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Department of Mathematics

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Master of Science Degree in Mathematics

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Program Description

The Department of Mathematics at The University of Tennessee at Chattanooga offers a Master of Science degree in mathematics, with concentrations in applied mathematics, applied statistics, pre-professional mathematics, and education. This program is designed to provide individuals with an in-depth understanding in their chosen area, further preparing them for work in industry, government, and education, or for further graduate studies. Completion of the program requires thirty-six (36) semester credit hours, which includes an area of application or an internship. There is also an option of composing a final thesis. Students must maintain a minimum institutional cumulative GPA of 3.0, and are subject to all regulations of the UTC Graduate School.

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Faculty and the Department

The Department of Mathematics has 20 full time faculty members holding professorial rank, all of whom hold the Ph.D. degree. The graduate faculty has 11 members and their research interests span a wide variety of mathematical interests. These include linear algebra and matrix theory, modern algebra, graph theory, numerical analysis, functional analysis, ordinary and partial differential equations and difference equations, operations research, statistics and mathematics education. The Department is highly active in research as demonstrated by publications in national and international refereed journals, invited and contributed presentations at national and international conferences, service on editorial boards, and refereeing and reviewing activities. In 2005-06, more than twenty papers appeared in print, several more were accepted for publication, and more than 25 papers were presented at national and international conferences. In 2008, 28 journal articles appeared in refereed journals.

The department currently has 51 declared majors, an active Pi Mu Epsilon fraternity, and a weekly colloquium series. Even though final approval for the MS degree was awarded just two weeks before the start of the fall 2009 term, there are two full time graduate students employed as teaching assistants along with a number of students taking graduate level math courses on a part time basis. With an endowment of over $1 million, the Department is able to offer very competitive assistantships and fellowships for graduate study.

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Admission

Individuals must meet the admission requirements of the UTC Graduate School as stated in the Graduate Catalog (PDF, see Page 8). Please note that the minimum GPA on all undergraduate work will be 2.7 effective in Fall 2010. In addition, students must have a strong mathematical background at the undergraduate level, as evidenced by successful completion of critical coursework or by a baccalaureate degree in mathematics from a regionally accredited institution. Requirements may be higher for a graduate of an unaccredited institution.

Admission is a two-step process involving application to the Graduate School and application to the Department of Mathematics.

  1. Application to the Graduate School can be done online
  2. Application to the Department requires to submission of:
    • A letter of application explaining reasons why the candidate wishes to pursue graduate study in Mathematics,
    • Two letters of recommendation from individuals who are familiar with the applicant's scholastic ability and/or professional work experience,
    and if the applicant is applying for assistantships or fellowships
    • Submission of the scores on the verbal and quantitative part of the GRE

Application materials to the department should be sent to the Mathematics Graduate Program Coordinator. E-mail submission of application letters and letters of recommendation is acceptable.

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Critical undergraduate coursework required for admission

Differential and Integral Calculus with Laboratory (8 hours), Multivariable Calculus (3 hours), Differential Equations (3 hours), Elementary Linear Algebra (3 hours), Analysis (3 hours), Probability and Statistics (3 hours), Modern Algebra (3 hours), a course in Computer Science (3 hours), and two additional upper-level mathematics courses (6 hours). In addition, at least one course should emphasize mathematical proofs. Students whose academic background is considered inadequate may be asked to complete additional coursework. In addition, a GPA of 3.0 (on a 4.0 scale) is required on all upper level mathematics courses.

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General Degree Requirements

  1. Credit hours: A minimum of thirty six (36) semester hours is required. At least twenty four (24) must be in mathematics at the 5000 level.
  2. Core Courses: Zero to nine (0-9) hours, depending on whether these courses were taken at the undergraduate level:
    1. Introduction to Analysis II (Math 4500 at UTC or equivalent)
    2. Linear Algebra and Matrix Theory (Math 4200 at UTC or equivalent)
    3. Complex Analysis (Math 4570 at UTC or equivalent)
  3. Concentration requirements: Twelve (12) hours chosen from one of four areas, including at least one two-semester sequence defined under that concentration. See Concentrations.
  4. Area of Application or Internship: A minimum of six (6) hours. See Area of Applicaion or Internship.
  5. Electives: As needed to complete thirty six (36) hours. This may include three (3) hours for a special project, or as many as six (6) hours for a thesis. See Electives.

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Concentrations

Students must choose one of the following concentrations:

  1. Applied Mathematics (12 hours)
    One of the following six-hour sequences:
    1. Numerical Analysis I and II - MATH 5600 (3) and 5610 (3)
    2. Numerical Solutions of PDEs I and II - MATH 5620 (3) and 5630 (3)
    3. Applied Math for Science and Engineering I and II - MATH 5470 (3) and 5480 (3)
    Plus six additional hours chosen from MATH 5451, 5461, 5580, 5470, 5480, 5600, 5610, 5620, 5630, 5910.
  2. Applied Statistics (12 hours)
    One six-hour sequence consisting of two courses chosen from:
    1. Linear Regression and Time Series - MATH 5121 (3)
    2. Analysis of Variance - MATH 5110 (3)
    3. Design of Experiments - MATH 5120 (3)
    Plus six additional hours chosen from MATH 5111, 5311, 5121, 5321, 5150, 5110, 5120, 5320, 5910.
  3. Pre-Professional Mathematics (12 hours)
    This concentration is recommended for students wishing to pursue the Ph.D. in Mathematics. It is strongly suggested that students choosing this concentration consider writing a master's thesis. Two six-hour sequences are required to give the student both breadth and depth in mathematics. In addition to the sequences described above under the Applied Mathematics and Applied Statistics concentrations, the following serve as appropriate sequences for this concentration (only):
    1. Graph Theory - MATH 5721 (3) and Number Theory - MATH 5271 (3)
    2. Linear Algebra & Matrix Theory - MATH 5201 (3) and Advanced Matrix Theory - MATH 5200 (3)
    3. Modern Algebra I and II - MATH 5250 (3) and 5260 (3)
    4. Advanced Differential Equations - MATH 5451 (3) and Partial Differential Equations - MATH 5461 (3)
    5. Operations Research (Nonlinear) - MATH 5321 (3) and Operations Research III - MATH 5320 (3)
  4. Education (12 hours)
    In order to ensure that students choosing the Education concentration have a broad mathematics background, they must complete at least one course selected from a required sequence in each of the other three concentrations above (9 hours total), plus a second course (3 hours) to complete one of those sequences. In addition, students must complete 12 hours of Education courses; two of these courses (6 hours) count as the Area of Application described below. If not already taken, it is strongly recommended that these twelve hours be chosen from the following list of courses, since these are required for teacher licensure in Tennessee:
    1. Social and Historical Foundations of Education - EDUC 520 (3)
    2. Human Development Applied to Education - EDUC 521 (3)
    3. Instructional Planning and Evaluation - EDUC 522 (3)
    4. Teaching in Diverse Classrooms - EDUC 514 (3)
    5. Literacy Instruction for Middle/High School Learners - EDUC 563 (3)
    6. Educational Technology - EDUC 575 (3)
    If all these courses have been completed, other graduate courses from the College of Health, Education and Professional Studies may be chosen with the consent of the student's graduate program committee to complete the twelve hours.

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Area of Application and Internships

Students must complete a minimum of six (6) credit hours in an area of application or an internship. The student and his or her graduate program committee will jointly decide upon the area of application or internship, and must be approved by the Graduate Coordinating Committee. It should be consonant with the chosen concentration. An oral presentation and a written report on the internship or area of application are required. Typically, students choosing an area of application will complete coursework in another department or college such as Business, Economics, Computer Science, Engineering, Physics, Chemistry, or Biology. In keeping with the interdisciplinary nature of this program, if a student chooses an area of application, the Graduate Coordinating Committee will ask that a representative from the outside area be added as an additional member of the student's graduate program committee. Students choosing the internship option will usually collaborate with a local business. Options include businesses in the health insurance field, industrial and manufacturing industries, engineering firms, etc.

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Electives

Students must complete additional elective hours as needed to complete the degree. Any of the courses listed under the concentrations above may serve as electives. In addition, a special project (3 hours) or a thesis (6 hours) may be chosen to fulfill part of these elective hours. Prior to enrolling in MATH 5910 (Special Project in Mathematics), MATH 5980 (Research), or MATH 5990 (Thesis), a student choosing to do a project or thesis must have the topic approved by his or her graduate program committee and the Graduate Coordinating Committee, and must submit the committee form to the Graduate School for final approval.

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Course Scheduling

A full-time student can complete the degree requirements in four semesters. Courses will typically be offered at times to maximize their availability for employed students. Typical programs of study for each concentration are given below; these are only samples.

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Sample Course Schedule for Each Concentration

  1. Applied Mathematics Concentration
    • First Year (Fall):
      • MATH 5571 - Introductory Complex Variables (core)
      • MATH 5600 - Numerical Analysis I (concentration sequence)
      • MATH 5461 - Partial Differential Equations (elective)
    • First Year (Spring):
      • MATH 5501 - Analysis II (core)
      • MATH 5610 - Numerical Analysis II (concentration sequence)
      • MATH 5200 - Advanced Matrix Theory (elective)
    • Second Year (Fall):
      • MATH 5620 - Numerical Solution of PDE I (concentration)
      • MATH 5470 - Applied Math for Science and Engineering I (elective)
      • ENCM 501 - Introduction to Computational Fluid Dynamics (application)
    • Second Year (Spring):
      • MATH 5630 - Numerical Solution of PDE II (concentration)
      • MATH 5480 - Applied Math for Science and Engineering II (elective)
      • ENCM 510 - Computational Fluid Dynamics I (application)
  2. Applied Statistics Concentration
    • First Year (Fall):
      • MATH 5321 - Operations Research (Nonlinear) (concentration)
      • MATH 5571 - Introductory Complex Variables (core)
      • MATH 5110 - Analysis of Variance (concentration sequence)
    • First Year (Spring):
      • MATH 5501 - Analysis II (core)
      • MATH 5200 - Advanced Matrix Theory (elective)
      • MATH 5120 - Design of Experiments (concentration sequence)
    • Second Year (Fall):
      • MATH 5320 - Operations Research III (concentration)
      • MATH 5600 - Numerical Analysis I (elective)
      • MATH 5910 - Special Topics in Applied Statistics (elective)
    • Second Year (Spring):
      • MATH 5150 - Biostatistics (elective)
      • MATH 5920 - Graduate Internship in Mathematics (6 hours)
  3. Pre-Professional Mathematics Concentration
    • First Year (Fall):
      • MATH 5201 - Linear Algebra and Matrix Theory (core)
      • MATH 5110 - Analysis of Variance (concentration sequence)
      • MATH 5600 - Numerical Analysis I (elective)
    • First Year (Spring):
      • MATH 5271 - Number Theory (elective)
      • MATH 5120 - Design of Experiments (concentration sequence)
      • MATH 5200 - Advanced Matrix Theory (elective)
    • Second Year (Fall):
      • ECON 501 - Concepts in Economics (application)
      • MATH 5250 - Modern Algebra I (concentration sequence)
      • MATH 5980 - Research (3 hours)
    • Second Year (Spring):
      • ECON 510 - Macroeconomic Analysis for Business (application)
      • MATH 5260 - Modern Algebra II (concentration sequence)
      • MATH 5990 - Thesis (3 hours)
  4. Education Concentration
    • First Year (Fall):
      • EDUC 520 - Social and Historical Foundations of Education (concentration)
      • MATH 5571 - Introductory Complex Variables (core)
      • MATH 5201 - Linear Algebra and Matrix Theory (core)
    • First Year (Spring):
      • EDUC 521 - Human Development Applied to Education (concentration)
      • MATH 5501 - Modern Analysis (core)
      • MATH 5200 - Advanced Matrix Theory (elective)
    • Second Year (Fall):
      • EDUC 522 - Instructional Planning and Evaluation (concentration)
      • MATH 5250 - Modern Algebra I (concentration sequence)
      • MATH 5600 - Numerical Analysis I (concentration)
    • Second Year (Spring):
      • EDUC 514 - Teaching in Diverse Classrooms (concentration)
      • MATH 5260 - Modern Algebra II (concentration sequence)
      • MATH 5150 - Biostatistics (concentration)

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Financial Aid, Assistantships, and Fellowships

Financial support for graduate study is available for some full time students through Graduate Teaching Assistantships. Since students in the MS degree program either will have a bachelor's degree in mathematics, or will have a bachelor's degree in a related area (engineering, physics, or mathematics education) with the mathematics course work equivalent to a bachelors degree in mathematics, they satisfy SACS criteria to teach developmental mathematics courses. Typically, a TA would teach two sections per semester and would be paid $12,000 per academic year. In addition, there would be a full waiver of tuition.

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New Four-Digit Course Numbers Effective Fall 2010

Beginning in the fall 2010 semester, UTC is renumbering courses from a 3 digit to a 4 digit pattern. This table gives the old and new numbers. This table should help in identifying those courses offered in the coming semesters.

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Tentative Course Offerings in Spring, Summer, and Fall 2010

The tentative Spring 2010 graduate course schedule is given below. (Updated: 3 November 2009.)

The tentative Summer 2010 graduate course schedule is to offer MATH 401 Mathematics of Interest in Summer II (June 4 - July 6).

The tentative Fall 2010 graduate course schedule is given below. (Updated: 3 November 2009.)

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