Mathematics Courses

Credits: 3

An introductory course for entering mathematics majors. Through presentations, discussions and problem solving the question "What is Mathematics?".
Credits: 1

Designed for the liberal arts student, this course investigates the meaning and methods of mathematics. By viewing mathematics as a search for patterns, a way of thinking, and a part of our cultural heritage, it emphasizes the various roles of mathematics. Mathematical ideas from geometry, number theory, and algebra are presented that support the proposition that mathematics is much more than just a collection of techniques for obtaining answers with standard problems. Offered spring, odd years
Credits: 3

This course is designed primarily for the student who needs a foundation in algebra and trigonometry for the study of calculus. The concept of function and graphical representation of functions is stressed. Topics covered: real numbers; algebra of real numbers including equations and inequalities; functions and their graphs including polynomials, rational expressions, logarithmic and exponential, trigonometric; algebra of the trigonometric functions including identities, equations, polar coordinates, complex numbers, systems of equations.
Credits: 4

Topics considered: basic algebra, systems of equations, matrix algebra, linear programming, finite probability. Problem solving and the use of mathematical reasoning in investigating relevant applications from business and the social sciences form an integral part of the course.Prerequisites: Three years of high school mathematics including intermediate algebra. Offered spring, even years
Credits: 3

This course is intended for education majors and is designed to provide a mathematical treatment of the fundamental concepts of arithmetic, algebra, and number theory as they relate to the elementary school mathematics curriculum.
Credits: 3

This course is intended for education majors and is designed to provide a mathematical treatment of the fundamental concepts of probability, statistics, and elementary geometry as they relate to the elementary school mathematics curriculum.
Credits: 3

This course will help students learn how to think about statistics and probability, how to identify the tools needed to study a particular problem and how to read and critically evaluate quantitative information presented in the media. The course format involves extensive reading and discussion of newspaper and journal articles, computer activities, writing assignments, and student projects.
Credits: 3

Credits: 1-3

Credits: 1-6

The student will be introduced to the mathematics of linear systems and to the concepts, methods and applications of calculus. Mathematical questions arising in business and the life and social sciences will be modeled and solved using these tools. Topics to be covered include linear systems of equations, matrix techniques, functions, limits, continuity, differentiation and integration. The approach will be graphical, numerical and analytic.
Credits: 4

Topics studied are limits and continuity; derivatives and antiderivatives of the algebraic, exponential, logarithmic, trigonometric, and inverse functions; the definite integral; and the fundamental theorem of the calculus.
Credits: 4

Topics studied are methods of integration, applications of definite integrals, sequences, improper integrals, and series, parametric equations and polar coordinates.
Credits: 4

Vector calculus, functions of several variables, partial derivatives, multiple integrals, space analytic geometry, and line integrals.
Credits: 4

A continuation of first semester calculus, with an emphasis on modeling and applications of mathematics and statistics to the biological sciences. Topics to be covered include exponential and logarithmic functions, differential equations, matrices, systems of differential equations, and an introduction to probability and statistics.
Credits: 4

This course serves as an introductory programming course for Mathematics majors. Basic programming techniques for solving problems typically encountered by mathematicians will be developed. The course covers basic procedural techniques such as algorithms, variables, input/output, data types, selection, iteration, functions and graphing. Good programming and commenting practices will be emphasized. The programming language for the course will be a mathematical programming language.
Credits: 3

Study of matrices, matrix operations, and systems of linear equations, with an introduction to vector spaces and linear transformations. Elementary applications of linear algebra are included.
Credits: 3

This course covers the basic tools of mathematics and computer science - logic, proof techniques, set theory, functions, inductive processes, counting techniques - with applications to such areas as formal languages, circuit theory and graph theory.
Credits: 3

The course will provide an introduction to the language of advanced mathematics and to mathematical proof. It will emphasize rigorous argument and the practice of proof in various mathematical contexts. Topics will include logic, set theory, cardinality, methods of proof, and induction. Other mathematical topics chosen at the discretion of the instructor will be included as material through which proving skills will be honed.
Credits: 3

This course introduces object oriented programming, a programming style useful for constructing large and/or complicated programs. The course covers the practice of object oriented programming in a current language (which may change as the field evolves), and underlying concepts of objects, classes, inheritance, and object oriented design patterns. The course considers applications in such areas as graphical user interfaces, data structures, simulations, games, etc.
Credits: 3

Basic concepts of probability theory and statistical inference. A knowledge of calculus is not required.
Credits: 3

An introduction to statistics with emphasis on applications. Topics include the description of data with numerical summaries and graphs, the production of data through sampling and experimental design, techniques of making inferences from data such as confidence intervals and hypothesis tests for both categorical and quantitative data. The course includes an introduction to computer analysis of data with a statistical computing package.
Credits: 3

Credits: 0-6

Credits: 1-6

The goal of the course will be to present the important concepts and theorems of mathematical logic and to explain their significance to mathematics. Specific results will include compactness, completeness and incompleteness theorems, with applications including switching circuits and nonstandard analysis.
Credits: 3

This course will examine the Zermelo-Fraenkel axioms for set theory and discuss the relationship between set theory and classical mathematics. Other topics will be chosen from the following: ordinal and cardinal numbers, the Axiom of Choice, the consistency and independence of the continuum hypothesis, and large cardinals. Prerequisites:MATH 239. Offered fall, even years
Credits: 3

A survey of the mathematical analysis of the time and space resources required to execute algorithms. Starting with the asymptotic analysis of resource needs of specific algorithms, the course builds to a study of lower bounds associated with problems, and culminates in an in-depth study of abstract resource-complexity classes such as P, NP, and PSPACE. Prerequisites: MATH 239. Not offered on a regular basis.
Credits: 3

This course covers the theoretical limits on what algorithms can and cannot compute. Topics include finite automata, regular languages, push-down automata, context-free languages, Turing machines, decidability, the structure of the classes of computable and incomputable problems, and the relationships between computability and the logical limits of mathematics.
Credits: 3

The purpose of this course is to introduce students to the fundamentals of graph theory and its applications. Topics covered include graphs, graph isomorphisms, trees, graph matrices and eigenvalues, strongly regular graphs, graph colorings, chromatic polynomials, planar graphs and the Four Color theorem. Students will use software to store, visualize, and manipulate graph models, and as a tool to explore basic properties of graphs.
Credits: 3

As calculus seeks to develop proficiency in analysis problem solving, the aim of this course is to develop proficiency in basic combinatorial problem solving and reasoning. Topics include: Enumeration, generating functions, sieve formulas, recurrence relations, graph theory, network analysis, trees, search theory, and block designs. Prerequisites: MATH 222, MATH 233 and either MATH 237 or MATH 239. Offered fall, even years
Credits: 3

An introduction to classical number theory dealing with such topics as divisibility, prime and composite numbers, Diophantine equations, the congruence notation and its applications, quadratic residues. Prerequisites: MATH 222 and MATH 239. Offered spring, odd years
Credits: 3

A study of the underlying theory of elementary calculus. Topics include the structure and properties of the real numbers, sequences, functions, limits, continuity, the derivative, the Riemann integral, and Taylor's theorems.
Credits: 3

A continuation of MATH 324 covering Riemann-Stieltjes integration, sequences and series of functions, special functions, and functions of several variables. Prerequisites: MATH 324. Offered every spring.
Credits: 3

A study of the methods of solving ordinary differential equations, and some of the applications of these equations in the physical sciences and geometry.
Credits: 3

A continuation of MATH 326 covering the existence theory of systems of ordinary differential equations, phase plane analysis, stability theory, and boundary value problems. An introduction to chaos theory, Lyapunov's Theorem, and Green's functions may be included if time permits.
Credits: 3

A study of the basic properties of groups, rings, and integral domains, including the fundamental theorem of group homomorphisms. The concepts basic to the development of algebraic systems are studied initially.
Credits: 3

The course introduces the student to the techniques for the formulation and solution of linear programming problems and their corresponding dual problems. It is intended to be a broad overview of deterministic linear programming and operations research. Topics to be covered include the Simplex Method, the Dual Simplex Method, Sensitivity Analysis, Network Optimization Methods, (Deterministic) Dynamic Programming, Game Theory and Branch and Bound Methods for Integer Programming. Additional topics may be selected from the Cutting Plane Methods for Integer Programming, the Transportation Problem, the Assignment Problem, Graphs and Networks, the Network Simplex Method, the Ellipsoid Algorithm and the Critical Path Method when time permits.
Credits: 3

An advanced look at vector spaces and linear transformations, with emphasis on the analysis of the eigenvalues of a linear transformation and on the concept of orthogonality. Applications, such as the solutions of linear systems of ordinary differential equations, are included.
Credits: 3

This course presents an investigation of the axiomatic foundations for several approaches to the study of modern geometry. Euclidean geometry, geometric transformations, and non-Euclidean geometries will be discussed.
Credits: 3

detailed examination of topological spaces and mappings. The properties of compactness, connectedness, and separation are studied. Further topics from general, geometric, or algebraic topology will also be discussed. Prerequisites: MATH 223 and MATH 239. Offered fall, even years
Credits: 3

Computer and mathematical models are increasingly important tools used to understand complex biological systems. Under the guidance of biology and mathematics professors, students will work both individually and in groups to develop, analyze and present models of various biological systems ranging from disease models and diffusion processes to ecosystem dynamics. The course involves two hours of lectures and a two hour computer-based laboratory.
Credits: 0-3

Topics include probability definitions and theorems; discrete and continuous random variables including the binomial, geometric, Poisson, and normal random variables; and the applications of statistical topics such as sampling distributions, estimation, confidence intervals, and tests of hypothesis. Both the theory and applications of probability will be included with applications of statistics.
Credits: 3

This course serves as an advanced statistical and algorithmic modeling course. The course includes the processes of model building using two disciplines, statistical learning and machine learning. Emphasis is placed on mathematics and algorithms. The topics include linear and non-linear regression methods, supervised and unsupervised learning methods including industry-standard methods, model improvement and ensemble methods, and handling large data issues. Students will gain mathematical foundations and data science skills with state-of-the-art programming languages such as R and Python, will learn to build high performance predictive models involving real-world data, and will produce a written data analysis report with an oral presentation.
Credits: 3

This course serves as an advanced applied statistics course. The course will enhance students’ statistical modeling knowledge and skills in multivariate and advanced settings with possibly interdisciplinary applications. Topics include a review of multiple linear regression and multi-sample analysis, a review of random variables, vector and matrix algebra, the theory of multivariate statistics, exploratory and confirmatory factor analysis, classification and clustering methods, multivariate data analysis techniques, model building and improvement methods, and individually chosen cutting-edge statistical models. Methodologies and applications are studied with real-word data along with state-of-the-art statistical software packages such as R and SAS/SPSS.
Credits: 3

This course provides an introduction to numerical methods and the analysis of these methods. Topics include floating point arithmetic, error analysis, solution of non-linear equations, interpolation and approximation, numerical differentiation and integration, and the solution of linear systems.
Credits: 3

This course provides an investigation of advanced topics in numerical analysis. Topics include the numerical solution of ordinary differential equations, boundary value problems, curve fitting, and eigenvalue analysis. Prerequisites: MATH 345. Offered spring, even years
Credits: 3

In this course, the student will research a mathematical topic and prepare for an oral presentation based on that research. Students will learn about research resources such as journals and electronic databases, mathematical writing conventions and presentation techniques. Students will prepare a talk of at least one half hour in length to be presented in a public forum.
Credits: 1

The course develops and expands upon certain topics in multivariate calculus. This includes the algebra and geometry of vectors, real and vector functions of one and several variables, curves, scalar and vector fields, vector differential and integral calculus, applications to geometry.
Credits: 3

Topics include probability definitions and theorems; discrete and continuous random variables including the binomial, hypergeometric, Poisson and normal random variables. Both the theory and applications of probability will be included.
Credits: 3

Sampling distributions, point and interval estimation, and tests of hypothesis. Topics also include: regression and correlation, the analysis of variance, and nonparametric statistics.
Credits: 3

This advanced course in statistics focuses on two topics crucial to the study of actuarial science. Topics in Regression include simple and multiple regression (including testing, estimation, and confidence procedures), modeling, variable screening, residual analysis and special topics in regression modeling. Topics in Time Series include linear time series models, auto-regressive, moving average and ARIMA models, estimation, data analysis and forecasting with time series models, forecast errors and confidence intervals. Case studies and analysis of real data will be included.
Credits: 3

The purpose of this course is to develop knowledge of the fundamental tools of probability that are useful for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. A thorough command of the supporting calculus is assumed. Additionally, a very basic knowledge of insurance and risk management is assumed.
Credits: 0-3

A study of complex numbers, complex differentiation and integration, mappings, power series, residues, and harmonic functions, with particular emphasis on those topics which are useful in applied mathematics. Optional topics: conformal mappings and analytic continuation.
Credits: 3

An introduction to those equations which play a central role in many problems in applied math and in physical and engineering sciences. Topics include first-order equations, the most useful second-order equations (e.g.:Laplace's wave and diffusion), and some methods for solving such equations, including numerical techniques. Modeling for the motion of a vibrating string and conduction of heat in a solid body are emphasized.
Credits: 3

The goal of this course is to provide the student interested in Actuarial Science, an understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. Students will also be given an introduction to financial instruments, including derivatives, and the concept of no-arbitrage as it relates to financial mathematics.
Credits: 0-3

An exploration of an advanced topic that extends the breadth and/or depth of the undergraduate mathematical experience.
Credits: 3

An exploration of an advanced algebraic topic that extends the breadth and/or depth of the undergraduate mathematical experience.
Credits: 3

This course is an introduction to the basics of digital images, Fourier analysis, wavelets, and computing in an applications first approach. Digitized photographs (or sound files) are stored as very large matrices and manipulated initially using basic linear algebra. Basic programming in Matlab, Maple, or Mathematica will be introduced as a means of performing the manipulations and a discovery tool. Wavelet transforms are used to aid in compressing or enhancing digital photographs, de-noising sound files, and compression using the JPEG2000 standard. Each student in the course will work on a final project that will involve coding, writing up the results in a paper, and presenting the results at the end of the semester.
Credits: 3

A discussion course dealing with selected areas of biomathematics based on current literature and/or guest speakers.
Credits: 1

An introduction to the mathematical and computational modeling of the visible world. Topics include vector representations of three-dimensional geometry; parametric and implicit forms of lines and surfaces; affine transformations; projections from three dimensions to two; rendering equations that model reflection, transmission, and absorption of light. Realistic models of real or imagined scenes will be created using these techniques, and drawn using a computer programming language.
Credits: 3

This course shows how habits of thought from mathematics lead to powerful ways of constructing correct computer programs. Specifically, it explores how mathematical proof based on careful and precise definitions is applied to proving algorithms correct, and how such reasoning and its results can be expressed through object oriented programming. Examples come from linear algebra, graph theory, or similar areas of mathematics.
Credits: 3

Credits: 0-6

The history of mathematics is traced from antiquity to the achievements of twenty-first century mathematicians. Applications to secondary and elementary school teaching are included.
Credits: 3

Independent research, directed by a member of the Department of Mathematics. Results of the research are to be reported in (l) a written thesis, and (2) an oral presentation in a Mathematics Department Colloquium or other approved forum. To be eligible a student must have a 3.7 cumulative grade point average in the major and a 3.0 overall. The Department can make special exceptions. Prerequisites: Enrollment is by invitation of the Department. Offered by individual arrangement
Credits: 3-6

Credits: 1-12

A course of study in which a student works individually on a project under the supervision of a faculty member. A Math 398 project will emphasize research on a topic that is outside the purview of the curriculum as contained in regular course offerings. Additionally, students must go beyond the textbook, to engage in reading, inquiry, and discovery that reflects creative mathematical research. All such projects must be approved by the chair as suitable for Math 398. Prerequisite: permission of instructor. Offered by individual arrangement.
Credits: 1-3

A course of study in which students work individually under the supervision of a faculty member. Prerequisites: Permission of instructor. (l to 3 semester hours.) Offered by individual arrangement
Credits: 1-3

Credits: 3

Credits: 1-15

Designed for teachers who desire to renew and to strengthen their knowledge of elementary calculus as well as for those who wish to probe the subject at a greater depth. Beginning with familiar material, the course attempts to develop the intermediate supporting theory. Topics covered include limit theory, differentiation, properties of continuous functions, and the theory of Riemann integration. Prerequisites: A course in analysis.
Credits: 3

Classical Algebra is an introduction to number theory and higher algebra within an historical context. The course may be used as a mathematics elective by students in the M.S. program in secondary mathematics. By permission of the department, it is open to undergraduates and will be available for 300-level mathematics credit to students who have not had both Number Theory (MATH 319) and Abstract Algebra (MATH 330).
Credits: 3

Many models can be formulated as a system of linear equations. The main emphasis of this course is to investigate a number of models that can be solved using matrix techniques and linear algebra. Applications may include, but are not limited to, Least Squares Fitting of Data, Markov Chains, and Population Growth Models. Prerequisites: A course in Elementary Linear Algebra.
Credits: 3

The concept of a geometric transformation is studied in conjunction with the basic structure of a group and properties of a space that remain invariant under specified transformations. Isometric and similarity transformations of the plane will be studied in depth in both a synthetic and analytic framework. As time permits, inversions, affine, projective, and topological transformations will be investigated. Prerequisites: A course in geometry.
Credits: 3

Presents the discovery of non-Euclidean geometry and the subsequent reformulation of the foundations of Euclidean geometry. Euclid's geometry, modern axiomatics, Hilbert's geometry and hyperbolic geometry are studied with a view of expanding the students' knowledge and perception of geometry, but also to gain an appreciation for Euclid's original work. Prerequisites: A course in geometry.
Credits: 3

The course will cover the fundamentals of combinatorics, beginning with elementary counting techniques (combinations and permutations) and including such topics as generating functions, Polya's enumeration formula, and graph theory. There will be an emphasis on discrete modeling. Prerequisites: A course in either Discrete Mathematics or Probability Theory.
Credits: 3

The course will cover basic statistical methods including the chi-square test, regression and correlation, analysis of variance and experimental design, and non parametric statistics. The emphasis is on the art of statistical thinking and data analysis based on real-world problems. The use of the computer and their peripheral devices as tools to understanding the statistical concepts will be included in this course. Prerequisites: One undergraduate course in Probability and Statistics.
Credits: 3

A chronological development of the fundamental principles of modern mathematics. The underlying concepts that form a basis for the axiomatic development of geometry, algebra, and analysis are discussed within the scope of the mathematics curriculum. Prerequisites: One course in each of the areas: algebra, analysis, geometry.
Credits: 3

Problems arising in a variety of fields will be investigated from a mathematical modeling perspective. The basic mathematical concepts and techniques widely used in Applied Mathematics and Numerical Analysis will be studied in the context of the applications. Numerical methods, involving the use of calculators and/or computer technology, which aid in the investigation, will be introduced dependent on the specific application. Prerequisites: Calculus III and Elementary Linear Algebra.
Credits: 3

Credits: 1-12

Credits: 1-12

Credits: 0-6