MATHEMATICS

Department of Mathematics

Keith E. Mellinger, Chair
Janusz Konieczny, Career Advisor for Pure Mathematics
Jangwoon Lee, Career Advisor for Applied Mathematics
Debra L. Hydorn, Career Advisor for Statistics

Faculty

Professors

Yuan-Jen Chiang
Debra L. Hydorn
Janusz Konieczny
J. Larry Lehman
Marie P. Sheckels
Suzanne Sumner

Associate Professors

Manning G. Collier
Keith E. Mellinger

Assistant Professors

Julius N. Esunge
Randall D. Helmstutler
Jangwoon Lee

Senior Lecturer

Patricia M. Dean

The Mathematics Program

The interests and expertise of the mathematics faculty cover a broad range of mathematical areas, including algebra, analysis, topology (modern geometry), discrete mathematics (mathematics of computer science), number theory, statistics, and applied mathematics. With this spectrum of faculty knowledge, the student is afforded an opportunity to learn the contemporary view of mathematics. Inside the classroom, student comprehension is the main concern of the faculty. Outside the classroom, the faculty offers opportunities for independent study, undergraduate research, and internship supervision.

Courses in mathematics vary from the theoretical to the applied. Thus, a major in mathematics can be a foundation for a career in industry, government, teaching, or the pursuit of a higher degree in graduate school. The department faculty encourages double majors, giving students entrance to a wide variety of fields upon graduation.

University of Mary Washington hosts a chapter of Pi Mu Epsilon, a national honorary mathematics fraternity, and a chapter of the Mathematical Association of America. The Oscar Schultz Award in Mathematics represents the department’s top academic honor and is given annually to a junior or senior in the department. The recipients of the Meredith C. Loughran ’94 Scholarship are selected based on their meritorious academic record, citizenship and leadership in public service. The Louise W. Robertson, M.D. ’56 Scholarship is awarded to a student majoring in mathematics or a health field.

Qualified mathematics majors having at least a 3.5 GPA in mathematics courses and an overall GPA of at least 3.0 may graduate with Honors in Mathematics by completing a directed study or undergraduate research which culminates in an approved Honors thesis.

Requirements for the Mathematics Major

Thirty-six (36) credits are required. Eighteen (18) credits must be from the following mathematics courses: 223, 224, 300, 431, 471 and either 432, 442, or 472. An additional six (6) credits must be 400-level with at most three (3) credits of directed study (491/492). An additional nine (9) credits must be from mathematics courses at the 300- or 400-level. The remaining three (3) credits must be from: mathematics courses numbered 210 or above; computer science courses numbered 220 or above; physics courses numbered 105 or above; Philosophy 306. No internship (499) credits will count for the major. At most six (6) credits of directed study (491/492) will count for the major.

Mathematics Course Offerings

110 – Finite Mathematics with Applications (3)

Includes topics such as sets, logic, probability, statistics, and counting. Other topics are at the discretion of the instructor. Designed for the non-major.

111 – Precalculus (3)

Emphasis on elementary functions including rational, exponential, logarithmic and trigonometric functions. Designed for students who intend to take calculus.

115 – Introduction to Mathematical Modeling (3)

Mathematical topics include linear functions, linear regression, curve fitting, probability models, and difference equations. Emphasis on environmental issues such as population growth, pollution, natural disasters, epidemics, genetics, and patterns in nature.

121 – Calculus I (3)

First course in calculus. Includes functions, limits, derivatives, and applications. May include some proofs.

122 – Calculus II (3)

Prerequisite: Mathematics 121. Includes antiderivatives, definite integrals and their applications, the fundamental theorem of calculus, derivatives and integrals of inverse functions, and techniques of integration. (Prospective mathematics majors should take this course during their freshman year.)

200 – Introduction to Statistics (3)

First course in statistical methods. Includes descriptive and inferential techniques and probability, with examples from diverse fields. Topics vary with instructor and may also include sampling methods, regression analysis, and computer applications.

201 – Introduction to Discrete Mathematics (3)

Designed to prepare prospective mathematics majors for advanced study in the field by introducing them to a higher level of mathematical abstraction. Topics include sets and logic, functions and relations, methods of mathematical proof including mathematical induction, and elementary counting techniques. (Prospective mathematics majors should take this course during their freshman year.)

204 – Mathematical Concepts and Methods I (4)

Prerequisite: Education 203. Mathematical concepts and methods of teaching for the elementary school. Topics include number systems and their properties, problem solving, and topics in number theory. Course intended for students certifying to teach grades PreK-6. Significant field experience required. (3 lecture credits, 1 practicum credit).

205 – Selected Topics in Mathematics (3)

Prerequisite: Course dependent. Opportunity for additional study of lower-level topics in mathematics.

207 – History of Mathematics (3)

The history of mathematics begins with the early numbering systems and mathematics of the Egyptians and the Babylonians. The course then turns to the Greeks and their emphasis on logical deduction and geometry. The Arabs develop algebra in the Middle Ages, and calculus is created during the Age of Reason. The development of individual branches of mathematics then is studied (probability, number theory, non-Euclidean geometry, set theory, and topology). The course ends with the Computer Age and implications for the future.

210 – Statistical Methods (3)

Prerequisite: Mathematics 200. Second course in statistical methods. Includes one-way and higher ANOVA, multiple regression, categorical data analysis, and nonparametric methods with examples from diverse fields. Topics vary with instructor and may also include time series and survival analysis.

223 – Calculus III (3)

Prerequisite: Mathematics 122. Includes parametric equations, polar coordinates, improper integrals, l’Hôpital’s rule, sequences, and infinite series.

224 – Multivariable Calculus (3)

Prerequisite: Mathematics 122. Includes vectors in two- and three-dimensional space, vector-valued functions, functions of several variables, partial derivatives, multiple integrals, and line integrals.

300 – Linear Algebra (3)

Prerequisites: Mathematics 122 and either Mathematics 201 or Computer Science 125. An introduction to linear algebra. Usually includes matrix algebra, systems of equations, vector spaces, inner product spaces, linear transformations, and eigenspaces.

312 – Differential Equations (3)

Prerequisite: Mathematics 122. Ordinary differential equations which may include Laplace transformations, linear differential equations, applications, approximations, and linear systems of equations.

321 – Number Theory (3)

Prerequisite: Mathematics 201 or Computer Science 125. An elementary, theoretical study of the properties of the integers.

325 – Discrete Mathematics (3)

Prerequisite: Mathematics 201 or Computer Science 125. Includes topics such as discrete probability, graph theory, recurrence relations, topics from number theory, semigroups, formal languages and grammars, finite automata, Turing machines, and coding theory.

330 – Foundations of Advanced Mathematics (3)

Prerequisite: Any Mathematics course numbered 223 or higher. Introduction to mathematical reasoning and rigor. Includes topics such as basic logic, set theory, mathematical induction, relations, functions, sequences, cardinality, elementary number theory, and axiomatic construction of the real numbers. Emphasis placed on reading mathematics, understanding mathematical concepts, and writing proofs.

351, 352 – Numerical Analysis (3, 3)

Prerequisite: Mathematics 300 or Mathematics 312 or Computer Science 220. Numerical methods applied to solutions of equations, interpolation, differentiation, integration, and solutions of differential equations and linear systems. Only in sequence.

372 – Modern Geometry (3)

Prerequisite: Math 300. Axiomatic development of various geometries including modern Euclidean geometry, finite geometries, hyperbolic geometry, and elliptic geometry. Topics could also include convexity, transformational geometry, projective geometry, and constructability.

381, 382 – Probability and Statistical Inference (3, 3)

Prerequisite: Mathematics 223. An introduction to probability theory and calculus-based statistics including probability distributions of discrete and continuous random variables, functions of random variables, methods of estimation, and statistical inference. Only in sequence.

411- Chaotic Dynamical Systems (3)

Prerequisite: Mathematics 223. Chaotic dynamical systems including iteration, graphical analysis, periodic points, bifurcations, the transition to chaos, fractals, Julia sets and the Mandelbrot set.

412 – Complex Variables (3)

Corequisite: Mathematics 471. Analytic functions, Cauchy-Riemann conditions, integration, power series, calculus of residues, conformal mappings and applications.

431, 432 – Abstract Algebra (3, 3)

Prerequisite: Mathematics 300. Mathematical systems including groups, rings, fields, and vector spaces. Only in sequence.

441, 442 – Topology (3, 3)

Prerequisite: Mathematics 300 or 325; 431 is also a prerequisite for 442. Math 441 includes topics from point-set topology such as continuity, connectedness, compactness, and product and quotient constructions. Math 442 serves as an introduction to algebraic topology including homotopy theory, covering spaces, and topological groups. Only in sequence.

461 – Topics in Mathematics (3)

Prerequisite: Course dependent. Topics such as partial differential equations, optimization, Fourier series, ring theory, cryptology, algebraic number theory, coding theory, and modeling. May be taken up to three times for credit.

471, 472 – Real Analysis (3, 3)

Prerequisites: Mathematics 223 and 300. A rigorous, real analysis approach to the theory of calculus. Only in sequence.

491, 492 – Directed Study (1-3, 1-3)

Prerequisite: Departmental permission. Individual study beyond the scope of normal course offerings, done under the direction of a faculty member. May lead to graduation with Honors in Mathematics.

499 – Internship (credits variable)

Supervised off-campus experience, developed in consultation with the department. Does not count in the major program.