# Mathematics and Statistics

J. Mark Dorrepaal, Chair

Glenn Lasseigne, Chief Departmental Advisor

## Bachelor of Science—Mathematics Major

The Department of Mathematics and Statistics offers a program of study consisting of three optional tracks, each of which leads to the degree of Bachelor of Science with a major in mathematics. In order to graduate from the program all students must complete the requirements of at least one of these tracks. The optional tracks enable students to emphasize studies in Applied Mathematics, Statistics/Biostatistics, or Mathematics for Secondary School Teachers. The track for secondary school teachers is intended for those who wish to pursue a career in teaching mathematics at the high school level and leads to teaching licensure in the Commonwealth of Virginia. The applied mathematics and statistics/biostatistics tracks are intended for those who wish to pursue graduate work in the mathematical or statistical sciences, or otherwise obtain employment in a mathematics or statistics-related field. Students in these tracks may also obtain teacher licensure by fulfilling the requirements of the Darden College of Education outlined under the teaching track. The requirements of each basic area along with the professional education courses needed for teacher licensure in the Commonwealth of Virginia are listed below.

### Requirements

### Lower Division General Education

Composition ^{*} | 6 | |

Oral Communication | 3 | |

Mathematics | 6 | |

Precalculus I | ||

Precalculus II | ||

Language and Culture | 0-6 | |

Information Literacy and Research | 3 | |

Introduction to Information Literacy and Research for Scientists | ||

Human Creativity | 3 | |

Interpreting the Past | 3 | |

Literature | 3 | |

Human Behavior | 3 | |

Philosophy and Ethics (PHIL 120P recommended) | 3 | |

The Nature of Science ^{**} | 8 | |

Impact of Technology (Satisfied by TLED 430 for teacher education) | 0-3 | |

Total Hours | 41-50 |

* | A grade of C or better is required in both courses. |

** | The eight credit hours of Nature of Science with labs need not be in the same science. However, PHYS 231N-PHYS 232N are recommended for the applied mathematics option; either BIOL 108N-BIOL 109N or BIOL 115N-BIOL 116N are recommended for the statistics/biostatistics option. |

Other Required courses | ||

CS 150 | Problem Solving and Programming I | 4 |

Mathematics Core Course Requirements ^{*} | ||

MATH 211 | Calculus I | 4 |

MATH 212 | Calculus II | 4 |

MATH 307 | Ordinary Differential Equations | 3 |

MATH 311W | Abstract Algebra | 3 |

MATH 312 | Calculus III | 4 |

MATH 316 | Introductory Linear Algebra | 3 |

MATH 317 | Calculus IV: Introductory Analysis | 3 |

STAT 310 | Introductory Data Analysis ^{**} | 3 |

or STAT 431 | Theory of Statistics | |

STAT 330 | An Introduction to Probability and Statistics ^{***} | 3 |

or STAT 331 | Theory of Probability | |

Total Hours | 34 |

* | A grade of C+ or higher is required in these courses. In addition, a grade of C or higher is required in mathematics and statistics prerequisite courses to advance to the next course. |

** | Statistics/Biostatistics majors take both. |

*** | Statistics/Biostatistics majors take STAT 331. |

All students are required to choose one of the following options:

#### Applied Mathematics

MATH 401 | Partial Differential Equations | 3 |

MATH 408 | Applied Numerical Methods I | 3 |

MATH 422 | Applied Complex Variables | 3 |

MATH 400-level electives: | 9 | |

No more than One of the following may be selected: | ||

History of Mathematics | ||

Fundamental Concepts of Geometry | ||

Number Theory and Discrete Mathematics | ||

Total Hours | 18 |

#### Statistics/Biostatistics

STAT 310 | Introductory Data Analysis | 3 |

or STAT 431 | Theory of Statistics | |

STAT 405 | Introduction to Data Handling | 3 |

STAT 400-level electives | 12 | |

Total Hours | 18 |

#### Mathematics for Secondary for Secondary School Teachers

This option is for students seeking teaching licensure (see below for additional information).

### Elective Credit

Elective credit may be needed to meet the minimum requirement of 120 credit hours for the applied mathematics and statistics/biostatistics options.

## Math Teaching Licensure

Due to changing University requirements, national accreditation standards, and the Virginia Board of Education licensure regulations, the teacher preparation programs in the College of Sciences are under constant revision. Any changes resulting from these factors supersede the program requirements described in this Catalog. Students are encouraged to obtain current program information from their advisors and the Teacher Education Services website at __www.odu.edu/tes__.

### Admission

Students must first declare the mathematics teacher preparation track as their major with the mathematics departmental advisor. All students must apply for and be admitted into the approved mathematics teacher preparation program. Students must meet the required criteria for admission by passing the Virginia Board of Education prescribed assessments and earn the minimum required grade point averages (GPA).

### Virginia Board of Education prescribed assessments

- A passing PRAXIS I composite score of 532 or
- Qualifying SAT or ACT test scores or
- PRAXIS I Math test score of 178 and a composite Virginia Communication and Literacy (VCLA) score of 470 or
- SAT Mathematics test score of 530 and a composite Virginia Communication and Literacy (VCLA) score of 470 or
- ACT Mathematics test score of 22 and a composite Virginia Communication and Literacy (VCLA) score of 470

To review more information on the Virginia Board of Education prescribed assessments, visit the Teacher Education Services website, www.odu.edu/tes.

### Required grade point averages (GPA)

- A cumulative GPA of 2.75 is required.
- A major/content GPA of 2.75 is required. No grade lower than C+ is accepted for the core math courses. No grade lower than C- is accepted for the remaining math courses.
- A professional education GPA of 2.75 is required. All professional education courses must be passed with a grade of C- or higher.

Although students may enroll in a limited number of education courses, students must be admitted into the approved mathematics teacher preparation program prior to enrolling in any instructional strategies practicum education course. Students must also meet with an education advisor in the Office of Teacher Education Services.

### Continuance

Students must maintain a cumulative GPA of 2.75, a major/content GPA of 2.75 and a professional education GPA of 2.75. Mathematics core courses must be passed with a grade of C+ or higher. The remaining courses required for the major and in the professional education core must be completed with a grade of C- or higher for continuance. A professional education GPA of 2.75 is required for continuance. Students must take and pass the Virginia Communication and Literacy Assessment (VCLA) and the PRAXIS II Math Content examination prior to or while enrolled in the instructional strategies course. All assessments must be passed prior to the start of the Teacher Candidate Internship Orientation session.

### Virginia Board of Education prescribed assessments

Virginia Communication and Literacy Assessment (VCLA) – a passing composite score of 470 is required on this reading and writing assessment

PRAXIS II Mathematics: Content Knowledge (test code: 0061) – passing score of 147 is required

To review more information on the Virginia Board of Education prescribed assessments visit the Teacher Education Services website, www.odu.edu/tes.

### Graduation

Requirements for graduation include completion of ENGL 110C and ENGL 211C or 221C or 231C with a grade of C or better, completion of the Senior Assessment, a minimum cumulative 2.75 GPA, in the major area, and in the professional education core, with no grade less than C+ in the math core courses and no grade less than C- in the remaining courses in the major and the professional education core, successful completion of the Teacher Candidate Internship and a minimum of 126 credit hours to include a minimum of 32 credit hours overall and 12 credit hours in upper-level courses in the major program from Old Dominion University.

### Course Requirements for the Mathematics for Secondary School Teachers Option

MATH 400 | History of Mathematics | 3 |

MATH 404 | Fundamental Concepts of Geometry | 3 |

MATH 406 | Number Theory and Discrete Mathematics | 3 |

MATH 417 | Intermediate Real Analysis I | 3 |

or MATH 422 | Applied Complex Variables | |

MATH 400-level electives | 6 | |

Total Hours | 18 |

### Professional Education core courses and requirements

TLED 301 | Foundations and Introduction to Assessment of Education | 3 |

TLED 360 | Classroom Management and Discipline | 2 |

TLED 408 | Reading and Writing in Content Areas | 3 |

TLED 430 | PK-12 Instructional Technology ^{*} | 3 |

STEM 453 | Developing Instructional Strategies for Teaching in the Middle/High School: Mathematics | 3 |

TLED 483 | Seminar in Teacher Education ^{**} | 1 |

TLED 485 | Teacher Candidate Internship (student teaching) | 12 |

SPED 313 | Fundamentals of Human Growth and Development: Birth through Adolescence | 3 |

SPED 406 | Students with Diverse Learning Needs in the General Education Classroom | 3 |

Total Hours | 33 |

* | Satisfies impact of technology requirement. |

** | Corequisite with STEM 453. |

### UPPER DIVISION GENERAL EDUCATION

The professional education core satisfies this requirement.

- Option A. Approved Disciplinary Minor (a minimum of 12 hours determined by the department), or second degree or second major.
- Option B: Interdisciplinary Minor (specifically 12 hours, 3 of which may be in the major)
- Option C. International Business and Regional Courses or an approved Certification Program such as teaching licensure
- Option D. Two Upper-Division Courses from outside the College of Sciences and not required by the major (6 hours)

Requirements for graduation for the applied mathematics and statistic tracks include a minimum cumulative grade point average of 2.00 overall and in the major, 120 credit hours, which must include both a minimum 30 credit hours overall and 12 credit hours in upper-level courses in the major program from Old Dominion University*, completion of ENGL 110C and ENGL 211C or 221C or 231C with a grade of C or better, and completion of the Senior Assessment.

* The teaching licensure program requires a minimum of 126 credit hours, which must include 32 credit hours from Old Dominion University.

### Practicum

Any student who wishes to receive a practicum or internship experience may do so as an integral part of the degree program. Students in the secondary school teacher track are required to complete both a practicum and a student teaching internship as part of the degree requirements. Otherwise, students may substitute the practicum experience for one of the optional courses listed in the other two tracks.

## Minor in Mathematics

Students may pursue a minor in mathematics with an emphasis in one of the three following areas: applied mathematics, statistics/biostatistics or actuarial mathematics.

The applied mathematics option consists of the following:

MATH 307 | Ordinary Differential Equations | 3 |

MATH 312 | Calculus III | 4 |

MATH 317 | Calculus IV: Introductory Analysis | 3 |

Select two of the following: | 6 | |

Introductory Linear Algebra | ||

Partial Differential Equations | ||

Applied Numerical Methods I | ||

Applied Numerical Methods II | ||

Intermediate Real Analysis I | ||

Applied Mathematics I: Biomathematics | ||

Applied Mathematics II: Mathematical Modeling | ||

Applied Complex Variables | ||

Applied Mathematics III: Elasticity | ||

Applied Mathematics IV: Fluid Mechanics | ||

Mathematics in Nature | ||

Or approved topics courses | ||

Total Hours | 16 |

The statistics/biostatistics option consists of 12 hours of statistics at the 300/400 level, of which at most six hours can be at the 300 level. STAT 306 cannot be applied to this option.

The actuarial mathematics option consists of the following:

MATH 312 | Calculus III | 4 |

MATH 316 | Introductory Linear Algebra | 3 |

STAT 330 | An Introduction to Probability and Statistics | 3 |

or STAT 331 | Theory of Probability | |

MATH 408 | Applied Numerical Methods I | 3 |

or STAT 431 | Theory of Statistics | |

Total Hours | 13 |

At least nine credit hours in the chosen option must be taken through courses offered by Old Dominion University. Students must have an overall grade point average of at least 2.00 in the courses required for the minor in their chosen option exclusive of 100/200-level courses and prerequisite courses.

## Advanced Placement

Students who have achieved a qualifying score on the Calculus AB or Calculus BC advanced placement examinations receive credit for MATH 211 (and MATH 162M and MATH 163). Credit for MATH 162M and MATH 163 is also given for qualifying scores on the placement tests administered by the University Testing Center. Refer to the Academic Testing and the Experiential Learning Credit Options at the Undergraduate Level sections of this Catalog. Advanced placement credit is not available for MATH 102M.

### MATHEMATICAL SCIENCES Courses

**MATH 101M. An Introduction to Mathematics for Critical Thinking. 3 Credits.**

This course fulfills the math general education requirement for some majors in the College of Arts and Letters and the College of Education. It can also be used as a preparation for STAT 130M. An introduction to the ways in which modern mathematics can be used to analyze the modern world and make logical decisions. Topics include problem solving, sets, logic, consumer mathematics (loans, mortgages, annuities), elementary statistics, chaos and fractals.

**MATH 102M. College Algebra. 3 Credits.**

A basic course in algebra that emphasizes applications and problem-solving skills. Topics include properties of the real numbers, graphing of equations and inequalities, the algebra of rational expressions, and properties of exponentials and logarithms. This course fulfills the math general education requirement and can be used as a preparation for MATH 162M. MATH 101M is not a prerequisite for MATH 102M. Not open to students with credit for MATH 162M.

**MATH 103M. College Algebra with Supplemental Instruction. 3 Credits.**

This course covers the same content as MATH 102M. It is designed for students who must complete MATH 102M as part of their degree program, but who do not meet the prerequisites for MATH 102M (Math SAT greater than 450 and High School GPA of 3.0 or greater). MATH 103M may be used interchangeably with MATH 102M and may be used as a prerequisite requirement for any course that requires MATH 102M as a prerequisite. MATH 103M will require registration for a supplemental instruction session each week. Prerequisites: Math SAT less than or equal to 450, OR, High School GPA less than 3.0.

**MATH 162M. Precalculus I. 3 Credits.**

The first course in a two-course sequence designed to provide a strong preparation for calculus. Topics include algebraic operations, equations and inequalities, graphs and functions, polynomial functions, theory of equations, systems of equations, exponential functions, and logarithmic functions. Prerequisite: qualifying score on SAT or ACT, or qualifying score on a placement test administered by the University Testing Center or a grade of C or better in MATH 102M or MATH 103M.

**MATH 163. Precalculus II. 3 Credits.**

Lecture 3 hours; recitation 1 hour; 3 credits. Prerequisite: A grade of C or better in MATH 162M. The second course in a two-course sequence designed to provide strong preparation for calculus. Topics include exponential and logarithmic functions/equations, trigonometric functions/equations, trigonometric identities, laws of sines and cosines, vectors, polar representation of complex numbers, binomial theorem, and conic sections.

**MATH 166. Precalculus I and II. 4 Credits.**

A one-semester precalculus course covering the topics of MATH 162M and MATH 163 at an accelerated pace. Not available to students with credit in MATH 163. Prerequisites: A grade of C or better in MATH 102M or MATH 103M.

**MATH 200. Calculus for Business and Economics. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: A grade of C or better in MATH 162M. The derivative and optimization, exponential functions and growth, and integration with applications to future value and consumer's and producer's surplus.

**MATH 211. Calculus I. 4 Credits.**

Lecture 4 hours; laboratory 1 hour; 4 credits. Prerequisites: A grade of C or better in MATH 163 or MATH 166. A first course in calculus and analytic geometry. Topics include differentiation and integration of algebraic and transcendental functions of one variable and applications.

**MATH 212. Calculus II. 4 Credits.**

Lecture 4 hours; laboratory 1 hour; 4 credits. Prerequisite: A grade of C or better in MATH 211. A second course in calculus and analytic geometry. Topics include techniques of integration, polar coordinates, infinite series, solid geometry, vectors, lines and planes.

**MATH 280. Transfer Credit for Ordinary Differential Equations. 3 Credits.**

3 credits. This course is a VCCS transfer credit vehicle. Students who have earned transferable credit in MATH 279 or 291 at any member institution of the VCCS will be granted credit for MATH 280. The course will not be offered for credit by Old Dominion University. Cannot be used to substitute for MATH 307 for MATH majors or minors.

**MATH 285. Transfer Credit for Calculus III. 4 Credits.**

4 credits. This course is a VCCS transfer credit vehicle. Students who have earned transferable credit for MATH 275 or 277 at any member institution of the VCCS will be granted credit for MATH 285. The course will not be offered for credit by Old Dominion University. Cannot be used to substitute for MATH 312 for MATH majors or minors.

**MATH 295. Topics in Mathematics. 1-5 Credits.**

1-5 credits. Prerequisite: departmental permission.

**MATH 300. Number Systems. 3 Credits.**

Sets and systems of numbers, prime, integer, rational, irrational, real, complex and their properties. Representation of numbers. Divisibility, congruence, modular arithmetic, elementary number theory and symbolic logic. (May not be used to satisfy the upper-division elective requirement of the math majors program.) Prerequisite: A grade of C or better in MATH 102M or MATH 103M or MATH 162M.

**MATH 302. Geometry. 3 Credits.**

Elementary plane and solid Euclidean geometry with proofs and applications. Topics include angles, triangles, congruence, quadrilaterals, circles, similarity, perimeter, area, volume, polygons, plane and solid constructions. Geometer's Sketchpad software used to discover geometric properties. (May not be used to satisfy the upper-division elective requirement of the math majors program.) Prerequisite: A grade of C or better in MATH 102M or MATH 103M or MATH 162M.

**MATH 305. Discrete Math. 3 Credits.**

Topics: Vectors and matrices, linear programming, operations on sets, combinatorics, permutations, combinations, elementary probability, logic, relations and functions, induction, graphs and trees, applications. (May not be used to satisfy the upper-division elective requirement of the math majors program.) Prerequisite: A grade of C or better in MATH 102M or MATH 103M or MATH 162M.

**MATH 307. Ordinary Differential Equations. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: A grade of C or better in MATH 212. Topics include first order differential equations and systems, second and higher order linear equations, solution by series and Laplace transform, and applications.

**MATH 311W. Abstract Algebra. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: A grade of C or better in ENGL 211C or 221C or 231C; MATH 212 or departmental permission. Topics include introduction to logic and methods of proof; sets, relations, and functions; elementary group and ring theory. (This is a writing intensive course.).

**MATH 312. Calculus III. 4 Credits.**

Lecture 4 hours; laboratory 1 hour; 4 credits. Prerequisite: A grade of C or better in MATH 212. A third course in calculus and analytic geometry. Topics include vector functions, partial derivatives, multiple integrals and an introduction to vector calculus.

**MATH 316. Introductory Linear Algebra. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: A grade of C or better in MATH 212. An introduction to linear algebra. Topics include matrices, vectors, vector spaces, linear transformations, eigenvalues and eigenvectors.

**MATH 317. Calculus IV: Introductory Analysis. 3 Credits.**

Lecture 3 hours; recitation 1 hour; 3 credits. Prerequisite: A grade of C or better in MATH 212. An introduction to real analysis. Topics covered include completeness and topological properties of real line, theory of sequences, limits of functions, continuity, Fundamental Theorem of calculus, Leibniz’s rule.

**MATH 335. Number Systems and Discrete Mathematics. 3 Credits.**

Estimation and other applications to real world problems, using elementary principles of algebra, geometry, number theory, number systems, and discrete mathematics. (May not be used to satisfy the upper-division elective requirement of the math majors program.) Prerequisite: A grade of C or better in MATH 102M or MATH 103M or MATH 162M.

**MATH 367. Cooperative Education. 1-3 Credits.**

1-3 credits ( may be repeated for credit). Prerequisite: approval by the department and Career Management in accordance with the policy for granting credit for Cooperative Education programs. Available for pass/fail grading only. Student participation for credit based on the academic relevance of the work experience, criteria, and evaluative procedures as formally determined by the department and Career Management prior to the semester in which the work experience is to take place. (qualifies as a CAP experience).

**MATH 395. Topics in Mathematics. 1-3 Credits.**

1-3 credits. Prerequisite: departmental permission.

**MATH 399. Putnam Exam Problems and Related Topics. 1 Credit.**

Lecture 1 hour; 1 credit. Prerequisite: A grade of C or better in MATH 212. This course is designed to help students prepare for the Putnum Exam - an annual national mathematical competition. Problems from previous Putnam Exams and materials related to the solution of such problems will be considered.

**MATH 400/500. History of Mathematics. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: MATH 311W or 316 or 317. This course considers some of the major events in the development of mathematics from ancient times through the seventeenth century, including the discovery of incommensurability, the origins of the axiomatic method, trigonometry, solution of equations, calculation of areas and volumes, analytic geometry, probability, and calculus. Students will be graded on tests which consist mostly of problems typical of the periods considered.

**MATH 401/501. Partial Differential Equations. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisites: A grade of C or better in MATH 307 and 312. Not available to students with credit in MATH 691. Separation of variable techniques, Sturm-Liouville systems, generalized Fourier series, orthogonal functions of the trigonometric, Legendre and Bessel type boundary value problems associated with the wave equation and the heat conduction equation in various coordinate systems, applications to physics and engineering.

**MATH 404/504. Fundamental Concepts of Geometry. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: MATH 311W. The fundamentals of projective, Euclidean and non-Euclidean geometry are explored by the synthetic method and the algebraic method.

**MATH 406/506. Number Theory and Discrete Mathematics. 3 Credits.**

Prerequisites: MATH 311W and MATH 316. A survey course. Topics include the prime number theorem, congruences, Diophantine equations, continued fractions, quadratic reciprocity, combinatorics, logic, graphs, trees, algorithms, coding and linear programming.

**MATH 408/508. Applied Numerical Methods I. 3 Credits.**

An introduction to the numerical methods commonly used by scientists and engineers. Topics include solutions of equations of one variable, direct methods for solving linear systems, matrix factorization, stability analysis, iterative techniques, polynomial interpolation, numerical differentiation and integration, approximation theory, and initial and boundary value problems for ordinary differential equations. Prerequisites: A grade of C or better in MATH 316; CS 150 or equivalent programming ability also required.

**MATH 409/509. Applied Numerical Methods II. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisites: A grade of C or better in MATH 408/508. Topics include least squares problems, the QR factorization, the conjugate gradient method, Householder transformation and the QR method for approximating eigenvalues and singular values of a matrix. For applications, the finite difference method and the finite element method for solving partial differential equations, trigonometric interpolation and FFT as well as introductory study of optimization are discussed.

**MATH 417/517. Intermediate Real Analysis I. 3 Credits.**

A rigorous course in classical real analysis. Topics include the topology of Euclidean n-space, properties of vector valued functions of several variables such as limits, continuity, differentiability and integrability, pointwise and uniform convergence of sequences and series of functions; Fourier series. Prerequisite: a grade of C or better in MATH 317.

**MATH 418/518. Intermediate Real Analysis I. 3 Credits.**

A rigorous course in classical real analysis. Topics include the topology of Euclidean n-space, properties of vector valued functions of several variables such as limits, continuity, differentiability and integrability, pointwise and uniform convergence of sequences and series of functions; Fourier series. Prerequisite: A grade of C or better in MATH 417.

**MATH 420/520. Applied Mathematics I: Biomathematics. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: A grade of C or better in MATH 307. An introduction to current developments in the mathematical investigation of biological problems. Topics include scaling systems of differential equations, stability, perturbation methods, bifurcation phenomena and wave propagation. Applications are chosen from interacting populations, transport and reaction diffusion kinetics, transmission of nerve impulses, and cardiovascular modeling.

**MATH 421/521. Applied Mathematics II: Mathematical Modeling. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisites: A grade of C or better in MATH 307, 312, 316, and 317. A one semester course in formulating, evaluating and validating mathematical models of physical phenomena. Models of traffic flow, mechanical vibrations, combustion, quantum mechanics, wave propagation or other fields of applied mathematics will be examined. Techniques learned in previous courses are used to simplify, analyze and solve these models. New methods introduced include phase-plane analysis, characteristics, calculus of variations and perturbation methods.

**MATH 422/522. Applied Complex Variables. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: A grade of C or better in MATH 312. Not available to students with credit in MATH 692. Topics include complex numbers, analytical functions and their properties, derivatives, integrals, series representations, residues and conformal mappings. Applications of the calculus of residues and mapping techniques to the solution of boundary value problems in physics and engineering.

**MATH 427/527. Applied Mathematics III: Elasticity. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisites: A grade of C or better in MATH 307 and 312. An introduction to the mathematical theory of linear and non-linear elastic continua. Topics include vectors, tensors, deformation, stress, nonlinear constitutive theory, exact solutions, infinitesimal theory, antiplane strain, plane strain, plane stress, extension, torsion, bending and elastic wave propagation.

**MATH 428/528. Applied Mathematics IV: Fluid Mechanics. 3 Credits.**

Lecture 3 hours: 3 credits. Corequisite: MATH 401/501. Prerequisites: A grade of C or better in MATH 307 and 312. A mathematical investigation of the differential equations governing fluid flow with an emphasis on steady state incompressible flows. The Navier-Stokes equations are derived and some exact solutions are presented including the potential flow solutions. Topics therefore include classical ideal fluid flow and its complex variable representation, various approximations to the Navier-Stokes equations, boundary layer theory, and also surface and internal gravity wave motion, aspects of hydrodynamic stability theory and convection. Other topics may be introduced by the instructor.

**MATH 457/557. Mathematics in Nature. 3 Credits.**

Lecture 3 hours; 3 credits. Prerequisite: A grade of C or better in MATH 307. A calculus and differential equations based description of many patterns observable in the natural world including wave motion in the air, oceans, rivers, and puddles; rainbows, halos and other meteorological phenomena; arrangement of leaves, petals and branches; height of trees; river meanders; animal and insect markings; mudcracks; spider webs; and others. Partial differential equations will be discussed as needed but a knowledge of ordinary differential equations will be assumed.

**MATH 496/596. Topics in Mathematics. 1-3 Credits.**

1-3 credits. Prerequisite: permission of the instructor.

**MATH 498/598. Tutorial Work in Special Topics in Mathematics. 1-3 Credits.**

1-3 credits. Prerequisite: permission of the instructor. Independent study under the direction of an instructor including library research and reports.

### STATISTICS Courses

**STAT 130M. Elementary Statistics. 3 Credits.**

Topics include: data description, elementary probability, binomial and normal distributions, interval estimation, hypothesis testing, and correlation. The role of probability in inference is emphasized. Prerequisites: qualifying score on a placement test administered by the University Testing Center, qualifying SAT or ACT score, a C or better in MATH 101M, or a higher level math course.

**STAT 306. Introductory Statistics. 3 Credits.**

A general probability and statistics course designed specifically to accommodate the needs of school teachers and health professionals. Topics include: descriptive statistics, basic probability, discrete random variables, continuous random variables, interval estimation, regression and correlation, hypothesis testing, and applications. (May not be used to satisfy the upper-division elective requirement of the math major program.) Prerequisites: A grade of C or better in MATH 102M or MATH 162M.

**STAT 310. Introductory Data Analysis. 3 Credits.**

Topics include measures of location, dispersion, and strength of relationship; parametric and nonparametric tests of location; one-way analysis of variance; complete block designs; simple and multiple regression; correlation; measures of association for categorical data. Microsoft EXCEL will be used extensively as an aid in data analysis. Written interpretation of results will be a routine component of daily assignments. Prerequisites: A grade of C or better in STAT 130M or MATH 211.

**STAT 330. An Introduction to Probability and Statistics. 3 Credits.**

Topics include: descriptive statistics, probability theory and probability distributions, mathematical expectation and its role in decision making, hypothesis testing, point and interval estimation, numerous applications. (Not open to students with credit in STAT 331.) Prerequisites: A grade of C or better in MATH 211.

**STAT 331. Theory of Probability. 3 Credits.**

An introduction to probability theory including probability functions, continuous and discrete random variables, combinatorics, special probability distributions, moment generating functions, and limit laws. Prerequisites: A grade of C or better in MATH 211.

**STAT 405/505. Introduction to Data Handling. 3 Credits.**

Prerequisites: grade of C or better in STAT 130M or equivalent and a grade of C or better in MATH 316 or equivalent or permission of instructor. Use of SAS and R to handle data sets. Topics for SAS include data input, creating permanent data sets, merging data sets, creating new variables, sorting, printing, charting, formatting, IML programming, macro programming, and an overview of proc SQL and other statistical procedures. Topics for R include data structure, control structure, writing functions, and graphics.

**STAT 431/531. Theory of Statistics. 3 Credits.**

Topics include point and interval estimation, tests of hypotheses, introduction to linear models, likelihood techniques, and regression and correlation analysis. Prerequisites: A grade of C or better in STAT 331 or departmental permission.

**STAT 432/532. Sampling Theory. 3 Credits.**

Sampling from finite populations is discussed. Topics such as simple random sampling, stratified random sampling and ratio and regression estimation are included. Also discussed are aspects of systematic sampling, cluster sampling, and multi-stage sampling. Prerequisites: A grade of C or better in STAT 431/STAT 531.

**STAT 435/535. Design and Analysis of Experiments. 3 Credits.**

Topics include analysis of variance with one or more factors, multiple comparisons, randomized blocks, Latin squares and related designs: multifactor factorial experiments; blocking and confounding in the 2(k) factorial design; two-level fractional factorial designs. Statistical software will be used to analyze real life data. Prerequisites: A grade of C or better in STAT 405 or STAT 505 and STAT 437 or STAT 537.

**STAT 437/537. Applied Regression Analysis. 3 Credits.**

Topics include theory of least squares, simple linear regression, multiple regression (including its matrix formulation), applications of these techniques to real life data, residual analysis, selection of variables, multicollinearity issues, regression on dummy variables, and analysis of covariance. Prerequisite: A grade of C or better in STAT 330 or STAT 310 or STAT 431/STAT 531.

**STAT 440/540. Clinical Trials. 3 Credits.**

An introduction to statistical methods used in the design, conduct, and analysis of clinical trials. Topics include: study designs, treatment allocation, sample size and power, clinical life tables, log rank test, cross-over designs, and sequential methods of monitoring clinical trials. Prerequisites: A grade of C or better in STAT 431/STAT 531.

**STAT 442/542. Environmental Statistics. 3 Credits.**

Topics include nonlinear and generalized linear models, quantitative risk assessment, analysis of stimulus-response and spatially correlated data, methods of combining data from several independent studies. Regression settings are emphasized where one or more predictor variables are used to make inferences on an outcome variable of interest. Applications include modeling growth inhibition of organisms exposed to environmental toxins, spatial associations of like species, risk estimation, and spatial prediction. SAS is used extensively in the course. Prerequisites: A grade of C or better in STAT 431/STAT 531 or permission of the instructor; STAT 437 or STAT 537 recommended.

**STAT 447/547. Analysis of Longitudinal Data. 3 Credits.**

Topics include general linear models, weighted least squares (WLS), maximum likelihood (ML), restricted maximum likelihood (REML) methods of estimation, analysis of continuous response repeated measures data, parametric models for covariance structure, generalized estimating equations (GEE) and quasi least squares (QLS), models for discrete longitudinal data: marginal, random effects, and transition models. Limitations of existing approaches will be discussed. Emphasis will be on the application of these tools to data related to the biological and health sciences. Methods will be implemented using statistical software. Prerequisites: A grade of C or better in STAT 431/STAT 531. Pre- or corequisite: STAT 405/STAT 505.

**STAT 449/549. Nonparametric Statistics. 3 Credits.**

Topics include the theory and applications of binomial tests and rank tests, including the tests of McNemar, Mann-Whitney, Friedman, Kruskal-Wallis, and Smirnov. Prerequisites: A grade of C or better in STAT 330 or STAT 331 or departmental permission.

**STAT 450/550. Categorical Data Analysis. 3 Credits.**

Topics include relative risk and odds ratio measures for 2 x 2 tables, the chi-square and Mantel-Haenszel tests, Fisher's exact test, analysis of sets of 2 x 2 tables using Cochran-Mantel-Haenszel methodology, analysis of I x J and sets of I x J tables for both nominal and ordinal data, logistic regression including the logit and probit models, and building and applying loglinear models. Emphasis will be on the application of these statistical tools to data related to the health and social sciences. Interpretation of computer output will be stressed. Prerequisites: A grade of C or better in STAT 431/STAT 531. Pre- or corequisite: STAT 405/STAT 505.

**STAT 460/560. Statistical Simulation/Programming Using Statistical Software Packages. 3 Credits.**

Prerequisites: A grade of C or better in STAT 405/505 and two of STAT 435/STAT 535, STAT 437/STAT 537, STAT 447/STAT 547 and STAT 450/STAT 550. This course is a data-based tour of advanced statistical techniques using software packages, exploring a catalog of data sets (simulated or otherwise) spanning a variety of fields and applications, including data suitable for regression, ANOVA, time series modeling, longitudinal data analysis, and multivariate techniques. Approaches will include parametric, nonparametric, simulation, and bootstrapping. SAS and R (S-plus) will be used extensively, with some other specialized products. For writing actual (not packaged) code, PROC IML and R will be used. This is a finishing course for applied statisticians, highly recommended for students planning a career in statistical programming and simulation.

**STAT 497/597. Topics in Statistics. 1-3 Credits.**

The advanced study of selected topics. Prerequisites: permission of the instructor.