Douglas Rall has been a faculty member at Furman since he finished his Ph.D. in 1976. His primary upper-level teaching interests are in algebra, graph theory, combinatorics, and number theory, but during his career, he has taught nearly all of the courses in the Mathematics Department. In 1990, Dr. Rall was awarded the Alester B. Furman, Jr. & Janie Earle Furman Award for Meritorious Teaching. He served as Mathematics Department Chair (1998-2002) and Furman University Faculty Chair (1999-2001).

Name Title Description

MTH-110

Finite Mathematics

Topics include: set theory, combinatorics, probability, statistics, matrix algebra, linear programming, Markov chains, graph theory, and mathematics of finance. A student cannot receive credit for this course after credit has been received for MTH-260 or any mathematics course numbered greater than MTH-302.

MTH-145

Calc for Life & Social Science

Introduction to the methods of differential and integral calculus with an emphasis on applications in the management, life, and social sciences. Topics include limits and continuity, differentiation and integration of functions of one variable, exponential and logarithmic functions, and applications.

MTH-150

Analytic Geometry/Calculus I

First course in the standard calculus sequence. Introduction to the theory, methods, and applications of differential calculus and an introduction to the definite integral. Topics include: algebraic and trigonometric functions, limits and continuity, rules for differentiation, applications of the derivative, antiderivatives, and the definition and basic properties of the definite integral.

MTH-151

Analytic Geometry/Calculus II

The second course in the standard calculus sequence. An introduction to the logarithmic and exponential functions, the applications of the definite integral, techniques of integration, indeterminate forms, improper integrals, numerical methods, and infinite series.

MTH-160

Vectors and Matrices

Introduction to the theory of vectors and matrices. Among the topics included are: vectors, vector operations, the geometry of Euclidean space, systems of equations, matrices, matrix operations, special transformations, eigenvalues, and applications of matrix theory.

MTH-255

Differential Equations

Introduction to the theory, methods, and applications of ordinary differential equations, including first- and higher-order differential equations, series solutions, systems, approximate methods, Laplace transforms, and phase plane analysis.

MTH-260

Higher Mathematics Transition

Introduction to the main ideas and proof techniques of mathematics with an emphasis on reading, writing and understanding mathematical reasoning. Among the topics covered are logic, proof techniques, sets, cardinality, combinatorial enumeration, mathematical induction, relations, functions, and others selected by the instructor.

MTH-320

Number Theory

Introduction to the arithmetic properties of the integers including divisibility, congruences, diophantine equations, primes and their distribution, quadratic forms and quadratic reciprocity. Additional topics will be chosen from continued fractions, cryptography, partitions, elliptic curves, modular forms and number fields.

MTH-330

Combinatorics & Graph Theory

A study of the primary methods and fundamental ideas of combinatorics and graph theory. Topics covered include generating functions, set partitions, recurrence relations, inclusion-exclusion, trees, graph connectivity, independence, and graph colorings. Additional topics will be chosen from Ramsey theory, set systems, planarity, directed graphs, matchings, and Hamiltonian and Eulerian graphs.

MTH-460

Modern Algebra

A theoretical introduction to some of the basic ideas of modern abstract algebra. Included is a study of groups, rings, domains, polynomial rings and fields as well as an investigation of their sub-structures and of the fundamental homomorphism theorems.

MTH-461

Topics in Algebra

An in-depth investigation of selected topics in abstract algebra.

Douglas Rall has published more than 60 research papers, mostly in the area of graph theory and combinatorial optimization, and one book, "Topics in Graph Theory: Graphs and Their Cartesian Product." The Simons Foundation supports his research through a "Collaboration Grant for Mathematicians." Collaborative research with other mathematicians from the United States and a number of foreign countries has been a very enjoyable and rewarding part of his professional life. Dr. Rall is a Foundation Fellow of the Institute of Combinatorics and its Applications and serves on the editorial board of the journal Discussiones Mathematicae Graph Theory.

Education
Ph.D.
University of Iowa
M.S.
University of Iowa
B.A.
University of Iowa

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