# Mathematics and Statistics

**Department Head: Dr. Mohsen Razzaghi
Graduate Coordinator: Dr. Corlis Johnson**

410 Allen Hall

Drawer MA

Mississippi State, MS 39762

Telephone: 662-325-3414

Fax: 662-325-0005

E-mail: office@math.msstate.edu

Website: http://math.msstate.edu

## Mathematics

### Admission Criteria

Graduate study is offered in the Department of Mathematics and Statistics leading to the degrees of Master of Science in Mathematics and Doctor of Philosophy in Mathematical Sciences. For unrestricted admission to the master’s degree program, a degree applicant must submit three letters of recommendation and transcripts from all former institutions attended. The applicant must present the equivalent of an undergraduate major in mathematics, as described in the general catalog, with a minimum grade point average of 2.75 on a 4.00 scale on the last two years of undergraduate academic work. In addition, a student is expected to possess those qualities that, in the judgment of the departmental graduate faculty, indicate that the applicant has the ability to do graduate work at the appropriate level. A minimum score of 477 PBT (153 CBT or 53 iBT) on the Test of English as a Foreign Language (TOEFL) or a score of 4.5 on the International English Language Testing Systems (IELTS) is required of international students (with some exceptions). An applicant for the Ph.D. program must meet the requirements for admission to the master’s degree program and submit a satisfactory score on the Graduate Record Examination (GRE) General Test. The department awards a limited number of teaching assistantships. It is recommended that teaching assistantship applicants who do not have English as their native language must submit a score of at least 600 PBT (100 iBT) on the TOEFL or 7.5 on the IELTS.

### Provisional Admission

An applicant who has not fully met the GPA requirement stipulated by the University may be admitted on a provisional basis. The provisionally-admitted student is eligible for a change to regular status after receiving a 3.00 GPA on the first 9 hours of graduate courses at Mississippi State University (with no grade lower than a C). The first 9 hours of graduate courses must be within the student's program of study. Courses with an S grade, transfer credits, or credits earned while in Unclassified status cannot be used to satisfy this requirement. If a 3.00 is not attained, the provisional student **shall **be dismissed from the graduate program. Academic departments may set higher standards for students to fulfill provisional requirements; a student admitted with provisional status should contact the graduate coordinator for the program’s specific requirements. **While in the provisional status, a student is not eligible to hold a graduate assistantship.**

### Academic Performance

Continuous enrollment in the University or in a specific graduate program is dependent upon a satisfactory evaluation of academic performance and progress toward the completion of a specified degree. A student’s progress is considered satisfactory unless judged to be unsatisfactory by the department and/or the dean of the college offering the program.

Unsatisfactory progress in a degree program may be defined as one or more of the following.

- A student’s failure to maintain a B average on all graduate courses attempted after admission to the program
- Failure of a Master’s Core Examination or a Ph.D. Comprehensive Area Examination
- Failure of the preliminary examination

In January, May, and August of each year, the Graduate Coordinating Committee will review the academic records of students who were admitted with contingent or provisional status, are currently on probation, have earned a grade of D, F, or U during the previous semester, or have earned more than two grades below B. The Graduate Coordinating Committee will consider making a recommendation to the Dean of the Graduate School that a student be dismissed from his/her degree program if any of the following conditions exist.

- The student’s progress in his/her degree program is deemed unsatisfactory
- The student is not making satisfactory progress toward satisfying any condition of his/her contingent admission
- The student is on academic probation and cannot meet the requirements for good academic standing within the next 9 credit hours taken in the student’s program of study

Any of the following will result in a recommendation for dismissal from a graduate degree program.

- Two failures on the Master’s Core Examination or a Ph.D. Comprehensive Area Examination
- Failure of a student in provisional status to achieve a 3.00 GPA on the first 9 hours of regular graduate level coursework taken at Mississippi State University
- More than two grades below a B
- A grade of D, F, or U in any course (graduate or undergraduate) taken while the student is enrolled in a graduate program in mathematics or statistics

The student and advisor (if different from the graduate coordinator) will be notified in writing when the first and second unsatisfactory grades are received. A student enrolled in a graduate program in the Department of Mathematics and Statistics will be placed on academic probation if the student fails to maintain a 3.00 GPA or earns a grade below a B in a prerequisite course. To be removed from academic probation, the student must achieve an overall GPA of 3.00 or higher on coursework taken toward the degree.

To be eligible for the preliminary/comprehensive examination, a graduate student must maintain an overall B average in all graduate courses attempted while in a specific program. Individual programs may have additional requirements.

## Statistics

### Admission Criteria

Graduate study is offered in the Department of Mathematics and Statistics leading to the degrees of Master of Science in Statistics and Doctor of Philosophy in Mathematical Sciences. Admission to the master’s degree program in statistics is open to graduates in all disciplines. An applicant must submit three letters of recommendation and transcripts from all former institutions attended. The student must present the equivalent of a bachelor’s degree, with a minimum grade point average of 2.75 on a 4.00 scale on the last two years of undergraduate academic work. In addition, a student is expected to possess those qualities that, in the judgment of the departmental graduate faculty, indicate that the applicant has the ability to do graduate work at the appropriate level. A minimum score of 477 PBT (53 iBT) on the Test of English as a Foreign Language (TOEFL) or 4.5 on the International English Language Testing Systems (IELTS) is required of international students (with some exceptions). An applicant for the Ph.D. program must meet the requirements for admission to the master’s degree program and submit a satisfactory score on the Graduate Record Examination (GRE) General Test. The department awards a limited number of teaching assistantships. It is recommended that teaching assistantship applicants who do not have English as their native language must submit a score of at least 600 PBT (100 iBT) on the TOEFL or 7.5 on the IELTS.

### Provisional Admission

An applicant who has not fully met the GPA requirement stipulated by the University may be admitted on a provisional basis. The provisionally-admitted student is eligible for a change to regular status after receiving a 3.00 GPA on the first 9 hours of graduate courses at Mississippi State University (with no grade lower than a C). The first 9 hours of graduate courses must be within the student's program of study. Courses with an S grade, transfer credits, or credits earned while in Unclassified status cannot be used to satisfy this requirement. If a 3.00 is not attained, the provisional student **shall **be dismissed from the graduate program. Academic departments may set higher standards for students to fulfill provisional requirements; a student admitted with provisional status should contact the graduate coordinator for the program’s specific requirements. **While in the provisional status, a student is not eligible to hold a graduate assistantship.**

### Academic Performance

Continuous enrollment in the University or in a specific graduate program is dependent upon a satisfactory evaluation of academic performance and progress toward the completion of a specified degree. A student’s progress is considered satisfactory unless judged to be unsatisfactory by the department and/or the dean of the college offering the program.

Unsatisfactory progress in a degree program may be defined as one or more of the following.

- A student’s failure to maintain a B average on all graduate courses attempted after admission to the program
- Failure of a Master’s Core Examination or a Ph.D. Comprehensive Area Examination
- Failure of the preliminary examination

In January, May, and August of each year, the Graduate Coordinating Committee will review the academic records of students who were admitted with contingent or provisional status, are currently on probation, have earned a grade of D, F, or U during the previous semester, or have earned more than two grades below B. The Graduate Coordinating Committee will consider making a recommendation to the Dean of the Graduate School that a student be dismissed from his/her degree program if any of the following conditions exist.

- The student’s progress in his/her degree program is deemed unsatisfactory
- The student is not making satisfactory progress toward satisfying any condition of his/her contingent admission
- The student is on academic probation and cannot meet the requirements for good academic standing within the next 9 credit hours taken in the student’s program of study

Any of the following will result in a recommendation for dismissal from a graduate degree program.

- Two failures on the Master’s Core Examination or a Ph.D. Comprehensive Area Examination
- Failure of a student in provisional status to achieve a 3.00 GPA on the first 9 hours of regular graduate level coursework taken at Mississippi State University
- More than two grades below a B
- A grade of D, F, or U in any course (graduate or undergraduate) taken while the student is enrolled in a graduate program in mathematics or statistics

The student and advisor (if different from the graduate coordinator) will be notified in writing when the first and second unsatisfactory grades are received.

A student enrolled in a graduate program in the Department of Mathematics and Statistics will be placed on academic probation if the student fails to maintain a 3.00 GPA or earns a grade below a B in a prerequisite course. To be removed from academic probation, the student must achieve an overall GPA of 3.00 or higher on coursework taken toward the degree.

To be eligible for the preliminary/comprehensive examination, a graduate student must maintain an overall B average in all graduate courses attempted while in a specific program. Individual programs may have additional requirements.

#### Prerequisite Courses

The master’s degree program in Statistics requires as prerequisite expertise in the following: Matrix Algebra, Computer Concepts, and Calculus at the level of MA 2743 Calculus IV.

## Master of Science in Mathematics - Thesis

MA 6153 | Matrices and Linear Algebra ^{1} | 3 |

MA 6753 | Applied Complex Variables ^{1} | 3 |

MA 6933 | Mathematical Analysis I ^{1} | 3 |

MA 6163 | Group Theory | 3 |

or MA 6943 | Mathematical Analysis II | |

MA /ST 6543 | Introduction to Mathematical Statistics I | 3 |

or MA 6313 | Numerical Analysis I | |

MA XXXX | Additional graduate-level coursework | 15 |

MA 8000 | Thesis Research/ Thesis in Mathematics | 6 |

Total Hours | 36 |

^{1} | Requires an examination. |

## Master of Science in Mathematics - Non-Thesis

MA 6153 | Matrices and Linear Algebra ^{1} | 3 |

MA 6753 | Applied Complex Variables ^{1} | 3 |

MA 6933 | Mathematical Analysis I ^{1} | 3 |

MA 6163 | Group Theory | 3 |

or MA 6943 | Mathematical Analysis II | |

MA /ST 6543 | Introduction to Mathematical Statistics I | 3 |

or MA 6313 | Numerical Analysis I | |

MA XXXX | Additional graduate-level coursework | 18 |

MA 7000 | Directed Individual Study in Mathematics ^{2} | 3 |

Total Hours | 36 |

^{1} | Requires an examination. |

^{2} | A project is required. |

## Doctor of Philosophy in Mathematical Sciences - Mathematics

Graduate-level coursework in each of four areas of mathematics and/or statistics | 24 | |

Graduate-level coursework in area of specialization | 9-12 | |

MA 9000 | Dissertation Research /Dissertation in Mathematics | 20 |

Total Hours | 53-56 |

Comprehensive area examinations, a preliminary examination, a dissertation, and dissertation defense are required. Before taking the preliminary examination, a Ph.D. student must satisfy the departmental foreign language requirement.

Research areas for the Ph.D. include

- applied and computational mathematics,
- ordinary and partial differential equations,
- functional analysis and operator theory,
- topology,
- graph theory,
- geometric combinatorics, and
- statistics.

For further details and specific degree requirements contact the Graduate Coordinator.

## Master of Science in Statistics - Thesis

ST 8533 | Applied Probability ^{1} | 3 |

ST 8603 | Applied Statistics ^{1} | 3 |

ST 6543 | Introduction to Mathematical Statistics I ^{1} | 3 |

ST 6573 | Introduction to Mathematical Statistics II ^{1} | 3 |

ST 8613 | Linear Models I ^{1} | 3 |

ST 8000 | Thesis Research/ Thesis in Statistics | 6 |

ST XXXX | Additional graduate-level coursework | 15 |

Total Hours | 36 |

^{1} | Requires an examination over these core courses. |

## Master of Science in Statistics - Non-Thesis

ST 8533 | Applied Probability ^{1} | 3 |

ST 8603 | Applied Statistics ^{1} | 3 |

ST 6543 | Introduction to Mathematical Statistics I ^{1} | 3 |

ST 6573 | Introduction to Mathematical Statistics II ^{1} | 3 |

ST 8613 | Linear Models I ^{1} | 3 |

ST XXXX | Additional graduate-level coursework | 18 |

ST 7000 | Directed Individual Study in Statistics ^{2} | 3 |

Total Hours | 36 |

^{1} | Requires an examination over these core courses. |

^{2} | A project is required. |

In addition, there is ample flexibility in the non-thesis option to allow a graduate student with special interest in an area of statistical application to acquire an area of emphasis in that particular applied field.

## Doctor of Philosophy in Mathematical Sciences - Statistics

Graduate-level coursework in each of four areas of mathematics and/or statistics | 24 | |

Graduate-level coursework in area of specialization | 9-12 | |

ST 9000 | Dissertation Research /Dissertation in Statistics | 20 |

Total Hours | 53-56 |

Comprehensive area examinations, a preliminary examination, a dissertation, and dissertation defense are required. Before taking the preliminary examination, a Ph.D. student must satisfy the departmental foreign language requirement.

Research areas for the Ph.D. include

- linear models,
- multivariate statistics,
- probability theory and stochastic processes, and
- statistical methods.

Many applied courses are offered that are suitable for a minor in statistics at the master’s or doctoral level.

For further details and specific degree requirements, contact the Graduate Coordinator.

## Mathematics

**MA 6133 Discrete Mathematics: 3 hours.**

(Prerequisites: MA 3163 or consent of instructor). Three hours lecture. Sets, relations, functions, combinatorics, review of group and ring theory, Burnside's theorem, Polya's counting theory, group codes, finite fields, cyclic codes, and error-correcting codes

**MA 6143 Graph Theory: 3 hours.**

(Prerequisites: MA 3113 or consent of instructor). Three hours lecture. Basic concepts, graphs, and matrices, algebraic graph theory, planarity and nonplanarity, Hamiltonian graphs, digraphs, network flows, and applications

**MA 6153 Matrices and Linear Algebra: 3 hours.**

(Prerequisites: MA 3113 and MA 3253). Three hours lecture. Linear transformations and matrices; eigen values and similarity transformations; linear functionals, bilinear and quadratic forms; orthogonal and unitary transformations; normal matrices; applications of linear algebra

**MA 6163 Group Theory: 3 hours.**

(Prerequisite: MA 3163 or consent of the instructor). Three hours lecture. Elementary properties: normal subgroups; factor groups; homomorphisms and isomorphisms; Abelian groups; Sylow theorems; composition series; solvable groups

**MA 6173 Number Theory: 3 hours.**

(Prerequisite: MA 3113). Three hours lecture. Divisibility: congruences; quadratic reciprocity; Diophantine equations; continued fractions

**MA 6243 Data Analysis I: 3 hours.**

(Prerequisite:MA 2743. Corequisite:MA 3113). Three hours lecture. Data description and descriptive statistics, probability and probability distributions, parametric one-sample and two-sample inference procedures, simple linear regression, one-way ANOVA. Use of SAS. (Same as ST 4243/6243)

**MA 6253 Data Analysis II: 3 hours.**

(Prerequisite:MA 4243/6243 and MA 3113). Three hours lecture. Multiple linear regression; fixed, mixed, and random effect models;block designs; two-factor analysis of variance;three-factor analysis of variance;analysis of covariance. Use of SAS. (Same as ST 4253/6253)

**MA 6313 Numerical Analysis I: 3 hours.**

(Prerequisites: CSE 1233 or equivalent, MA 3113, and MA 2743). Three hours lecture. Matrix operations; error analysis; norms of vectors and matrices; transformations; matrix functions; numerical solutions of systems of linear equations; stability; matrix inversion; eigen value problems; approximations

**MA 6323 Numerical Analysis II: 3 hours.**

(Prerequisites: CSE 1233 or equivalent. MA 3113 and MA 3253). Three hours lecture. Numerical solution of equations; error analysis; finite difference methods; numerical differentiation and integration; series expansions; difference equations; numerical solution of differential equations

**MA 6373 Introduction to Partial Differential Equations: 3 hours.**

(Prerequisite: MA 3253). Three hours lecture. Linear operators: linear first order equations; the wave equation; Green's function and Sturm-Liouville problems; Fourier series; the heat equation; Laplace's equation

**MA 6523 Introduction to Probability: 3 hours.**

(Prerequisite: MA 2733). Three hours lecture. Basic concepts of probability, conditional probability, independence, random variables, discrete and continuous probability distributions, moment generating function, moments, special distributions, central limit theorem. (Same as ST 4523/6523)

**MA 6533 Introduction to Probability and Random Processes: 3 hours.**

(Prerequisites: MA 3113 and MA 2743). Three hours lecture. Probability, law of large numbers, central limit theorem, sampling distributions, confidence intervals, hypothesis testing, linear regression, random processes, correlation functions, frequency and time domain analysis. (Credit can not be earned for this course and MA/ST 4523/6523)

**MA 6543 Introduction to Mathematical Statistics I: 3 hours.**

(Prerequisite: MA 2743.) Three hours lecture. Combinatorics; probability, random variables, discrete and continuous distributions, generating functions, moments, special distributions, multivariate distributions, independence, distributions of functions of random variables. (Same as ST 4543/6543.)

**MA 6573 Introduction to Mathematical Statistics II: 3 hours.**

(Prerequisite: MA 4543/6543.) Three hours lecture. Continuation of MA-ST 4543/6543. Transformations, sampling distributions, limiting distributions, point estimation, interval estimation, hypothesis testing, likelihood ratio tests, analysis of variance, regression, chi-square tests. (Same as ST 4573/6573.)

**MA 6633 Advanced Calculus I: 3 hours.**

(Prerequisite: MA 2743 and MA 3053). Three hours lecture. Theoretical investigation of functions; limits; differentiability and related topics in calculus

**MA 6643 Advanced Calculus II: 3 hours.**

(Prerequisite: MA 4633/6633). Three hours lecture. Rigorous development of the definite integral; sequences and series of functions; convergence criteria; improper integrals

**MA 6733 Linear Programming: 3 hours.**

(Prerequisites:MA 3113).Three hours lecture. Theory and application of linear programming; simplex algorithm,revised simplex algorithm, duality and sensitivity analysis, transportation and assignment problem algorithms,interger and goal programming. (Same as IE 4733/6733)

**MA 6753 Applied Complex Variables: 3 hours.**

(Prerequisite: MA 2743). Three hours lecture. Analytic functions: Taylor and Laurent expansions; Cauchy theorems and integrals; residues; contour integration; introduction to conformal mapping

**MA 6933 Mathematical Analysis I: 3 hours.**

(Prerequisite: MA 4633/6633 or equivalent). Three hours lecture. Metric and topological spaces; functions of bounded variation and differentiability in normed spaces

**MA 6943 Mathematical Analysis II: 3 hours.**

(Prerequisite: MA 4933/6933). Three hours lecture. Riemann-Stieltjes integration, sequences and series of functions; implicit function theorem; multiple integration

**MA 6953 Elementary Topology: 3 hours.**

(Prerequisite: MA 4633/6633). Three hours lecture. Definition of a topological space, metric space, continuity in metric spaces and topological spaces; sequences; accumulation points; compactness, separability

**MA 6990 Special Topics in Mathematics: 1-9 hours.**

Credit and title to be arranged. This course is to be used on a limited basis to offer developing subject matter areas not covered in existing courses. (Courses limited to two offerings under one title within two academic years)

**MA 7000 Directed Individual Study in Mathematics: 1-6 hours.**

Hours and credits to be arranged

**MA 8000 Thesis Research/ Thesis in Mathematics: 1-13 hours.**

Hours and credits to be arranged

**MA 8113 Modern Higher Algebra I: 3 hours.**

(Prerequisite: MA 4163/6163). Three hours lecture. A study of the basic mathematical systems with emphasis on rings, fields, and vector spaces

**MA 8123 Modern Higher Algebra II: 3 hours.**

(Prerequisite: MA 8113). Three hours lecture. A continuation of the topics introduced in MA 8113

**MA 8203 Foundations of Applied Mathematics I: 3 hours.**

(Prerequisites: MA 3113, MA 3253 or consent of instructor.) Three hours lecture. Principles of applied mathematics including topics from perturbation theory, calculus of variations, and partial differential equations. Emphasis of applications from heat transfer, mechanics, fluids

**MA 8213 Foundations of Applied Mathematics II: 3 hours.**

(Prerequisite: MA 8203). Three hours lecture. A continuation of MA 8203 including topics from wave propagation, stability, and similarity methods

**MA 8253 Operational Mathematics: 3 hours.**

(Prerequisite: MA 4753/6753). Three hours lecture. Theory and applications of Laplace, Fourier, and other integral transformations: introduction to the theory of generalized functions

**MA 8273 Special Functions: 3 hours.**

Three hours lecture. Infinite products: asymptotic series; origin and properties of the special functions of mathematical physics

**MA 8283 Calculus of Variations: 3 hours.**

Three hours lecture. Functionals: weak and strong extrema; necessary conditions for extrema; sufficient conditions for extrema; constrained extrema; direct methods; applications

**MA 8293 Integral Equations: 3 hours.**

Three hours lecture. Equations of Fredholm type: symmetric kernels; Hilbert-Schmidt theory; singular integral equations; applications; selected topics

**MA 8313 Ordinary Differential Equations I: 3 hours.**

Three hours lecture. Linear systems of differential equations; existence and uniqueness; second order systems; systems with constant coefficients; periodic systems; matrix comparison theorems; applications and selected topics

**MA 8323 Ordinary Differential Equations II: 3 hours.**

(Prerequisite: MA 8313). Three hours lecture. Existence, uniqueness, continuation of solutions of nonlinear systems; properties of solutions of linear and nonlinear equations including boundedness, oscillation, asymptotic behavior, stability, and periodicity; application

**MA 8333 Partial Differential Equations I: 3 hours.**

(Prerequisite: MA 4373/6373 or consent of instructor). Three hours lecture. Solution techniques; existence and uniqueness of solutions to elliptic, parabolic, and hyperbolic equations; Green's functions

**MA 8343 Partial Differential Equations II: 3 hours.**

(Prerequisite: MA 8333). Three hours lecture. A continuation of the topics introduced in MA 8333

**MA 8363 Numerical Solution of Systems of Nonlinear Equations: 3 hours.**

(Prerequisites: MA 4313/6313 and MA 4323/6323). Three hours lecture. Basic concepts in the numerical solution of systems of nonlinear equations with applications to unconstrained optimization

**MA 8383 Numerical Solution of Ordinary Differential Equations I: 3 hours.**

(Prerequisites: MA 4313/6313 and MA 4323/6323). Three hours lecture. General single-step, multistep, multivalue, and extrapolation methods for systems of nonlinear equations; convergence; error bounds; error estimates; stability; methods for stiff systems; current literature

**MA 8443 Numerical Solution of Partial Differential Equations I: 3 hours.**

(Prerequisites: MA 4313/6313, MA 4323/6323, and MA 4373/6373 or consent of instructor). Three hours lecture. Basic concepts in the finite difference and finite element methods; methods for parabolic equations; analysis of stability and convergence

**MA 8453 Numerical Solution of Partial Differential Equations II: 3 hours.**

(Prerequisite: MA 8443). Three hours lecture. Methods for elliptic equations; iterative procedures; integral equation methods; methods for hyperbolic equations; stability; dissipation and dispersion

**MA 8463 Numerical Linear Algebra: 3 hours.**

(Prerequisite: MA 4323/6323). Three hours lecture. Basic concepts of numerical linear algebra

**MA 8633 Real Analysis I: 3 hours.**

(Prerequisite: MA 4943/6943). Three hours lecture. Lebesgue measure and Lebesgue integrals; convergence theorems, differentiation and L spaces

**MA 8643 Real Analysis II: 3 hours.**

(Prerequisite: MA 8633). Three hours lecture. General measures; the Radon-Nikodym theorem and other topics

**MA 8663 Functional Analysis I: 3 hours.**

(Prerequisite: MA 8643). Three hours lecture. Hilbert spaces; Banach spaces; locally convex spaces; Hahn-Banach and closed graph theorems; principle of uniform boundedness; weak topologies

**MA 8673 Functional Analysis II: 3 hours.**

(Prerequisite: MA 8663). Three hours lecture. Continuation of topics introduced in MA 8663

**MA 8713 Complex Analysis I: 3 hours.**

(Prerequisite MA 4943/6943 or consent of instructor). Three hours lecture. Complex numbers: functions of a complex variable; continuity; differentiation and integration of complex functions; transformations in the complex plane

**MA 8723 Complex Analysis II: 3 hours.**

(Prerequisite: MA 8713). Three hours lecture. Series; analytic continuation; Riemann surfaces; theory of residues

**MA 8913 Introduction to Topology I: 3 hours.**

(Prerequisite: MA 4643/6643 or MA 4953/6953). Three hours lecture. Basic general topology; introduction of homotopy and homology groups

**MA 8923 Introduction to Topology II: 3 hours.**

(Prerequisite: MA 8913). Three hours lecture. Continuation of topics introduced in MA 8913

**MA 8981 Teaching Seminar: 1 hour.**

One hour lecture. Preparation for service as instructors in mathematics and statistics courses; includes practice lectures and exam preparation. (May be taken for credit more than once.)

**MA 8990 Special Topics in Mathematics: 1-9 hours.**

Credit and title to be arranged. This course is to be used on a limited basis to offer developing subject matter areas not covered in existing courses. (Courses limited to two offerings under one title within two academic years)

**MA 9000 Dissertation Research /Dissertation in Mathematics: 1-13 hours.**

Hours and credits to be arranged

**MA 9313 Selected Topics in Ordinary Differential Equations: 3 hours.**

(Prerequisite: MA 8313 and consent of instructor). (May be taken for credit more than once). Three hours lecture. Topics to be chosen from such areas as Bifurcation Theory, Biological Modeling, Control Theory, Dynamical Systems, Functional Differential Equations, Nonlinear Oscillations, and Quantitative Behavior

**MA 9333 Selected Topics in Partial Differential Equations: 3 hours.**

(Prerequisite: MA 8333 and consent of instructor). (May be taken for credit more than once). Three hours lecture. Topics to be chosen from such areas as Bifurcation Theory, Boundary Integral Methods, Evolution Equations, Maximum and Variational Principles, and Spectral Methods

**MA 9413 Selected Topics in Numerical Analysis: 3 hours.**

(Prerequisite: Consent of instructor). (May be taken for credit more than once). Three hours lecture. Current topics in Numerical Analysis. The subject matter may vary from year to year

**MA 9633 Selected Topics in Analysis: 3 hours.**

(Prerequisite: MA 8643 and consent of instructor). (May be taken for credit more than once). Three hours lecture. Topics will be chosen from areas of analysis of current interest

## Statistics

**ST 6111 Seminar in Statistical Packages: 1 hour.**

One hour lecture. Introduction to the statistical computer packages available at MSU

**ST 6211 Statistical Consulting: 1 hour.**

(Prerequisite: Consent of the department). Provides students with the opportunity to participate as statistical consultants on real projects; consultants are required to attend a weekly staff meeting. (May be repeated for credit.)

**ST 6213 Nonparametric Methods: 3 hours.**

(Prerequisite: An introductory course in statistical methods). Three hours lecture. Nonparametric and distribution-free methods, including inferences for proportions, contingency table analysis, goodness of fit tests, statistical methods based on rank order, and measures of association

**ST 6243 Data Analysis I: 3 hours.**

(Prerequisite:MA 2743, Corequisite MA 3113). Three hours lecture. Data description and descriptive statistics, probability and probability descriptions, parametric one-sample and two-sample inference procedures, simple linear regression, one-way ANOVA. Use of SAS. (Same as MA 4243/6243)

**ST 6253 Data Analysis II: 3 hours.**

(Prerequisite:MA/ST 4243/6243 and MA 3113). Three hours lecture. Multiple linear regression fixed, mixed, and random effect models;block design;two-factor analysis of variance;three-factor analysis of variance; analysis of covariance. Use of SAS. (Same as MA 4253/6253)

**ST 6313 Introduction to Spatial Statistics: 3 hours.**

(Prerequisite: Grade of C or better in ST 3123, or equivalent). Two hours lecture. Two hours laboratory. Spatial data analysis; kriging, block kriging, cokriging, variogram models;median polish and universal kriging for mean-nonstationary data;spatial autoregressive models; estimation and testing; spatial sampling

**ST 6523 Introduction to Probability: 3 hours.**

(Prerequisite: MA 2733). Three hours lecture. Basic concepts of probability, conditional probability, independence, random variables, discrete and continuous probability distributions, moment generating function, moments, special distributions, central limit theorem. (Same as MA 4523/6523)

**ST 6543 Introduction to Mathematical Statistics I: 3 hours.**

(Prerequisite: MA 2743). Three hours lecture. Combinatorics; probability, random variables, discrete and continuous distributions, generating functions, moments, special distributions, multivariate distributions, independence, distributions of functions of random variables. (Same as MA 4543/6543)

**ST 6573 Introduction to Mathematical Statistics II: 3 hours.**

(Prerequisite: ST 4543/6543). Three hours lecture. Continuation of ST 4543/6543. Transformations, sampling distributions, limiting distributions, point estimation, interval estimation, hypothesis testing, likelihood ratio tests, analysis of variance, regression, chi-square tests. (Same as MA 4573/6573)

**ST 6990 Special Topics in Statistics: 1-9 hours.**

Credit and title to be arranged. This course is to be used on a limited basis to offer developing subject matter areas not covered in existing courses. (Courses limited to two offerings under one title within two academic years)

**ST 7000 Directed Individual Study in Statistics: 1-6 hours.**

Hours and credits to be arranged

**ST 8000 Thesis Research/ Thesis in Statistics: 1-13 hours.**

Hours and credits to be arranged

**ST 8114 Statistical Methods: 4 hours.**

(Prerequisite: MA 1313). Three hours lecture. Two hours laboratory. Fall and Spring semesters. Descriptive statistics; sampling distributions; inferences for one and two populations; completely random, block, Latin square, split-plot designs; factorials; simple linear regression; chi-square tests

**ST 8214 Design and Analysis of Experiments: 4 hours.**

(Prerequisite: ST 8114) Three hours lecture. Three hours laboratory. Offered spring semester. Procedures in planning and analyzing experiments; simple, multiple, and curvilinear regression; factorial arrangement of treatments; confounding; fractional replication; block designs; lattices; split-plots

**ST 8253 Regression Analysis: 3 hours.**

(Prerequisite: ST 8114 or equivalent). Three hours lecture. Fall and Spring semesters. Simple linear regression analysis and related inferences, remedial measures, multiple and polynomial regression, use of indicator variables, variable selection methods, and use of computer

**ST 8263 Advanced Regression Analysis: 3 hours.**

(Prerequisite: ST 8253). Three hours lecture. Continuation of ST 8253, including variable selection methods, optimization techniques, biased estimation methods such as ridge regression, non-linear regression, model validation methodology, indicator variables, design models

**ST 8313 Introduction to Survey Sampling: 3 hours.**

(Prerequisite: ST 8114). Three hours lecture. Topics include: design, planning, execution, and analysis of sample surveys; simple random, stratified random, cluster, and systematic sampling; ratio and regression estimation

**ST 8353 Statistical Computations: 3 hours.**

(Prerequisite: ST 8114). Three hours lecture. Applications of computer packages, including data screening, t-tests and Hotelling's T", analysis of designed experiments, regression analysis, contingency table analysis, projects, and report writing

**ST 8413 Multivariate Statistical Methods: 3 hours.**

(Prerequisite: ST 8253). Three hours lecture. Multivariate normal; multiple and partial correlation; principal components; factor analysis; rotation; canonical correlation; discriminant analysis; Hotelling's T"; cluster analysis; multidimensional scaling; multivariate analysis of variance

**ST 8433 Multivariate Statistical Analysis: 3 hours.**

(Prerequisites: ST 8413 and ST 8613 or consent of instructor). Three hours lecture. Theory of multivariate statistical methodology, including multivariate normal and Wishart distributions, Hotelling’s T2, classification, multivariate analysis of variance and covariance, canonical correlation, principal components analysis

**ST 8533 Applied Probability: 3 hours.**

(Prerequisite: ST 4543/6543). Three hours lecture. An introduction to the applications of probability theory. Topics include Markov Chains, Poisson Processes, and Renewal, Queueing, and Reliability theories. Other topics as time permits

**ST 8553 Advanced Probability Theory: 3 hours.**

(Prerequisites: ST 6543 and MA 8633 or consent of instructor). Three hours lecture. A measure-theoretic presentation of the theory of probability including independence and conditioning, convergence theorems, characteristics functions, and limit theorems

**ST 8563 Advanced Stochastic Processes: 3 hours.**

(Prerequisite: ST 8553 or consent of instructor). Three hours lecture. Continuation of ST 8553, including Markov processes, second-order processes, stationary processes, Ergodic theory, martingales, stopping lines, and Brownian motion

**ST 8603 Applied Statistics: 3 hours.**

(Prerequisite: ST 4253/6253 or equivalent). Three hours lecture. Advanced analysis of experimental data. Topics include mixed and random models, incomplete block design, changeover trials, experiments, analysis of covariance, and repeated measures design

**ST 8613 Linear Models I: 3 hours.**

(Prerequisites: ST 4253/6253 and ST 4573/6573) . Three hours lecture. Random vectors, multivariate normal, distribution of quadratic forms, estimation and statistical inferences relative to the general linear model of full rank, theory of hypothesis testing

**ST 8633 Linear Models II: 3 hours.**

(Prerequisite: ST 8613). Three hours lecture. Continuation of ST 8613, including generalized inverses; general linear model not of full rank, related inferences, applications; computing techniques; design models, analyses, hypothesis testing; variance-component models

**ST 8733 Advanced Statistical Inference I.: 3 hours.**

Prerequisites: MA/ST 4573/6573 or consent of instructor). Three hours lecture. Theoretical statistics, including sufficiency and completeness, UMVU estimators, likelihood estimation, Bayesian estimation, UMP tests, likelihood-based tests, sequential tests, optimality, and asymptotic properties

**ST 8743 8743 Advanced Statistical Inference II: 3 hours.**

(Prerequisites: ST 8733 or consent of instructor). Three hours lecture. Theoretical statistics, including order statistics, power functions, efficiency, asymptotic theory, nonparametric rank- based hypothesis testing, permutation testing, M estimation, jackknife procedure, and bootstrap procedure

**ST 8853 Advanced Design of Experiments I: 3 hours.**

(Prerequisite: ST 8603 or ST 8214). Three hours lecture. Noise reducing designs; incomplete block designs; factorial experiments, Yates' algorithms, confounding systems; fractional replication; pooling of experiments; nested designs; repeated measurement designs; messy data analyses

**ST 8863 Advanced Design of Experiments II: 3 hours.**

(Prerequisites: ST 8853 and ST 8613). Three hours lecture. Continuation of ST 8853, including analysis of covariance, split-plot designs and variants, applications of the general linear model, response surface methodology, randomization models, pseudo-factors, and cross-over design

**ST 8913 Recent Developments in Statistics: 3 hours.**

(Prerequisite: Consent of instructor). New results in statistical theory and/or statistical methodology; advanced work organized around topics not usually considered in the other courses

**ST 8951 Seminar in Statistics: 1 hour.**

(Prerequisite: Consent of Instructor). (May be repeated for credit). Review of literature on assigned topics; discussions and presentations of papers

**ST 8990 Special Topics in Statistics: 1-9 hours.**

**ST 9000 Dissertation Research /Dissertation in Statistics: 1-13 hours.**

Hours and credits to be arranged