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
Suzanne Sumner

Associate Professors

Manning G. Collier
Randall D. Helmstutler
Keith E. Mellinger

Assistant Professors

Julius N. Esunge
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. Majors in other disciplines can be enhanced with one of our Minors in Mathematics or Applied Mathematics.

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. Four additional scholarships are available. The recipients of the Meredith C. Loughran ’94 Scholarship are selected based on their meritorious academic record, citizenship and leadership in public service. The Merrilyn Sawyer Dodson/class of 1968 scholarship and the Mary Farley Talley ’66 scholarship each recognize the scholastic achievements of mathematics majors, while 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 207 or above; computer science courses numbered 220 (except Computer Science 302) 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.

Requirements for the Mathematics Minor

Eighteen (18) credits are required. Any course numbered Math 207 or higher counts toward the minor, with the exception of internship credits (Math 499). At least 12 credits must be earned from mathematics courses numbered 300 and above. At most three credits of Math 491 (directed study) may be counted toward the mathematics minor.

Requirements for the Applied Mathematics Minor

Eighteen (18) credits are required. Six credits come from Mathematics 223 and 312; nine additional upper level credits must come from Mathematics 300, 351, 352, 381, 382, 411, 461 (with departmental approval), and 491/492 (with departmental approval); the final three credits may be taken from any course in the additional upper level list above or Mathematics 224, 280, Computer Science 220, or any 300/400 level course in a related discipline with mathematics department approval. At most three credits of Math 491 (directed study) may be counted toward the applied mathematics minor.

Mathematics Course Offerings (MATH)

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: MATH 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: EDUC 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 (1-3)

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.

223 – Calculus III (3)

Prerequisite: MATH 122. Includes analytic geometry, parametric equations, polar coordinates, improper integrals, L’Hôpital’s rule, sequences, and infinite series.

224 – Multivariable Calculus (3)

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

280 – Statistical Methods (3)

Prerequisite: MATH 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.

300 – Linear Algebra (3)

Prerequisites: MATH 122 and either MATH 201 or CPSC 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: MATH 122. Ordinary differential equations which may include Laplace transformations, linear differential equations, applications, approximations, and linear systems of equations.

321 – Number Theory (3)

Prerequisite: MATH 201 or CPSC 125. An elementary, theoretical study of the properties of the integers.

325 – Discrete Mathematics (3)

Prerequisite: MATH 201 or CPSC 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: MATH 223 and either MATH 300 or MATH 312. 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 and non-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: MATH 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: MATH 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: MATH 471. Analytic functions, Cauchy-Riemann conditions, integration, power series, calculus of residues, conformal mappings and applications.

431, 432 – Abstract Algebra (3, 3)

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

441, 442 – Topology (3, 3)

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

MATH 481  – Theory of Interest (3)

This course introduces the mathematical concepts underlying the theory of interest. Topics include  measurement of interest (including accumulated and present value factors), annuities, yield rates, amortization schedules and sinking funds, bonds and related securities, derivative instruments, and hedging and investment strategies.

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 or minors.

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