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. A Mathematics Education concentration
is designed for mathematics teachers who wish to significantly increase their mathematical
knowledge and/or teach dual enrollment courses and for individuals with a bachelor's
degree who eventually wish to obtain a terminal degree related to mathematics education.
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.
Related Media
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MTSU College of Graduate Studies
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 and Data 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.
Mathematics Education concentration curriculum will increase students' mathematical knowledge as applied
to the teaching profession at the secondary and early tertiary levels. Secondary school
mathematics teachers will be prepared to teach high school courses with more mathematical
rigor; to transition to community college teaching; and to teach dual enrollment courses.
Graduates, regardless of teaching experience, will also be prepared to enter a terminal
degree program in mathematics education.
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 four concentrations for the Master of Science (M.S.) in Mathematics:
Actuarial and Financial Mathematics, General Mathematics, Industrial Mathematics,
Mathematics Education, Research Preparation, or Mathematic Education.
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.
Actuarial Science
Mathematics, Actuarial and Financial Mathematics Concentration, M.S.
Don Hong, Program Director
(615) 904-8339
Don.Hong@mtsu.edu
The Actuarial and Financial Mathematics concentration is for students who need specialized training in actuarial and financial mathematics as well as internship experience.
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 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). Once this initial application has been accepted, the applicant will receive directions on how to enter the graduate portal to be able to submit other materials.
- 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 Actuarial and Financial Mathematics requires completion of a minimum of 36 semester hours.
Candidate must
- participate in the graduate seminar and give an oral presentation of an approved topic;
- successfully complete a master's thesis or engage in internship or a written comprehensive examination (may be taken no more than twice).
Curriculum: Mathematics, Actuarial and Financial Mathematics
The following illustrates the minimum coursework requirements.
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.
Required Concentration Courses (9 hours)
ACSI 6020 - Construction and Evaluation of Actuarial Models
3credit hours
Prerequisite: ACSI 6010 or permission of instructor. Topics include construction of empirical models, construction and selection of parametric models, construction of models in presence of truncation and censoring, interpolation and smoothing, credibility theory, and simulation.
ACSI 6030 - Actuarial Models for Life Contingencies
3credit hours
Prerequisites: STAT 3150 and ACSI 4230 or MATH 6604 or permission of instructor. Topics include survival distributions, life tables, life insurance, life annuities, and pensions, premiums and reserves, multiple lives, multiple decrements, models including expenses.
ACSI 6040 - Actuarial Models for Financial Economics
3credit hours
Prerequisite: ACSI 4200/ACSI 5200 or MATH 6603 or permission of instructor. Topics include applications of stochastic processes to actuarial models, Poisson process, Markov process, interest rate models, arbitrage free models, valuation of derivative securities, financial risk management.
Thesis/Internship Option
Students may opt in a thesis or internship option. Students who write a master's thesis (MATH 6640) or engage in an internship (ACSI 6910) may substitute one math core course by one of the following data analysis and programming courses in order to prepare them for thesis research or internship working.
For the thesis option, students should enroll in MATH 6640 for at least 3 credit hours.
For the internship credits to be awarded, the location must be approved by the faculty advisor and the internship work must be related to actuarial science. Students must keep a portfolio during the internship and do a presentation upon completion of the internship.
Comprehensive exam will be waived if students write a master's thesis or engage in an internship.
Elective Concentration Courses (12-18 hours)
12-18 hours approved by advisor. Courses should be chosen from the following list of courses:
ACSI 5140 - Mathematical Foundations of Actuarial Science
3credit hours
Prerequisite: STAT 3150 or consent of instructor. Integrates probability and risk management topics into fundamental tools for assessing risk in an actuarial environment. Probability topics include random variables, distributions, conditional probability, independence, and central limit theorems. Risk topics include frequency and severity. Insurance concepts such as retention, deductible, coinsurance, and risk premiums.
ACSI 5200 - Introduction to Mathematics of Investment
3credit hours
(Same as MATH 5200.) Prerequisite: MATH 1920 or consent of instructor. Models and methods to analyze investments in bonds, treasury bills, stocks, and other derivatives. Topics include obtaining the price of bonds, stocks, and options; sensitivity analysis; investment performance assessment; portfolio analysis; capital asset pricing model; and mathematical modeling of investor preference and attitude toward risk.
ACSI 5220 - Mathematics of Corporate Finance
3credit hours
Prerequisites: ACSI/MATH 4200/ACSI 5200/MATH 5200 and ECON 2410, 2420, or consent of instructor. Mathematics of capital budgeting and evaluation models in corporate finance. Topics include net present values, internal rate of return, profitability index; evaluation of projects, corporations, and stocks; capital asset pricing model; cost of capital; quantification of risk and uncertainty; capital budgeting; capital structure; income statement and financial planning.
ACSI 5230 - Mathematics of Compound Interest
3credit hours
Prerequisites: ECON 2410, ECON 2420, ACSI/MATH 4200/ACSI 5200/MATH 5200, or consent of instructor. Topics include measurement of interest (including accumulating and present value factors), annuities certain, yield rates, amortization schedules, sinking funds, and bonds and related securities.
ACSI 5240 - Mathematics of Interest Theory, Economics, and Finance
3credit hours
Prerequisites: ACSI 4230/ACSI 5230 or consent of instructor. Applies calculus and theory of interest tools to intermediate topics in microeconomics and macroeconomics and topics in finance. Topics include pricing activities, the simplified Keynesian model, interest and discount rates, valuation of payment streams, yield rates, amortization, cash flows and internal rate of return, stock and bond valuation, portfolio risks, the Capital Asset Pricing Model (CAPM), efficient markets, capital structure, leverage, financial performance measurement, and basic option pricing and the Black-Scholes model.
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. 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. Concepts and models for long term actuarial mathematics. 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 5530 - Rate Making and Loss Reserving
3credit hours
Prerequisite: ACSI 4200 or consent of the instructor. Introduces the daily work as a P&C actuary in rate making and loss reserving, summarizing loss run data, compiling of loss triangles, computing loss development factors, incurred method, paid method, case method, Bornhuetter-Ferguson method, trend losses, rate making on losses and exposure, IBNR reserving, make loss payments plan, reporting and communication of analysis results.
ACSI 5630 - Mathematics of Risk Management
3credit hours
Prerequisite: ACSI/MATH 4200/ACSI 5200/MATH 5200. Topics chosen from mathematical modeling of volatility; pricing of bonds and stocks; duration and complexity; asset/liability management; forward contract, future contract, options; spreads, collars and other hedging strategies; option pricing models, Black-Scholes formula, Greeks, Delta hedge, Delta-Gamma hedge; hedge portfolio and hedge ratio.
ACSI 5640 - Mathematics of Options, Futures, and Other Derivatives
3credit hours
Prerequisites: ACSI/MATH 4630/ACSI 5630/5630 and 4200/ACSI 5200/MATH 5200. Topics chosen from lognormal model; Black-Scholes equation; volatility; risk neutral pricing; simulation; interest rate models; pricing of bonds, option on bonds, interest rate caps, and other interest rate derivatives.
ACSI 6010 - Introduction to Loss Models
3credit hours
Prerequisite: STAT 5190 or consent of instructor. Topics include statistical distributions for modeling insurance claims frequency and severity, aggregate claim distributions, effect of coverage modifications and inflations, and risk measures.
ACSI 6110 - Predictive Analysis
3credit hours
Prerequisite: ACSI 5140 or consent of instructor. Topics include generalized linear models, logistic regression, discriminant analysis, support vector machines, ridge regression, lasso, sparse modeling, variable selection, model selection, and other selected topics from computational statistics, machine learning, and data mining.
ACSI 6600 - Problems in Actuarial Science
1 to 6credit hours
Prerequisites: Mathematical maturity, preparation in actuarial science (normally nine semester hours of graduate study in actuarial science), and consent of instructor. Students wishing to enroll must select a topic in actuarial science prior to the semester in which ACSI 6600 is taken. Topics include, but are not limited to, applications of principles of actuarial mathematics to group and health insurance, retirement benefits, quantitative risk management, rate making, statistical methods in actuarial data analysis, interest rate models and their applications. Students must submit a written report. Course may be taken up to two times provided that the projects are completely different. Credits may total 1-12 hours.Credit will be based on the difficulty and complexity of the project as determined by the instructor. Pass/Fail grading.
ACSI 6910 - Internship in Actuarial Science
3credit hours
Prerequisites: Major in actuarial science; approval of program director; a plan of activities with the associated firm prior to registration. Practical experience in a specific area of actuarial industry for 250 hours. Pass/Fail.
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 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 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.
STAT 5190 - Mathematical Statistics II
3credit hours
Prerequisite: STAT 3150 or equivalent. Theory of statistical inference. Topics include sampling distributions, decision theory, estimation, test of hypothesis, regression analysis, analysis of variance, and selected applications.
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 5700 - Analysis of Large-Scale Data Sets
3credit hours
The analysis and applications of large-scale data sets. Scalable machine learning and data mining applications in a practical clinical environment. Statistical software used in the application of these techniques.
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 7400 - Computational Statistics
3credit hours
Prerequisites: COMS 6100 and MATH 2530 or equivalent. Statistical visualization and other computationally intensive methods. The role of computation as a fundamental tool of discovery in data analysis, statistical inference, and development of statistical theory and methods. Monte Carlo studies in statistics, computational inference, tools for identification of structure in data, numerical methods in statistics, estimation of functions (orthogonal polynomials, splines, etc.), statistical models, graphical methods, data fitting and data mining, and machine learning techniques.
General Mathematics
Mathematics, General Mathematics Concentration, M.S.
James Hart, Program Director
(615) 898-2402
James.Hart@mtsu.edu
The General Mathematics concentration is for students desiring a broad background in mathematics.
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 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). Once this initial application has been accepted, the applicant will receive directions on how to enter the graduate portal to be able to submit other materials.
- 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 a minimum of 36 semester hours.
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
The following illustrates the minimum coursework requirements. In addition, a maximum of 9 hours of thesis research may be required to fulfill degree requirements.
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 three of the following 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. Models and methods to analyze investments in bonds, treasury bills, stocks, and other derivatives. Topics include obtaining the price of bonds, stocks, and options; sensitivity analysis; investment performance assessment; portfolio analysis; capital asset pricing model; 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. 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. Concepts and models for long term actuarial mathematics. 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. Topics chosen from mathematical modeling of volatility; pricing of bonds and stocks; duration and complexity; asset/liability management; forward contract, future contract, options; spreads, collars and other hedging strategies; option pricing models, Black-Scholes formula, Greeks, Delta hedge, Delta-Gamma hedge; hedge portfolio and hedge ratio.
ACSI 5640 - Mathematics of Options, Futures, and Other Derivatives
3credit hours
Prerequisites: ACSI/MATH 4630/ACSI 5630/5630 and 4200/ACSI 5200/MATH 5200. Topics chosen from lognormal model; Black-Scholes equation; volatility; risk neutral pricing; simulation; interest rate models; pricing of bonds, option on bonds, interest rate caps, and other interest rate derivatives.
ACSI 6010 - Introduction to Loss Models
3credit hours
Prerequisite: STAT 5190 or consent of instructor. Topics include statistical distributions for modeling insurance claims frequency and severity, aggregate claim distributions, effect of coverage modifications and inflations, and risk measures.
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 (6-9 hours)
- Six to nine additional hours approved by advisor.
Thesis (3-9 hours)
- The master's thesis is an option in this concentration. See MATH 6640 Thesis Research (1 to 6 credits).
Industrial Mathematics
Mathematics, Industrial Mathematics Concentration, M.S.
James Hart, Program Director
(615) 898-2402
James.Hart@mtsu.edu
The Industrial Mathematics concentration is for students interested in positions in industry or who want to further graduate work in applied mathematics.
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 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). Once this initial application has been accepted, the applicant will receive directions on how to enter the graduate portal to be able to submit other materials.
- 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 a minimum of 36 semester hours.
Candidate must successfully complete a master's thesis or a written comprehensive examination (may be taken no more than twice).
Curriculum: Mathematics, Industrial Mathematics
The following illustrates the minimum coursework requirements. In addition, a maximum of 9 hours of thesis research may be required to fulfill degree requirements.
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 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)
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.
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 (6-9 hours)
- Six to nine additional hours chosen from the list above list
Thesis (3-9 hours)
The master's thesis is an option in this concentration. See MATH 6640, Thesis Research (1 to 6 credits).
Mathematics Education
Mathematics, Mathematics Education, M.S.
James Hart, Program Director
(615) 898-2402
James.Hart@mtsu.edu
The Mathematics Education concentration is for students who desire to increase their mathematical knowledge as applied to the teaching profession at the secondary and early tertiary levels.
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 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 fee (online at www.mtsu.edu/graduate/apply.php). Once this initial application has been accepted, the applicant will receive directions on how to enter the graduate portal to be able to submit other materials.
- 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 Mathematics Education requires completion of a minimum of 36 semester hours.
Candidate must successfully complete a written comprehensive examination (may be taken no more than twice).
Curriculum: Mathematics, Mathematics Education
The following illustrates the minimum coursework requirements.
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.
Students who choose the Thesis Option
Students who choose the Thesis Option may substitute one of the following courses for a core course:
STAT 6020 - Applied Statistical Methods
3credit hours
Prerequisites: MATH 1530, MATH 2050, or STAT 3150 or permission of instructor. Contemporary and medical research methodology for biostatistics. Descriptive and inferential statistics including parametric and nonparametric hypothesis testing methods, sample size, statistical significance and power, survival curve analysis, relative risk, odds ratios, chi square modeling, and analysis of variance. Data will be analyzed using statistical software.
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.
Concentration Courses (15 hours)
15 hours of approved courses in mathematical sciences from the following list:
MATH 5530 - Abstract Algebra II
3credit hours
Prerequisite: MATH 4510 or MATH 5510. Theory of rings, fields, integral domains, matrices, and vector spaces.
MATH 6320 - Mathematical Problem Solving
3credit hours
Prerequisite: Permission of instructor. A basis for reflection on teaching and learning mathematics. Problem-solving strategies and heuristics. Focuses on all branches of mathematics, providing an opportunity to synthesize mathematical knowledge.
MATH 6330 - Algebra from an Advanced Perspective
3credit hours
Prerequisite: Permission of instructor. Review and extension of algebraic skills and concepts as they relate to the teaching and learning of algebra. Focus on algebraic thinking and problem solving, algebraic systems, functions, graphing, and linear algebra.
MATH 6340 - Geometry from an Advanced Perspective
3credit hours
Prerequisite: Permission of instructor. Investigations into the foundations of plane, solid, and coordinate geometry, motion geometry, similarities and congruencies, measurement and the application of geometry. Instruction will model the suggested pedagogy appropriate for school mathematics.
MATH 6350 - Probability and Statistics from an Advanced Perspective
3credit hours
Prerequisite: Permission of instructor. Relation to school mathematics. Development of central tendency and variation, concepts of chance including sample space, randomness, conditional probability, and independence.
MATH 6900 - Research in Mathematics Education
3credit hours
Prerequisite: Permission of instructor. Examines factors influencing research and critical analyses of selected research in mathematics education. Studies representing different methodologies critiqued.
Cognate (12 hours)
12 hours of approved courses from the following list: The master's thesis is an option in this concentration (MATH 6640, 1-6 credits)
MATH 6360 - Technology Tools for School Mathematics
3credit hours
Integrates technology into the teaching and learning process for teachers of middle and secondary school mathematics. Investigates a variety of mathematical subject matter appropriate for middle and secondary school students via technology. Lessons designed for use with a variety of technologies, including graphing calculators, dynamic geometry software, spreadsheets, authoring software, presentation software, and the World Wide Web. Highly individualized due to varying backgrounds and interests of students.
MATH 6380 - Current Trends in Mathematics Education
3credit hours
Prerequisite: Permission of instructor. Innovative topics or critical issues related to the teaching and learning of mathematics. Includes history of mathematics education, pedagogical content knowledge, assessment and evaluation, and technologies.
FOED 6030 - School and Community Relations
3credit hours
The reciprocal relationship of the two and the skills necessary for analyzing problems and utilizing data and technical skills in planning effective school-community relations programs.
FOED 6630 - Educational Tests and Measurements
3credit hours
Basic concepts in educational measurement and evaluation; evaluation as a part of the teaching-learning process; utilization of evaluation for instructional improvement.
SPSE 6050 - Instructional Leadership
3credit hours
Research on student learning, effective teaching, and effective schools. Attention given to processes for promoting school improvement.
SPSE 6430 - Introduction to Curriculum Development
3credit hours
Opportunity to study, discuss, and evaluate modern practices and procedures in curriculum development and reorganization in schools and school systems.
Research Preparation
Mathematics, Research Preparation Concentration, M.S.
James Hart, Program Director
(615) 898-2402
James.Hart@mtsu.edu
The Research Preparation concentration is for students wishing to pursue the Ph.D. in Mathematics.
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 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). Once this initial application has been accepted, the applicant will receive directions on how to enter the graduate portal to be able to submit other materials.
- 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 a minimum of 36 semester hours.
Candidate must successfully complete a written comprehensive examination (may be taken no more than twice).
Curriculum: Mathematics, Research Preparation
The following illustrates the minimum coursework requirements. In addition, a maximum of 9 hours of thesis research may be required to fulfill degree requirements.
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 (6 hours)
- Six hours approved by advisor
Thesis (3-9 hours)
MATH 6640 - Thesis Research
1 to 6credit hours
Selection of a research problem, review of pertinent literature, collection and analysis of data, and composition of thesis. Once enrolled, student should register for at least one credit hour of master's research each semester until completion. S/U grading.
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