# Mathematics

**Degrees Offered**

- Bachelor of Arts
- Bachelor of Science

**Area of Emphasis**

****Students enrolled in the B.A. or the B.S. in Mathematics have the opportunity to earn an area of emphasis.

- Actuarial Science

Students may not earn both a Bachelor of Arts and a Bachelor of Science in Mathematics.

**Nature of Program**

The Department of Mathematics provides a curriculum with programs for:

- Students wishing to earn an undergraduate major or minor in mathematics
- Students enrolled in elementary and secondary teacher programs
- Students interested in the applications of mathematics to the fields of computer science, statistics, engineering, physical, natural and social science, and business and economics
- Non-science majors, to educate them in the ideals and objectives of mathematics

**Placement into Mathematics Courses**

To enroll in a freshman-level mathematics course, a student must demonstrate a satisfactory understanding of background material, either in the prerequisite courses specified in this catalog or by satisfactory performance on the SAT/ACT tests, or on the Quantitative Reasoning Assessment (QRA). The QRA is given during orientation for freshman and transfer students. It is also given before classes begin each semester. Students intending to take the QRA before classes begin must register for the exam prior to the day the test is given. Sign-up can be done by visiting the department website. There is no fee for the exam. The QRA may only be taken twice during a four-year period. Students who do not meet the prerequisites will be dropped from their math class during the first week of classes.

**Math Learning Center**

The Department of Mathematics offers help to students in mathematics courses through its Math Learning Center, located in room 301 Armstrong Hall. The Math Learning Center is a free, drop-in help center for students enrolled in undergraduate math classes through calculus. Hours are posted at the beginning of each semester and announced in mathematics classes. The phone number is (304) 293-7273.

Students who earn a degree in the Eberly College of Arts and Sciences must complete the University requirements, the College requirements for their specific degree program, and their major requirements.

**Minors**

All students have the possibility of earning one or more minors; view a list of all available minors and their requirements here. Please note that students may not earn a minor in their major field.

**Certificate of Global Engagement**

Students in the Eberly College, regardless of their major, can earn a Certificate of Global Engagement. Completion of the Certificate demonstrates the student’s knowledge of diverse cultures, as well as the ability to communicate and interact effectively with people of different cultural backgrounds. Students will be required to apply their knowledge of contemporary issues and global social contexts to their course work and their broader citizenship. For details regarding Certificate requirements, please visit the Eberly College page.

**Admission Requirements**

Some entering freshmen can be admitted directly into the major based on high school GPA and results of standardized tests. Others will be advised in the Center for Learning, Advising, and Student Success until they meet milestones set by the department: completion of MATH 154 or MATH 155 with C- or higher and 2.0 overall GPA. Please contact an adviser in the department for details.

**Benchmark Expectations**

By the 5th semester, students should have completed calculus courses through MATH 261 and have completed or be enrolled in MATH 283. Normally, students must register for 9 hours of math each subsequent term. All majors must meet with a math department adviser each semester. Students who fail to meet these benchmarks may be removed from their major.

**For specific information on the following programs please see the links to the right:**

- Mathematics B.A.
- Mathematics B.S.

**Major Learning Outcomes**

**mathematics**

Upon successful completion of the B.A. or B.S. degree, **Mathematics** majors will demonstrate the following competencies:

- Students will communicate mathematics in both written and oral forms.
- Students will construct valid proofs.
- Students will demonstrate their ability to comprehend and to synthesize professional mathematical discourse (such as upper level textbooks, monographs, journal articles, unpublished faculty research, technical reports, etc.).
- Students will prepare a clear and concise written project and orally present advanced mathematical concepts effectively and professionally.

- Students will have a clear understanding of fundamental concepts and general understanding in a breadth of advanced topics in mathematics.
- Students will demonstrate basic skills in specific mathematics topics (Algebra, Trigonometry, Calculus, Differential Equations, and Linear Algebra).
- Students will demonstrate a breadth of knowledge of upper level mathematics topics.
- Students will be exposed to the use of mathematics in various applications and professions.

- Students will apply mathematical knowledge.
- Students will demonstrate their ability to understand and construct mathematical models to solve problems.
- Students will apply mathematics they have learned to new and different areas.

### Mathematics Minor

### MINOR CODE - U024

There are two possible tracks for the Mathematics minor.

Successful completion of the minor requires that the student receive a grade of at least a C in each of the mathematics courses presented for the minor, or a cumulative grade point average of at least 2.25 in these courses.

TRACK ONE | ||

Core Courses: | 15-19 | |

Select one of the following : | ||

Calculus 1a with Precalculus and Calculus 1b with Precalculus | ||

Calculus 1 | ||

and: | ||

Calculus 2 | ||

Multivariable Calculus | ||

Introduction to the Concepts of Mathematics | ||

Upper-Division Electives: | 9 | |

Select one of the following: | ||

Introduction to Algebraic Structures | ||

Introduction to Linear Algebra | ||

Introduction to Analysis and Topology | ||

Introduction to Real Analysis 1 | ||

and: | ||

Two additional courses chosen from STAT 461, or any Math course numbered 300 or above ^{*} | ||

Total Hours | 24-28 |

TRACK TWO | ||

Core Courses | 16-20 | |

Select one of the following: | ||

Calculus 1a with Precalculus and Calculus 1b with Precalculus | ||

Calculus 1 | ||

and: | ||

Calculus 2 | ||

Multivariable Calculus | ||

Elementary Differential Equations | ||

Upper-Division Electives: | 9 | |

Select one of the following: | ||

Applied Modern Algebra | ||

Numerical Analysis 1 | ||

Complex Variables | ||

Partial Differential Equations | ||

Two additional courses chosen from STAT 461, or any Math course numbered 300 or above ^{*} | ||

Total Hours | 25-29 |

* |

**MATH 112. Quantitative Skill and Reasoning 1. 1 Hour.**

Part one of a two-part introductory study of quantitative and reasoning skills needed for success in science, technology, engineering, and mathematics coursework.

**MATH 121. Intro Concepts Of Mathematics. 3 Hours.**

(Designed for non-science majors who do not need the techniques of mathematics for other course work in their programs.) Topics in modern mathematics.

**MATH 122. Quantitative Skills and Reasoning. 0-2 Hours.**

PR: Minimum HEPC-defined ACT/SAT Math or equivalent assessment score, or satisfactory performance on placement test. An introductory study of quantitative and reasoning skills needed for success in science, technology, engineering, and mathematics.

**MATH 124. Algebra with Applications. 3 Hours.**

PR: Satisfactory performance on departmental placement test; or satisfy the minimum ACT/SAT Math score; or a grade of C- or better in MATH 122. Study of algebra with an emphasis on applications for science, business, technology, and social science. Topics include graphing and solving problems using linear, quadratic, square-root, logarithmic, and exponential functions, solving equations, performing operations on matrices.

**MATH 126. College Algebra. 3 Hours.**

PR: Satisfy the minimum ACT/SAT math score, or satisfactory performance on departmental placement examination, or a minimum grade of C- in MATH 122. Introduces the foundations of analysis designed to precede the calculus sequence with emphasis on functions and graphs. Topics include properties of absolute value, polynomial, rational, exponential, logarithmic functions, and techniques for solving equations and inequalities.

**MATH 128. Plane Trigonometry. 3 Hours.**

PR: MATH 124 or MATH 126 with a minimum grade of C- in each. (This course is not open to students who have credit for MATH 129 or equivalent.) Trigonometric functions, identities, vectors, complex numbers, and trigonometric equations. Pre-requisite(s) and/or co-requisite(s) may differ on regional campuses.

**MATH 129. Pre-Calculus Mathematics. 4 Hours.**

PR: Satisfy the minimum ACT/SAT math score, or satisfactory performance on departmental placement test. A treatment of algebra, analytic geometry, and trigonometry. Not open to students who have credit for the equivalent of either MATH 126 or 128. Pre-requisite(s) and/or co-requisite(s) may differ on regional campuses.

**MATH 150. Applied Calculus. 3 Hours.**

PR: Satisfy the minimum ACT/SAT math score, or satisfactory performance on departmental placement examination, or C- in MATH 124 or MATH 126 or MATH 129. For students in other disciplines needing calculus for applications.Limits of sequences and functions, continuity derivatives, and integrals of polynomials, rational functions, and exponential and logarithmic functions, partial derivatives, maxima and minima. Pre-requisite(s) and/or co-requisite(s) may differ on regional campuses.

**MATH 153. Calculus 1a with Precalculus. 4 Hours.**

PR: Satisfy the minimum ACT/SAT math score, or satisfactory performance on departmental placement examination, or C- in (MATH 126 and MATH 128) or in MATH 129. Introduction to limits, continuity, derivatives, and applications of derivative.

**MATH 154. Calculus 1b with Precalculus. 4 Hours.**

PR: MATH 153 with a minimum grade of C-. Introduction to applications of derivatives, antiderivatives, and definite integrals.

**MATH 155. Calculus 1. 4 Hours.**

PR: Satisfy the minimum ACT/SAT math score, or satisfactory performance on deparmental placement examination, or C- in MATH 129. Introduction to limits, continuity, derivatives, antiderivatives, definite integrals, and applications of the derivative. Not open to students who have earned credit in MATH 153 and/or MATH 154.

**MATH 156. Calculus 2. 4 Hours.**

PR: A minimum grade of C- in MATH 154 or MATH 155. Techniques of integration, application of the definite integral, polar coordinates, indeterminate forms, and infinite series.

**MATH 191. First-Year Seminar. 1-3 Hours.**

Engages students in active learning strategies that enable effective transition to college life at WVU. Students will explore school, college and university programs, policies and services relevant to academic success. Provides active learning activities that enable effective transition to the academic environment. Students examine school, college and university programs, policies and services.

**MATH 218. History of Mathematics. 3 Hours.**

PR: MATH 155 with a minimum grade of C-. Development of mathematics through calculus, with emphasis on mathematical theories and techniques of each period and their historical evolution. (Not offered on a regular basis.).

**MATH 222. Numerical and Symbolic Methods in Mathematics and Statistics. 3 Hours.**

PR: MATH 156 with a minimum grade of C-. Data manipulation, data visualization in two and three dimensions including animation, scientific programming using a high level language, symbolic manipulators and other packages. Applications to problems in mathematics and statistics. (Equivalent to STAT 222.).

**MATH 231. Algebra and Geometry for Elementary Teachers. 3 Hours.**

PR: MATH 126. (For elementary education majors only.) Algebra, real numbers, and geometry applied to graphing, problem solving, probability and statistics, calculations, and the computer.

**MATH 232. Number and Algebra for Teachers. 3 Hours.**

PR: A minimum grade of C- in MATH 124 or MATH 126 or MATH 150 or MATH 153 or MATH 155. (Open to pre- service elementary education majors only.) Use of properties of real numbers and algebra to illuminate conceptual understanding and enhance problem solving techniques. The use of technology is infused throughout the course.

**MATH 233. Measurement and Geometry for Teachers. 3 Hours.**

PR: MATH 232 with a minimum grade of C-. (Open to pre-service elementary education majors only.) Use of properties of real numbers, algebra, measurement and geometry to illuminate conceptual understanding and enhance problem solving techniques. The use of technology and manipulatives is infused throughout the course.

**MATH 238. Modern Geometry for Teachers. 3 Hours.**

PR: MATH 156 with a minimum grade of C- or consent. (For prospective high school mathematics teachers.) Foundations of geometry. Special topics from Euclidean, projective, and non-Euclidean geometries.

**MATH 251. Multivariable Calculus. 4 Hours.**

PR: MATH 156 with a minimum grade of C-. Introduction to solid analytic geometry, vector algebra, and calculus of several variables.

**MATH 261. Elementary Differential Equations. 4 Hours.**

PR: MATH 251 with a minimum grade of C-. Ordinary differential equations, Laplace transforms, partial differential equations, Fourier series, and applications.

**MATH 283. Introduction to the Concepts of Mathematics. 3 Hours.**

PR: MATH 156 or consent. Elementary logic, basic theory, relations and functions, equivalence relations and decomposition of sets, order relations, and cardinality. Emphasis on learning to prove theorems.

**MATH 293. Special Topics. 0-6 Hours.**

PR: Consent. Investigation of topics not covered in regularly scheduled courses.

**MATH 318. Perspectives on Mathematics and Science. 3 Hours.**

PR: MATH 150 or MATH 153 or MATH 155. This course explores knowledge generation in the sciences and mathematics by referencing the philosophy, history, and methods of those disciplines. It is designed to prepare future teachers with background, rationales, and strategies necessary to enhance student knowledge and interest in these areas, providing deeper understanding of the underlying mathematics in science, and of mathematics in general.

**MATH 341. Introduction to Algebraic Structures. 3 Hours.**

PR: MATH 283 or consent. A study of groups, rings, and fields together with their substructures, quotients and products, morphisms; the fundamental homomorphism theorems.

**MATH 343. Introduction to Linear Algebra. 3 Hours.**

PR: MATH 156. Introduction to vector spaces as an algebraic system. Emphasis on axiomatic development and linear transformation. Examples from geometry and calculus.

**MATH 363. Mathematical Foundations of Actuarial Science. 3 Hours.**

PR: MATH 156 with a minimum grade of C-. Concepts from calculus and probability as they pertain to actuarial sciences. The calculus portion covers limits, derivatives, integrals, power series and polar coordinates. The probability portion covers basic and conditional probability, Bayes' theorem, discrete and continuous variables and distributions, and bivariate distributions. Focus is on word problems of the type covered by the SOA/CAS Exam P/1.

**MATH 364. Mathematics of Compound Interest. 3 Hours.**

PR: MATH 156 or MATH 150. A problem-solving course focusing on the measurement of interest, annuities, amortization schedules, and sinking funds, and the valuation of bonds and other securities.

**MATH 367. Applied Mathematical Analysis. 3 Hours.**

PR: MATH 261. The algebra and differential calculus of vectors, solution of the partial differential equations of mathematical physics, and application of functions of a complex variable.

**MATH 373. Introduction to Cryptography. 3 Hours.**

PR: MATH 155. Introduces students to the art of confidential communication the mathematical background and the practical skills in making and breaking secret codes.

**MATH 375. Applied Modern Algebra. 3 Hours.**

PR: MATH 156. Finite fields, algebraic coding theory, Boolean algebras, monoids, finite state, and Turing machines.

**MATH 376. Foundations, Functions and Regression Models. 3 Hours.**

PR or CONC: MATH 156. In-depth study of topics taught by teachers of secondary school mathematics. Emphasizes development of the concept of function, exploring function patterns in data sets, and connections between these topics and topics of mathematics associated with the secondary school curriculum. Integrates use of appropriate technology in developing lessons that help students master the concepts of functions, data, and real world applications.

**MATH 377. Operations Research. 3 Hours.**

PR: MATH 156. Linear programming, multi-objective optimization and goal programming, discrete dynamic programming, network flows, discrete optimization models and methods, nonlinear programming.

**MATH 378. Discrete Mathematics. 3 Hours.**

PR: MATH 283. Permutations, combinations, binominal theorem, inclusion- exclusion formula, recurrence relations, generating functions, elementary graph theory (connectivity, paths, circuits, trees, vertex and edge coloring, graph algorithms) matching theory, and discrete optimization. (Equiv. to CS 426.).

**MATH 381. Introduction to Analysis and Topology. 3 Hours.**

PR: MATH 283 or consent. Introduction to metric and topological spaces. Topics include: continuity, convergence, separation, compactness, and connectedness.

**MATH 420. Numerical Analysis 1. 3 Hours.**

PR: MATH 251 and (either a programming language or MATH 222.) Computer arithmetic, roots of equations, interpolation, Gaussian elimination, numerical integration and differentiation. Numerical solution of initial value problems for ordinary differential equations. Least square approximations. (Equiv. to CS 460.).

**MATH 421. Numerical Analysis 2. 3 Hours.**

PR: (MATH 420 or CS 460) and (MATH 441 or MATH 343). Solutions of linear systems by direct and iterative methods. Calculation of eigenvalues, eigenvectors, and inverses of matrices. Applications to ordinary and partial differential equations.

**MATH 441. Applied Linear Algebra. 3 Hours.**

PR: MATH 251. Matrix algebra with emphasis on algorithmic techniques and applications to physical models. Topics include solution of large systems of equations, orthogonal projections and least squares, and eigenvalue problems.

**MATH 442. Advanced Algebraic Structures. 3 Hours.**

PR: MATH 341. Continuing study of groups, rings, and fields together with their substructures, quotients, and products. Morphisms with an emphasis on the fundamental homomorphism theorems.

**MATH 451. Introduction to Real Analysis 1. 3 Hours.**

PR: MATH 283. A study of sequences, convergence, limits, continuity, definite integral, derivative, differentials, functional dependence, multiple integrals, sequences, and series of functions.

**MATH 452. Introduction to Real Analysis 2. 3 Hours.**

PR: MATH 451. A study of sequences, convergence, limits, continuity, definite integral, derivative, differentials, functional dependence, multiple integrals, sequences and series of functions.

**MATH 456. Complex Variables. 3 Hours.**

PR: MATH 261. Complex numbers, functions of a complex variable; analytic functions; the logarithm and related functions; power series; Laurent series and residues; conformal mapping and applications.

**MATH 464. Deterministic Mathematical Modeling. 3 Hours.**

PR: MATH 222 and MATH 261 and MATH 420; or consent. An introduction to mathematical modeling of deterministic systems. Topics include growth and decay models, equilibrium models, optimal control and utility, and model validation. Applications from chemistry, physics, biology, economics, and the environment will be considered.

**MATH 465. Partial Differential Equations. 3 Hours.**

PR: MATH 261. Introduces students in mathematics, engineering, and the sciences to methods of applied mathematics. First and second order equations, canonical forms, wave, heat, and Laplace's equations, and representation of solutions.

**MATH 469. Seminar in Applied Mathematics. 1-12 Hours.**

PR: Consent. Selected topics in applied mathematics.

**MATH 490. Teaching Practicum. 1-3 Hours.**

PR: Consent. Teaching practice as a tutor or assistant.

**MATH 491. Professional Field Experience. 1-18 Hours.**

PR: Consent. (May be repeated up to a maximum of 18 hours.) Prearranged experiential learning program, to be planned, supervised, and evaluated for credit by faculty and field supervisors. Involves temporary placement with public or private enterprise for professional competence development.

**MATH 493. Special Topics. 1-6 Hours.**

PR: Consent. Investigation of topics not covered in regularly scheduled courses.

**MATH 494. Seminar. 1-3 Hours.**

PR: Consent. Presentation and discussion of topics of mutual concern to students and faculty.

**MATH 495. Independent Study. 1-6 Hours.**

Faculty supervised study of topics not available through regular course offerings.

**MATH 496. Senior Thesis. 1-3 Hours.**

PR: Consent.

**MATH 498. Honors. 1-3 Hours.**

PR: Students in Honors Program and consent by the honors director. Independent reading, study, or research.

### Faculty

#### Chair

- Edgar Fuller - Ph.D. (University of Georgia)

#### Professors

- Ian Christie - Ph.D. (University of Dundee)

Numerical partial differential equations - Krzysztof Ciesielski

Analysis, Topology, Set theory, MRI imaging - Harvey Diamond - Ph.D. (MIT)

Graduate Program Director. Approximation theory, Applied mathematics - Harry Gingold - D.Sc. (Israel Institute of Technology)

Differential equations, Asymptotic methods - John Goldwasser

Combinatorics, Graph theory - Jack T. Goodykoontz Jr. - Ph.D. (University of Kentucky)

Emeritus - Henry W. Gould - M.A. (University of Virginia)

Emeritus - Harumi Hattori - Ph.D. (Rensselaer Polytechnic Institute)

Differential equations, Continuum mechanics - Caulton L. Irwin - Ph.D. (Emory University)

Associate director, N.R.C.C.E. Variational methods, Optimization, Applied mathematics - Jin Bai Kim

Emeritus - Hong-Jian Lai

Associate Chair. Graph theory, Matroid theory - Dening Li

Partial differential equations - Michael E. Mays - Ph.D. (Penn. State University)

Director of IML. Number theor. - Sam B. Nadler Jr. - Ph.D.

Emeritus - Laura Pyzdrowski - Ed.D. (West Virginia University)

Mathematics Education - Sherman D. Riemenschneider - Ph.D. (Syracuse University)

Emeritus - William H. Simons

Emeritus - Jerzy Wojciechowski - Ph.D. (University of Cambridge)

Combinatorics, Graph theory - Cun-Quan Zhang

Graph theory, Combinatorics

#### Adjunct Professor

- Yuesheng Xu

Integral equations, Wavelet theory

#### Associate Professors

- Edgar Fuller - Ph.D. (University of Georgia)

Chair. Knot theory, Machine learning, Mathematics education - Gary H. Ganser

Applied mathematics, Fluid mechanics - Rong Luo

Graph Theory - Betty L. Miller - M.S. (West Virginia University)

Emeritus - James E. Miller - Ph.D. (Univiversity of Kentucky)

Emeritus - David Miller - Ph.D. (Oklahoma State University)

Undergraduate Program Director. Mathematics Education - James E. Moseley

Partial differential equations, Modeling

#### Assistant Professors

- Jessica Deshler - Ph.D. (University of New Mexico)

Mathematics education - Nicole Engelke-Infante

Mathematics Education - Adam Halasz - Ph.D. (State University of New York at Stony Brook)

Molecular systems biology, Monte Carlo methods, Mathematical physics - Vicki Sealey - Ph.D. (Arizona State University)

Mathematics education - Charis Tsikkou

PDE's - Adrian Tudorascu - Ph.D. (Carnegie Mellon University)

Analysis, PDE's, and fluid dynamics