Florida Institute of Technology
High Tech with a Human Touch
Mathematical Sciences
Graduate Programs
Catalog Table of Contents
| Degree Programs | Major Codes |
|---|---|
| Graduate Certificate in Teaching | 8004 |
| MS - Applied Mathematics | 8073 |
| Ph.D. - Applied Mathematics | 9073 |
| Ph.D. - Operations Research | 9074 |
Graduate Certificate—Teaching*
| Major Code: | 8004 | Degree Awarded: | Specialist in Education |
|---|---|---|---|
| Delivery Mode(s): | Location(s): | Main Campus - Melbourne | |
| Admission Status: | Graduate | Age Restriction: | No |
The graduate certificate is for students seeking an alternative route to professional certification in Florida. This certificate program is a subset of the MAT degree program and is designed for individuals who hold bachelor’s degrees in content areas and are current teachers with 3-year temporary teaching certificates. It consists of six graduate courses that prepare teachers for state certification. The certificate may be completed in two regular terms and a summer session. The credit hours may be applied within five years of completion to the MAT.
Admission Requirements
An applicant must have a bachelor’s degree in mathematics or science, or in an area in which state certification is sought, from an accredited college or university, and be currently teaching with temporary certification.
Certificate Requirements*
The Graduate Certificate requires passing the six courses (18 credit hours) listed below with a grade point average of at least 3.0. All courses must be taken at Florida Tech.
| EDS 5051 | Methods and Management of Middle and High School Teaching | 3 |
| EDS 5055 | Foundations and Management of Classroom Instruction | 3 |
| EDS 5060 | ESOL Teaching Strategies | 3 |
| EDS 5067 | Measurement and Evaluation | 3 |
| EDS 5071 | Methods and Strategies of Teching Middle and High School Science or EDS 5072 Methods and Strategies of Teaching Middle and High School Mathematics or EDS 5073 Methods and Strategies for Teaching Specific Middle and High School Content | 3 |
| EDS 5135 | Reading in the Content Area |
3 |
TOTAL CREDITS REQUIRED 18
*Curriculum guided by state requirements and subject to change.
Master of Science in Applied Mathematics
| Major Code: | 8073 | Degree Awarded: | Master of Science |
|---|---|---|---|
| Delivery Mode(s): | Classroom | Location(s): | Main Campus - Melbourne |
| Admission Status: | Graduate | Age Restriction: | No |
The master’s degree program in mathematics is designed to produce mathematicians with competence in analysis who have breadth and versatility in mathematics and its applications in related fields. To this end, students entering the master’s program in mathematics are required to select an applied field in which they wish to develop some expertise and to complete six credit hours toward the degree from approved courses outside the mathematics curriculum. In addition, the master’s program is organized so that students will have the freedom to select some of their mathematics electives to develop their own special interests and to complement their choice of applied field. The flexibility in the elective part of the curriculum allows some students the opportunity to achieve a breadth of experience in mathematics and its uses in physical and engineering sciences, computer science or operations research. At the same time, it will allow other students to achieve more knowledge in a particular area in which they may wish to develop expertise. In either case, the program is organized to help students obtain an appropriate background for industrial employment or to pursue further graduate studies toward the doctoral degree. In either case, students will benefit from the range of options that are available in the applied mathematics master’s program.
Students are encouraged to consider which combination of elective mathematics courses are appropriate for their choice of applied specialization and to discuss the program with their advisers as soon as graduate study begins.
Admission Requirements
Applicants should have the equivalent of an undergraduate major in mathematics and must have completed undergraduate courses in differential equations and statistics, and have proficiency in a high-level programming language. (Programming languages are noncredit courses for graduate mathematics students.) Applications from graduates with undergraduate majors in the physical sciences or graduate students seeking a second master’s degree are welcome. In such cases, however, it may be necessary for applicants to take courses in addition to the 30-credit degree requirement in those subjects where their backgrounds are deficient.
Degree Requirements
The master of science degree in mathematics requires a minimum of 30 credit hours of work beyond the bachelor’s degree. For the thesis option, six credit hours of thesis are required. The thesis should demonstrate the candidate’s abilities in the areas of reading and understanding mathematical literature, independent learning and written expression. Theses that combine mathematics with its applications in a related field are encouraged. A nonthesis option candidate must successfully complete a final program examination.
Curriculum
Core Areas (18 credit hours)
| Analysis | 6 |
| Linear Algebra | 3 |
| Numerical and Computational Mathematics | 3 |
| Probability and Statistics | 3 |
| Differential Equations | 3 |
Elective Courses (6 credit hours)
Courses in mathematics or in other scientific or engineering courses with a high degree of mathematical content. Six credit hours of electives can be devoted to writing a thesis, except in the case of students pursuing a fast track or accelerated master’s program. The selection of elective courses must have the approval of the department head.
Applied Field (6 credit hours)
This requirement consists of courses outside the mathematics program. The applied field courses must be at the 5000-level or above. The selection of applied field courses must have the approval of the department head. Normally, only those subjects involving an appropriate degree of mathematical content are approved as applied field courses in a mathematics program.
Master’s Thesis (6 credit hours)
The thesis is expected to be completed in two terms. The master’s thesis in mathematics is expected to be a thorough investigation of a well-defined problem.
Doctor of Philosophy in Applied Mathematics
| Major Code: | 9073 | Degree Awarded: | Doctor of Philosophy |
|---|---|---|---|
| Delivery Mode(s): | Classroom | Location(s): | Main Campus - Melbourne |
| Admission Status: | Graduate | Age Restriction: | No |
The doctoral program in mathematics is designed to produce a mathematician with a broad background in analysis and a strong field of specialization in nonlinear analysis, applied analysis, or numerical analysis and scientific computing. This combination of training will prepare the student for a career in a variety of areas, such as government or industrial research, or academic research and teaching. Doctoral graduates have the necessary experience in areas of application to be able to work successfully with other members of multidisciplinary research teams. Graduates also have the critical ability to think independently and analytically. They are able to make significant contributions to knowledge in their chosen fields of inquiry.
A preliminary program of study should be prepared by the student and adviser during the first semester of graduate studies. The final doctoral program of study must be approved by the student’s advisory committee and program chair.
Admission Requirements
Applicants for the doctoral program in mathematics usually have a bachelor’s or master’s degree in mathematics. However, applications are also invited from graduates in physical and engineering sciences. In these cases, necessary undergraduate courses have to be taken to remove deficiencies before the student enters the doctoral program. In evaluating international applicants, due consideration is given to academic standards in the country in which the graduate studies were performed. Graduate teaching assistants carry on a variety of teaching assignments and in view of this, evidence of good English-speaking skills is an important criterion in processing the applications. For admission, a student should have a superior academic record and letters of recommendation. Preference will be given to applicants who have good scores on the GRE.
General admission requirements and the process for applying are presented in the Academic Overview section of the university catalog.
Degree Requirements
The degree of doctor of philosophy (Ph.D.) is conferred primarily in recognition of the breadth of scientific accomplishment and the power to investigate scientific problems independently, rather than for the completion of a definite course of studies. Although demanding a strong mathematical orientation, the doctoral program in mathematics does not fall within the traditional boundaries of a single academic unit and the scope is quite broad. Consequently, every course in a student’s program of study is evaluated not only as to content, but also as to the way in which it complements other courses and furnishes breadth and depth to the program. The work should consist of advanced studies and scientific research that lead to a significant contribution and knowledge of a particular area.
Each student must pass a preliminary examination covering the core courses, complete an approved program of studies, pass the comprehensive examination (usually oral), complete a program of significant original research work and defend a dissertation concerning the research work completed.
General degree requirements are presented in the Academic Overview section of the university catalog.
Curriculum
After a bachelor’s degree in mathematical sciences, a minimum of 75 credit hours is required for the doctoral program, including the courses listed below:
Core Areas (30 credit hours)
| Linear Algebra | 3 |
| Real and Complex Variables | 9 |
| Numerical and Computational Mathematics | 6 |
| Probability and Statistics | 6 |
| Differential Equations | 6 |
Areas of Specialization (21–27 credit hours)
Areas of specialization include nonlinear analysis; stochastic analysis; optimization; numerical analysis and scientific computing; and statistics
Considerable flexibility is allowed in the selection of courses in core areas and areas of specialization. Selected course offerings from the mathematics department and other areas of science and engineering may be taken to fulfill the requirements.
Doctoral Dissertation
The dissertation consists of 24–30 credit hours of work and is expected to be completed within two years. The doctoral dissertation is expected to represent original research in mathematics. It may present new theoretical developments or new areas of application or both. The dissertation should contain results that constitute a significant contribution to the literature of the field of investigation. These results should be worthy of publication in an established technical journal.
Doctor of Philosophy in Operations Research
| Major Code: | 9074 | Degree Awarded: | Doctor of Philosophy |
|---|---|---|---|
| Delivery Mode(s): | Classroom | Location(s): | Main Campus - Melbourne |
| Admission Status: | Graduate | Age Restriction: | No |
The doctor of philosophy program provides a more advanced level of education, as well as demonstrated ability to perform independent research. These additional strengths should qualify the graduate for vital positions of leadership in industry, business, government and academia.
Admission Requirements
An applicant for the doctoral program will normally have completed a master’s degree in operations research or a related discipline. If the master’s degree is not in operations research, then the student will be required to take the core courses for Florida Tech’s master’s degree in operations research. These courses may be used toward fulfilling the credit requirements for the Ph.D. in operations research. Students also will be required to pass a written qualifying examination equivalent to Florida Tech’s master’s final program examination.
General admission requirements are discussed in the Academic Overview section of the university catalog.
Degree Requirements
A minimum of 48 credit hours beyond the requirements for the master’s degree is required to earn the doctoral degree. These credits include 24 credit hours of dissertation research in addition to normal coursework.
Each student must complete an approved program of study, pass a comprehensive examination, complete a program of significant original research, and defend a dissertation concerning the research.
General degree requirements are presented in the Academic Overview section of the university catalog.
Curriculum
The individual doctoral program of study must be approved by the student’s doctoral committee and the program chair. Students who have not taken MTH 5051 and MTH 5102, or their equivalents, will be required to take them. Students are also required to take at least two courses from the Computation/Computer Science list.
The doctoral program in operations research does not fall within the traditional boundaries of a single discipline. The scope is broad and interdisciplinary. Consequently, every course in a student’s program of study is evaluated in terms of how it complements other courses and provides breadth and depth to the program. Considerable latitude is permitted in course selection, provided the core requirements for operations research/mathematics/computation are met. The remaining courses are selected in collaboration with the doctoral committee according to the interests and research objectives of the student. The student may opt to concentrate study in the area of human-centered design (described below).
| Computation Electives | ||
| MTH 5301 | Numerical Analysis | |
| MTH 5305 | Numerical Linear Algebra | |
| MTH 5320 | Neural Networks | |
| ORP 5050 | Discrete System Simulation | |
Human-Centered Design
The program in human-centered design (HCD) is offered for students who wish to carry out advanced research, innovation and leadership in the academic world, as well as fill equivalent positions in industry and government. The program may be completed through one of three areas: aerospace engineering, operations research or computer science. Other research areas within the field may be pursued depending on current trends in the Human-Centered Design Institute (HCDI) of Florida Tech.
The program is designed to attract students who have the greatest potential for expanding the frontiers of knowledge and art of HCD, and in transferring this knowledge and art to others. It is open to graduate students who have a strong interest in people and are ready to learn about applied human and social sciences. HCD requires significant breadth and depth of understanding in engineering, mathematics and science, the mastery of several specialized subjects and the creativity to extend the body of knowledge and art on a particular subject through significant original research.
Each candidate is expected to publish major portions of their dissertation in refereed conferences and journals, and is strongly encouraged to actively participate in research activities of the HCDI while pursuing the degree. The student’s advisory committee and the director of the HCDI must approve the doctoral program of study.