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Applied and Computational Mathematics MS

Nathan Cahill, Graduate Program Director
(585) 475-5144, nathan.cahill@rit.edu

http://www.rit.edu/cos/sms/academics.html

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.

[arrow] Click to view program requirements in the Quarter Calendar

Quarter Curriculum - For Reference Only

Effective fall 2013, RIT will convert 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)

CourseQtr. 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

CourseSem. 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)

CourseQtr. 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

CourseSem. 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)

CourseQtr. 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

CourseSem. 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)

CourseQtr. 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.