**(330) 941-3302**

Students may select mathematics as their major for the following degree programs:

- Bachelor of Science (BS)
- Bachelor of Science in Education (BSEd)

In addition to satisfying general University requirements, all students majoring in mathematics must complete the following core courses:

COURSE | TITLE | S.H. |
---|---|---|

MATH 1571 | Calculus 1 | 4 |

MATH 1572 | Calculus 2 | 4 |

MATH 2673 | Calculus 3 | 4 |

MATH 3715 | Discrete Mathematics | 3 |

MATH 3720 | Linear Algebra and Matrix Theory | 3 |

MATH 3721 | Abstract Algebra 1 | 4 |

MATH 3751 | Real Analysis 1 | 4 |

STAT 3743 | Probability and Statistics | 4 |

CSIS 2610 | Programming and Problem-Solving | 4 |

Intermediate-level (2600) proficiency in a foreign language | ||

Select one of the following: | 2 | |

Senior Undergraduate Research Project | ||

Thesis | ||

STEM Internship |

In addition, students must complete 12 additional semester hours in mathematics at the 3700-level or above,with at least two courses chosen from the 4800-level. The total number of hours of mathematics is 40 semester hours.

In selecting appropriate courses, the student should consult a department advisor, since certain courses are recommended according to whether the student contemplates graduate study in mathematics or statistics, secondary school teaching, or a career in business, industry, or government. The following courses are recommended based upon the student's interest and career goals:

**Traditional Mathematics**: In addition to the core, students seeking classical training in mathematics are recommended to take MATH 4822, MATH 4880, and MATH 5852 and one additional 4800-level course in mathematics. The minor course of study may be any discipline. Suggested minors include biology, chemistry, computer science, economics, geology, physics, psychology, one engineering specialty (from chemical, civil, electrical, industrial, mechanical), or statistics. Students will study the nature of mathematics in fields such as algebra, real analysis, complex analysis, and topology. Connections to, and generalizations of, earlier formulations of mathematical concepts will constantly occur. Generally, new results in mathematics are developed and proven by those with a Ph.D. in mathematics. Students planning to pursue a Ph.D. will be well prepared for graduate school with these courses and should also study at least one of the languages French, Russian, or German.

**Applied Mathematics**: Applied mathematics courses emphasize areas of mathematics used in government and industry. Students learn mathematical models for the study of physical and computational processes. Mathematical techniques are also used to study uncertainty, scheduling, and decision theory. Many graduates find employment in consulting firms and large corporations where computing and mathematical problem solving skills are valued. Students are also prepared to pursue a master's degree in applied mathematics.

In addition to the core, students interested in applied mathematics are recommended to take MATH 3705, 3760, two electives from MATH 4855, MATH 5825, MATH 5835, MATH 5845, MATH 5861, and MATH 6942, and complete a recognized minor in any discipline. Suggested minors include statistics, computer science, engineering, physics, geology, chemistry, biology, logistics, economics, or geoscience.

**Statistics**: Statistical techniques are utilized in many fields of research such as medicine, biology, business, and sociology. Statisticians learn proper methodology for collecting, summarizing, and interpreting data subject to sampling variability. The increase in affordable computing and the ease of statistical software have placed statistical expertise in demand. Generally, students interested in statistics pursue further study at the graduate level, but positions are available for students upon completion of a bachelor’s degree.

In addition to the core, students interested in statistics are recommended to take MATH 3760, MATH 5845, and complete a minor in statistics that would consist of STAT courses STAT 3743, STAT 4817, STAT 4843, STAT 4844, and two elective courses which can be chosen from the STAT courses STAT 5840, STAT 5846, STAT 5847, STAT 5849 and STAT 5895. One of the elective courses may be chosen from outside the Department of Mathematics and Statistics with the permission of the chairperson. Such a course can be ECON 5824 or ISEN 3720 or another statistics-related course.

**Actuarial Mathematics**: Students interested in using mathematics and statistics to quantify risk and develop models to better predict and study risk should consider actuarial mathematics. Actuaries work for insurance companies, investment and consulting firms, as well as the government and seek to find ways to manage risk and avoid potential exposure to excessive risk. Actuaries assess pension plans, mortality rates, and accident rates. Students will study the mathematical and statistical foundations of actuarial models as they prepare for the examination sequence to become a licensed actuary.

In addition to the core, students interested in actuarial mathematics are recommended to take STAT 5800, STAT 4844, STAT 4888, and STAT 5802 and complete a minor in actuarial science that would consist of STAT courses STAT 4817 and STAT 4843, ECON courses ECON 2610 and ECON 2630, FIN 3720, and either STAT 4848 or ECON 5824.

**Accelerated 4+1 Program**: Undergraduate students can apply for admission into the accelerated program for the MS in Mathematics after completing 78 undergraduate semester hours with a GPA of 3.3 or higher. After being admitted to the accelerated MS program, students can take a maximum of nine semester hours of graduate coursework that can count toward both a bachelor’s and master’s degree from the Department of Mathematics and Statistics. The courses chosen to count for both undergraduate and graduate coursework must be approved by the Graduate Executive Committee within the Department upon admission into the program. An additional six hours of graduate coursework can be completed as an undergraduate and used exclusively for graduate credit. This allows the student to graduate with a master’s degree with one year of additional full-time study beyond the bachelor’s degree.

**Chair**

**Angela Spalsbury**, Ph.D., Chair

**Professors**

**Annette M. Burden**, Ph.D., Professor

**Guang-Hwa (Andy) Chang**, Ph.D., Professor

**Neil Flowers**, Ph.D., Assistant Professor

**Richard G. Goldthwait**, Ph.D., Assistant Professor

**Jozsi Z. Jalics**, Ph.D., Associate Professor

**G. Jay Kerns**, Ph.D., Professor

**Lucy Xiaojing Kerns**, Ph.D., Assistant Professor

**Thomas L. Madsen**, Ph.D., Assistant Professor

**Nguyet Thi Nguyen**, Ph.D., Assistant Professor

**Anita C. O'Mellan**, Ph.D., Professor

**David H. Pollack**, Ph.D., Associate Professor

**Alicia Prieto Langarica**, Ph.D., Associate Professor

**Stephen Rodabaugh**, Ph.D., Professor

**Thomas Smotzer**, Ph.D., Professor

**Angela Spalsbury**, Ph.D., Professor

**Jamal K. Tartir**, Ph.D., Professor

**Padraic ("Paddy") W. Taylor**, Ph.D., Associate Professor

**Thomas P. Wakefield**, Ph.D., Associate Professor

**Eric J. Wingler**, Ph.D., Professor

**George Yates**, Ph.D., Professor

**Instructor**

**Lori A. Carlson**, M.S., Instructor

## Mathematics

**MATH 1501 Elementary Algebraic Models 5 s.h.**

Arithmetic of integers and of rational numbers; linear equations and inequalities in one variable; polynomials, factoring, algebraic fractions, radicals and quadratic equations; linear systems in two variables; graphs. Does not count toward a degree.**Prereq.:** Level 10 on Math Placement Test.

**MATH 1505 Intermediate Algebra with Applications 5 s.h.**

This course is intended to prepare STEM students for their college-level mathematics requirement. Topics include linear and nonlinear equations and inequalities; problem solving; relations of function types that include linear, polynomial, radical, rational, exponential, and logarithmic; applications. Math Placement Level 10 or higher. Does not count toward a degree.

**MATH 1507 Intermediate Algebra 3 s.h.**

Topics include functions of the following: linear, polynomial, rational, exponential, and logarithmic. Emphasis on function relations and graphing by algebraic techniques and technology. Solving linear, nonlinear equations and inequalities. Does not count toward a degree.**Prereq.:** MATH 1501 or Level 20 on Math Placement Test.

**MATH 1510 College Algebra 4 s.h.**

This course is primarily intended to prepare STEM students (along with MATH 1511) for MATH 1570 or 1571 and business students for MATH 1552. Topics include real numbers, equations and inequalities, linear, quadratic, polynomial, exponential, and logarithmic functions, graphing techniques, systems of equations, and applications. The course fulfills the general education requirements for mathematics.**Prereq.:** MATH 1505 or MATH 1507 with a "C" or better or Math Placement Level 35 or higher.**Gen Ed**: Math Substitute.

**MATH 1511 Trigonometry 3 s.h.**

This course, along with MATH 1510 is primarily intended to prepare STEM students for MATH 1570 or MATH 1571. Topics include algebraic structure and graphs of trigonometric functions and inverse trigonometric functions, angle measurements, similar triangles, trigonometric identities, vectors, complex numbers, polar coordinates and solving trigonometric equations with applications.**Prereq.:** MATH 1505 or MATH 1507 or Math Placement Level 35.**Gen Ed**: Math Substitute.

**MATH 1513 Algebra and Transcendental Function 5 s.h.**

Function concepts including trigonometric, exponential, and logarithmic functions. Application problems and graphing. Supplemental topics.**Prereq.:** Math Placement Level 45 or higher.**Gen Ed**: Math Substitute.

**MATH 1552 Applied Mathematics for Management 4 s.h.**

Apply functions, linear systems, linear programming to business including use of technology; mathematics of finance and an introduction to limits, derivatives and integrals with business applications. No credit for students who have completed MATH 1570 or MATH 1571.**Prereq.:** MATH 1510 or at least Level 45 on the Mathematics Placement Test.**Gen Ed**: Math Substitute.

**MATH 1564 Foundations of Middle School Mathematics 1 4 s.h.**

Conceptual foundations of topics from number theory, operations, functions, algebra, geometry, measurement, probability, and data analysis. Emphasis on multiple approaches and representations, problem solving, and communication of mathematical reasoning. Includes inquiry-based laboratory experiences with manipulatives and computing technology.**Prereq.:** At least Level 40 on the Mathematics Placement Test or concurrent registration in MATH 1507 (for both).

**MATH 1570 Applied Calculus 1 4 s.h.**

The elements of differential and integral calculus, with emphasis on applications. Analytical geometry, differentiation and integration techniques and series representations. Introduction to differential equations, transform calculus, and Fourier analysis. This is a basic methods course particularly adapted for those who require applied topics in mathematics. Not applicable toward the Mathematics major. Credit will not be given for both MATH 1549 and MATH 1570. **Prereq.:** MATH 1513, or MATH 1510 and MATH 1511, or at least Level 50 on the Mathematics Placement Test.**Gen Ed**: Math Substitute.

**MATH 1571 Calculus 1 4 s.h.**

A sequence of integrated courses in analytic geometry and calculus. A detailed study of limits, derivatives, and integrals of functions of one and several variables with applications.**Prereq.:** MATH 1513, minimum grade of "C", or MATH 1510 and MATH 1511, minimum grade of "C" in both courses, or at least Level 70 on the Mathematics Placement Test.**Gen Ed**: Math Substitute.

**MATH 1572 Calculus 2 4 s.h.**

A sequence of integrated courses in analytic geometry and calculus. A detailed study of limits, derivatives, and integrals of functions of one and several variables with applications.**Prereq.:** MATH 1571.**Gen Ed**: Math Substitute.

**MATH 1580H Honors Biomathematics 1 2 s.h.**

Counting techniques, probability, matrices and linear systems. Emphasis on the role of mathematical models in explaining and predicting phenomena in life sciences.**Prereq.:** Admission to NEOMED-YSU program.

**MATH 1581H Honors Biomathematics 2 4 s.h.**

A study of functions, differential and integral calculus. Emphasis on the role of mathematical models in explaining and predicting phenomena in life sciences. Credit will not be given for both MATH 1581H and MATH 1571.**Prereq.:** Admission to NEOMED-YSU program.**Gen Ed**: Math Substitute.

**MATH 1585H Honors Calculus 1 5 s.h.**

A sequence of honors courses in analytical geometry and calculus which cover essentially the same material as MATH 1571, MATH 1572, MATH 2673, in two semesters instead of three. A detailed study of limits, derivatives, and integrals of functions of one and several variables and their applications. This sequence will be offered at most once during each academic year.**Prereq.:** Level 90 on the Mathematics Placement Test.**Gen Ed**: Math Substitute.

**MATH 1586H Honors Calculus Laboratory 1 1 s.h.**

Introduction to mathematical modeling of topics covered in calculus. Emphasizes the use of technology such as computer algebra systems, technical document processing, and graphics software for solving problems and reporting solutions.**Prereq.:** MATH 1571 or concurrent with MATH 1585H.

**MATH 2623 Quantitative Reasoning 3 s.h.**

Mathematics models emphasizing basic ideas in mathematics and statistics, stressing concept formation rather than manipulative skills. Credit will not be given for both MATH 2623 and MATH 2625.**Prereq.:** MATH 1501 or Level 20 on the Mathematics Placement Test.**Gen Ed**: Mathematics.

**MATH 2623H Honors Quantitative Reasoning 3 s.h.**

Mathematics models emphasizing basic ideas in mathematics and statistics, stressing concept formation rather than manipulative skills. Credit will not be given for both MATH 2623 and MATH 2625.**Prereq.:** MATH 1501 or Level 20 on the Mathematics Placement Test.**Gen Ed**: Mathematics.

**MATH 2651 Mathematics for Early Childhood Teachers 1 3 s.h.**

A conceptual development of mathematics topics underlying today's Pre-K-grade 3 curriculum. Emphasis on multiple approaches, problem solving, and communication of mathematics. Incorporates classroom activities, manipulatives, technology, and activities developmentally appropriate for young children.**Prereq.:** MATH 1501 or Level 20 on the Mathematics Placement Test.

**MATH 2652 Mathematics for Early Childhood Teachers 2 3 s.h.**

A conceptual development of mathematics topics underlying today's Pre-K-grade 3 curriculum. Emphasis on multiple approaches, problem solving, and communication of mathematics. Incorporates classroom activities, manipulatives, technology, and activities developmentally appropriate for young children.**Prereq.:** MATH 2651.**Gen Ed**: Math Substitute.

**MATH 2665 Foundations of Middle School Mathematics 2 4 s.h.**

Conceptual foundations of topics from number theory, operations, functions, algebra, geometry, measurement, probability, and data analysis. Emphasis on multiple approaches and representations, problem solving, and communication of mathematical reasoning. Includes inquiry-based laboratory experiences with manipulatives and computing technology.**Prereq.:** At least Level 40 on the Mathematics Placement Test or concurrent registration in MATH 1507 (for both).**Gen Ed**: Math Substitute.

**MATH 2670 Applied Calculus 2 5 s.h.**

The elements of differential and integral calculus, with emphasis on applications. Analytical geometry, differentiation and integration techniques and series representations. Introduction to differential equations, transform calculus, and Fourier analysis. This is a basic methods course particularly adapted for those who require applied topics in mathematics. Not applicable toward the Mathematics major. Credit will not be given for both MATH 1549 and MATH 1570.**Prereq.:** MATH 1570.**Gen Ed**: Math Substitute.

**MATH 2673 Calculus 3 4 s.h.**

A sequence of integrated courses in analytic geometry and calculus. A detailed study of limits, derivatives, and integrals of functions of one and several variables with applications.**Prereq.:** MATH 1572.

**MATH 2686H Honors Calculus 2 5 s.h.**

A sequence of honors courses in analytical geometry and calculus which cover essentially the same material as MATH 1571, 1572, 2673, in two semesters instead of three. A detailed study of limits, derivatives, and integrals of functions of one and several variables and their applications. This sequence will be offered at most once during each academic year.**Prereq.:** MATH 1585H.**Gen Ed**: Math Substitute.

**MATH 2687H Honors Calculus Laboratory 2 1 s.h.**

Introduction to mathematical modeling of topics covered in calculus. Emphasizes the use of technology such as computer algebra systems, technical document processing, and graphics software for solving problems and reporting solutions.**Prereq.:** MATH 1572 or concurrent with MATH 1586H.

**MATH 3701 Biomathematics Seminar 1 s.h.**

Introduction to interdisciplinary research in biology and mathematics. Topics include current research by faculty and students, cross disciplinary communication, report writing, technical presentations, literature reading, laboratory techniques and safety. May be repeated once. Listed also as BIOL 3701.**Prereq.:** MATH 1571 or BIOL 2601 or BIOL 2602.

**MATH 3702 Problem Solving Seminar for Secondary Mathematics 3 s.h.**

Approaches to and practice with problem solving with examples from a broad spectrum of mathematics. Emphases include problems at the level of the Praxis II examination for mathematics and problems suitable for high school contests such as the American Mathematics Competition 10 and 12.**Prereq.:** MATH 1572 or consent of instructor.

**MATH 3705 Differential Equations 3 s.h.**

Methods and theory of solving differential equations with applications. Existence, uniqueness. First order equations. Higher order linear equations. Introduction to partial differential equations and boundary value problems, including Laplace's equation.**Prereq.:** MATH 2673.

**MATH 3705H Honors Differential Equations 3 s.h.**

Methods and theory of solving differential equations with applications. Existence, uniqueness. First order equations. Higher order linear equations. Introduction to partial differential equations and boundary value problems, including Laplace's equation.**Prereq.:** MATH 2673.

**MATH 3715 Discrete Mathematics 3 s.h.**

A course in discrete mathematical structures to prepare students for advanced courses. Topics include set theory, functions and relations, logic and quantifiers, truth tables and Boolean expressions, induction and other techniques of proof, and graphs. Credit will not be given for both CSCI 3710 and MATH 3715.**Prereq.:** MATH 1572.

**MATH 3720 Linear Algebra and Matrix Theory 3 s.h.**

Matrices; matrix operations; linear transformations; applications.**Prereq.:** MATH 1572.

**MATH 3721 Abstract Algebra 1 4 s.h.**

Introduction to abstract algebra investigating fundamental concepts in group and ring theory. Topics include groups, subgroups, cyclic groups, permutation groups, cosets, direct products, homomorphisms, factor groups, rings, integral domains and polynomial rings.**Prereq.:** MATH 3715 and MATH 3720.

**MATH 3750 History of Mathematics 3 s.h.**

A survey of the historical development of mathematics.**Prereq.:** MATH 3715.

**MATH 3751 Real Analysis 1 4 s.h.**

Introduction to the properties of the real number system and metrics and metric properties, with critical analysis of limits, continuity, differentiability, integration, and other fundamental concepts underlying the calculus.**Prereq.:** MATH 2673 and MATH 3715.

**MATH 3760 Numerical Analysis 1 3 s.h.**

The theory and techniques of numerical computation. The solution of a single equation, interpolation methods, numerical differentiation and integration, direct methods for solving linear systems.**Prereq.:** MATH 3720 and CSIS 2610.

**MATH 3767 Algebra/Geometry for Middle School Teachers 1 4 s.h.**

An integrated, conceptual, and function-centered approach to the foundations of algebra, geometry, and trigonometry for preservice middle childhood mathematics specialists. Emphasis on multiple approaches and representations, problem solving, and communication of mathematical reasoning. Includes inquiry-based laboratory experiences. Not applicable to the mathematics major.**Prereq.:** MATH 1564 and either 40 on the Mathematics Placement test or MATH 1507.

**MATH 3768 Algebra/Geometry for Middle School Teachers 2 4 s.h.**

An integrated, conceptual, and function-centered approach to the foundations of algebra, geometry, and trigonometry for preservice middle childhood mathematics specialists. Emphasis on multiple approaches and representations, problem solving, and communication of mathematical reasoning. Includes inquiry-based laboratory experiences. Not applicable to the mathematics major.**Prereq.:** MATH 2665 and either 40 on the Mathematics Placement test or MATH 1507.

**MATH 3785 Numerical Methods 3 s.h.**

Matrices, matrix operations, and the application of numerical methods. Not applicable to the Mathematics major.**Prereq.:** MATH 2670 and ENTC 1505, or equivalent.

**MATH 3795 Topics in Mathematics 2-3 s.h.**

The study of a mathematical topic or the development of a special area of mathematics. May be repeated once.**Prereq.:** MATH 1549 or MATH 1570 or MATH 1571 or MATH 2623 or MATH 2651.

**MATH 4822 Abstract Algebra 2 3 s.h.**

A continuation of MATH 3721 with special emphasis on fields. Additional topics in pure or applied algebra.**Prereq.:** MATH 3721 or equivalent.

**MATH 4823 Abstract Algebra 3 3 s.h.**

This course introduces advanced topics in field theory. Topics may include principal ideal domains, irreducibility, quotient rings, algebraic extensions, finite fields, splitting fields, and the Galois group.**Prereq.:** MATH 4822.

**MATH 4830 Foundations of Geometry 3 s.h.**

The development of Euclidean and non-Euclidean geometries from postulate systems.**Prereq.:** MATH 3715.

**MATH 4832 Euclidean Transformations 3 s.h.**

General properties of functions and transformations; isometries and transformations of the Euclidean plane; the complex plane, its geometry and subfields; transformational, analytical, and vector approaches to Euclidean geometry; connections to other branches of mathematics and applications.**Prereq.:** MATH 3720 and MATH 4830.

**MATH 4843 Theory of Probability 3 s.h.**

The mathematical foundation of probability theory including the study of discrete and continuous distributions. Other topics selected from limit theorems, generating functions, applications. Credit will not be given for MATH 4843 and STAT 4843.**Prereq.:** STAT 3743 and MATH 2673.

**MATH 4855 Ordinary Differential Equations 3 s.h.**

A second course in differential equations with emphasis on nonlinear problems and qualitative methods or on boundary value problems. Topics are chosen from: proofs of fundamental theorems, phase plane analysis, limit cycles and the Poincare-Bendixon theorem, biological models, stability via Liapunov functions, asymptotic methods, and boundary value problems.**Prereq.:** MATH 3705 and MATH 3720.

**MATH 4857 Partial Differential Equations 3 s.h.**

Introduction to partial differential equations (PDE) including solution techniques and applications. Classifications of the basic types of PDE's (hyperbolic, parabolic and elliptic) and dependence on boundary and initial conditions. Topics include Fourier series, integral transforms (Fourier, Laplace), and applications in vibrations, electricity, heat transfer, fluids or other selected topics.**Prereq.:** MATH 3705 and MATH 3720.

**MATH 4869 Functions, Calculus, and Applications for Middle School Teachers 3 s.h.**

Polynomial and exponential functions, limits, derivatives, integrals, and applications. Interpretation of slope and area in graphs of functions from applied settings. Applications of limits to the derivations of geometric formulas. Relations between tables, graphs, and the symbolic representation of functions.**Prereq.:** MATH 3767 or consent of instructor.

**MATH 4870 Mathematics Seminar for Middle School Teachers 2 s.h.**

Approaches to and practice with problem solving from a broad spectrum of mathematics. Equal emphasis on problems suitable for contests in the seventh or eighth grade (such as the American Mathematics Competition 8 and MathCounts) and at the level of the Praxis II examination for Middle School Mathematics. May be repeated 2 times.**Prereq.:** MATH 2624 or MATH 2625 or STAT 2601; MATH 3767; MATH 3768; and either MATH 4869 or concurrent registration in MATH 4869.

**MATH 4875 Complex Variables 3 s.h.**

Complex numbers and their geometric representation, analytic functions of a complex variable, contour integration, Taylor and Laurent series, residues and poles, conformal mapping.**Prereq.:** MATH 3751 or equivalent.

**MATH 4880 Introduction to Topology 3 s.h.**

An introduction to the basic concepts of general topology: compactness, connectedness, and continuity in topological spaces.**Prereq.:** MATH 3721 and MATH 3751.

**MATH 4882 Biomathematics Research 1-2 s.h.**

Interdisciplinary and individualized study of a topic in biology and mathematics. Student project mentored jointly by faculty in biology and mathematics. May be repeated once. Grading is Traditional/PR. Listed also as BIOL 4882.**Prereq.:** MATH 3701, BIOL 3701, senior status and permission of the department chairperson.

**MATH 4884 Mathematical Logic 3 s.h.**

An introduction to the study of theories in formalized languages and to the theory of models.**Prereq.:** MATH 3721 or PHIL 3719.

**MATH 4896 Senior Undergraduate Research Project 2 s.h.**

Individualized study of a topic in mathematics culminating in a written report and an oral presentation at a national or regional meeting or a local seminar. May be repeated once.**Prereq.:** 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751 and permission of the department chairperson.**Gen Ed**: Capstone.

**MATH 4897H Thesis 2 s.h.**

Individualized study of a topic in mathematics culminating in a written report and an oral presentation at a national or regional meeting or a local seminar.**Prereq.:** 24 s.h. of mathematics applicable to the mathematics major including both MATH 3721 and MATH 3751 and permission of the department chairperson.

**MATH 5821 Topics in Abstract Algebra 4 s.h.**

A course in abstract algebra aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3721 and MATH 5821.**Prereq.:** MATH 3715 and MATH 3720.

**MATH 5825 Advanced Linear Algebra 3 s.h.**

A study of abstract vector spaces, linear transformations, duality, canonical forms, the spectral theorem, and inner product spaces.**Prereq.:** MATH 3721.

**MATH 5828 Number Theory 3 s.h.**

A study of congruences, Diophantine equations, quadratic residues, special number theory functions, and selected applications.**Prereq.:** MATH 3721.

**MATH 5835 Introduction to Combinatorics and Graph Theory 3 s.h.**

The pigeonhole principle; permutations, combinations, the binomial theorem; the inclusion-exclusion principle; recurrence relations; graphs and digraphs, paths and cycles, trees, bipartite graphs and matchings.**Prereq.:** MATH 3715 and MATH 3720.

**MATH 5845 Operations Research 3 s.h.**

An introduction to operations research with emphasis on mathematical methods. Topics may include: linear programming, sensitivity analysis, duality theory, transportation problems, assignment problems, transshipment problems, and network problems.**Prereq.:** MATH 3715 and MATH 3720.

**MATH 5851 Topics in Analysis 4 s.h.**

A course in analysis aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3751 and MATH 5851.**Prereq.:** MATH 2673, MATH 3720, and MATH 3715.

**MATH 5852 Real Analysis 2 3 s.h.**

Uniform convergence of sequences of functions and some consequences; functions on n-space: derivatives in vector spaces, mean value theorem, Taylor's formula, inverse mapping theorem, implicit mapping theorem.**Prereq.:** MATH 3720 and MATH 3751 or equivalent.

**MATH 5860 Topics in Numerical Analysis 3 s.h.**

A course in numerical analysis aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3760 and MATH 5860.**Prereq.:** MATH 3720 and CSIS 2610.

**MATH 5861 Numerical Analysis 2 3 s.h.**

Numerical methods of initial-value problems, eigenvalue problems, iterative methods for linear and nonlinear systems of equations, and methods involving least squares, orthogonal polynomials, and fast Fourier transforms.**Prereq.:** MATH 2673 and MATH 3760 or equivalent.

**MATH 5875 Complex Variables 3 s.h.**

Complex numbers and their geometric representation, analytic functions of a complex variable, contour integration, Taylor and Laurent series, residues and poles, conformal mapping.**Prereq.:** MATH 3751 or equivalent.

## Statistics

**STAT 2601 Introductory Statistics 3 s.h.**

Designed for students from different disciplines who desire an introduction to statistical reasoning. Topics include collecting and summarizing data, concepts of randomness and sampling, statistical inference and reasoning, correlation and regression.**Prereq.:** MATH 1507 or level 35 on the Math Placement Test.**Gen Ed**: Math Substitute, Math Substitute.

**STAT 2625 Stat Lit and Crit Reasoning 4 s.h.**

An introduction to statistics and its applications. Topics include descriptive statistics, experimental design, probability sampling distribution, statistical inference, correlation and regression. Emphasis on applications, critical reasoning, and data analysis using statistical software. Credit will not be given for both MATH 2623 and MATH 2625.**Prereq.:** MATH 1501 or at least Level 20 on the Mathematics Placement Test.

**STAT 3717 Statistical Methods 4 s.h.**

Probability and statistics designed for students majoring in the natural sciences. Topics include descriptive statistics, probability, estimation, testing hypotheses, analysis of variance, regression and nonparametric statistics. Use of personal computers with computer software will be required. Credit will not be given for both STAT 3717 and STAT 3743.**Prereq.:** MATH 1549 or MATH 1570 or MATH 1571 or MATH 1585H or equivalent.

**STAT 3743 Probability and Statistics 4 s.h.**

A calculus-based probability and statistics course. Topics include descriptive statistics, probability models and related concepts and applications, statistical estimation, and hypothesis testing. Credit will not be given for both STAT 3717 and STAT 3743.**Prereq.:** MATH 1572 or MATH 1585H.

**STAT 3781H Honors Biostatistics 3 s.h.**

Descriptive statistics, testing hypotheses, analysis of count data, correlation, regression, nonparametric statistics, and analysis of variance with applications relating to biological and health sciences.**Prereq.:** MATH 1580H and MATH 1581H, or equivalent.

**STAT 4800 M Found Actuarial Sci 3 s.h.**

**STAT 4804 Actuarial Models 1 3 s.h.**

The statistical foundation of actuarial contingency models including the study of survival and severity distributions. Other topics selected from life insurance and annuities, benefit premiums, reserves, and applications.**Prereq.:** STAT 3743 or consent of department chairperson.

**STAT 4805 Actuarial Models 2 3 s.h.**

The statistical foundation of actuarial contingency models including the analysis of benefit reserves. Other topics selected from multiple life functions and decrement models, insurance models, and applications.**Prereq.:** STAT 3743 or consent of department chairperson.

**STAT 4814 Statistical Data Mining 3 s.h.**

**STAT 4817 Applied Statistics 3 s.h.**

Application of regression, survey sampling, analysis of variance, design and analysis of experiments, and related topics.**Prereq.:** STAT 3717 or STAT 3743 or equivalent.

**STAT 4820 Modern Decision Making 3 s.h.**

**STAT 4843 Theory of Probability 3 s.h.**

The mathematical foundation of probability theory including the study of discrete and continuous distributions. Other topics selected from limit theorems, generating functions, stochastic processes, and applications. Listed also as MATH 4843. Credit for STAT 4843 will not be given to students with MATH 4843.**Prereq.:** STAT 3743 and MATH 2673 or consent of department chairperson.

**STAT 4844 Theory of Statistics 3 s.h.**

The mathematical theory of statistical inferences including likelihood principle, sufficient statistics, theory of statistical estimation, hypothesis testing and related topics.**Prereq.:** MATH 4843.

**STAT 4845 Stochastic Process Models 3 s.h.**

Introduction to the mathematical foundations of the theory and application of stochastic processes. Topics include Markov processes, Poisson processes, queueing theory, and simulation. Other topics selected from limit theorems, Brownian Motion, and stationary processes.**Prereq.:** STAT 4843, MATH 4843.

**STAT 4848 Applied Regression Time Series 3 s.h.**

Statistical methods for regression and time series analysis. Topics include applied linear regression with model fitting and diagnostics, data analysis, and forecasting with time series models.**Prereq.:** STAT 3717 or STAT 3743.

**STAT 4857 Statistical Consulting 3 s.h.**

**STAT 4888 Actuarial Models in Financial Economics 3 s.h.**

An introduction to actuarial models in financial economics. Topics include the Black-Scholes framework for pricing derivatives, the binomial pricing model, and interest rate models.**Prereq.:** STAT 4843.

**STAT 4893 Statistical Internship 2 s.h.**

**STAT 4896 Statistical Project 2 s.h.**

Individualized study of a topic in statistics culminating in a written report and an oral presentation. May be repeated once.**Prereq.:** STAT 4817 and permission of chairperson.**Gen Ed**: Capstone, Capstone.

**STAT 5800 Mathematical Foundations of Actuarial Science 3 s.h.**

A survey of probability theory and an introduction to risk management. Emphasis of the course will be on problem solving with applications in actuarial science.**Prereq.:** MATH 4843, STAT 4843 or consent of instructor.

**STAT 5802 Theory of Interest 3 s.h.**

Mathematical theory and techniques in analysis of interest. Topics include measurement of interest, force of interest, annuities, amortization, pricing of investment products, and applications to actuarial sciences.**Prereq.:** MATH 1572 and any 3700 level MATH, STAT, ECON, or FIN course.

**STAT 5806 Seminar in Actuarial Science 2-3 s.h.**

Approaches to and practice with problem solving in actuarial science. Topics may include financial mathematics, financial economics, or actuarial modeling. May be repeated once. Not applicable to the mathematics major.**Prereq.:** MATH 4843, STAT 4843 or consent of the instructor.

**STAT 5814 Statistical Data Mining 3 s.h.**

A systematic introduction to data mining with emphasis on various data mining problems and their solutions. Topics include data mining processes and issues, exploratory data analysis, supervised and unsupervised learning, classification, and prediction methods.**Prereq.:** STAT 3717 or STAT 3743, or consent of department chairperson.

**STAT 5817 Applied Statistics 3 s.h.**

**STAT 5819 Bayesian Statistics 3 s.h.**

An introduction to the Bayesian approach to statistical inference for data analysis in a variety of applications. Data analysis using statistical software will be emphasized. Topics include: comparison of Bayesian and frequentist methods, Bayesian model specification, prior specification, basics of decision theory, Markov chain Monte Carlo, Bayes factor, empirical Bayes, Bayesian linear regression and generalized linear models, hierarchical models.**Prereq.:** STAT 3717 or STAT 3743 or STAT 4817 or STAT 6940 or equivalent.

**STAT 5840 Statistical Computing 3 s.h.**

Computational methods used in statistics. Topics include generation and testing of random numbers, computer intensive methods, and simulation studies.**Prereq.:** STAT 3717 or STAT 3743.

**STAT 5843 Theory of Probability 3 s.h.**

**STAT 5844 Theory of Statistics 3 s.h.**

**STAT 5846 Categorical Data Analysis 3 s.h.**

Discrete distributions, contingency table analysis, odds ratios, relative risk, logistic regression, hierarchical models.**Prereq.:** STAT 4817 or STAT 4844.

**STAT 5847 Nonparametric Statistics 3 s.h.**

Nonparametric statistical inference including tests of hypotheses for one sample, two or more related independent samples, dependence, goodness-of-fit, trend, and related topics.**Prereq.:** STAT 3717 or STAT 3743 or equivalent.

**STAT 5848 Applied Regression Time Series 3 s.h.**

**STAT 5849 Multivariate Statistical Analysis 3 s.h.**

The statistical analysis of multivariate observations. Topics include multivariate probability distribution theory, regression, analysis of variance, and techniques in data analysis.**Prereq.:** MATH 3720 and STAT 4844 or equivalent.

**STAT 5857 Statistical Consulting 3 s.h.**

The objective of this course is to cultivate the skills necessary to competently engage in statistical consulting. Topics include problem solving, study design, power and sample size, data management, selection and application of statistical methods, ethical practice, and effective visual and literal communication of results.**Prereq.:** STAT 4817 or equivalent.