Furman University

110 Finite Mathematics
GER: MR (Mathematics & Formal Reasoning)
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 301 or greater. Satisfies the pre-fall 2008 general education requirement in mathematics for the bachelor of arts degree only. 4 credits.

140 Integrated Precalculus/Calculus I
Introduction to the theory and methods of differential calculus. Topics include functions, graphs, limits, continuity and derivatives. Enrollment by department established criteria only. May not be enrolled on a pass-fail basis. 4 credits.

141 Integrated Precalculus/Calculus II
GER: MR (Mathematics & Formal Reasoning)
Prerequisite: MTH-140
Introduction to applications of the derivative and the theory and applications of the definite integral. Topics include: trigonometric functions and their derivatives, applications of derivatives, antiderivatives, the definite integral and applications of the integral. Satisfies the pre-fall 2008 general education requirement in mathematics. 4 credits.

150 Analytic Geometry and Calculus I
GER: MR (Mathematics & Formal Reasoning)
Prerequisite: criteria established by department
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. Satisfies the pre-fall 2008 general education requirement in mathematics. 4 credits.

151 Analytic Geometry and Calculus II
Prerequisite: MTH-141 or 150
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. 4 credits.

160 Vectors and Matrices
Prerequisite: MTH-151
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. 4 credits.

235 Operations Research
Prerequisite: MTH-160
Application of mathematical modeling and analytical methods to make better decisions. Topics include modeling, algorithm design, discrete linear function optimization with linear constraints, convexity, duality, sensitivity analysis, and optimality criteria. 4 credits.

241 Introduction to Statistics
Prerequisite: MTH-110, 141 or 150
Non-calculus based course in elementary probability and statistics. Counting problems, probability, various distributions, random variables, estimation, hypothesis testing, regression and correlation, analysis of variance, and nonparametric methods. A student cannot receive credit for this course and ECN-225 or MTH-341. 4 credits.

250 Vector Calculus
Prerequisite: MTH-160
Introduction to multivariate and vector calculus. Topics include vector functions and the differential and integral calculus of functions of several variables including Green’s Theorem and Stokes’ Theorem. 4 credits.

255 Differential Equations
Prerequisite: MTH-160
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. 4 credits.

260 Introduction to Discrete Mathematics
Prerequisite: MTH-151
Introduction to the main ideas and proof techniques of discrete mathematics. Among the topics covered are mathematical logic, relations, functions, partitions, recursion, induction, combinatorial principles, inclusion/exclusion, enumeration, and introductory graph theory (trees, connectivity, planarity, colorings, etc.). 4 credits.

301 Mathematics for Elementary School Teachers I
Problem solving and mathematical reasoning; sets and set operations; functions; numeration systems; the systems of whole numbers, integers, and rational numbers; algorithms; mental computation; elementary number theory; teaching strategies, materials, and technologies for these topics in grades pre-K-6. 4 credits.

302 Mathematics for Elementary School Teachers II
Prerequisite: MTH-301
Decimals and percents; elementary probability; descriptive statistics; geometry of shapes in two and three dimensions; congruence and similarity; measurement; geometric transformations; teaching strategies, materials, and technologies for these topics in grades pre-K-6 and field-based experiences in area schools. 4 credits.

320 Number Theory
Prerequisite: MTH-260
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. 4 credits.

325 Modern Geometry
Prerequisite: MTH-260
Development of Euclidean and non-Euclidean geometries. Topics include axiom systems, models, congruence theorems, parallel postulates, and the philosophical and historical background to geometry. 4 credits.

330 Combinatorics and Graph Theory
Prerequisite: MTH-260
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. 4 credits.

335 Mathematical Models and Applications
Prerequisite: MTH-250 and 255
A selection of mathematical models using various continuous and discrete methods and having applications in business and the social and biological sciences. Included are ecological models, epidemic models, Richardson’s arms race model, and population growth models. Other topics discussed are linear programming, voting problems, and Markov chains. 4 credits.

340 Probability
Prerequisite: MTH-250
Calculus-based course in probability, covering counting, discrete and continuous probability, random variables, important probability distributions, joint distributions, expectation, moment generating functions, and applications of probability. 4 credits.

341 Mathematical Statistics
Prerequisite: MTH-340
Calculus based course in statistics covering sampling, estimation, hypothesis testing, chi-square tests, regression, correlation, analysis of variance, experimental design, and nonparametric statistics. 4 credits.

350 Complex Variables
Prerequisite: MTH-250
Study of the complex plane and the calculus of functions of a complex variable. Topics to be considered include the algebra and geometry of complex numbers, limits and derivatives of functions of a complex variable, the Cauchy- Riemann equations, contour integrals, Taylor and Laurent series, and residues. 4 credits.

360 Linear Algebra and Matrix Theory
Prerequisite: MTH-160 and 260
Study of finite dimensional real vector spaces, linear transformations, determinants, inner product spaces, eigenvalues and eigenvectors. 4 credits.

420 Topology
Prerequisite: MTH-260
Introduction to concepts in topology including the following: topological spaces, metric spaces, continuity, homeomorphisms, neighborhoods, closed sets and closure, basis and sub-basis for a topology, subspaces, product spaces, connectivity, compactness, and separation axioms. 4 credits.

450 Real Analysis
Prerequisite: MTH-260
A theoretical introduction to some of the basic ideas of real analysis: real numbers and the topology of the real line, sequences and series of real numbers, limits of functions, continuity, uniform continuity, differentiation, the Riemann integral, and sequences and series of functions. 4 credits.

451 Topics in Analysis
Prerequisite: MTH-450
An in-depth investigation of selected topics in analysis. 4 credits.

460 Modern Algebra
Prerequisite: MTH-260
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. 4 credits.

461 Topics in Algebra
Prerequisite: MTH-460
An in-depth investigation of selected topics in abstract algebra. 4 credits.

504 Directed Independent Study
Study of an area of mathematics of interest to the student that is not part of one of the listed courses. The student must choose a faculty member to direct the study and, together with this faculty member, prepare a description of the material to be covered and submit it to the department chair for approval. Variable credit.