. Topics include stature, sex, and ancestry estimation from skeletal remains, DNA analysis, fingerprint, toolmark, and bloodstream analysis. Students develop their own simple programs in an appropriate programming language to build and verify models and use existing programs to investigate the processing and analysis of physical evidence.

ISC 5305. Scientific Programming (3). Prerequisites: Working knowledge of one programming language (C++, Fortran, Java), or instructor permission. This course focuses on object-oriented coding in C++, Java and Fortran 90 with applications to scientific programming. Discussion of class hierarchies, pointers, function and operator overloading and portability. Examples include computational grids and multidimensional arrays.

ISC 5307. Scientific Visualization (3). Prerequisites: CGS 4406, ISC 5305, or instructor permission. The course covers the theory and practice of scientific visualization. Students learn how to use state-of-the-art visualization toolkits, create their own visualization tools, represent both 2-D and 3-D data sets, and evaluate the effectiveness of their visualizations.

ISC 5308. Computational Aspects of Data Assimilation (3). Prerequisites: MAC 2311, MAC 2312, MAS 3105, ISC 5305, or instructor permission. This course explores common methods of data assimilation, such as Kalman filtering, ensemble filter, particle and hybrid filters, and variational methods. These methods are introduced and derived in the context of both variational and estimation theory with an emphasis on computational aspects, using simple models and current research materials.

ISC 5314. Verification and Validation in Computational Science (3). Prerequisites: MAC 2312, MAS 3105, or ISC 5315; or instructor permission. This course covers the theory and practice of verification and validation in computational sciences. Students learn basic terminology, are exposed to procedures and practical methods used in software implementation validation and in solution verification, employ exact and manufactured solutions, and explore elements of software quality assurance. The course introduces essential data analysis techniques and reviews software development and maintenance tools. Examples from physical sciences and engineering are used to illustrate aspects of code variation, including validation hierarchy, validation benchmarks, uncertainty quantification and simulation code predictive capabilities. The computational laboratory is an essential part of this course.

ISC 5315. Applied Computational Science I (4). Prerequisites: ISC 5305; MAP 2302; or instructor permission. This course provides students with high-performance computational tools necessary to investigate problems arising in science and engineering, with an emphasis on combining them to accomplish more complex tasks. A combination of course work and lab work provides the proper blend of theory and practice with problems culled from the applied sciences. Topics include numerical solutions to ODEs and PDEs, data handling, interpolation and approximation, and visualization.

ISC 5316. Applied Computational Science II (4). Prerequisite: ISC 5315 or instructor permission. This course provides students with high-performance computational tools necessary to investigate problems arising in science and engineering, with an emphasis on combining them to accomplish more complex tasks. A combination of course work and lab work provides the proper blend of theory and practice with problems culled from the applied sciences. Topics include mesh generation, stochastic methods, basic parallel algorithms and programming, numerical optimization, and nonlinear solvers.

ISC 5317. Computational Evolutionary Biology (4). Prerequisites: ISC 5224, ISC 5306, or instructor permission. This course presents computational methods for evolutionary inferences. Topics include the underlying models, the algorithms that analyze models, and the creation of software to carry out the analysis.

ISC 5318. High-Performance Computing (3). Prerequisites: ISC 5305 or equivalent or instructor permission. This course introduces high-performance computing, term which refers to the use of parallel supercomputers, computer clusters, as well as software and hardware in order to speed up computations. Students learn to write faster code that is highly optimized for modern multi-core processors and clusters, using modern software-development tools and performance analyzers, specialized algorithms, parallelization strategies, and advanced parallel programming constructs.

ISC 5326. Introduction to Game Design and Simulator Design (3). This course introduces basic techniques used to design and implement computer games and/or simulation environments. Topics include a historical overview of computer games and simulators, game documents, description and use of a game engine, practical modeling of objects and terrain, as well as the use of audio. Physics and artificial intelligence in games are covered briefly. Programming is based on a scripting language. The course is divided into lectures and practical assignments. Course topics are assimilated through the design of a 3D game to be designed and implemented in a team environment.

ISC 5415. Computational Space Physics (3). Prerequisites: MAC 2312, MAS 3105, or instructor permission. This course offers an introduction to numerical methods in the context of observational and theoretical astrophysics. The course covers interpolation, approximation, minimization and optimization, solution of linear systems of equations, random number generation, function integration, numerical differentiation, numerical integration of ordinary differential equations, stiff systems of ODEs, survey of methods for partial differential equations (Poisson equation, heat diffusion, and hydrodynamics).

ISC 5425. Introduction to Bioinformatics (4). Bioinformatics provides a quantitative framework for understanding how the genomic sequence and its variations affect the phenotype. This course is designed for biologists and biochemists seeking to improve their quantitative data interpretation skills, and for mathematicians, computer scientists and other quantitative scientists seeking to learn more about computational biology. Laboratory exercises are designed to reinforce classroom learning.

ISC 5473. Introduction to Density Functional Theory (3). Prerequisites: CHM 3400; PHY 3101; MAC 2312; MAP 2302; or MAP 3305; or Instructor permission. Note: Basic knowledge of quantum mechanics or differential equations is preferred. Prior programming skills are not required. This course introduces density functional theory (DFT), which is widely used in industry and academia to calculate the properties of molecules and materials. This course covers basic concepts of DFT, the numerical implementation of DFT, building molecules and crystals for DFT simulations, and operating open-source DFT software.

ISC 5906r. Directed Individual Study in Computational Science (1–12). Prerequisite: Instructor permission. The course covers selected topics as designated by the students and the directing professor. May be repeated to a maximum of twenty-four semester hours.

ISC 5907r. Directed Individual Study in Computational Science (1–12). (S/U grade only). Study on a selected topic as designated by the student and the directing professor. May be repeated to a maximum of twenty-four semester hours.

ISC 5934r. Introductory Seminar on Research in Computational Science (1). (S/U grade only). A series of lectures given by faculty on research being conducted in the Department of Scientific Computing.

ISC 5935r. Selected Topics in Computational Science (3–12). (S/U grade only). Selected research topics that are not covered by other courses. May be repeated to a maximum of twelve semester hours.

ISC 5939r. Advanced Graduate Student Seminar in Computational Science (1–3). (S/U grade only). A series of lectures given by faculty, students or outside scholars on research and research methods related to computational science. May be repeated within the same term to a maximum of twelve semester hours.

ISC 5948r. Graduate Internship in Computational Science (3–6). (S/U grade only). Supervised internship individually arranged to accommodate professional development. May be repeated to a maximum of six semester hours.

ISC 5975r. Thesis (3–12). (S/U grade only). A minimum of six semester hours is required.

ISC 6981r. Dissertation (1–12). (S/U grade only). Prerequisite: Advisor approval. A minimum of twenty-four semester hours is required for Ph.D. degree.

ISC 8963r. Master's Comprehensive Examination (0). (P/F grade only.) Prerequisite: Advisor approval. May be repeated with instructor permission.

ISC 8964r. Doctoral Qualifying Examination (0). (P/F grade only.) Prerequisite: Advisor approval. May be repeated with instructor permission.

ISC 8965r. Doctoral Preliminary Examination (0). (P/F grade only.) Prerequisite: Advisor approval. May be repeated with instructor permission.

ISC 8977r. Master's Thesis Defense (0). (P/F grade only.) Prerequisite: Advisor approval. May be repeated with instructor permission.

ISC 8982r. Dissertation Defense (0). (P/F grade only.) Prerequisite: Advisor approval. May be repeated with instructor permission.

MAD 5420. Numerical Optimization (3). Prerequisites: MAC 2313; MAS 3105; C, C++, or Fortran. This course covers unconstrained minimization: one-dimensional, multivariate, including steepest-descent, Newton's method, Quasi-Newton methods, conjugate-gradient methods, and relevant theoretical convergence theorems. Constrained minimization: Kuhn-Tucker theorems, penalty and barrier methods, duality, and augmented Lagrangian methods. Introduction to global minimization.

MAD 5427. Numerical Optimal Control of Partial Differential Equations (3). Prerequisites: MAD 5739; MAS 3105. This course covers Euler Lagrange equations, adjoint method algorithm, optimal control of systems governed by elliptic, parabolic, hyperbolic PDEs, control of initial and boundary conditions, adjoint sensitivity analysis, optimal parameter estimation, Kalman filter for parameter identification, and automatic differentiation techniques.

MAP 5395. Finite Element Methods (3). Prerequisites: MAD 5738 and, C++ or Fortran. This course covers the methods of weighted residuals, finite element analysis of one and two-dimensional problems, isoparametric elements, time-dependent problems, algorithms for parabolic and hyperbolic problems, applications, advanced Galerkin techniques.