Nathan Cahill, Graduate Program Director

(585) 475-5144, nathan.cahill@rit.edu

## Program overview

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 options in discrete mathematics, dynamical systems, and scientific computing. Students will 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.

## Curriculum

#### Applied and computational mathematics (discrete mathematics option), MS degree, typical course sequence

Course | Sem. Cr. Hrs. | |
---|---|---|

First Year |
||

MATH-611 | Numerical Analysis | 3 |

MATH-651 | Combinatorics and Graph Theory I | 3 |

MATH-671 | Number Theory | 3 |

MATH-601 | Methods of Applied Mathematics | 3 |

MATH-605 | Stochastic Processes | 3 |

MATH-652 | Combinatorics and Graph Theory II | 3 |

Second Year |
||

MATH-771 | Mathematics of Cryptography | 3 |

Electives | 6 | |

MATH-790 | Thesis | 9 |

Total Semester Credit Hours |
36 |

#### Applied and computational mathematics (dynamical systems option), MS degree, typical course sequence

Course | Sem. Cr. Hrs. | |
---|---|---|

First Year |
||

MATH-611 | Numerical Analysis | 3 |

MATH-651 | Combinatorics and Graph Theory I | 3 |

MATH-631 | Dynamical Systems | 3 |

MATH-601 | Methods of Applied Mathematics | 3 |

MATH-605 | Stochastic Processes | 3 |

MATH-731 | Advanced Dynamical Systems | 3 |

Second Year |
||

MATH-741 | Partial Differential Equations I | 3 |

Electives | 6 | |

MATH-790 | Thesis | 9 |

Total Semester Credit Hours |
36 |

#### Applied and computational mathematics (scientific computing option), MS degree, typical course sequence

Course | Sem. Cr. Hrs. | |
---|---|---|

First Year |
||

MATH-611 | Numerical Analysis | 3 |

MATH-651 | Combinatorics and Graph Theory I | 3 |

Elective | 3 | |

MATH-601 | Methods of Applied Mathematics | 3 |

MATH-605 | Stochastic Processes | 3 |

MATH-612 | Numerical Linear Algebra | 3 |

Second Year |
||

MATH-711 | Advanced Methods in Scientific Computing | 3 |

MATH-712 | Numerical Methods for PDEs | 3 |

Elective | 3 | |

MATH-790 | Thesis | 9 |

Total Semester Credit Hours |
36 |

## Admission requirements

To be considered for admission to the MS program in applied and computational mathematics, candidates must fulfill the following requirements:

- Hold a baccalaureate degree from an accredited institution in mathematics or any related field (applicant's should have completed course work in multivariable calculus, differential equations, matrix theory, and probability and statistics. Knowledge of a programming language is required.),
- Submit official transcripts (in English) of all previously completed undergraduate and graduate course work,
- Submit a personal statement of educational objectives,
- Have an undergraduate cumulative GPA of 3.0 or higher,
- Submit two letters of recommendation, and
- Complete a graduate application.
- International applicants whose primary language is not English must submit scores from the Test of English as a Foreign Language (TOEFL). A minimum score of 550 (paper-based) or 79-80 (Internet-based) is required. International English Language Testing System (IELTS) scores will be accepted in place of the TOEFL exam. Minimum scores will vary; however, the absolute minimum score required for unconditional acceptance is 6.5. For additional information about the IELTS, please visit www.ielts.org. Those who cannot take the TOEFL will be required to take the Michigan Test of English Proficiency at RIT and obtain a score of 80 or higher.

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.

## Additional information

#### Student’s advisory committee

Upon admission to the program, the student chooses an adviser and forms an advisory committee. This committee will oversee the academic aspects of the student’s program, including the selection of a concentration and appropriate courses to fulfill the program’s requirements.

#### Cooperative education

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.

#### Part-time study

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.

#### Nonmatriculated students

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 in to the program from courses taken at RIT is limited for nonmatriculated students.

### Quarter Curriculum - For Reference Only

Effective fall 2013, RIT converted its academic calendar from quarters to semesters. The following content has been made available as reference only. Currently matriculated students who began their academic programs in quarters should consult their academic adviser for guidance and course selection.

### Program overview

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 School of Mathematical Sciences offers an interdisciplinary master of science degree in applied and computational mathematics. The objective of the program is to provide 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. Since this is an interdisciplinary program, students have the opportunity to choose from a wide variety of courses.

### Curriculum

The program consists of 48 quarter credit hours of study. Four core courses, usually completed in the first three quarters, provide a focus on some of the ideas of applied mathematics. A concentration and a corresponding course of study are formulated by the student in consultation with an advisory committee. The student completes a total of 20 quarter credit hours by taking a set of five specialized courses offered in the School of Mathematical Sciences, as well as other departments. Concentrations include dynamical systems, discrete mathematics, computational biomathematics, and scientific computing. Other concentrations may be created with approval of the program director.

**Semester conversion**

Effective fall 2013, RIT will convert its academic calendar from quarters to semesters. Each program and its associated courses have been sent to the New York State Department of Education for approval of the semester plan. For reference, the following charts illustrate the typical course sequence for this program in both quarters and semesters. Students should consult their graduate program adviser with questions regarding planning and course selection.

#### Applied and computational mathematics (discrete mathematics option), MS degree, typical course sequence (quarters)

Course | Qtr. Cr. Hrs. | |
---|---|---|

First Year |
||

1016-713 | Mathematical Methods in Scientific Computing | 4 |

1016-725 | Stochastic Processes | 4 |

1016-802 | Methods of Applied Mathematics | 4 |

1016-767 | Combinatorics | 4 |

1016-768 | Graph Theory | 4 |

1016-785 | Number Theory | 4 |

1016-764 | Topics in Logic, Sets, and Computability | 4 |

Choose one of the following electives: | 4 | |

1016-711 | Numerical Analysis | |

1016-720 | Complex Variables | |

1016-789 | Mathematics of Cryptography | 4 |

1016-879 | Thesis | 12 |

Total Quarter Credit Hours |
48 |

#### Applied and computational mathematics (discrete mathematics option), MS degree, typical course sequence (semesters), effective fall 2013

Course | Sem. Cr. Hrs. | |
---|---|---|

First Year |
||

MATH-611 | Numerical Analysis | 3 |

MATH-651 | Combinatorics and Graph Theory I | 3 |

MATH-671 | Number Theory | 3 |

MATH-601 | Methods of Applied Mathematics | 3 |

MATH-605 | Stochastic Processes | 3 |

MATH-652 | Combinatorics and Graph Theory II | 3 |

Second Year |
||

MATH-771 | Mathematics of Cryptography | 3 |

Electives | 6 | |

MATH-790 | Thesis | 9 |

Total Semester Credit Hours |
36 |

#### Applied and computational mathematics (dynamical systems option), MS degree, typical course sequence (quarters)

Course | Qtr. Cr. Hrs. | |
---|---|---|

First Year |
||

1016-713 | Mathematical Methods in Scientific Computing | 4 |

1016-725 | Stochastic Processes | 4 |

1016-802 | Methods of Applied Mathematics | 4 |

1016-767 | Combinatorics | 4 |

1016-706 | Advanced Differential Equations | 4 |

1016-707 | Dynamical Systems | 4 |

1016-807 | Boundary Value Problems | 4 |

Choose two of the following electives | 8 | |

1016-711 | Numerical Analysis | |

1016-720 | Complex Variables | |

1016-709 | Chaotic Dynamical Systems | |

1016-879 | Thesis | 12 |

Total Quarter Credit Hours |
48 |

#### Applied and computational mathematics (dynamical systems option), MS degree, typical course sequence (semesters), effective fall 2013

Course | Sem. Cr. Hrs. | |
---|---|---|

First Year |
||

MATH-611 | Numerical Analysis | 3 |

MATH-651 | Combinatorics and Graph Theory I | 3 |

MATH-631 | Dynamical Systems | 3 |

MATH-601 | Methods of Applied Mathematics | 3 |

MATH-605 | Stochastic Processes | 3 |

MATH-731 | Advanced Dynamical Systems | 3 |

Second Year |
||

MATH-741 | Partial Differential Equations I | 3 |

Electives | 6 | |

MATH-790 | Thesis | 9 |

Total Semester Credit Hours |
36 |

#### Applied and computational mathematics (scientific computing option), MS degree, typical course sequence (quarters)

Course | Qtr. Cr. Hrs. | |
---|---|---|

First Year |
||

1016-713 | Mathematical Methods in Scientific Computing | 4 |

1016-725 | Stochastic Processes | 4 |

1016-802 | Methods of Applied Mathematics | 4 |

1016-767 | Combinatorics | 4 |

1016-712 | Numerical Linear Algebra | 4 |

1016-807 | Boundary Value Problems | 4 |

1016-811 | Numerical Partial Differential Equations | 4 |

1016-711 | Numerical Analysis | 4 |

1016-720 | Complex Variables | 4 |

1016-879 | Thesis | 12 |

Total Quarter Credit Hours |
48 |

#### Applied and computational mathematics (scientific computing option), MS degree, typical course sequence (semesters), effective fall 2013

Course | Sem. Cr. Hrs. | |
---|---|---|

First Year |
||

MATH-611 | Numerical Analysis | 3 |

MATH-651 | Combinatorics and Graph Theory I | 3 |

MATH-xxx | Elective | 3 |

MATH-601 | Methods of Applied Mathematics | 3 |

MATH-605 | Stochastic Processes | 3 |

MATH-612 | Numerical Linear Algebra | 3 |

Second Year |
||

MATH-711 | Advanced Methods in Scientific Computing | 3 |

MATH-712 | Numerical Methods for PDEs | 3 |

Elective | 3 | |

MATH-790 | Thesis | 9 |

Total Semester Credit Hours |
36 |

#### Applied and computational mathematics (computational biomathematics option), MS degree, typical course sequence (quarters)

Course | Qtr. Cr. Hrs. | |
---|---|---|

First Year |
||

1016-713 | Mathematical Methods in Scientific Computing | 4 |

1016-725 | Stochastic Processes | 4 |

1016-802 | Methods of Applied Mathematics | 4 |

1016-767 | Combinatorics | 4 |

1016-707 | Dynamical Systems | 4 |

1016-719 | Biostatistics | 4 |

1016-862 | Mathematical Biology | 4 |

1016-711 | Numerical Analysis | 4 |

1016-720 | Complex Variables | 4 |

1016-879 | Thesis | 12 |

Total Quarter Credit Hours |
48 |

The program includes a thesis, which requires the student to present 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.

### Admission requirements

To be considered to admission to the MS program in applied and computational mathematics, candidates must fulfill the following requirements:

- Hold a baccalaureate degree from an accredited institution in mathematics or any related field. The prerequisite courses are multivariable calculus, differential equations, matrix theory, and probability and statistics. Knowledge of a programming language is required.
- Submit official transcripts (in English) of all previously completed undergraduate and graduate course work,
- Submit a personal statement of educational objectives,
- Have an undergraduate cumulative GPA of 3.0 or higher,
- Submit two letters of recommendation, and
- Complete a graduate application.
- International applicants whose primary language is not English must submit scores from the Test of English as a Foreign Language (TOEFL). A minimum score of 550 (paper-based), 213 (computer-based), or 79-80 (Internet-based) is required. International English Language Testing System (IELTS) scores will be accepted in place of the TOEFL exam. Minimum scores will vary; however, the absolute minimum score required for unconditional acceptance is 6.5. For additional information about the IELTS, please visit www.ielts.org. Those who cannot take the TOEFL will be required to take the Michigan Test of English Proficiency at RIT and obtain a score of 80 or higher.

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.

### Additional information

#### Student’s advisory committee

Upon admission to the program, the student chooses an adviser and forms an advisory committee. This committee will oversee the academic aspects of the student’s program, including the selection of a concentration and appropriate courses to fulfill the program’s requirements.

#### Cooperative education

The optional cooperative education program enables the student 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 quarter.

#### Part-time study

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 graduate program may normally be completed in two years of part-time study.

#### Nonmatriculated students

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 instructor. Courses taken for credit may be applied toward the master’s degree if the student is formally admitted to the graduate program at a later date. However, a maximum of 12 quarter credit hours may be transferred to the degree program from courses taken at RIT as a nonmatriculated student.