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# Mathematics M.S.

As the technical sophistication of most professions increases, there is growing need for individuals capable of “speaking the language” of mathematics. Mathematicians increasingly are sought to probe and expand mathematical theory, as engineering and empirical science delve deeper into nature. Individuals also are needed to teach the math skills that have expanded into virtually every field. MTSU’s Master of Science in Mathematics gets students involved in both the understanding and creation of advanced mathematics through quality instruction, opportunities for research, and close faculty-student interaction. A General Mathematics concentration is aimed at students desiring a broad background in mathematics. The Industrial Mathematics concentration is designed for students interested in positions in industry or further graduate work in applied mathematics. A Research Preparation concentration, which requires a thesis, is intended for students wishing to pursue the Ph.D. in Mathematics.

### Weekly seminars help grad find passion for graph theory

Hays Whitlatch earned his M.S. in Mathematics at MTSU following a recommendation from a co-worker and began work on his doctorate at the University of South Carolina in fall 2014. Whitlatch had moved to the Nashville area for a job following his undergraduate studies at the University of Iowa. "It was a great recommendation," he says. "One thing that I really liked about MTSU is that professors are willing to invest much time into curious students such as myself." One of these curious moments led him to the weekly Discrete Mathematics seminars where he discovered a passion for graph theory. Whitlatch, who wrote his thesis on "Isoperimetric Constants in Planar Graphs with Hyperbolic Properties," ultimately wants to teach and research in a university environment. His graduate teaching assistantship helped him both financially and in his development as an educator.

### Zhang award-winning thesis focuses on cancer, imaging data

MTSU alum Fengqing “Zoe” Zhang (M.S. in Mathematics, 2010) joined Drexel University as assistant professor in fall 2014 after finishing her Ph.D. in Statistics at Northwestern University. She completed her MTSU master's thesis on "Imaging Mass Spectrometry Data Analysis with Applications in Cancer Study" under the supervision of Dr. Don Hong. The work led to three journal publications and earned the 2011 Master’s Thesis Award for Digital Scholarship from the Conference of Southern Graduate Schools. Reviewers called it "cutting-edge" because linking spectroscopy technology and the applied-statistical method is relatively new work. “During my master’s study, I had the chance to attend various seminars and to present my work at regional and national conferences,” Zhang says. “My training in mathematics, statistics, and teaching at MTSU provided a foundation for my later study and research.” She holds a B.S. in Electrical Engineering from Beijing University of Aeronautics and Astronautics.

A majority of M.S. in Mathematics graduates go on to pursue their doctoral degrees at a number of universities. Several students have also entered Ph.D. programs at MTSU in either the Computational Science or the Mathematics and Science Education Ph.D. programs.

**General Mathematics** concentration students usually work in fields which require the specialized thinking
skills that mathematicians develop but which do not necessarily require a highly specialized
mathematics background.

**Research Preparation** curriculum gives students a strong background in what is called pure mathematics
for a career in academics and mathematical research.

**Industrial Mathematics** students focus on applied mathematics to work in fields which make heavy use of mathematical
modeling. Mathematicians work with programmers to develop highly specialized software
tools for engineering and medical applications. Mathematicians help develop or enhance
sophisticated models for understanding weather, chemical, biological, or economic
processes; and mathematicians create entirely new mathematical tools to probe frontiers
in physics, structural design, and other pursuits.

## Doctoral programs accepting recent MTSU alumni include

- Middle Tennessee State University
- Northwestern University
- University of South Carolina
- University of Tennessee-Knoxville
- University of Toledo

## Graduate

Students may choose from three concentrations for the Master of Science (M.S.) in Mathematics: General Mathematics, Industrial Mathematics, or Research Preparation.

A minor in Mathematics is also available at the graduate level.The Department of Mathematical Sciences also offers courses in the Master of Science in Professional Science degree, which includes concentrations in Biostatistics and Actuarial Sciences.

Applicants for the M.S. in Mathematics must have

- Acceptable scores on the GRE or MAT. (Successful applicants typically have combined GRE scores of 291 [current scale] or 900 [former scale] or above, or MAT scores of 402 or greater.)
- A bachelor’s degree from an accredited university or college.
- An acceptable grade point average for all college work taken.
- 21 semester hours of college-level mathematics (including calculus), with at least 9 hours of mathematics beyond calculus.

**For complete curriculum details, click on the REQUIREMENTS tab above.**

## Undergraduate

Undergraduate students interested in mathematical modeling and problem solving can pursue a Bachelor of Science (B.S.) degree with a major in Mathematics, choosing one of three concentrations: Actuarial Science, Mathematics Education, or Professional Mathematics.

Undergraduate minors are available in three areas: Mathematics; Statistics; and Mathematics for Managerial, Social, and Life Sciences.

## General Mathematics

# Mathematics, General Mathematics Concentration, M.S.

**James Hart, Program Director
(615) 898-2402James.Hart@mtsu.edu**

Three concentrations are offered under the Master of Science: General Mathematics (students desiring a broad background in mathematics should pursue this concentration); Industrial Mathematics (students interested in positions in industry or further graduate work in applied mathematics should pursue this concentration); and Research Preparation (students wishing to pursue the Ph.D. in Mathematics should choose this concentration).

Please see undergraduate catalog for information regarding undergraduate programs.

### Admission Requirements

Admission normally requires completion of the GRE or MAT with acceptable scores. (Successful applicants typically have combined GRE scores of 291 [current scale] or 900 [former scale] or above or MAT scores of 402 or greater.)

Applicant must

- have earned a bachelor's degree from an accredited university or college;
- have an acceptable grade point average for all college work taken;
- have completed 21 semester hours of college-level mathematics (including calculus), with at least 9 hours of mathematics beyond calculus.

### Application Procedures

*All application materials are to be submitted to the College of Graduate Studies.*

Applicant must

- submit application with the appropriate application fee (online at
**www.mtsu.edu/graduate/apply.php**); - submit official scores on the GRE or MAT;
- submit official transcripts of all previous college work.
- two letters of recommendation are also recommended, but not required.

### Degree Requirements

The Master of Science in Mathematics with a concentration in General Mathematics requires completion of 36 hours consisting of a 9-hour core, 18 hours in the concentration, and a 9-hour cognate approved by the advisor.

Candidate must successfully complete a master's thesis or a written comprehensive examination (may be taken no more than twice).

### Curriculum: Mathematics, General Mathematics Concentration

Candidate must complete 36 hours in the following course of study:

### Core Courses (9 hours)

### MATH 6120 - Advanced Linear Algebra

**3credit hours**Prerequisite: MATH 2010. Continuation of linear algebra topics in MATH 2010 including advanced topics in inner product spaces and structure of linear operators.

### MATH 6170 - Sets and Logic

**3credit hours**Includes topics in three categories: 1) Propositions, predicates, quantifiers, truth tables, tautologies, and methods of mathematical proof including mathematical induction. 2) Sets, relations, functions, graphs, cardinality, and the Axiom of Choice. 3) Applications of these foundations to selected results in algebra and analysis as time permits. It is recommended that this course be taken early in the graduate program.

### MATH 6190 - Analysis I

**3credit hours**Prerequisite: MATH 4250 or equivalent. Rigorous treatment of limits, continuity, differentiation, and integration; infinite series; introduction to metric spaces.

### Concentration Courses (18 hours)

Eighteen (18) hours from approved courses in mathematical sciences including at least one course from each of three different groups:

### Actuarial and Financial Mathematics:

### ACSI 5200 - Introduction to Mathematics of Investment

**3credit hours**(Same as MATH 5200.) Prerequisite: MATH 1920 or consent of instructor. Calculus and probability/statistics used to model and analyze investments in bonds, treasury bills, stocks, and other derivatives. Topics include obtaining the price of a bond as a function of interest rate, developing formulas for duration and convexity to study the sensitivity of price to interest rate, and mathematical modeling of investor preference and attitude toward risk.

### MATH 5200 - Introduction to Mathematics of Investment

**3credit hours**(Same as ACSI 5200.) Prerequisite: MATH 1920 or consent of instructor. Calculus and probability/statistics used to model and analyze investments in bonds, treasury bills, stocks, and other derivatives. Topics include obtaining the price of a bond as a function of interest rate, developing formulas for duration and convexity to study the sensitivity of price to interest rate, and mathematical modeling of investor preference and attitude toward risk.

### ACSI 5330 - Actuarial Mathematics I

**3credit hours**Prerequisites: ACSI 4230/ACSI 5230 and STAT 4190 or consent of instructor. First of a two-semester sequence; a preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 3. Topics include survival distributions and life tables, life insurance, life annuities, and net premiums.

### ACSI 5340 - Actuarial Mathematics II

**3credit hours**Prerequisite: ACSI 4230/ACSI 5230 and STAT 4190 or consent of instructor. Second of a two-semester sequence; a preparatory course for the Society of Actuaries/Casualty Actuarial Society Course/Exam 3. Topics chosen from net premium reserves, multiple life functions, multiple decrement models, valuation theory and pension plans, and insurance models (including expenses and nonforfeiture benefits and dividends).

### ACSI 5630 - Mathematics of Risk Management

**3credit hours**Prerequisite: ACSI/MATH 4200/ACSI 5200/MATH 5200. A preparatory course for the Society of Actuaries Course 6. Topics include mathematical modeling of volatility; pricing of bonds, stocks, and other derivatives with uncertainty; benchmark portfolios; asset/liability management for property/casualty insurers; liability associated with a financially distressed company. Heath-Jarrow-Morton and Cox-Ingersoll-Ross models studied.

### ACSI 5640 - Mathematics of Options, Futures, and Other Derivatives

**3credit hours**Prerequisites: ACSI/MATH 4630/ACSI 5630/5630 and 4200/ACSI 5200/MATH 5200. A preparatory course for the Society of Actuaries Course 6. Topics include risk management using options, interest rate swaps, interest rate caps, Black-Scholes analysis, Taylor series expansion to obtain hedge parameters, portfolio insurance, numerical procedures, interest rate derivatives, and use of Black's model.

### ACSI 6010 - Credibility Theory and Loss Distributions

**3credit hours**Prerequisite: STAT 5190 or consent of instructor. A preparatory course for Exam Part 4B of the Casualty Actuarial Society. Topics include Bayes Theorem and its relationship to credibility theory and analysis of statistical distributions for modeling insurance claims by size.

### MATH 6603 - Problems in Mathematics-Mathematics of Finance

**1 to 9credit hours**Prerequisite: Mathematical maturity, preparation in the area, and normally nine semester hours of graduate study. Problems course dealing with theory methods and applications.

### MATH 6604 - Problems in Mathematics-Mathematics of Life Contingencies

**1 to 9credit hours**Prerequisite: Mathematical maturity, preparation in the area, and normally nine semester hours of graduate study. Problems course dealing with theory methods and applications.

### Algebra/Number Theory:

### MATH 5420 - Number Theory

**3credit hours**Divisibility congruences, quadratic residues, Diophantine equations, quadratic forms, and continued fractions.

### MATH 5530 - Abstract Algebra II

**3credit hours**Prerequisite: MATH 4510 or MATH 5510. Theory of rings, fields, integral domains, matrices, and vector spaces.

### MATH 6140 - Selected Topics of Modern Mathematics: Algebra

**3credit hours**Prerequisite: MATH 5530 or consent of instructor. Extension of previous work in algebra with emphasis on topics not treated in other courses.

### MATH 6510 - Advanced Algebra

**3credit hours**Prerequisite: MATH 5530. Polynomial rings, theory of fields, vector spaces and intermediate group theory necessary for Galois theory, and Galois theory.

### Analysis:

### MATH 6141 - Selected Topics of Modern Mathematics: Analysis

**3credit hours**Prerequisite: MATH 6200 or consent of instructor. Extension of previous work in analysis with emphasis on topics not treated in other courses.

### MATH 6200 - Analysis II

**3credit hours**Prerequisite: MATH 6190 or equivalent. A continuation of MATH 6190. Lebesgue measure, Lebesgue integral, functions of bounded variation.

### MATH 6210 - Complex Variables

**3credit hours**Prerequisite: MATH 6190. Theory of functions of complex variables and their application in mathematics and physics.

### MATH 6250 - Real Analysis

**3credit hours**Prerequisite: MATH 6200. A continuation of MATH 6200. Advanced topics in real analysis. Abstract measure and integration theory. Introduction to functional analysis.

### Combinatorics/Graph Theory:

### MATH 5700 - Combinatorics and Graph Theory

**3credit hours**Prerequisite: MATH 2010 or 3080. Selected topics in combinatorics and graph theory emphasizing combinatorial problem solving and algorithmic proof.

### MATH 6700 - Advanced Combinatorics and Graph Theory

**3credit hours**Prerequisite: MATH 4700/MATH 5700. Selected topics in combinatorics and graph theory extending topics studied in MATH 4700/MATH 5700.

### Geometry/Topology:

### MATH 5270 - Introduction to Topology

**3credit hours**Prerequisites: MATH 3110 and a previous upper-division course in which the student has been required to write proofs. Fundamental concepts of topology including continuity, compactness, connectedness, separation axioms, and metric spaces.

### MATH 6142 - Selected Topics in Modern Mathematics: Topology

**3credit hours**Prerequisite: MATH 4270 or MATH 5270 or consent of instructor. Extension of previous work in topology with emphasis on topics not treated in other courses.

### MATH 6400 - Advanced Geometry

**3credit hours**Prerequisite: MATH 3070 or consent of instructor. Detailed study of one or more of the various branches of geometry including non-Euclidean geometry, projective geometry, algebraic geometry, and differential geometry.

### Industrial Mathematics:

### MATH 5310 - Numerical Analysis I

**3credit hours**Prerequisite: CSCI 3180 or equivalent. Application of computer-oriented numerical algorithms to algebraic equations, differential and integral equations, and linear algebra. Rigorous mathematical treatment of error included.

### MATH 5320 - Numerical Analysis II

**3credit hours**Prerequisite: CSCI 3180 or equivalent. Application of computer-oriented numerical algorithms to algebraic equations, differential and integral equations, and linear algebra. Rigorous mathematical treatment of error included.

### MATH 6260 - Advanced Differential Equations I

**3credit hours**Prerequisites: MATH 3120 and 4250. Qualitative and quantitative analysis of systems of differential equations. Gradient systems, Sturm-Liouville problems. Elementary techniques for boundary value problems of partial differential equations.

### MATH 6270 - Advanced Differential Equations II

**3credit hours**Prerequisite: MATH 6260. Solution techniques for boundary value problems. Problems involve heat, wave, and potential equations. Topics include the method of characteristics, series solutions, integral transforms, and Green's functions.

### MATH 6300 - Optimization

**3credit hours**Prerequisite: MATH 5320 or consent of instructor. Constrained and unconstrained optimization problems, including the generalized least squares problem and Eigenvalue problems. Methods include orthogonalization, conjugate gradient, and quasi-Newton algorithms.

### MATH 6310 - Control Theory

**3credit hours**Prerequisite: MATH 6260 or consent of instructor. Vector space applications to system analysis; observability, controllability, and stabilization of systems; feedback systems; Lyapunov methods; optimal control, and the calculus variations.

### Statistics:

### STAT 5200 - Statistical Methods for Forecasting

**3credit hours**Prerequisite: STAT 4190. Application of the regression model in forecasting regression and exponential smoothing methods to forecast nonseasonal time-series, seasonal series and globally constant seasonal models, stochastic time series models; and forecast evaluation. (Offers preparation to actuarial science students for the Society of Actuaries Exam #120 and Exam Part 3A administered by the Casualty Actuarial Society.)

### STAT 5320 - Probability and Stochastic Processes

**3credit hours**Prerequisite: Two semesters of calculus and STAT 3150 (or MATH 2050) or consent of instructor. Theoretical basis for stochastic processes and use as models of real-world phenomena. Topics include Markov chains, Poisson processes, and Brownian motion and stationary processes. Applications include Gambler's Ruin, birth and death models, hitting times, stock option pricing, and the Black-Scholes model.

### STAT 5360 - Regression Analysis

**3credit hours**Prerequisites: MATH 2050 and STAT 3150 or equivalent. Theory and application of regression models. Approaches to model building and data analysis treated. Computation and interpretation of results facilitated through use of statistical software packages.

### STAT 5370 - Nonparametric Statistics

**3credit hours**Prerequisite: STAT 3150 or equivalent. Statistical tests that require no assertions about parameters or about the form of the population from which the samples are drawn. A wide range of practical problems.

### STAT 5380 - Experimental Design

**3credit hours**Prerequisite: STAT 3150 or equivalent. Topics include one-way analysis of variance, multiple comparison, multifactor analysis of variance, and various practical issues in experimental design. Computation and interpretation of results are facilitated through the use of statistical software packages.

### STAT 6160 - Advanced Mathematical Statistics I

**3credit hours**Prerequisite: Two semesters of calculus or permission of instructor. Introduction to theoretical probability used in statistics with an emphasis on the mathematical theory. A rigorous treatment of random variables, their probability distributions, and mathematical exceptions in a univariate and multivariate setting. Includes conditional probabilities, stochastic independence, sampling theory, and limit laws.

### STAT 6180 - Advanced Mathematical Statistics II

**3credit hours**Prerequisite: STAT 6160 or permission of instructor. Theory of estimation and hypothesis tests. Topics include minimum variance unbiased estimation, methods of estimation, most powerful tests, likelihood ratio tests, decision theory, and sequential test procedures.

### STAT 6602 - Problems in Statistics-Regression Analysis

**3credit hours**Prerequisite: Mathematical maturity, preparation in the area and (normally) nine semester hours of graduate study. Problems course dealing with theory, methods, and applications.

### STAT 6603 - Problems in Statistics-Nonparametric Statistics

**3credit hours**Prerequisite: Mathematical maturity, preparation in the area and (normally) nine semester hours of graduate study. Problems course dealing with theory, methods, and applications.

### STAT 6604 - Problems in Statistics-Experimental Design

**3credit hours**Prerequisite: Mathematical maturity, preparation in the area and (normally) nine semester hours of graduate study. Problems course dealing with theory, methods, and applications.

### Cognate (9 hours)

Nine (9) additional hours approved by advisor. The master’s thesis is an option in this concentration. See MATH 6640 Thesis Research (1 to 6 credits).

### Program Notes

Candidate must

- file a degree plan in the College of Graduate Studies prior to entry into the program;
- file a Notice of Intent to Graduate form in the College of Graduate Studies within the first two weeks of the term in which candidate intends to graduate.

## Industrial Mathematics

# Mathematics, Industrial Mathematics Concentration, M.S.

**James Hart, Program Director
(615) 898-2402James.Hart@mtsu.edu**

Three concentrations are offered under the Master of Science: General Mathematics (students desiring a broad background in mathematics should pursue this concentration); Industrial Mathematics (students interested in positions in industry or further graduate work in applied mathematics should pursue this concentration); and Research Preparation (students wishing to pursue the Ph.D. in Mathematics should choose this concentration).

Please see undergraduate catalog for information regarding undergraduate programs.

### Admission Requirements

Admission normally requires completion of the GRE or MAT with acceptable scores. (Successful applicants typically have combined GRE scores of 291 [current scale] or 900 [former scale] or above or MAT scores of 402 or greater.)

Applicant must

- have earned a bachelor's degree from an accredited university or college;
- have an acceptable grade point average for all college work taken;
- have completed 21 semester hours of college-level mathematics (including calculus), with at least 9 hours of mathematics beyond calculus.

### Application Procedures

*All application materials are to be submitted to the College of Graduate Studies.*

Applicant must

- submit application with the appropriate application fee (online at
**www.mtsu.edu/graduate/apply.php**); - submit official scores on the GRE or MAT;
- submit official transcripts of all previous college work;
- two letters of recommendation are recommended, but not required

### Degree Requirements

The Master of Science in Mathematics with a concentration in Industrial Mathematics requires completion of 36 hours of graduate courses consisting of a 9-hour core, 18 hours in the concentration, and a 9-hour cognate approved by the advisor.

Candidate must successfully complete a master's thesis or a written comprehensive examination (may be taken no more than twice).

### Curriculum: Mathematics, Industrial Mathematics

Students interested in positions in industry or further graduate work in applied mathematics should pursue this concentration. In addition to the core, students must complete the concentration and a cognate (36 hours) as outlined below:

### Core (9 hours)

### MATH 6120 - Advanced Linear Algebra

**3credit hours**Prerequisite: MATH 2010. Continuation of linear algebra topics in MATH 2010 including advanced topics in inner product spaces and structure of linear operators.

### MATH 6170 - Sets and Logic

**3credit hours**Includes topics in three categories: 1) Propositions, predicates, quantifiers, truth tables, tautologies, and methods of mathematical proof including mathematical induction. 2) Sets, relations, functions, graphs, cardinality, and the Axiom of Choice. 3) Applications of these foundations to selected results in algebra and analysis as time permits. It is recommended that this course be taken early in the graduate program.

### MATH 6190 - Analysis I

**3credit hours**Prerequisite: MATH 4250 or equivalent. Rigorous treatment of limits, continuity, differentiation, and integration; infinite series; introduction to metric spaces.

### Concentration (18 hours)

Eighteen (18) hours including

### MATH 5310 - Numerical Analysis I

**3credit hours**Prerequisite: CSCI 3180 or equivalent. Application of computer-oriented numerical algorithms to algebraic equations, differential and integral equations, and linear algebra. Rigorous mathematical treatment of error included.

### MATH 5320 - Numerical Analysis II

**3credit hours**

### MATH 6260 - Advanced Differential Equations I

**3credit hours**Prerequisites: MATH 3120 and 4250. Qualitative and quantitative analysis of systems of differential equations. Gradient systems, Sturm-Liouville problems. Elementary techniques for boundary value problems of partial differential equations.

### MATH 6270 - Advanced Differential Equations II

**3credit hours**Prerequisite: MATH 6260. Solution techniques for boundary value problems. Problems involve heat, wave, and potential equations. Topics include the method of characteristics, series solutions, integral transforms, and Green's functions.

### plus two courses from

### MATH 6210 - Complex Variables

**3credit hours**Prerequisite: MATH 6190. Theory of functions of complex variables and their application in mathematics and physics.

### MATH 6300 - Optimization

**3credit hours**Prerequisite: MATH 5320 or consent of instructor. Constrained and unconstrained optimization problems, including the generalized least squares problem and Eigenvalue problems. Methods include orthogonalization, conjugate gradient, and quasi-Newton algorithms.

### MATH 6310 - Control Theory

**3credit hours**Prerequisite: MATH 6260 or consent of instructor. Vector space applications to system analysis; observability, controllability, and stabilization of systems; feedback systems; Lyapunov methods; optimal control, and the calculus variations.

### MATH 6400 - Advanced Geometry

**3credit hours**Prerequisite: MATH 3070 or consent of instructor. Detailed study of one or more of the various branches of geometry including non-Euclidean geometry, projective geometry, algebraic geometry, and differential geometry.

### STAT 6180 - Advanced Mathematical Statistics II

**3credit hours**Prerequisite: STAT 6160 or permission of instructor. Theory of estimation and hypothesis tests. Topics include minimum variance unbiased estimation, methods of estimation, most powerful tests, likelihood ratio tests, decision theory, and sequential test procedures.

### MATH 6700 - Advanced Combinatorics and Graph Theory

**3credit hours**Prerequisite: MATH 4700/MATH 5700. Selected topics in combinatorics and graph theory extending topics studied in MATH 4700/MATH 5700.

### STAT 6160 - Advanced Mathematical Statistics I

**3credit hours**Prerequisite: Two semesters of calculus or permission of instructor. Introduction to theoretical probability used in statistics with an emphasis on the mathematical theory. A rigorous treatment of random variables, their probability distributions, and mathematical exceptions in a univariate and multivariate setting. Includes conditional probabilities, stochastic independence, sampling theory, and limit laws.

### Cognate (9 hours)

Nine (9) additional hours chosen from the above list; MATH 6640, and/or courses from relevant disciplines approved by advisor. The master’s thesis is an option in this concentration. See MATH 6640 Thesis Research (1 to 6 credits).

### Program Notes

Candidate must

- file a degree plan in the College of Graduate Studies prior to entry into the program;
- file a Notice of Intent to Graduate form in the College of Graduate Studies within the first two weeks of the term in which candidate intends to graduate.

## Research Preparation

# Mathematics, Research Preparation Concentration, M.S.

**James Hart, Program Director
(615) 898-2402James.Hart@mtsu.edu**

Three concentrations are offered under the Master of Science: General Mathematics (students desiring a broad background in mathematics should pursue this concentration); Industrial Mathematics (students interested in positions in industry or further graduate work in applied mathematics should pursue this concentration); and Research Preparation (students wishing to pursue the Ph.D. in Mathematics should choose this concentration).

Please see undergraduate catalog for information regarding undergraduate programs.

### Admission Requirements

Admission normally requires completion of the GRE or MAT with acceptable scores. (Successful applicants typically have combined GRE scores of 291 [current scale] or 900 [former scale] or above or MAT scores of 402 or greater.)

Applicant must

- have earned a bachelor's degree from an accredited university or college;
- have an acceptable grade point average for all college work taken;
- have completed 21 semester hours of college-level mathematics (including calculus), with at least 9 hours of mathematics beyond calculus.

### Application Procedures

*All application materials are to be submitted to the College of Graduate Studies.*

Master of Science in Mathematics applicants must

- submit application with the appropriate application fee (online at
**www.mtsu.edu/graduate/apply.php**); - submit official scores on the GRE or MAT;
- submit official transcripts of all previous college work;
- two letters of recommendation are recommended, but not required.

### Degree Requirements

The Master of Science in Mathematics with a concentration in Research Preparation requires completion of 36 hours consisting of a 9-hour core, 18 hours in the concentration, and a 9-hour cognate approved by the advisor.

Candidate must successfully complete a written comprehensive examination (may be taken no more than twice).

### Curriculum: Mathematics, Research Preparation

### Required Core Courses (9 hours)

### MATH 6120 - Advanced Linear Algebra

**3credit hours**Prerequisite: MATH 2010. Continuation of linear algebra topics in MATH 2010 including advanced topics in inner product spaces and structure of linear operators.

### MATH 6170 - Sets and Logic

**3credit hours**Includes topics in three categories: 1) Propositions, predicates, quantifiers, truth tables, tautologies, and methods of mathematical proof including mathematical induction. 2) Sets, relations, functions, graphs, cardinality, and the Axiom of Choice. 3) Applications of these foundations to selected results in algebra and analysis as time permits. It is recommended that this course be taken early in the graduate program.

### MATH 6190 - Analysis I

**3credit hours**Prerequisite: MATH 4250 or equivalent. Rigorous treatment of limits, continuity, differentiation, and integration; infinite series; introduction to metric spaces.

### Concentration (18 hours)

### MATH 5270 - Introduction to Topology

**3credit hours**Prerequisites: MATH 3110 and a previous upper-division course in which the student has been required to write proofs. Fundamental concepts of topology including continuity, compactness, connectedness, separation axioms, and metric spaces.

### MATH 5530 - Abstract Algebra II

**3credit hours**Prerequisite: MATH 4510 or MATH 5510. Theory of rings, fields, integral domains, matrices, and vector spaces.

### MATH 5700 - Combinatorics and Graph Theory

**3credit hours**Prerequisite: MATH 2010 or 3080. Selected topics in combinatorics and graph theory emphasizing combinatorial problem solving and algorithmic proof.

### MATH 6200 - Analysis II

**3credit hours**Prerequisite: MATH 6190 or equivalent. A continuation of MATH 6190. Lebesgue measure, Lebesgue integral, functions of bounded variation.

### MATH 6140 - Selected Topics of Modern Mathematics: Algebra

**3credit hours**Prerequisite: MATH 5530 or consent of instructor. Extension of previous work in algebra with emphasis on topics not treated in other courses.

### MATH 6210 - Complex Variables

**3credit hours**Prerequisite: MATH 6190. Theory of functions of complex variables and their application in mathematics and physics.

### Cognate (9 hours)

Nine (9) hours including MATH 6640 and six (6) additional hours approved by advisor.

### Program Notes

Candidate must

- file a degree plan in the College of Graduate Studies prior to entry into the program;
- file a Notice of Intent to Graduate form in the College of Graduate Studies within the first two weeks of the term in which candidate intends to graduate.

### Contact and Student Information

**James Hart**

James.Hart@mtsu.edu

615-898-2402

**James Hart**

James.Hart@mtsu.edu

615-898-2402

**Department of Mathematical Sciences**MTSU BOX 34

1301 East Main Street

Murfreesboro, Tennessee 37132

**College of Graduate Studies**

Middle Tennessee State University

MTSU Box 42

1301 East Main Street

Murfreesboro, TN 37132

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