Overview & Purpose

The Computational Science track is the third specialization offered in our MMS degree program. It utilizes the wide range of departments and units on campus that present opportunities to collaborate in computational projects. Most prominently, the College of Engineering comprises eleven departments (including computer science) with nearly 300 faculty. The department of mathematics maintains several collaborations with the school of engineering ranging from fluid dynamics to computational topology. Demands for mathematical expertise in computational methods arise also in much of the research conducted at our Mathematical Biosciences Institute.. Other units on campus that can potentially provide practical experiences for this specialization are, for example, the departments of Statistics, Economics, Physics, Chemistry, or Earth Sciences. In addition researchers and students in computational sciences can gain access to the resources of the Ohio Supercomputer Center.

The curriculum of the this track provides students with the mathematical tools in numerical analysis, finite element methods, and applied differential equations to tackle computational challenges in a broad range of applied subjects. Students are expected to take additional courses chosen from areas such as computational electromagnetics, mechanics, fluid and aerodynamics, as well as signal processing, algorithms and graphics, or mathematical computational methods in order to gain valuable exposure in a computational discipline outside of mathematics. Most of these courses are currently offered by the college of engineering but other options are being explored and can be proposed by students and advisors.

Employment prospects for graduates exist in many branches of industry, particularly those concerned with simulation, imagining, and a variety of data-heavy engineering applications. Possible employment in the public sector may focus on applications in environmental, atmospheric, oceanographic, economic, or epidemiological analysis as well as data security and encryption.

As with other MMS tracks, this program also provides a strong mathematical foundation for students planning to apply later to PhD programs in applied mathematics, computer science, or engineering. Generally the rigorous formation in mathematics combined with training in independent work open up new employment opportunities of graduates in jobs that require quantitative analysis even if unrelated to computational sciences.

Find below basic information about the curriculum of the program, prerequisites, and support. For further information about admission, contact our Graduate Office at grad-info@math.osu.edu.

If you have further questions about the curriculum or content of courses please contact Prof Ching-Shan Chou, Prof Chiu-Yen Kao, or Prof Saleh Tanveer.

Curriculum

The curriculum consists of about twelve quarter-long courses over two years. Besides satisfactory completion of these courses students are required to write a Master's thesis for graduation. See here a

Mathematics Courses

The mathematical part of the required curriculum consists of six courses described below. There maybe some flexibility in the order these are taken although the one indicate in the sample schedule is strongly recommended.

• A year-long sequence in Applied Differential Equations trains students in ordinary and partial differential equations techniques with strong emphasis on applications to mathematical modeling. Topics include bifurcation theory as well as nonlinear and chaotic dynamics.
• A three-semester long course sequence in Numerical Analysis, Computational Partial Differential Equations, and Numerical Linear Algebra equip students with a wide range of mathematical skills and methods that are at the core of this track.
• The Introduction to Finite Element Methods teaches central method in computing that is heavily used in industry and engineering. It is co-taught by the department of mathematics and the college of engineering.

Electives & Concentrations

This track requires a more substantial set of elective than other MMS tracks. In particular, students should concentrate their studies on a more specifically defined topic within computational mathematics through their choices of electives. Further consideration are as follows:

• Electives must cover at least 12 credits (about four courses).
• At least two and preferably three should be in the same sub-concentration indicated in the elective list of the sample schedule.
• The selection of electives should be done in close coordination and with approval of student's advisor.

Internship & Thesis & Course Option

In the summer between the first and second year students are expected to complete an interdisciplinary practical experience. It will typically be co-mentored by one mathematics faculty and one faculty from an applied department. The area of the latter would usually be in engineering or physical science, but other areas such as economics or life science are also possible. These internships are arranged by the faculty advisor and program leaders.

In their second year students will write a mathematical thesis on a topic in computational science under the supervision of a faculty member of the mathematics department as well as a faculty from a non-math department. Typically advisors, co-advisors, and thesis topics are found as a result of the summer internships. The thesis is to be completed and defended in the spring quarter of the second year.

Subject to approval by the Graduation Studies Committee, students can also request to graduate with the "Course Option", which would be formally treated as a non-thesis option master degree. In this option students will not complete a formal internship and thesis but take 21 instead of 12 credit hours of elective courses (that is, about seven elective courses). In addition students will take an examination which contains both a written and oral portion. The written portion will be 2-3 week project-like assignment. The oral portion will focus both on the written project and general knowledge in computational mathematics. As for the regular thesis option the second faculty member on the examination committee (besides the advisor from mathematics) will typically be from and engineering or physical science department.

The course option is considered an exceptional route to degree, that is to be used if a student wishes to explore directions in mathematical computation for which collaborations and projects have yet to be developed. Generally though students and advisors are expected to follow the regular whenever feasible.

Application Requirements

All application information can be found at http://www.math.ohio-state.edu/graduate/apply. Specific requirements for the Mathematical Biology specialization are as follows:

• Bachelor degree with courses taken in multivariable calculus, differential equations, and linear algebra. Most of our applicants are math majors but majors with significant math requirements are also welcome.
• Undergraduate GPA of 3.0 or higher.
• A substantial background (e.g., in the form of a minor) in an engineering or physical science discipline is strongly recommended.
• Students from non-English speaking countries need to have excellent English skills. Both TOEFL and GRE General Test scores must be presented. (Neither test is required for domestic students).
• GRE Subject Test scores are useful but are not required or expected.

Admission & Support

Students are admitted in the autumn. Generally admission will come with the offer of a Graduate Teaching Associateship (GTA), although we may also consider exceptions (for example, OSU grad students that already hold GA positions in other programs).

Support

Students will generally be offered support as GTAs. A typical teaching load includes two recitations meeting twice a week. Support includes the following:

• Waiver of all instructional tuition fees.
• Waiver also of summer tuition fees.
• Stipend salary for a 9-month period of at least $1850/month.
• Stipend support also during the Headstart program.

Admission

We will admit around six students each year to this specialization of the M.M.S. program. Students are expected to arrive five weeks before the start of the autumn term in order to participate in our teaching preparation program, which is prerequisite for holding a GTA appointment. Further academic activities are scheduled during this time on an individual basis.