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.
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.
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.
Students may choose from three concentrations for the Master of Science (M.S.) in Mathematics: General Mathematics, Industrial Mathematics, or Research Preparation.
MTSU also offers the Master of Science in Teaching (M.S.T.) with a major in Mathematics and concentrations in Middle Grade Mathematics and Secondary Mathematics.
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
For complete curriculum details, click on the REQUIREMENTS tab above.
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 Industrial Mathematics Research Preparation
The Department of Mathematical Sciences offers the Master of Science with a major in Mathematics, the Master of Science in Teaching with a major in Mathematics, and a minor in Mathematics at the graduate level.
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).
Two concentrations are offered under the Master of Science in Teaching: Middle Grade Mathematics and Secondary Mathematics.
The department also offers courses in the Master of Science in Professional Science degree. Students interested in a concentration in Biostatistics or in Actuarial Sciences should refer to the Master's of Science in Professional Science program.
Please see undergraduate catalog for information regarding undergraduate programs.
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
All application materials are to be submitted to the College of Graduate Studies.
Applicant must
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
Candidate must complete 36 hours in the following course of study:
3 credit hours
Prerequisite: MATH 2010. Continuation of linear algebra topics in MATH 2010 including advanced topics in inner product spaces and structure of linear operators.
3 credit 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.
3 credit hours
Prerequisite: MATH 4250 or equivalent. Rigorous treatment of limits, continuity, differentiation, and integration; infinite series; introduction to metric spaces.
Eighteen (18) hours from approved courses in mathematical sciences including at least one course from each of three different groups:
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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).
3 credit 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.
3 credit 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.
3 credit 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.
1 to 9 credit hours
Prerequisite: Mathematical maturity, preparation in the area, and normally nine semester hours of graduate study. Problems course dealing with theory methods and applications.
1 to 9 credit hours
Prerequisite: Mathematical maturity, preparation in the area, and normally nine semester hours of graduate study. Problems course dealing with theory methods and applications.
3 credit hours
Divisibility congruences, quadratic residues, Diophantine equations, quadratic forms, and continued fractions.
3 credit hours
Prerequisite: MATH 4510 or MATH 5510. Theory of rings, fields, integral domains, matrices, and vector spaces.
3 credit hours
Prerequisite: MATH 5530 or consent of instructor. Extension of previous work in algebra with emphasis on topics not treated in other courses.
3 credit hours
Prerequisite: MATH 5530. Polynomial rings, theory of fields, vector spaces and intermediate group theory necessary for Galois theory, and Galois theory.
3 credit hours
Prerequisite: MATH 6200 or consent of instructor. Extension of previous work in analysis with emphasis on topics not treated in other courses.
3 credit hours
Prerequisite: MATH 6190 or equivalent. A continuation of MATH 6190. Lebesgue measure, Lebesgue integral, functions of bounded variation.
3 credit hours
Prerequisite: MATH 6190. Theory of functions of complex variables and their application in mathematics and physics.
3 credit hours
Prerequisite: MATH 6200. A continuation of MATH 6200. Advanced topics in real analysis. Abstract measure and integration theory. Introduction to functional analysis.
3 credit hours
Prerequisite: MATH 2010 or 3080. Selected topics in combinatorics and graph theory emphasizing combinatorial problem solving and algorithmic proof.
3 credit hours
Prerequisite: MATH 4700/MATH 5700. Selected topics in combinatorics and graph theory extending topics studied in MATH 4700/MATH 5700.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.)
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit 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.
3 credit hours
Prerequisite: Mathematical maturity, preparation in the area and (normally) nine semester hours of graduate study. Problems course dealing with theory, methods, and applications.
3 credit hours
Prerequisite: Mathematical maturity, preparation in the area and (normally) nine semester hours of graduate study. Problems course dealing with theory, methods, and applications.
3 credit hours
Prerequisite: Mathematical maturity, preparation in the area and (normally) nine semester hours of graduate study. Problems course dealing with theory, methods, and applications.
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).
Candidate must
The Department of Mathematical Sciences offers the Master of Science with a major in Mathematics, the Master of Science in Teaching with a major in Mathematics, and a minor in Mathematics at the graduate level.
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).
Two concentrations are offered under the Master of Science in Teaching: Middle Grade Mathematics and Secondary Mathematics.
The department also offers courses in the Master of Science in Professional Science degree. Students interested in a concentration in Biostatistics or in Actuarial Sciences should refer to the Master's of Science in Professional Science program.
Please see undergraduate catalog for information regarding undergraduate programs.
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
All application materials are to be submitted to the College of Graduate Studies.
Master of Science in Mathematics applicants must
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
3 credit hours
Prerequisite: MATH 2010. Continuation of linear algebra topics in MATH 2010 including advanced topics in inner product spaces and structure of linear operators.
3 credit 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.
3 credit hours
Prerequisite: MATH 4250 or equivalent. Rigorous treatment of limits, continuity, differentiation, and integration; infinite series; introduction to metric spaces.
3 credit 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.
3 credit hours
Prerequisite: MATH 4510 or MATH 5510. Theory of rings, fields, integral domains, matrices, and vector spaces.
3 credit hours
Prerequisite: MATH 2010 or 3080. Selected topics in combinatorics and graph theory emphasizing combinatorial problem solving and algorithmic proof.
3 credit hours
Prerequisite: MATH 6190 or equivalent. A continuation of MATH 6190. Lebesgue measure, Lebesgue integral, functions of bounded variation.
3 credit hours
Prerequisite: MATH 5530 or consent of instructor. Extension of previous work in algebra with emphasis on topics not treated in other courses.
3 credit hours
Prerequisite: MATH 6190. Theory of functions of complex variables and their application in mathematics and physics.
Nine (9) hours including MATH 6640 and six (6) additional hours approved by advisor.
Candidate must
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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