Mathematics Department Course Offerings

MATH 100 : Math Test course
  Credits: 3

MATH 101 : Welcome Mathematics Majors
An introductory course for entering mathematics majors. Through presentations, discussions and problem solving the question "What is Mathematics?". Offered every fall   Credits: 1

MATH 104 : R/Mathematical Ideas
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

MATH 112 : Precalculus
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. Prerequisites: Three years of high school mathematics, including intermediate algebra. Offered every semester   Credits: 4

MATH 113 : R/Finite Math for Society
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

MATH 140 : Math Concepts for Elem Educ I
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. Offered every semester   Credits: 3

MATH 141 : R/Math Concepts for Elem Ed II
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. Prerequisites: MATH 140. Offered every semester   Credits: 3

MATH 160 : R/Elements of Chance
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. (Those who have completed MATH 242, 260, or 360 may not enroll in this class for credit. Those majoring in mathematics may only receive free elective credit for the course.) Prerequisites: Three years of high school mathematics including intermediate algebra. Offered every fall   Credits: 3

MATH 188 : Experimental:
  Credits: 1-3

MATH 199 : Directed Study
  Credits: 1-6

MATH 213 : R/Applied Calculus I
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. Prerequisites: Precalculus or the equivalent. Not available to students with credit for MATH 221. Offered every semester   Credits: 4

MATH 221 : R/Calculus I
Topics studied are limits and continuity; derivatives and antiderivatives of the algebraic and trigonometric functions; the definite integral; and the fundamental theorem of the calculus. Prerequisites: MATH 112 or Precalculus with trigonometry or the equivalent. Offered every semester   Credits: 4

MATH 222 : Calculus II
Derivatives and antiderivatives of the transcendental functions, methods of integration, applications of definite integrals, sequences, improper integrals, and series. Prerequisites: MATH 221. Offered every semester   Credits: 4

MATH 223 : Calculus III
Vector calculus, functions of several variables, partial derivatives, multiple integrals, space analytic geometry, and line integrals. Prerequisites: MATH 222. Offered every semester   Credits: 4

MATH 228 : Calculus II for Biologists
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. Prerequisites: MATH 221. Offered every spring   Credits: 4

MATH 230 : Programming&MathProblemSolving
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 such as Matlab. Restricted to Math majors only. Corequisite/Prequisite: MATH 222.   Credits: 3

MATH 233 : Linear Algebra I
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. Prerequisites: MATH 213 or MATH 221 or permission of instructor. Offered every semester   Credits: 3

MATH 237 : R/Intro toDiscrete Mathematics
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. NOTE: This course is not available for credit to students with credit for MATH 239. Prerequisites: Four years of high school mathematics. Offered every fall   Credits: 3

MATH 239 : Intro to Mathematical Proof
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. Prerequisites: MATH 222 or permission of the department. Offered every semester   Credits: 3

MATH 242 : R/Elem of Probability & Stat
Basic concepts of probability theory and statistical inference. A knowledge of calculus is not required. (Those who have completed MATH 360 may not enroll in this course for credit, and no student may receive credit for more than one 200-level statistics course, including credit for more than one of the following courses: ECON 205, GEOG 278, MATH 242, PLSC 251, PSYC 250, and SOCL 211.) Prerequisites: Three years of high school mathematics including intermediate algebra. Not offered on a regular basis   Credits: 3

MATH 262 : R/Applied Statistics
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. (Those who have completed MATH 360 may not enroll in this course for credit, and no student may reveive credit for more than one 200-level statisticcs course, including credit for more than one of the following courses: BIOL 250, ECON 205, GEOG 278, MATH 242, MATH 262, PLSC 251, PSYC 250, and SOCL 211.) Offered every semester   Credits: 3

MATH 288 : Experimental:
  Credits: 0-6

MATH 299 : Directed Study
  Credits: 1-6

MATH 301 : Mathematical Logic
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. Prerequisites: MATH 239. Offered fall, odd years.   Credits: 3

MATH 302 : Set Theory
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

MATH 303 : TheoryComputational Complexity
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

MATH 304 : Theory of Computability
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 uncomputable problems, and the relationships between computability and the logical limits of mathematics. Prerequisites: MATH 239. Not offered on a regular basis.   Credits: 3

MATH 315 : Combinatorics
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

MATH 319 : Theory of Numbers
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

MATH 324 : Real Analysis I
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. Prerequisites: MATH 223 and MATH 239. Offered every semester   Credits: 3

MATH 325 : Real Analysis II
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

MATH 326 : Differential Equations
A study of the methods of solving ordinary differential equations, and some of the applications of these equations in the physical sciences and geometry. Prerequisites: MATH 223. Corequisites: MATH 233 or PHYS 228. Offered every semester   Credits: 3

MATH 328 : Thry of Ordinary Diff Equation
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. Prerequisites: MATH 233 and MATH 236. Offered fall, odd years   Credits: 3

MATH 330 : Abstract Algebra
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. Prerequisites: MATH 222, MATH 233, and MATH 239. Offered every semester   Credits: 3

MATH 332 : Linear Programming &Oper Resch
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 deterministric 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. Prerequisites: MATH 222, MATH 233,one of MATH 237 or MATH 239, and MATH 230 or permission of instructor. Offered spring, even years   Credits: 3

MATH 333 : Linear Algebra II
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. Prerequisites: MATH 223, MATH 233, and MATH 239. Offered every fall   Credits: 3

MATH 335 : Foundations of Geometry
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. Prerequisites: MATH 222 and MATH 239. Offered every spring   Credits: 3

MATH 338 : Topology
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

MATH 340 : Modeling Biological Systems
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. (Cross listed with BIOL 340.) Prerequisites: MATH 222 and at least one of the following: BIOL 203, BIOL 222, MATH 223 or permission of the instructor. Offered spring, even years and when demand is sufficient   Credits: 0-3

MATH 341 : Probability &AppliedStatistics
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. A student may not receive major credit for both MATH 341 and MATH 360. MATH 341 does NOT serve as a prerequisite for MATH 361. Prerequisite: MATH 223 or permission of instructor. Offered every spring   Credits: 3

MATH 345 : Numerical Analysis I
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.Prerequisites: MATH 222, MATH 233, MATH 239 or permission of the instructor, and MATH 230. Offered every fall   Credits: 3

MATH 346 : Numerical Analysis II
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

MATH 348 : Oral Presentation &Res Seminar
In this course, the student will research a mathematical topic and prepare for an oral presentation based on that research. The student will learn about research resources such as journals and electronic databases. Students will learn 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. Prerequisites: MATH 239 and permission of the instructor. Co-requisite: Student must be a mathematics major who is simultaneously enrolled in a 300 level mathematics course. Offered every spring or more often if demand in sufficient   Credits: 1

MATH 350 : Vector Analysis
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. Prerequisites: Math 223. Offered spring, odd years   Credits: 3

MATH 360 : Probability
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. A student may not receive credit for both MATH 341 and MATH 360. Prerequisites: MATH 223 or permission of the instructor. Offered every fall   Credits: 3

MATH 361 : Statistics
Sampling distributions, point and interval estimation, and tests of hypothesis. Topics also include: regression and correlation, the analysis of variance, and nonparametric statistics. Prerequisites: MATH 360 or permission of the instructor. Offered every spring   Credits: 3

MATH 363 : Regression & Time Series
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. Prerequisites: Math 361 or Econ 307, or permission of the instructor. Not offered on a regular basis.   Credits: 3

MATH 366 : Math Fdtn of Actuarial Sci
The purpose of this course is to develop knowledge of the fundamenal tools of probability that are useful for quantitatively assessing risk. The application of these tools to problems encountred in actuarial science is emphasized. A thorough command of the supporting calculus is assumed. Additionly, a very basic knowledge of insurance and risk management is assumed. Prerequisites: MATH 360 and permission of the instructor.   Credits: 0-3

MATH 371 : Intro to Complex Analysis
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. Prerequisites: MATH 223 and MATH 239 or permission of the instructor. Offered every fall   Credits: 3

MATH 372 : Partial Differential Equations
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. Prerequisites: MATH 326. Offered spring, even years   Credits: 3

MATH 380 : Topics in Math:
An exploration of an advanced topic that extends the breadth and/or depth of the undergraduate mathematical experience. May be taken twice under different subtitles. Prerequisites: Completion of five courses toward the major in Mathematics or permission of instructor. Not offered on a regular basis   Credits: 3

MATH 381 : Topics in Algebra:
An exploration of an advanced algebraic topic that extends the breadth and/or depth of the undergraduate mathematical experience. May be taken twice under different subtitles. Prerequisite: MATH 330 or permission of instructor. Not offered on a regular basis.   Credits: 3

MATH 382 : Intro-Wavelets&TheirApplicatns
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. Prerequisites: MATH 222, MATH 233, MATH 239, and MATH 230, or permission of instructor. Offered spring, odd years   Credits: 3

MATH 383 : Biomathematics Seminar
A discussion course dealing with selected areas of biomathematics based on current literature and/or guest speakers. Prerequisites: Permission of the instructor. May be taken multiple times for credit with the permission of instructor. Offered spring, even years   Credits: 1

MATH 384 : Computational Graphics
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. Prerequisites: MATH 223, MATH 230, and MATH 233. Not offered on a regular basis.   Credits: 3

MATH 388 : Experimental:
  Credits: 0-6

MATH 390 : History of Mathematics
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. Prerequisites: MATH 222. Offered every spring   Credits: 3

MATH 393 : Honors Thesis in Mathematics
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: 1-6

MATH 395 : Internship in Mathematics
  Credits: 1-12

MATH 398 : Directed Research:
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

MATH 399 : Directed Study
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

MATH 488 : Experimental:
  Credits: 3

MATH 499 : Directed Study
  Credits: 1-15

MATH 521 : Foundations of Calculus
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

MATH 532 : Classical Algebra
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

MATH 533 : Applied Matrix Techniques
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

MATH 535 : Transformational Geometry
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

MATH 536 : Euclidan &Non-Euclidn Geometry
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

MATH 537 : Applied Combinatorics
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

MATH 560 : Statistical Methods
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

MATH 570 : Hist &Fundmntl Concpts of Math
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

MATH 575 : Applied & Computational Math
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

MATH 599 : Directed Study:
  Credits: 1-12

MATH 699 : Directed Study:
  Credits: 1-12