Create innovative computing solutions, mathematical models, and dynamic systems to solve problems in industries such as engineering, biology, and more.
Sophisticated mathematical tools are increasingly used to solve problems in management science, engineering, biology, financial portfolio planning, facilities planning, control of dynamic systems, and design of composite materials. The goal is to find computing solutions to real-world problems. The applied and computational mathematics master’s degree refines your capabilities in applying mathematical models and methods to study a range of problems, with an emphasis on developing and implementing computing solutions.
The ideas of applied mathematics pervade several applications in a variety of businesses and industries as well as government. Sophisticated mathematical tools are increasingly used to develop new models, modify existing ones, and analyze system performance. This includes applications of mathematics to problems in management science, biology, portfolio planning, facilities planning, control of dynamic systems, and design of composite materials. The goal is to find computable solutions to real-world problems arising from these types of situations.
The master of science degree in applied and computational mathematics provides students with the capability to apply mathematical models and methods to study various problems that arise in industry and business, with an emphasis on developing computable solutions that can be implemented. The program offers concentrations in discrete mathematics, dynamical systems, and scientific computing. Electives may be selected from the graduate course offerings in the School of Mathematical Sciences or from other graduate programs, with approval from the graduate program director. Students complete a thesis, which includes the presentation of original ideas and solutions to a specific mathematical problem. The proposal for the thesis work and the results must be presented and defended before the advisory committee.
A classic scenario plays out in action films ranging from Baby Driver to The Italian Job: criminals evade aerial pursuit from the authorities by seamlessly blending in with other vehicles and their surroundings. The Air Force Office of Scientific Research (AFOSR) has RIT researchers utilizing hyperspectral video imaging systems that make sure it does not happen in real life.
Applied and computational mathematics, MS degree, typical course sequence
Sem. Cr. Hrs.
Choose four of the following core courses:
Methods of Applied Mathematics
This course is an introduction to classical techniques used in applied mathematics. Models arising in physics and engineering are introduced. Topics include dimensional analysis, scaling techniques, regular and singular perturbation theory, and calculus of variations.
Numerical Analysis I
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra.
This course is an introduction to stochastic processes especially those that appear in various applications. It covered basic properties and applications of Poisson processes, and Markov chains in discrete and continuous time.
Mathematical Modeling I
This course will introduce graduate students to the logical methodology of mathematical modeling. They will learn how to use an application field problem as a standard for defining equations that can be used to solve that problem, how to establish a nested hierarchy of models for an application field problem in order to clarify the problem’s context and facilitate its solution. Students will also learn how mathematical theory, closed-form solutions for special cases, and computational methods should be integrated into the modeling process in order to provide insight into application fields and solutions to particular problems. Students will study principles of model verification and validation, parameter identification and parameter sensitivity and their roles in mathematical modeling. In addition, students will be introduced to particular mathematical models of various types: stochastic models, PDE models, dynamical system models, graph-theoretic models, algebraic models, and perhaps other types of models. They will use these models to exemplify the broad principles and methods that they will learn in this course, and they will use these models to build up a stock of models that they can call upon as examples of good modeling practice.
This course introduces the fundamental concepts of graph theory. Topics to be studied include graph isomorphism, trees, network flows, connectivity in graphs, matchings, graph colorings, and planar graphs. Applications such as traffic routing and scheduling problems will be considered.
Mathematical Modeling II
This course will continue to expose students to the logical methodology of mathematical modeling. It will also provide them with numerous examples of mathematical models from various fields.
The course prepares students to engage in activities necessary for independent mathematical research and introduces students to a broad range of active interdisciplinary programs related to applied mathematics.
This course is a continuation of Graduate Seminar I. It prepares students to engage in activities necessary for independent mathematical research and introduces them to a broad range of active interdisciplinary programs related to applied mathematics.
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.
Total Semester Credit Hours
This course introduces the fundamental concepts of combinatorics. Topics to be studied include counting techniques, binomial coefficients, generating functions, partitions, the inclusionexclusion principle and partition theory.
This course is an introduction to the standard results and techniques of number theory. Topics include divisibility, congruences, Diophantine equations, Moebius inversion, quadratic reciprocity, and primitive roots. Cryptography and other applications will be discussed. Projects may be required.
Mathematics of Cryptography
This course is an introduction to the mathematical problems and techniques that serve as a foundation for modern cryptosystems. The topics include: classical cryptosystems computational number theory, primality tests, finite fields, private and public key encryption scheme (RSA, El-Gamal), and applications such as digital signatures, one way functions, and zero knowledge proofs. Use of elliptic curves in cryptography will also be covered.
This course is a study of dynamical systems theory. Basic definitions of dynamical systems are followed by a study of maps and time series. Stability theory of solutions of differential equations is studied. Asymptotic behavior of solutions is investigated through limit sets, attractors, Poincare-Bendixson theory, and index theory. The notion of local bifurcation is introduced and investigated. Chaotic systems are studied.
Partial Differential Equations I
This course uses methods of applied mathematics in the solution of problems in physics and engineering. Models such as heat flow and vibrating strings will be formulated from physical principles. Characteristics methods, maximum principles, Green's functions, D'Alembert formulas, weak solutions and distributions will be studied.
Partial Differential Equations II
This is a continuation of Partial Differential Equations I and deals with advanced methods for solving partial differential equations arising in physics and engineering problems. Topics to be covered include second order equations, Cauchy-Kovalevskaya theorem, the method of descent, spherical means, Duhamels principle, and Greens function in higher dimensions.
Numerical Analysis II
This course covers the solutions of initial value problems and boundary value problems, spectral techniques, simulation methods, optimization and techniques employed in modern scientific computing.
Numerical Methods for Partial Differential Equations
This is an advanced course in numerical methods that introduces students to computational techniques for solving partial differential equations, especially those arising in applications. Topics include: finite difference methods for hyperbolic, parabolic, and elliptic partial differential equations, consistency, stability and convergence of finite difference schemes.
Hold a baccalaureate degree (or equivalent) from an accredited university or college in mathematics or a related field.
Submit official transcripts (in English) of all previously completed undergraduate and graduate course work.
Have knowledge of a programming language.
Have a minimum cumulative GPA of 3.0 (or equivalent).
Submit a personal statement of educational objectives.
Submit two letters of recommendation from academic or professional sources.
International applicants whose native language is not English must submit scores from the TOEFL, IELTS, or PTE. A minimum TOEFL score of 79 (internet-based) is required. A minimum IELTS score of 6.5 is required. The English language test score requirement is waived for native speakers of English or for those submitting transcripts from degrees earned at American institutions.
Although Graduate Record Examination (GRE) scores are not required, submitting them may enhance a candidate's acceptance into the program.
A student may also be granted conditional admission and be required to complete bridge courses selected from among RIT’s existing undergraduate courses, as prescribed by the student’s adviser. Until these requirements are met, the candidate is considered a nonmatriculated student. The graduate program director evaluates the student’s qualifications to determine eligibility for conditional and provisional admission.
Cooperative education enables students to alternate periods of study on campus with periods of full-time, paid professional employment. Students may pursue a co-op position after their first semester. Co-op is optional for this program.
The program is ideal for practicing professionals who are interested in applying mathematical methods in their work and enhancing their career options. Most courses are scheduled in the late afternoon or early evening. The program may normally be completed in two years of part-time study.
A student with a bachelor’s degree from an approved undergraduate institution, and with the background necessary for specific courses, may take graduate courses as a nonmatriculated student with the permission of the graduate program director and the course instructor. Courses taken for credit may be applied toward the master’s degree if the student is formally admitted to the program at a later date. However, the number of credit hours that may be transferred into the program from courses taken at RIT is limited for nonmatriculated students.