# Department of Mathematics and Statistics

**Department Head: Mohsen Razzaghi
Associate Director and Graduate Coordinator: Corlis Johnson
Undergraduate Coordinator: Len Miller
Associate Undergraduate Coordinator for Advising: Robert Banik**

Office: 410 Allen Hall

The Department of Mathematics and Statistics offers a Bachelor of Arts degree and a Bachelor of Science degree. Both degrees are 124 hours. The department also offers undergraduate minors in mathematics and statistics which are described below.

Candidates for the Bachelor of Arts degree are required to complete a minimum of 36 hours of mathematics. Candidates for the Bachelor of Science degree are required to take a minimum of 42 hours of mathematics. Required courses for each degree are listed below. Students must also satisfy the General Education requirements and College Core requirements, including speech, computer literacy and writing requirements.

Mathematics courses below Calculus I (MA 1713), do not count toward a degree in mathematics. Entering freshmen who plan to major in mathematics but do not meet the prerequisites for MA 1713 are encouraged to take the necessary courses during the summer in order to avoid adding one or two semesters to their degree. Otherwise, students who wish to major in mathematics but who do not meet the prerequisites of MA 1713 should join the undeclared major until they are ready to take Calculus I. At that time, they will be assigned an advisor in the Department of Mathematics and Statistics.

For all degree programs, including minors, a student must have an overall C average and a C average in the math classes which count toward the degree. Moreover, students pursuing a B.A. or B.S. degree in mathematics must have at least a GPA of 2.5 in Calculus I-IV, Linear Algebra and Differential Equations (MA 1713, MA 1723, MA 2733, MA 2743, MA 3113 and MA 3253). Students who fail to meet this requirement must withdraw from the B.A. and B.S. degree programs in Mathematics, subject to appeal to the department’s undergraduate coordinator.

Regarding graduate study, the Department of Mathematics and Statistics offers a Master of Science in Mathematics, Master of Science in Statistics, and a Doctor of Philosophy in Mathematical Sciences. Major areas of study for the Doctor of Philosophy in Mathematical Sciences include applied and computational mathematics, ordinary and partial differential equations, functional analysis and operator theory, graph theory, geometric combinatorics, topology and statistics. Please see the graduate coordinator for more details.

## B.A. in Mathematics

### General Education and College Requirements

English Composition | ||

EN 1103 | English Composition I | 3 |

or EN 1163 | Accelerated Composition I | |

EN 1113 | English Composition II | 3 |

or EN 1173 | Accelerated Composition II | |

Foreign Language | ||

3 semesters - one Foreign Language - see advisor | 9 | |

Humanities | ||

Literature - see University/A&S Core | 3 | |

History - see University/A&S Core | 3 | |

Philosophy - see University/A&S Core | 3 | |

From at least 2 different areas of Humanities | 9 | |

Math | ||

See Major Core | 6 | |

Fine Arts | ||

See A&S Requirements | 3 | |

Natural Sciences | ||

BIO 1134 | Biology I | 4 |

or BIO 1144 | Biology II | |

AND | ||

CH 1213 | Chemistry I | 3 |

CH 1223 | Chemistry II | 3 |

CH 1211 | Investigations in Chemistry I | 1 |

OR | ||

Physics I | ||

Physics II | ||

Social Sciences Electives | ||

Courses must spread over at least 4 disciplines with a max of one Economics and a max of 2 in each remaining discipline; 6 hours need to be from A&S requirements. | 18 | |

Major Core | ||

Students should check for prerequisites for all courses and consult their advisor. | ||

MA 1713 | Calculus I | 3 |

MA 1723 | Calculus II | 3 |

MA 2733 | Calculus III | 3 |

MA 2743 | Calculus IV | 3 |

MA 3053 | Foundations of Mathematics | 3 |

MA 3113 | Introduction to Linear Algebra | 3 |

MA 3163 | Introduction to Modern Algebra | 3 |

MA 3253 | Differential Equations I | 3 |

MA 4633 | Advanced Calculus I | 3 |

Math Elective - 3000+ | 3 | |

Math Elective - 4000 | 3 | |

Oral Communication Requirement | ||

CO 1003 | Fundamentals of Public Speaking | 3 |

Writing Requirement | ||

MA 4213 | Senior Seminar in Mathematics | 3 |

Computer Literacy | ||

CSE 1233 | Computer Programming with C | 3 |

General Electives | ||

Consult advisor | 16-28 | |

Total Hours | 124 | |

(31 hours must be 3000/4000 from A&S) |

## B.S. in Mathematics

### General Education and College Requirements

English Composition | ||

EN 1103 | English Composition I | 3 |

or EN 1163 | Accelerated Composition I | |

EN 1113 | English Composition II | 3 |

or EN 1173 | Accelerated Composition II | |

Foreign Language | ||

2 semesters - one Foreign Language - see advisor | 6 | |

Humanities | ||

Literature - see University/A&S Core | 3 | |

History - see University/A&S Core | 3 | |

Math | ||

See Major Core | 6 | |

Fine Arts | ||

See A&S Requirements | 3 | |

Natural Sciences | ||

Choose one of three options: | 15-18 | |

Option 1 | ||

Physics I | ||

Physics II | ||

Physics III | ||

Chemistry I | ||

Chemistry II | ||

Investigations in Chemistry I | ||

Option 2 | ||

Physics I | ||

Physics II | ||

Physics III | ||

PLUS choose two of the following: | ||

Biology I | ||

Biology II | ||

Genetics I | ||

Option 3 | ||

Biology I | ||

Biology II | ||

Genetics I | ||

Chemistry I | ||

Chemistry II | ||

Investigations in Chemistry I | ||

Social Sciences | ||

See A&S Requirements | 6 | |

Major Core | ||

Students should check for prerequisites for all courses and consult their advisor. | ||

MA 1713 | Calculus I | 3 |

MA 1723 | Calculus II | 3 |

MA 2733 | Calculus III | 3 |

MA 2743 | Calculus IV | 3 |

MA 3053 | Foundations of Mathematics | 3 |

MA 3113 | Introduction to Linear Algebra | 3 |

MA 3163 | Introduction to Modern Algebra | 3 |

MA 3253 | Differential Equations I | 3 |

MA 4313 | Numerical Analysis I | 3 |

MA 4633 | Advanced Calculus I | 3 |

MA 4643 | Advanced Calculus II | 3 |

Math Elective (3000+) | 3 | |

Math Elective (4000) | 3 | |

Oral Communication Requirement | ||

CO 1003 | Fundamentals of Public Speaking | 3 |

Writing Requirement | ||

MA 4213 | Senior Seminar in Mathematics | 3 |

Computer Literacy | ||

CSE 1233 | Computer Programming with C | 3 |

General Electives | ||

Consult advisor | 30-40 | |

Total Hours | 124 | |

(31 hours must be 3000/4000 from A&S) |

### Math Minor

A minor in mathematics consists of

MA 1713 | Calculus I | 3 |

MA 1723 | Calculus II | 3 |

MA 2733 | Calculus III | 3 |

MA 2743 | Calculus IV | 3 |

MA 3113 | Introduction to Linear Algebra | 3 |

MA 3253 | Differential Equations I | 3 |

One additional math course at the 3000 level and one additional 4000-level math course |

## Statistics (ST)

**Major Advisor: Associate Professor Janice DuBien**

Office: 448 Allen Hall

Courses in statistics are designed to satisfy two objectives. The first objective is to provide graduate training for those students wishing to pursue a career as professional statisticians. Both graduate and undergraduate courses are available for this purpose. The second is to provide minors for students from other disciplines. A minor in statistics consists of

MA /ST 3123 | Introduction to Statistical Inference | 3 |

ST 4111 | Seminar in Statistical Packages | 1 |

ST 4213 | Nonparametric Methods | 3 |

or ST 4313 | Introduction to Spatial Statistics | |

Choose one of the following: | 3 | |

Introduction to Probability | ||

Introduction to Mathematical Statistics I | ||

ST 4243 | Data Analysis I | 3 |

ST 4253 | Data Analysis II | 3 |

Please notice that MA 2743 and MA 3113 are prerequisites for ST 4243 and ST 4253.

Graduate study is offered in the Department of Mathematics and Statistics leading to the degree of Master of Science in Mathematics, Master of Science in Statistics, and a Doctor of Philosophy in Mathematical Sciences. Many applied statistics courses are offered which are suitable for a minor in statistics at the master’s or doctoral level. Specific course requirements for the graduate minor in statistics may be obtained from the Graduate Coordinator of the Department of Mathematics and Statistics.

Admission to the master’s program in statistics is open to graduates in all disciplines. The program of study is a blend of both statistical theory and statistical methods. In addition, there is ample flexibility in the non-thesis option to allow a graduate student with special interests in an area of statistical application to minor in that particular applied field. The department awards a limited number of teaching assistantships. For further details, consult the Graduate Coordinator of the Department of Mathematics and Statistics.

### Mathematics Courses

**MA 0003 Developmental Mathematics: 3 hours.**

(MA 0003 is a developmental course designed to prepare a student for university mathematics courses at the level of MA 1313 College Algebra: credit received for this course will not be applicable toward a degree). Three hours lecture. Real numbers fractions, decimal fractions, percent, algebraic expressions, factoring, algebraic fractions, linear equations/inequalities, integral exponents, quadratic equations

**MA 0103 Intermediate Algebra: 3 hours.**

(MA 0103 is designed to prepare a student for MA 1313 College Algebra) Two hours lecture. Two hours laboratory. Real numbers, algebraic expressions, factoring, algebraic fractions,linear equations/inequalities, quadratic equations, Pythagorean Theorem. Does not count toward any degree. Students with a math subscore of 17 or 18 must take this course in the summer or spring terms at MSU, transfer credit from another institution, or test out of the course by taking a departmental test

**MA 1001 First Year Seminar: 1 hour.**

One hour lecture. First-year seminars explore a diverse arrary of topics that provide students with an opportunity to learn about a specific discipline from skilled faculty members

**MA 1313 College Algebra: 3 hours.**

(Students with credit in MA 1713 will not receive credit for this course; Prerequisite: ACT math subscore 19, or grade of C or better in MA 0103). Two hour lecture. Two hours laboratory. Review of fundamentals; linear and quadratic equations; inequalities; functions; simultaneous equations; topics in the theory of equations

**MA 1323 Trigonometry: 3 hours.**

(Students with credit in MA 1713 will not receive credit for this course; Prerequisite: ACT Math subscore 24 (or higher for some sections), or grade of C or better in MA 1313). Three hours lecture. The trigonometric functions: identities; trigonometric equations; applications

**MA 1413 Structure of the Real Number System: 3 hours.**

(Prerequisite: C or better in MA 1313 or an ACT Math sub-score or 24). Three hours lecture. The nature of mathematics; introductory logic; structure and development of the real number system. (For Elementary and Special Education majors only)

**MA 1423 Problem Solving with Real Numbers: 3 hours.**

(Prerequisite: C or better in MA 1413). Three hours lecture. Proportions, percent problems, probability, counting principles,statistics. (For Elementary of Special Education majors only)

**MA 1433 Informal Geometry and Measurement: 3 hours.**

(Prerequisites: C or better in both MA 1413 and MA 1423). Three hours lecture. Measurements and informal geometry. (For Elementary and Special Education majors only)

**MA 1453 Precalculus with Graphing Calculators: 3 hours.**

(Prerequisites:Math ACT 24 or C or better in MA 1323 or a score of at least 70 on the Precalculus Qualifying Exam). Three hours lecture. Properties, applications, and graphs of linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions;trigonometric identities, equations and inverses; inequalities. (Degree credit will not be granted for MA 1453 and either MA 1313 or MA 1323. This course is intended to prepare students to take MA 1713 Calculus I )

**MA 1613 Calculus for Business and Life Sciences I: 3 hours.**

(Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Three hours lecture. Algebraic and some transcendental functions, solutions of systems of linear equations, limits, continuity, derivatives, applications

**MA 1713 Calculus I: 3 hours.**

(Prerequisite: ACT Math subscore 26, or grade of C or better in 1323 or 1453). Three hours lecture. Analytic geometry; functions; limits; continuity; derivatives of algebraic functions; applications of the derivative. Honors section available

**MA 1723 Calculus II: 3 hours.**

(Prerequisite: Grade of C or better in MA 1713). Three hours lecture. Antidifferentiation; the definite integral; applications of the definite integral; differentiation and integration of transcendental functions. Honors section available

**MA 2113 Introduction to Statistics: 3 hours.**

(Prerequisite:ACT Math subscore 24 (or higher for some sections) or a grade of C or better in MA 1313 ). Two hours lecture.Two hours laboratory. Introduction to statistical techniques: descriptive statistics, random variables, probability distributions, estimation, confidence intervals, hypothesis testing, and measurement of association. Computer instruction for statistical analysis. (Same as ST 2113)

**MA 2733 Calculus III: 3 hours.**

(Prerequisite: Grade of C or better in MA 1723). Three hours lecture. Further methods of integration; polar coordinates; vectors; infinite series. Honors section available

**MA 2743 Calculus IV: 3 hours.**

(Prerequisite: Grade of C or better in MA 2733). Three hours lecture. Differential calculus of functions of several variables; multiple integration; vector calculus. Honors section available

**MA 2990 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 3053 Foundations of Mathematics: 3 hours.**

(Prerequisite: MA 1723). Three hours lecture. The logical structure of mathematics; the nature of a mathematical proof; applications to the basic principles of algebra and calculus

**MA 3113 Introduction to Linear Algebra: 3 hours.**

(Prerequisite: MA 1723). Three hours lecture. Vector spaces; matrices; linear transformations; systems of linear equations; characteristic values and characteristic vectors

**MA 3123 Introduction to Statistical Inference: 3 hours.**

(Prerequisite:ACT math subscore 24, or grade of C or better in MA 1313 ). Two hours lecture. Two hours laboratory. Basic concepts and methods of statistics, including descriptive statistics, probability, random variables, sampling distribution,estimation,hypothesis testing, introduction to analysis of variance, simple linear regression. (Same as ST 3123)

**MA 3163 Introduction to Modern Algebra: 3 hours.**

(Prerequisite: MA 3113 and MA 3053 ). Three hours lecture. Rings,integral domains, and fields with special emphasis on the integers, rational numbers, real numbers and complex numbers; theory of polynomials

**MA 3253 Differential Equations I: 3 hours.**

(Prerequisite: MA 2743 or coregistration in MA 2743). Origin and solution of differential equations; series solutions; Laplace Transform methods; applications

**MA 3353 Differential Equations II: 3 hours.**

(Prerequisite: MA 3253). Three hours lecture. Systems of differential equations; matrix representations; infinite series solution of ordinary differential equations; selected special functions; boundary-value problems; orthogonal functions: Fourier series

**MA 3463 Foundations of Geometry: 3 hours.**

(Prerequisite: MA 1723 and MA 3053) Three hours lecture. The structural nature of geometry; modern methods in geometry: finite geometrics

**MA 3513 History of Mathematics: 3 hours.**

(Prerequisite: MA 2733 or coregistration in MA 2733). Three hours lecture. A historical development of mathematicians and their most important contributions will be emphasized

**MA 4000 Directed Individual Study in Mathematics: 1-6 hours.**

Hours and credits to be arranged

**MA 4133 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 4143 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 4153 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 4163 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 4173 Number Theory: 3 hours.**

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

**MA 4213 Senior Seminar in Mathematics: 3 hours.**

(Prerequisites:MA 3163 and MA 3253 and MA 4633) Three hours lecture. Students explore topics in current mathematical research, write expository articles, and give oral presentations. Refinement of specialized writing skills needed for effective mathematical communication

**MA 4243 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 4253 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 4313 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 4323 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 4373 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 4523 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 4533 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 4543 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 4573 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 4633 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 4643 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 4733 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 4753 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 4933 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 4943 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 4953 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 4990 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 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. Courses numbered MA 8273, 8283, 8293 and 8313 have as prerequisites at least one of the courses MA 4633/6633, MA 4153/6153, 4753/6753

**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 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.**

**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 Courses

**ST 2113 Introduction to Statistics: 3 hours.**

(Prerequisite:ACT Math subscore 24 (or higher for some sections) or a grade of C or better in MA 1313).Two hours lecture. Two hours laboratory. Introduction to statistical techniques; descriptive statistics, random variables, probability distributions, estimation, confidence intervals, hypothesis testing, and measurement of association. Computer instruction for statistical analysis. (Same as MA 2113)

**ST 2990 Special Topics in Statistics: 1-9 hours.**

**ST 3123 Introduction to Statistical Inference: 3 hours.**

(Prerequisite: ACT math subscore 24, or grade of C or better in MA 1313 ). Two hours lecture, Two hours laboratory. Basic concepts and methods of statistics, including descriptive statistics, probability random variables, sampling distribution, estimation, hypothesis testing, introduction to analysis of variance, simple linear regression. (Same as MA 3123),

**ST 4000 Directed Individual Study in Statistics: 1-6 hours.**

Hours and credits to be arranged

**ST 4111 Seminar in Statistical Packages: 1 hour.**

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

**ST 4211 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 4213 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 4243 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 4253 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 4313 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 4523 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 4543 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 4573 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 4990 Special Topics in Statistics: 1-9 hours.**

**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.**

**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