math phd gatech

Limited Business Hours

The Office of Graduate Education will be participating in a week-long training from July 29 – August 2, 2024. During this week we will have limited business hours. The office will be closed on Monday, July 29 and on Thursday, August 1 from 1 p.m. until 4 p.m. We appreciate your patience with our response time during this week and will do our best to respond to all inquiries as quickly as we can.

Graduate Education

Office of graduate and postdoctoral education, mathematics, program contact.

Graduate Coordinator Georgia Institute of Technology 686 Cherry St. NW Skiles, Room 117 Atlanta, GA 30332-0340

Application Deadlines

December 15

Admittance Terms

Degree programs.

• Master's, Mathematics
• Ph.D., Mathematics

Areas of Research

• Applied and Computational Math
• Differential Equations
• Discrete Mathematics
• Dynamical Systems
• Geometry and Topology
• Mathematical Biology
• Mathematical Physics
• Probability and Statistics

Standardized Tests

TOEFL Requirements

• Institute Code: 5248
• Department Code: 72
• Internet-based: 96, with minimum section scores of 19

IELTS Academic Requirements

• Minimum Score Required: ≥ 7 (minimum band score for Reading, Listening, and Speaking is 6.5; minimum band score for Writing is 5.5)
• Official scores must be sent via the  IELTS electronic score delivery service to Georgia Institute of Technology, ​Graduate

GRE Requirements

• Institute Code: R5248
• Department Code: 0703
• GRE General Exam -  Optional for Fall 2023 admissions
• GRE Subject Exam -  Optional for Fall 2023 admissions
• Minimum Score Required:  N/A

Application Requirements

• Three Letters of Recommendation
• Statement of Purpose

Program Costs

• Go to " View Tuition Costs by Semester ," and select the semester you plan to start. Graduate-level programs are divided into sections: Graduate Rates–Atlanta Campus, Study Abroad, Specialty Graduate Programs, Executive Education Programs
• Find the degree and program you are interested in and click to access the program's tuition and fees by credit hour PDF.
• In the first column, determine the number of hours (or credits) you intend to take for your first semester.
• Determine if you will pay in-state or out-of-state tuition. Learn more about the difference between in-state and out-of-state . For example, if you are an in-state resident and planning to take six credits for the Master of Architecture degree, the tuition cost will be $4,518.
• The middle section of the document lists all mandatory Institute fees. To see your total tuition plus mandatory fees, refer to the last two columns of the PDF.

Program Links

The Office of Graduate Education has prepared an admissions checklist to help you navigate through the admissions process.

Mathematics (MATH)

MATH 6001. Introduction to Graduate Studies in Mathematics. 2 Credit Hours.

This course covers practical information helping students start their careers as a professional mathematician. It also satisfies the Georgia Tech RCR requirements for "in-person" training.

MATH 6014. Graph Theory and Combinatorial Structures. 3 Credit Hours.

Fundamentals, connectivity, matchings, colorings, extremal problems, Ramsey theory, planar graphs, perfect graphs. Applications to operations research and the design of efficient algorithms.

MATH 6021. Topology of Euclidean Spaces. 3 Credit Hours.

Metric spaces, normed linear spaces, convexity, and separation; polyhedra and simplicial complexes; surfaces; Brouwer fixed point theorem.

MATH 6112. Advanced Linear Algebra. 3 Credit Hours.

An advanced course in Linear Algebra and applications.

MATH 6121. Modern Abstract Algebra I. 3 Credit Hours.

Graduate-level linear and abstract algebra including groups, finite fields, classical matrix groups and bilinear forms, multilinear algebra, and matroids. First of two courses.

MATH 6122. Modern Abstract Algebra II. 3 Credit Hours.

Graduate-level linear and abstract algebra including rings, fields, modules, some algebraic number theory and Galois theory. Second of two courses.

MATH 6221. Probability Theory for Scientists and Engineers. 3 Credit Hours.

Classical introduction to probability theory including expectation, notions of convergence, laws of large numbers, independence, large deviations, conditional expectation, martingales, and Markov chains.

MATH 6235. Stochastic Processes in Finance II. 3 Credit Hours.

Advanced mathematical modeling of financial markets, derivative securities pricing, and portfolio optimization. Concepts from advanced probability and mathematics are introduced as needed.

MATH 6241. Probability I. 3 Credit Hours.

Develops the probability basis requisite in modern statistical theories and stochastic processes. Topics of this course include measure and integration foundations of probability, distribution functions, convergence concepts, laws of large numbers, and central limit theory. First of two courses.

MATH 6242. Probability II. 3 Credit Hours.

Develops the probability basis requisite in modern statistical theories and stochastic processes. Topics of this course include results for sums of independent random variables, Markov processes, martingales, Poisson processes, Brownian motion, conditional probability and conditional expectation, and topics from ergodic theory. Second of two classes.

MATH 6262. Advanced Statistical Inference I. 3 Credit Hours.

Basic theories of statistical estimation, including optimal estimation in finite samples and asymptotically optimal estimation. A careful mathematical treatment of the primary techniques of estimation utilized by statisticians.

MATH 6263. Testing Statistical Hypotheses. 3 Credit Hours.

Basic theories of testing statistical hypotheses, including a thorough treatment of testing in exponential class families. A careful mathematical treatment of the primary techniques of hypothesis testing utilized by statisticians.

MATH 6266. Linear Statistical Models. 3 Credit Hours.

Basic unifying theory underlying techniques of regression, analysis of variance and covariance, from a geometric point of view. Modern computational capabilities are exploited fully. Students apply the theory to real data through canned and coded programs.

MATH 6267. Multivariate Statistical Analysis. 3 Credit Hours.

Multivariate normal distribution theory, correlation and dependence analysis, regression and prediction, dimension-reduction methods, sampling distributions and related inference problems, selected applications in classification theory, multivariate process control, and pattern recognition.

MATH 6307. Ordinary Differential Equations I. 3 Credit Hours.

This sequence develops the qualitative theory for systems of ordinary differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, normal forms. First of two courses.

MATH 6308. Ordinary Differential Equations II. 3 Credit Hours.

This sequence develops the qualitative theory for systems of differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, and normal forms. Second of two courses.

MATH 6321. Functions of a Complex Variable I. 3 Credit Hours.

Complex integration, including Goursat's theorem; classification of singularities, the argument principle, the maximum principle; Riemann Mapping theorem; analytic continuation and Riemann surfaces; range of an analytic function, including Picard's theorem.

MATH 6337. Real Analysis I. 3 Credit Hours.

Lebesgue measure and integration, differentiation, abstract measure theory. Credit cannot be received for both MATH 6337 and MATH 6579 .

MATH 6338. Real Analysis II. 3 Credit Hours.

Continuation of MATH 6337 . L^p and Hilbert spaces, introduction to operator theory and functional analysis. Credit cannot be received for both MATH 6338 and MATH 6580 .

MATH 6341. Partial Differential Equations I. 3 Credit Hours.

Introduction to the mathematical theory of partial differential equations covering the basic linear models of science and exact solution techniques.

MATH 6342. Partial Differential Equations II. 3 Credit Hours.

This course covers the general mathematical theory of linear stationary and evolution problems plus selected topics chosen from the instructor's interests.

MATH 6421. Algebraic Geometry I. 3 Credit Hours.

The study of zero sets of polynomials: algebraic varieties, regular and rational mappings, the Zariski topology.

MATH 6422. Algebraic Geometry II. 3 Credit Hours.

A continuation of Algebraic Geometry I.

MATH 6441. Algebraic Topology I. 3 Credit Hours.

Simplicial homology. Chain complexes and acyclic carriers. Simplicial approximation. The exact homology sequence. Maps of spheres. Mayer-Vietoris sequence.

MATH 6442. Algebraic Topology II. 3 Credit Hours.

Continuation of MATH 6441 . Singular homology. Local homology and manifolds. CW complexes. Cohomology. Duality in manifolds.

MATH 6451. General Topology. 3 Credit Hours.

Introduction to topological and metric spaces. Continuity, compactness, convergence, completion. Product and quotient spaces. Elementary homotopy.

MATH 6452. Differential Topology. 3 Credit Hours.

Manifolds. Differentiable structures. Tangent bundles. Embeddings and immersions. Maps on manifolds. Transversality. Morse-Sard Theorem. Vector bundles.

MATH 6453. Geometric Topology. 3 Credit Hours.

Characteristic classes, Morse theory, three-manifolds, four-manifolds, symplectic and contact manifolds, knot theory.

MATH 6455. Differential Geometry I. 3 Credit Hours.

Core topics in differential, including: Lie groups, curvature, and relations with topology.

MATH 6456. Differential Geometry II. 3 Credit Hours.

Introduces students to topics of current interest in geometry.

MATH 6514. Industrial Mathematics I. 3 Credit Hours.

Applied mathematics techniques to solve real-world problems. Topics include mathematical modeling, asymptotic analysis, differential equations and scientific computation. Prepares the student for MATH 6515.

MATH 6579. Measure Theory for Scientists and Engineers. 3 Credit Hours.

An introduction to measure theory and Lebesgue integration with a focus on topics that tend to be of the most utility in science and engineering. Credit cannot be received for both MATH 6337 and MATH 6579 .

MATH 6580. Hilbert Spaces for Scientists and Engineers. 3 Credit Hours.

Structure of linear operators in infinite dimensional spaces, applications. Credit cannot be received for both MATH 6338 and MATH 6580 .

MATH 6583. Integral Equations and Transforms. 3 Credit Hours.

Volterra and Fredholm linear integral equations; relation to differential equations; solution methods; Fourier, Laplace, and Mellin transforms; applications to boundary value problems and integral equations.

MATH 6584. Special Functions of Higher Mathematics. 3 Credit Hours.

Gamma function; exponential function; orthogonal polynomials; Bessel, Legendre, and hypergeometric functions; application to singular ordinary differential equations; and separation of variables for partial differential equations.

MATH 6635. Numerical Methods in Finance. 3 Credit Hours.

Basic numerical and simulation techniques used in the pricing of derivative securities and in related problems in finance. Some programming experience required.

MATH 6640. Introduction to Numerical Methods for Partial Differential Equations. 3 Credit Hours.

Introduction to the implementation and analysis of numerical algorithms for the numerical solution of the classic partial differential equations of science and engineering. Must have knowledge of a computer programming language, familiarity with partial differential equations and elements of scientific computing.

MATH 6641. Advanced Numerical Methods for Partial Differential Equations. 3 Credit Hours.

Analysis and implementation of numerical methods for nonlinear partial differential equations including elliptic, hyperbolic, and/or parabolic problems. Must have knowledge of classic linear partial differential equations and exposure to numerical methods for partial differential equations at the level of MATH 6640 or numerical linear algebra at the level of MATH 6643 .

MATH 6643. Numerical Linear Algebra. 3 Credit Hours.

Introduction to the numerical solution of the classic problems of linear algebra including linear systems, least squares, Singular value decomposition, eigenvalue problems. Crosslisted with CSE 6643 .

MATH 6644. Iterative Methods for Systems of Equations. 3 Credit Hours.

Iterative methods for linear and nonlinear systems of equations including Jacobi, G-S, SOR, CG, multigrid, Newton quasi-Newton, updating, and gradient-based methods. Crosslisted with CSE 6644 .

MATH 6645. Numerical Approximation Theory. 3 Credit Hours.

Theoretical and computational aspects of polynomial, rational, trigonometric, spline, and wavelet approximation.

MATH 6646. Numerical Methods for Ordinary Differential Equations. 3 Credit Hours.

Analysis and implementation of numerical methods for initial and two-point boundary value problems for ordinary differential equations.

MATH 6647. Numerical Methods for Dynamical Systems. 3 Credit Hours.

Approximation of the dynamical structure of a differential equation and preservation of dynamical structure under discretization. Must be familiar with dynamical systems and numerical methods for initial and boundary value problems in ordinary differential equations.

MATH 6701. Math Methods of Applied Sciences I. 3 Credit Hours.

Review of linear algebra and ordinary differential equations, brief introduction to functions of a complex variable.

MATH 6702. Math Methods of Applied Sciences II. 3 Credit Hours.

Review of vector calculus and its applications to partial differential equations.

MATH 6705. Modeling and Dynamics. 3 Credit Hours.

Mathematical methods for solving problems in the life sciences. Models-based course on basic facts from the theory of ordinary differential equations and numerical methods of their solution. Introduction to the control theory, diffusion theory, maximization, minimization and curve fitting. Math majors may not use this course toward any degree in the School of Mathematics.

MATH 6710. Numerical Methods in Computational Science and Engineering I. 3 Credit Hours.

Introduction to numerical algorithms widely used in computational science and engineering. Numerical linear algebra, linear programming, and applications. Crosslisted with CSE 6710 .

MATH 6711. Numerical Methods in Computational Science and Engineering II. 3 Credit Hours.

Efficient numerical techniques for solving partial differential equations and large-scale systems of equations arising from discretization of partial differential equations or variational problems in applications in science and engineering. Crosslisted with CSE 6711 .

MATH 6759. Stochastic Processes in Finance I. 3 Credit Hours.

Mathematical modeling of financial markets, derivative securities pricing, and portfolio optimization. Concepts from probability and mathematics are introduced as needed. Crosslisted with ISYE 6759 .

MATH 6761. Stochastic Processes I. 3 Credit Hours.

Discrete time Markov chains, Poisson processes, and renewal processes. Transient and limiting behavior. Average cost and utility measures of systems. Algorithms for computing performance measures. Modeling of inventories, and flows in manufacturing and computer networks. Crosslisted with ISYE 6761 .

MATH 6762. Stochastic Processes II. 3 Credit Hours.

Continuous time Markov chains. Uniformization, transient and limiting behavior. Brownian motion and martingales. Optional sampling and convergence. Modeling of inventories, finance, flows in manufacturing and computer networks. Crosslisted with ISYE 6762 .

MATH 6767. Design and Implementation of Systems to Support. 3 Credit Hours.

Computational Finance Introduction to large scale system design to support computational finance for options, stocks, or other financial instruments. Some programming experience, and previous exposure to stocks, bonds, and options required. Crosslisted with ISYE 6767 .

MATH 6769. Fixed Income Securities. 3 Credit Hours.

Description, institutional features, and mathematical modeling of fixed income securities. Use of both deterministic and stochastic models. Crosslisted with ISYE 6769 .

MATH 6783. Statistical Techniques of Financial Data Analysis. 3 Credit Hours.

Fundamentals of statistical inference for models used in the modern analysis of financial data. Crosslisted with ISYE 6783 .

MATH 6785. The Practice of Quantitative and Computational Finance. 3 Credit Hours.

Case studies, visiting lecturers from financial institutions, student group projects of an advanced nature, and student reports, all centered around quantitative and computational finance. Crosslisted with ISYE and MGT 6785 .

MATH 6793. Advanced Topics in Quantitative and Computational Finance. 3 Credit Hours.

Advanced foundational material and analysis techniques in quantitative and computational finance. Crosslisted with ISYE 6793 .

MATH 6XXX. Mathematics Elective. 1-21 Credit Hours.

MATH 7000. Master's Thesis. 1-21 Credit Hours.

MATH 7012. Enumerative Combinatorics. 3 Credit Hours.

Fundamental methods of enumeration and asymptotic analysis, including the use of inclusion/exclusion, generating functions, and recurrence relations. Applications to strings over a finite alphabet and graphs.

MATH 7014. Advanced Graph Theory. 3 Credit Hours.

Advanced topics in graph theory. Selection of arguments varies every year.

MATH 7016. Combinatorics. 3 Credit Hours.

Fundamental combinatorial structures including hypergraphs, transversal sets, colorings, Sperner families, intersecting families, packings and coverings, perfect graphs, and Ramsey theory. Algebraic and topological methods, applications.

MATH 7018. Probabilistic Methods in Combinatorics. 3 Credit Hours.

Applications of probabilistic techniques in discrete mathematics, including classical ideas using expectation and variance as well as modern tools, such as martingale and correlation inequalities.

MATH 7244. Stochastic Processes and Stochastic Calculus I. 3 Credit Hours.

An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. First of two courses.

MATH 7245. Stochastic Processes and Stochastic Calculus II. 3 Credit Hours.

An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. Continuation of MATH 7244 .

MATH 7251. High-dimensional probability. 3 Credit Hours.

The goal of this PhD level graduate course is to provide a rigorous introduction to the methods of high-dimensional probability.

MATH 7252. High-dimensional statistics. 3 Credit Hours.

The goal of this PhD level graduate course is to provide a rigorous introduction to the methods of high-dimensional statistics.

MATH 7337. Harmonic Analysis. 3 Credit Hours.

Fourier analysis on the torus and Euclidean space.

MATH 7338. Functional Analysis. 3 Credit Hours.

Spectral theory of bounded and unbounded operators, major theorems of functional analysis, additional topics.

MATH 7339. Advanced Analysis. 3 Credit Hours.

A comprehensive overview of advanced material in analysis. This is a Repeatable Course with 5 different subtitles; Recommended prerequisites may vary with each offering.

MATH 7510. Graph Algorithms. 3 Credit Hours.

Algorithms for graph problems such as maximum flow, covering, matching, coloring, planarity, minimum cuts, shortest paths, and connectivity. Crosslisted with ISYE 7510 and CS 7510 .

MATH 7581. Calculus of Variations. 3 Credit Hours.

Minimization of functionals, Euler-Lagrange equations, sufficient conditions for a minimum; geodesic, isoperometric, and time of transit problems; variational principles of mechanics; applications to control theory.

MATH 7586. Tensor Analysis. 3 Credit Hours.

Review of linear algebra, multilinear algebra, algebra of tensors, co- and contravariant tensors, tensors in Riemann spaces, geometrical interpretation of skew tensors.

MATH 7999. Preparation for Doctoral Comprehensive Examination. 1-21 Credit Hours.

MATH 8305. Aural-Oral English Skills for Math ESL International Teaching Assistants. 2 Credit Hours.

Enhancement of English listening/speaking skills for SOM international graduate students, post-docs, and new faculty who speak English as their second language (ESL) and who will be teaching undergraduate students.

MATH 8306. Academic Communication for Intermediate ESL Math International Teaching Assistants. 2 Credit Hours.

Continued enhancement of English listening/speaking skills for current and future SOM graduate international teaching assistants and international lead instructors who speak English as their second language (ESL).

MATH 8307. Academic Communication for Advanced ESL Math International Teaching Assistants. 1 Credit Hour.

MATH 8801. Special Topics. 1 Credit Hour.

This course enables the School of Mathematics to comply with requests for courses in selected topics.

MATH 8802. Special Topics. 2 Credit Hours.

MATH 8803. Special Topics. 3 Credit Hours.

MATH 8804. Special Topics. 4 Credit Hours.

MATH 8805. Special Topics. 5 Credit Hours.

This course enables the school of Mathematics to comply with requests for courses in selected topics.

MATH 8811. Special Topics. 1 Credit Hour.

MATH 8812. Special Topics. 2 Credit Hours.

MATH 8813. Special Topics. 3 Credit Hours.

MATH 8814. Special Topics. 4 Credit Hours.

MATH 8815. Special Topics. 5 Credit Hours.

MATH 8821. Special Topics. 1 Credit Hour.

MATH 8822. Special Topics. 2 Credit Hours.

MATH 8823. Special Topics. 3 Credit Hours.

MATH 8824. Special Topics. 4 Credit Hours.

MATH 8825. Special Topics. 5 Credit Hours.

MATH 8831. Special Topics. 1 Credit Hour.

MATH 8832. Special Topics. 2 Credit Hours.

MATH 8833. Special Topics. 3 Credit Hours.

MATH 8834. Special Topics. 4 Credit Hours.

MATH 8835. Special Topics. 5 Credit Hours.

MATH 8841. Special Topics. 1 Credit Hour.

MATH 8842. Special Topics. 2 Credit Hours.

MATH 8843. Special Topics. 3 Credit Hours.

MATH 8844. Special Topics. 4 Credit Hours.

MATH 8845. Special Topics. 5 Credit Hours.

MATH 8851. Special Topics. 1 Credit Hour.

MATH 8852. Special Topics. 2 Credit Hours.

MATH 8853. Special Topics. 3 Credit Hours.

MATH 8854. Special Topics. 4 Credit Hours.

MATH 8855. Special Topics. 5 Credit Hours.

MATH 8863. Advanced Topics in Graph Theory. 3 Credit Hours.

Selection of topics vary with each offering.

MATH 8873. Special Topics. 3 Credit Hours.

MATH 8900. Special Problems. 1-21 Credit Hours.

MATH 8901. Special Problems. 1-21 Credit Hours.

MATH 8902. Special Problems. 1-21 Credit Hours.

MATH 8903. Special Problems. 1-21 Credit Hours.

MATH 8997. Teaching Assistantship. 1-9 Credit Hours.

For students holding graduate teaching assistantships.

MATH 8998. Research Assistantship. 1-9 Credit Hours.

For students holding graduate research assistantships.

MATH 9000. Doctoral Thesis. 1-21 Credit Hours.

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Guillermo Goldsztein

Professor, school of mathematics.

Professor Goldsztein is originally from Buenos Aires, Argentina. In 1992 he received his undergraduate degree in mathematics from the University of Buenos Aires and in 1997 a Ph.D. in mathematics from MIT. During the three following years (1997-2000), he was a postdoctoral scholar and lecturer in applied mathematics at CalTech. Since 2000, he has been a faculty member of the School of Mathematics of Georgia Tech, where he is now a full professor. Professor Goldsztein enjoys applying mathematics that can be used in other other fields of science such as computational biology, machine learning, and the intersection between math and physics. Machine learning is among his areas of expertise.

404.894.2286

Office Location: Skiles 112

• Computational Materials Science

computational mechanics

• Institute for Materials

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• Mathematical approaches to image processing. Variational functional and PDE based methods for various problems arising in image restorations and segmentation: denoising, deblurring, inpainting, color image, video, shape analysis, texture, multiphase image segmentation and various extensions.
• Identifying Differential equations from single set of given data, regularized k-means and data clustering.
• Numerical methods and scientific computing: New modeling of functionals, mathematical analysis and numerical simulations for applied problems.

H. Milton Stewart School of Industrial and Systems Engineering

College of engineering, ph.d. in operations research.

The core strength comprising the discipline of Operations Research (OR) at Georgia Tech resides in the Stewart School of Industrial and Systems Engineering (ISyE). One of the largest programs in the country, approximately half of the entire ISyE faculty is directly responsible for the OR program through teaching and research activities that span virtually every topic and sub-discipline related to the field's basic methodologies of optimization, stochastics/applied probability and simulation. Most important, the OR faculty in the School currently counts among its members some of the most important figures in their respective concentrations, also making the program one of the strongest anywhere.

Students pursuing a degree in Operations Research (OR) are exposed to a host of research activities in the School. As one would expect from a program as large as ours, the range and depth of these activities are substantial. Depending upon your taste, your background, or your career intentions, you can engage in research that spans from the most fundamental/theoretical to work that places greater emphasis on applications. No matter your inclination, as an OR student, you can generally find several faculty doing work in your chosen concentration.

Students are attracted to our OR degree from a variety of academic disciplines and specializations. Most prominent are applicants from mathematics/mathematical sciences, theoretical computer science, and various engineering majors such as electrical and industrial engineering. However, it is not uncommon to also find qualified students from fields such as physics, economics, and statistics.

New Ph.D. students are admitted for each Fall semester only, and the admissions process is coordinated by the Associate Chair for Graduate Studies. Decisions on applicants to our various Ph.D. programs are determined jointly by a committee of faculty members, potential faculty research advisors, and the Associate Chair. All applicants must select and apply to a specific degree program, although it is possible in some cases to switch programs after enrollment.

A prior Master's degree is not a requirement for admission into our Ph.D. programs, and students can earn an M.S. degree typically within the first two years of Ph.D. study. For those unsure about applying to a Master's program versus a Ph.D. program, please note that students in our Master's programs are not guaranteed admission into a Ph.D. program here; we do offer a simplified application scheme. If you are interested in research and a Ph.D. degree, you should apply to a Ph.D. program directly.

Application Requirements

• Transcripts : Transcripts of prior academic work are required, as is evidence of an earned Bachelor's degree. Applicant transcripts should demonstrate strong academic preparation and capability, especially in advanced mathematics and computing coursework. Those with less preparation in mathematics and engineering are expected to use coursework at Georgia Tech to quickly establish proficiency. 
• Graduate Record Examination (GRE) : Scores from the general test are required, and strong performance on the quantitative section is expected. Scores from the Mathematics Subject Test are not required, but can help a student demonstrate proficiency in advanced mathematics.  **The GRE is optional for the 2024 admissions cycle for Ph.D. applicants.**   However, if you decide not to submit GRE scores, the rest of your academic record should make up for the lack of the test score. If you have GRE test scores and wish to submit them for Fall 2023, they will be accepted and considered.  
• Statement of Purpose : The written statement of purpose should describe clearly why the applicant wishes to pursue the Ph.D., including research and career goals. While the statement should describe past experiences, it should also identify clearly the research area of interest to the applicant and the members of our faculty that might serve as research advisor(s).
• Resume: A resume outlining academic experience, research experience and accomplishments, industry experience, specific skills, and outside interests of the applicant is required.
• Letters of Reference:   Three (3) credible letters of reference are required that attest to the preparation of the applicant and the likelihood for success in a Ph.D. program. At least two (2) letters should be from faculty members.  

Each year, we receive many more applications from qualified students than we have the capacity to admit into our programs. To help admitted students learn more about our programs and meet potential research advisors, we hold an invitation-only Ph.D. Applicant Visit Day annually in early March.  

• Requirements
• Check Status

Career Paths

ISyE produces well-rounded graduates who go on to make an extraordinary mark on the world through their leadership in engineering and technology. With broad skill sets and innovative minds molded by the number one school of industrial engineering in the country, our graduates are out changing the world and paving the way for future generations..

A sample of companies our Ph.D. graduates launched their careers with

• BHP Billiton
• Norfolk Southern
• Descartes Associates
• GE Global Research
• JP Morgan Chase
• Suntrust Bank
• Delta Technologies
• Capital One
• United Airlines

A sample of academic institutions our Ph.D. graduates launched their careers with

• MIT (Sloan/ORC)
• Carnegie Mellon (Business, Statistics)
• Purdue (Industrial Engineering)
• Harvard (Statistics)
• Iowa (Business)
• Arkansas (Industrial Engineering)
• Texas-Austin (Operations Research)
• Northwestern (IEMS, Business)
• Lehigh (Industrial Engineering)
• Florida (Industrial Engineering)
• North Carolina-Chapel Hill (Operations Research, Business)
• Middle East Technical University [Turkey] (Industrial Engineering)
• Duke (Business)
• Chicago (Business)
• Minnesota (Industrial Engineering)
• University of Chile (Industrial Engineering)
• Texas A&M (Industrial Engineering)
• Virginia Tech (Industrial Engineering)

Prospective Student Resources

New student checklist, graduate orientation resources, graduate handbook, financial aid.

Yes, the IELTS exam is accepted. See here for score requirements:  https://www.grad.gatech.edu/english-proficiency  

Transfer credit is accepted only in rare cases, and must be approved by the Associate Chair of Graduate Studies, ISyE. The review and approval process typically takes place during a student’s first semester in the program. A maximum of six total credit hours are transferrable. 

You may begin your application here: http://www.grad.gatech.edu/apply-now

Applicants should track their status through the CollegeNet online status check found here: https://www.grad.gatech.edu/status-checking

All ISyE Ph.D. students receive some type of funding and this is typically via a graduate assistantship (GRA or GTA). Sometimes students are supported by external fellowships. Please see here for more information on support: https://www.isye.gatech.edu/academics/doctoral/current-students/financial-support  

It is common for Ph.D. students to earn a Master’s degree as they progress through their Ph.D. program of study. That is, appropriate courses taken as part of their Ph.D. program are often applied to satisfy relevant degree requirements for a single Master’s degree. The review and approval process must go through the Associate chair for Graduate Studies.  Ph.D. students will not however be granted multiple Master’s degrees from ISyE. 

No. All Ph.D. students studying in ISyE receive financial support in the form of a graduate assistantship. There is no separate application required.  https://www.isye.gatech.edu/academics/doctoral/prospective-students/financial-support

Yes. ISyE Ph.D. students must be enrolled in the Atlanta campus.

Exceptions are given to applicants from countries where English is the SOLE OFFICIAL language of instruction. An applicant is also exempt if they have studied for at least one academic year at a U.S. college or university. Please visit https://grad.gatech.edu/english-proficiency for further information on the English Proficiency requirements for international students.

Applicants are required to submit a Statement of Purpose describing his or her motivation for pursuing the Ph.D. in ISyE, including a description of current research interests. Additionally, all applicants are required to submit transcripts of prior academic coursework, official GRE exam scores, and three recommendation letters.  

Please review the Georgia Tech English Proficiency Requirements here: https://grad.gatech.edu/english-proficiency .

The best preparation for a Ph.D. in Industrial Engineering or Operations Research at Georgia Tech is a technical program in mathematics, industrial engineering, operations research, statistics, or computer science. Students are expected to have strong understanding of calculus, applied probability, statistics, linear algebra, and computing. Also desirable are proof-based mathematics courses.  

Please see our admissions page here for additional information:  https://www.isye.gatech.edu/academics/doctoral/phd-industrial-engineering/admissions

The application deadline for our Ph.D. program is December 15. We offer fall admission only and classes begin in August.

Copies of your transcripts should be uploaded with your online application. If you are admitted to the program and decide to enroll, you will be required to have official transcripts sent to the Office of Graduate Studies.

Graduate Studies Georgia Institute of Technology 631 Cherry St., Room 318 Atlanta, GA 30332-0321

Our goal is to have all Ph.D. applications reviewed and official admissions decisions out by the end of February. 

Please refer to our ISyE Graduate Handbook .

Please visit our website for information related to: Admissions, Curriculum, Specializations, Financial Support, Research Faculty, Placement, etc.  https://www.isye.gatech.edu/academics/doctoral/industrial-engineering

Academic recommendations are strongly preferred. We require a total of three and they should be very strong. 

Academic recommendation letters are strongly preferred.  We ask for three letters of recommendations and they should be very strong.    

Xingxing Yu Email: yu at math.gatech.edu Office: Skiles 238

Research interest

• Graph theory, graph algorithms, and extremal combinatorics

Research papers

• Fall 2023: MATH 6014, Graph Theory; Course material on Canvas

Former PhD students

• Sean Curran (2003, NSA)
• Laura Sheppardson (2003, The University of Mississippi)
• Wen Jiang (2006, Citigroup)
• Mark Bilinski (2008, Lousiana State University)
• Jie Ma (2011, UCLA)
• Tianjun Ye (2012, Oracle)
• Dawei He (2017, Yahoo)
• Yan Wang (2017, Facebook)
• Yanxi Hou (2017, Fudan University; co-adviser Liang Peng)
• Qiqin (Jill) Xie (2019, Fudan University)
• Shijie Xie (2019, Facebook)
• Dantong Zhu (2021, Uber)
• Yingjie Qian (2022, META)
• Youngho Yoo (2022, Texas A&M)
• Xiaofan Yuan (2022, Arizona State University)
• Xiaonan Liu (2023, Vanderbilt)
• Joshua Schroeder (2023, AoPS)
• Michael Wigal (2023, UIUC)

Current PhD students

• Xiying Du (2021 --), co-advised by Rose McCarty
• Rulin Shi (2022 --)
• Carlos Sanchez-Vargas (2023 --)
• Yanjia Li (2023 --)

I am an editor of

• Discrete Mathematics
• SCIENCE CHINA Mathematics
• Journal of Combinatorics
• CSIAM Transactions on Applied Mathematics
• SIAM. J. Discrete Mathematics (2005-2023)

Graduate Programs in School of Mathematics

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Daniel Guggenheim School of Aerospace Engineering

College of engineering, a legacy of lifting others up and breaking barriers along the way.

The early years and determination of Professor Marilyn Smith. 

Marilyn Smith in the early 1980's at Lockheed developing computational flight test analysis software. 

Professor Marilyn Smith was often overlooked and told ‘no’ simply because of her gender, but found support along the way, which propelled her to become one of the leading researchers in vertical lift. 

She made history as Lockheed Martin’s first woman flight test engineer and later as the first female faculty member hired by the Daniel Guggenheim School of Aerospace Engineering (AE) at Georgia Tech. 

Her journey was far from easy, which motivated her to dedicate her career to opening doors and paving the way for women who followed. Now, a new scholarship established in her honor will continue her legacy, helping future generations pursue excellence, just as she has.  

Born to Fly

Smith, AE 1982, M.S. AE 1985, Ph.D. AE 1994, was just two weeks old when she took her first flight. Her mother would joke when the future scholar chose aerospace, though Smith teased that she had other early influences. The flight was from the Châteauroux-Déols Air Force Base hospital to Laon, France, where her father worked as an airman, and her mom worked as a secretary. 

As the oldest of four daughters, Smith assumed the role of the “responsible one” and at a young age, learned to cook and help her mother alter clothing to earn money, all while making sure her younger sisters did their chores and stayed out of trouble. “When I was a kid, I was always tinkering with things. I watched Star Trek almost daily, much to my father’s chagrin, but I found an affinity for aerospace,” Smith said.

Despite her busy home life, she excelled in the classroom and skipped one grade. There was talk of skipping two grades, but the school system wouldn’t allow it.

Teachers and school administrators didn’t know what to do with me because I was so outside the mold

MARILYN SMITH

“By the time I got to high school, the junior high school administration had begun making changes to their policies because of my experience.”

At that time – the early 1970s, girls weren’t allowed to take drafting or woodshop classes. Instead, Smith was forced into home economics and sewing classes — skills she already possessed thanks to her mom. It wasn’t the last time people told, or tried to tell, Smith what she was supposed to do.

Not ‘Lady-Like’

As she got older, she grew increasingly tired of people telling her what she could and couldn’t do simply because she was a girl. She couldn’t be better than the boys. She couldn’t take a higher mathematics course and score higher than the boys.

That’s not “lady-like,” adults would tell her. It was a phrase she heard often, and one that fueled her determination to prove them wrong. Her response? “Watch me.” 

Encouragement from her high school geometry teacher helped her see that she could one day use her gifts to become an engineer.  

“He was a great teacher who let students go at their own pace, so I did two years’ worth of geometry in one year,” she said. “One day, he looked at me and said, ‘You’re an engineer,’ I didn’t know it was possible for me to become an engineer, but he was right - I am an engineer.” 

Smith (right) and a Lockheed executive, look over the C-5 wingbox structural fatigue test. 

Smith (middle) and colleagues look over the production floor of the Lockheed office in Marietta, Georgia. 

Earning Her (Yellow Jacket) Wings

When she was still a baby, her father left the Air Force and her family moved from Laon, France first to Burnettown, South Carolina then to North Augusta, South Carolina, where Smith grew up until she left for college.

The exceptional student felt the pressure when deciding what school she’d attend for the next chapter of her life. She was weighing her options between Purdue and Georgia Tech, both known for their engineering programs. 

“My mom really wanted me to go to Georgia Tech because it was closer to home,” said Smith, who grew up about three hours from Atlanta. The co-op opportunities at Georgia Tech ended up swaying her decision — and changed the trajectory of her life. 

Smith covered 92 percent of her undergraduate tuition through scholarships, part-time jobs, and a co-op position at Lockheed Martin. 

She did three co-op rotations at NASA Langley Research Center, the first rotation in space structures. During the second rotation she wrote a Fortran program to model and measure the algae in Rhode Island’s Narragansett Bay, while during the third rotation she supported the general aviation stall and spin program in the flight-testing unit. She later transferred to Lockheed (now Lockheed-Martin) in Marietta, Georgia where she became a flight test engineer. 

“My favorite part about co-oping at Lockheed was making enough money to both eat and pay for school, as well as remain close to campus so I could go to football games,” she said. 

Her first date to one of those football games was with an electrical engineering student named Robert. The Yellow Jackets lost the game against Clemson, but Robert won Smith’s heart and they married after they both graduated.  

In the classroom, she hadn’t considered specializing in rotorcraft, until she enrolled in her first class with Professor Robin Gray , a renowned rotorcraft expert. She thoroughly enjoyed his classes, and he eventually became one of her most influential mentors. 

“He told me to not let anything stop me from doing what I wanted and to always double-check my calculations,” Smith said, noting she continues to follow both rules to this day. 

Turbulence Ahead

Then, as now, getting a degree in aerospace engineering wasn’t easy. Yet, at times, it was far easier for Smith than battling the sexist beliefs   and behaviors of some of the people around her.

She still remembers walking on the flight line at Lockheed one day in her flight suit, jump boots, parachute, and helmet.

“The entire place just stopped,” she recalled. Tools clattered to the ground and people stared — stunned to see a woman flight test engineer.

“I knew I had just done something special because I was the first woman flight test engineer hired at Lockheed.”

Smith excelled at Lockheed and enjoyed what she was doing. She had never considered pursuing a graduate degree until an opportunity presented itself. The company had just started a new employee development program, which later became their Technical Fellows Program. 

She was one of two engineers in her division selected to pursue their choice of an MBA or a master’s degree in their technical field at Georgia Tech. She enrolled and found herself juggling full-time work and conducting innovative research. 

Smith showcasing a structural model of the NASP vehicle while working at the Georgia Tech Research Institute (GTRI)

As a graduate student, she carpooled from Lockheed Martin’s Marietta office to Georgia Tech with classmate and colleague Susan Kilrain , M.S. AE 1985, who later became a NASA astronaut. On those drives and on campus, they quickly became friends.

“Susan and I were friends.” Smith said. “We helped each other out, being two of very few women in aerospace and at Lockheed.”

When she finished her master’s degree in 1985, Smith became the 11 th woman to graduate from Tech with a master’s degree in aerospace engineering. Shortly after, she transferred to Lockheed’s Research and Development group where her work moved from conducting flight tests to running computational fluid dynamics, which is still a part of what she does today. 

After only a few weeks with Lockheed’s Advanced Flight Sciences group, the branch chief pulled her and four other engineers aside and said, “You five don’t have Ph.D.s, so I’ve arranged for you to pursue your doctorate part-time at Georgia Tech.”

Smith couldn’t believe she was returning to school yet again, but she was up for the challenge and wanted to be the best engineer she could be.

While earning her Ph.D., she moved to Arizona to work at McDonnell-Douglas Helicopter, became a mom, moved back to Georgia, and started working at the Georgia Tech Research Institute (GTRI). Along the way, she had to change her thesis topic three times. This year marks 30 years since she successfully defended her thesis, A Fourth Order Euler/Navier-Stokes Prediction Method for the Aerodynamics and Aeroelasticity of Hovering Rotor Blades. 

Smith spent seven years working on various aircraft projects at GTRI, under the leadership of fellow AE alumnus and former NASA Administrator Richard Truly , AE 1959. GTRI had launched a new program where its engineers could also teach at Georgia Tech, so after some encouragement from AE Professor Al Pierce , Smith found herself teaching the next generation of engineers at her alma mater.

Leading and Mentoring the Next Generation

In the fall of 1997, Smith joined the AE faculty full-time as an assistant professor, becoming the first female faculty member hired in the Daniel Guggenheim School of Aerospace Engineering. 

Navigating through Tech as a new faculty member wasn’t easy, but she found guidance through her office neighbor, Professor Dewey Hodges which began a 24-year mentorship and friendship. 

Over the course of her 27-year journey at Tech, Smith has conducted more than $200 million in research with the U.S. Army, U.S. Navy, and NASA, and published more than 300 technical papers. She’s taught aeroelasticity courses at both the undergraduate and graduate-level, advised more than 18 Ph.D. students who went on to earn their doctorates, and has five more in the pipeline. 

She’s served as a mentor to countless Georgia Tech students and has devoted time and attention to guiding young faculty members, too. 

“Working alongside Dr. Smith, I was not only exposed to the cutting-edge of vertical flight aerodynamics, but was also nurtured with a kind of guidance and support that is rare and invaluable,” said Carlota Bonnet , AE 2019, MSAE 2022, Ph.D.AE 2024. “Her mentorship extended beyond the technical intricacies of our field; she was there for me through the highs and lows of graduate school, offering wisdom and encouragement that helped me navigate the rigors of academic and personal growth.”

“Professor Smith was my favorite professor as an undergraduate student and was someone I considered both a role model and an inspiration,” said Kelly Griendling , AE lecturer and Triple Yellow Jacket. "I still consider her as such today.  I feel extraordinarily lucky that I now get to count her as a colleague, a mentor, and a friend.”

Prof. Marilyn Smith and Carlota Bonnet are all smiles at Bonnet's doctoral graduation ceremony, May 2024. 

Prof. Tim Lieuwen (right) and Kelly Griendling (left) award Prof. Marilyn Smith with a  custom glass helicopter for her service in teaching and research at Georgia Tech, March 2024.

Many of the talented researchers and students who work with Prof. Marilyn Smith (from left) - Walther Chong , Pranav Sridhar , Jeremy Seeyave , Sheldon Salins , Prof. Smith, Aaron Crawford , Carlota Bonnet , Brenden Oates , Zahra Mehtar , and McKenna Taylor. 

Related Stories

$40 Million NASA Award to Increase Rotorcraft Vertical Lift Technology Campus-Wide

Led by Professor Marilyn Smith, a new award from NASA will give Georgia Tech researchers easier and faster access to research and engineering funds to support advances in rotorcraft vertical flight technology. 

Cat-alysts of Community: Georgia Tech Campus Cats

Professor Marilyn Smith serves as the faculty advisor for the Georgia Tech Campus Cats which supplies food and water stations for the cats, tracking cat sightings, building weather shelters, and securing veterinary care as needed.

George W. Woodruff School of Mechanical Engineering

Ph.D. Student Receives Patent for Thermographic Breast Cancer Detection Device

July 19, 2024 By Mikey Fuller

Mammograms can be an effective resource for detecting breast cancer, but for some women, it can be an invasive and uncomfortable experience.

That’s why Gianna Slusher, Ph.D. student in the George W. Woodruff School of Mechanical Engineering, developed a device that could serve as an effective alternative to traditional early detection methods for breast cancer.

Slusher and her partner, Caitlin Reina, received an official patent for inventing a mounted thermographic imaging system that can be used at home to detect medical issues such as breast cancer.

The device includes a mount that can attach to a wall and a clamp that holds a smartphone or tablet. Through an app programmed by the pair, it uses thermal images as a non-invasive and radiation-free way to capture changes in breast temperature associated with cancerous tumors. The mount can be positioned in multiple discreet and various angles, which can allow for consistent imaging. The user would be instructed on the app to see a doctor if an anomaly is detected.

Slusher and Reina began working on the project at the Invention Factory – a summer program they attended at Cooper Union for the Advancement of Science and Art in New York City while the pair were working towards their bachelor's degrees in mechanical engineering.

Slusher hopes the thermal imaging system and ease of use can help women battle all types of breast cancer in the early stages from the convenience of their own home.

During the summer of the Invention Factory when the device was created, Slusher’s aunt was diagnosed with breast cancer, which Slusher says deeply influenced her work.“Her journey inspired the creation of this device, and I am pleased to share that she is now healthy!”

Now Slusher hopes the invention can help other women gain easier access to a solution to a problem that many women will face in their lifetime.

“As a woman in mechanical engineering, I have strived to use my education and research to contribute to efforts that benefit other women,” she says.

After graduating from Cooper Union, Slusher was inspired to continue her research at the Georgia Institute of Technology through the bioengineering Ph.D. program under the supervision of Andrei Fedorov , who serves as associate chair for graduate studies, professor, Rae S. and Frank H. Neely Chair,  and Regents' Entrepreneur in the Woodruff School.

The patent was filed independently by Slusher and Reina. However, Slusher credits her advisor, Fedorov, as a significant source of support and inspiration when it comes to innovation and design throughout her research.

Fedorov says Slusher embodies the Georgia Tech motto of “Progress and Service,” and is grateful the graduate program can attract such brilliant and caring students.

“Becoming a lead inventor on a patented technology speaks volumes about the student’s thoughtfulness and ingenuity, as well as fearlessness of an innovator,” Fedorov says. “It takes not only the engineering talent and confidence in one’s ability to innovate and invent, but also the passion for helping others.”

The next stages of the invention involve refining the technology, conducting clinical trials if necessary, and ultimately bringing the innovation to market. Slusher hopes the patent gains recognition and interest from potential collaborators and investors.

Slusher continues to research cancer technologies in her Ph.D. studies, but at a micro-level, focusing on therapeutic cells and microfluidic device design and fabrication. She is designing and fabricating devices aimed at enabling rapid processing and analyses of cell therapies, thereby making this life-changing treatment more easily monitored, manufactured, affordable, and accessible to all.

Slusher is undecided on her plans after completing her Ph.D., but hopes to continue working in a capacity that allows her the freedom to research and design topics that inspire her, and where she can contribute meaningfully to advancements in her field.  

Isabel Berry Earns Prestigious Department of Energy Fellowship

Chemistry Ph.D. student Isabel Berry has been named a U.S. Department of Energy Computational Science Graduate Fellow (DOE CSGF).

The program trains emerging leaders in computational science, providing opportunities and funding to students pursuing doctoral degrees in fields that use high-performance computing to solve complex science and engineering problems.

“I am honored to receive this fellowship,” says Berry. “In addition to the support for my Georgia Tech studies, I’m especially excited to participate in the three-month practicum where I’ll collaborate with leading DOE scientists.”

According to the DOE, the practicum takes place at one of 21 DOE laboratories or sites across the country, offering the fellows insights into how their scientific interests can translate to research areas important to the nation.  

At Georgia Tech, Berry is a graduate research assistant for the Sherrill Group , spearheading research on using quantum mechanics and high-performance computing to understand how drug molecules bind to proteins.

“Computational chemists are always trying to balance speed and accuracy. My current research focuses on accuracy–modeling proteins with thousands of atoms to understand why some drugs work better than others,” explains Berry. “One of the practicum benefits will be access to the DOE’s supercomputers. I’m looking forward to learning how these incredible computers can help us further implement data-driven approaches to screen potential drug candidates (small molecules) even more rapidly.”

The fellowship is renewable for up to four years. As of September 1, 2024, the DOE CSGF will have onboarded more than 675 students across 34 cohorts representing 84 Ph.D. institutions. There are a record 40 incoming fellows for 2024-2025, with Berry the sole recipient from Georgia Tech.

"Izzy is an amazing student. She came to Georgia Tech with a B.S. in Chemistry and minors in computer science, applied math, and physics—as well as research experience in computational biophysics,” says  David Sherrill , Regents’ Professor in the School of Chemistry and Biochemistry and the School of Computational Science and Engineering who oversees Berry’s work. “She is exactly the kind of interdisciplinary student the DOE wants to recognize with their Computational Science Graduate Fellowship. I'm thrilled she's received this prestigious recognition."

Laura S. Smith  Communications Officer II  College of Sciences