Mathematics Course Descriptions

For students who are required to take MATH 101 or MATH 102, the minimum number of credit hours to graduate is 123.

MATH 105 Elementary Statistics (3)
A noncalculus introduction to the fundamental concepts of probability and statistics. Topics include data collecting, displaying, summarizing, drawing inferences, set theory, probability, permutations and combinations, expectation, normal distribution, sampling distributions, point and interval estimation, significance testing and simple linear regression. Appropriate application software utilized. Prerequisite: MATH 101 or placement by department.(Fall and Spring)

MATH 108, 109 Concepts of Mathematics for Teachers I/II (3, 3)
This two-part sequence is designed for the elementary education major as an introduction to selected topics in mathematics. Topics include sets and set operations, number and numeration systems and their operations, algorithms, measurement, reasoning and problem solving, patterns and relations, geometry, probability and statistics. Open only to and required for students preparing to teach at the elementary school level. (108 Fall, 109 Spring)

MATH 110 Prelude to Mathematical Thought (3)
This course serves as an introduction to mathematical reasoning. Emphasis will be on reading and interpreting problems as well as developing fundamental problem-solving strategies. In addition, the course will familiarize students with mathematical notation and develop the writing skills needed to explain solutions with precision. Possible topics include puzzle problems, algebraic and logical reasoning, pattern recognition, and counting techniques. This course may be used to prepare for MATH 111. (Fall)

MATH 111 Mathematical Thought and Problem-Solving (3)
This course provides students with a mathematical approach to solving problems as well as an introduction to the nature of mathematics. The course seeks to improve facility with computations, mathematical notation, logical reasoning, and verbal expression of mathematical concepts. Content is selected from classical and modern areas of mathematics such as geometry, number theory, algebra, graph theory, fractals, and probability. The delivery of the content takes on a variety of forms including in-class activities, projects, discovery learning, and lecture. (Fall and Spring)

MATH 114 Precalculus Mathematics (3)
Designed to prepare students for the calculus sequence or for MATH 115. Topics include set theory, inequalities, systems of equations, basic analytic geometry, functions, logarithms and trigonometry. This course satisfies the core math requirement. Prerequisite: MATH 101 or placement by department. (Fall and Spring)

MATH 228 Discrete Mathematics (3)
Basic techniques and methods of reasoning for discrete problem solving. Topics include induction, set theory, elementary combinatorics, graph theory and applied algebra. Applications to computer science are emphasized. Prerequisite: MATH 101/102 or placement by department. (Same as CSCI and IFSY 228.) (Spring)

MATH 247 Calculus I (4)
An introduction to the fundamental concepts of differential and integral calculus with an emphasis on limits, continuity, derivatives and integrals of elementary functions. Applications to curve sketching, max-min values, related rates and areas will be given. Derivatives and integrals of elementary transcendental functions. Prerequisite:MATH 114 or placement by department. Students that placed into Math 101/102 may not take Calculus until they have completed MATH 114. (Fall and Spring)

MATH 248 Calculus (4)
Techniques and applications of integration. Topics include improper integrals, polar coordinates, parametric equations, plane analytic geometry, sequences, series and Taylor’s theorem. Prerequisite: MATH 247 or permission of instructor. (Fall and Spring)

MATH 249 Calculus III (4)
Vectors. Calculus of vector-valued functions. Calculus of functions of several variables. Lagrange multipliers. Multiple integration. Line and surface integrals, including Green’s theorem, Stokes’ theorem, and the divergence theorem. Prerequisite: MATH 248 or permission of instructor. (Fall)

MATH 285 Applied Statistics (3)
An introduction to principles and techniques of data analysis and statistical models. Topics include the methods of exploratory data analysis, the design of experiments, sampling, hypothesis testing, simple and multiple regression, and the analysis of variance. Prerequisite: MATH 247 or permission of instructor. (Spring, odd years)

MATH 332 Graph Theory (3)
An introduction to graph theory, covering both theory and practical applications. Topics include paths and cycles, bipartite graphs, digraphs, spanning trees, connectivity, matchings, coloring, planarity, Hamiltonian cycles, and graph classes. Prerequisite: MATH 248 or permission of the instructor. (On a rotating basis)

MATH 364 Linear Algebra (3)
Matrices and determinants with applications to systems of linear equations, including linear programming, vector spaces, linear transformation, eigenvalues and eigenvectors, and canonical forms. Prerequisite: MATH 247 or permission of instructor. (Spring, even years)

MATH 368 Algebraic Structures (3)
An introduction to the fundamental concepts of abstract algebra. Topics include abelian groups, permutation groups, cyclic groups, isomorphisms and Cayley’s Theorem. Includes an introduction to rings, ideals, integral domains, and fields. Prerequisite: MATH 248 or permission of instructor. (Spring, even years)

MATH 377 Foundations of Geometry (3)
Survey of geometries emphasizing the axiomatic/deductive approach. Includes finite geometries, fundamental concepts of Euclidean geometry in the plane and higher dimensions, some theorems leading to the modern synthetic approach, constructions and transformations, history of the parallel postulate and non-Euclidean geometries. Understanding and writing clear and consistent proofs are major course objectives. Prerequisite: MATH 228 and MATH 248 or permission of instructor. (Fall, even years)

MATH 384 Differential Equations (3)
Typical solution methods for first order or linear equations involving ordinary derivatives. Series approximation, Laplace transforms, Picard’s method and existence theorems. Prerequisite: MATH 249 or permission of instructor. (Spring, odd years)

MATH 387 Probability (3)
An introduction to the theory of probability. Topics include Kolmogorov’s axioms of probability, conditional probability and independence, finite combinatorics, discrete and continuous distributions, moments, jointly distributed random variables, limit theorems, generating functions, Markov chains and random walks. Prerequisites: MATH 228 and MATH 248 or permission of instructor. (Fall, even years)

MATH 390 Mathematical Statistics (3)
Topics include functions of random variables, transformations of random variables, order statistics, sampling theory and distributions, introduction to the theory of point estimation and statistical inference, confidence intervals, hypothesis testing, likelihood ratio tests, regression, correlation, analysis of variance and analysis of enumerative data. Prerequisite: MATH 387. (As needed)

MATH 436 Elementary Number Theory
Elementary number theory with a focus on both history and theory. Topics include the Euclidean Algorithm, Diophantine equations, the Fundamental Theorem of Arithmetic, congruences, number-theoretic functions, primitive roots, continued fractions, and the theorems of Fermat, Wilson, and Euler. Prerequisites: MATH 228 and MATH 247 or permission of instructor. (On a rotating basis)

MATH 447 Introduction to Real Analysis I (3)
A rigorous development of the fundamental concepts of analysis, including the real number system, functions, sequences, limits, continuity, convergence, differentiation, integration and series. Prerequisite: MATH 249 or permission of instructor. (Spring, odd years)

MATH 457 to Complex Analysis (3)
Complex number systems, limits, sequences, analytic functions, the Laplace equation, contour integrals, Cauchy integral theorems, power series, singularities and conformal mapping. Prerequisite: MATH 249 or permission of instructor. (Spring, even years)

MATH 472 Topology (3)
An introduction to point-set topology or algebraic topology. Possible topics include metric spaces, normal and regular spaces, compactness, connectedness, continuity of mappings, homotopy and homology groups, fixed-point theorems and knot theory. Prerequisite: MATH 249 or permission of instructor.  (On a rotating basis)

MATH 484 Numerical Methods (3)
Numerical methods for applications of mathematics. Topics include the numerical solution to nonlinear equations, interpolation, numerical differentiation and integration, and the numerical solution to differential equations. Oriented toward computer implementation using a programming language or a computer algebra system. Prerequisites: MATH 248 and CSCI 120 or permission of instructor. (Spring, even years)

MATH 488 Operations Research (3 credits)
An introduction to operations research. Topics will be selected from linear programming, network models, project scheduling, stochastic processes, game theory, queuing theory, decision analysis, non-linear programming, dynamic programming, simulation, and forecasting. Prerequisite: MATH 248 and CSCI 120 or permission of instructor. (Spring, odd years)

MATH 489 Modeling and Simulation (3)
Emphasis on the study of models and their applications to other disciplines. Topics may include population growth, epidemics, scheduling problems, predator-prey interaction, transportation, economic and stochastic models. Prerequisite: MATH 248 and CSCI 120 or permission of instructor. (Same as CSCI 489.) (As needed)

MATH 398 Independent Study (1-3)
Independent study in an area of mathematics selected to meet a student’s interest or need. Permission of the instructor, department chair and dean for academic affairs required. (As needed)

MATH 492, 493 Practicum (1-3)
An opportunity to gain practical experience in a work-related program. The nature of the work experience and the number of credits must be approved in advance by the department chair and the dean for academic affairs. (As needed)

MATH 495, 496 Seminar I, II (1, 1)
A course designed to enhance the comprehension of the fundamental concepts of higher mathematics and to develop an understanding of their organization. The course may involve applying ideas and techniques learned in earlier classes to solve mathematical and applied problems, and it may also involve directed reading and study in contemporary publications. (Spring)

MATH 497 Undergraduate Research in Mathematics (1-3)
Under the supervision of a faculty instructor, students conduct research on mathematical questions posed by the student or the instructor. Work may be done individually or in teams as determined by the instructor. The course prerequisites and enrollment limitation vary with the instructor and topic. Prerequisites: permission of instructor. (As needed)

MATH 499 Special Topics in Mathematics (3)
An intensive study or continuation of a field of mathematics. Some possible topics are differential equations, advanced complex number theory, or harmonic analysis. (As needed)