#
Mathematics Course Offerings

A listing of offered courses follows with prerequisites. Please note that some courses do have additional fees associated with them. The credit value of each course is represented by the number in brackets.

Undergraduate Course Offerings

Graduate Course Offerings

# Undergraduate Courses

### M 100, 200, 300, 400, 500 Cooperative Education Program [variable]

These courses are intended for students in the cooperative education program. The program is designed to provide students with a series of real-world problems that must be analyzed and modeled to provide solutions that are usable in their work environment. These courses carry 1–3 credits, with the actual number of credits awarded on the basis of work involvement. Cooperative education courses may be repeated for a total of up to 15 credits. All courses must be taken on a Pass/No Pass basis.

*Prerequisites:* Sophomore standing and 2.5 GPA.

### M 110 Modeling with Elementary Functions [3]

A study of linear, quadratic, cubic, exponential, and logistic equations and their use in modeling real-world phenomena; the graphing of functions; solving equations with one or more variables; and systems of linear equations. The solution of word problems is stressed throughout. This course may serve as preparation for M 112 but not for M 144.

*Prerequisite:* Two years of algebra.

### M 112 A Short Course in Calculus [3]

A one-semester introduction to the basic concepts and applications of differential and integral calculus. No credit given to students who have previously received credit for M 144 or its equivalent.

*Prerequisite:* M 110 or its equivalent.

### M 114 Everyday Statistics [3]

Designed to introduce basic concepts of probability, random sampling, data organization, measures of central tendency and variability, binomial and normal probability distributions, statistical inference, elements of hypothesis testing, one- and two- sample tests for means and proportions, chi-square tests for tabular data, an introduction to linear regression and correlation. *Prerequisite:* Two years of algebra.

### M 116 Contemporary Mathematics [3]

Designed to introduce the student to a variety of mathematical fields and some of their contemporary applications. Topics selected from logic, set theory, mathematical systems, recursive sequences, probability, statistics, game theory, linear programming, graph theory, computer programming, voting methods, and topology. *Prerequisite:* Two years of algebra.

### M 118 Introduction to Modern Mathematics [4]

Sets, operations on sets, historical background for numeration, system of natural numbers, number bases, systems of integers, rational numbers, real numbers, metric geometry, modular systems, groups, fields, rings, integral domains, relations, and functions. A two-hour laboratory period per week is included. Note: This course does not satisfy the mathematics portion of the general education requirements in Arts and Sciences. *Prerequisite:* Two years of algebra.

### M 140 Precalculus with Trigonometry [4]

A study of linear and quadratic equations and inequalities; the Cartesian coordinate system for the plane; and the algebra and graphing of functions with special emphasis on polynomial, exponential, and logarithmic functions. Definitions and graphs of the trigonometric functions; solutions of triangles; analytic trigonometry, including circular and inverse trigonometric functions. Solutions of word problems are stressed throughout. A programmable graphing calculator is required. The goal is to prepare students for M 144.

*Prerequisite:* Two years of algebra.

### M 144 Calculus I [4]

Functions; limits; continuity; differentiation of algebraic, trigonometric, logarithmic, and exponential functions; applications of derivatives; and an introduction to integration.

*Prerequisite:* M 140 or equivalent.

### M 145 Calculus II [4]

Techniques of integration, indeterminate forms, improper integrals, infinite sequences and series, and separable differential equations.

*Prerequisite:* M 144.

### M 220 Linear Algebra and Matrix Theory [3]

Linear equations and matrix algebra, determinants, vector spaces, linear independence and bases, linear transformations and their matrix representations, eigenvalues and eigenvectors, diagonalizable matrices. Selected topics from quadratic forms, linear programming, inner product spaces, or numerical linear algebra.

*Prerequisite:* M 145.

### 221W Discrete Mathematics I [4]

Topics include propositional calculus, combinatorics, graph isomorphisms, paths, planarity, colorability, trees and graph algorithms, occupancy problems, generating functions, and recurrence equations.

*Prerequisite:* M 145.

**(Writing-intensive course)**
### M 222W Discrete Mathematics II [4]

A formal introduction to the basic concepts of modern abstract mathematics. Topics include symbolic logic, predicate calculus, methods of proof, elements of set theory, functions, relations, cardinality, and graph theory.

*Prerequisite:* M 221W.

**(Writing-intensive course)**
### M 240 Calculus of Several Variables [4]

Vectors in three dimensions, curves and parametric equations in three dimensions, geometry of surfaces, differential calculus of functions of more than one variable with applications, multiple integrals and their applications, the differential and integral calculus of vector fields.

*Prerequisite:* M 145.

### M 242 Differential Equations [3]

Solutions of first-order linear, separable equations and applications; higher-order linear equations and applications. Nonhomogeneous equations; Laplace transforms and initial value problems; matrices, eigenvalues, and linear systems of differential equations. Qualitative analysis of equilibria and bifurcations.

*Prerequisite:* M 145.

### M 246 Applied Mathematics with Differential Equations for Civil Engineers [4]

Matrix algebra; first- and second-order linear differential equations, including numerical methods; an introduction to partial differential equations, including numerical methods; an introduction to probability and statistics. (A student may not receive credit for both this course and either M 242 or M 344.)

*Prerequisite:* M 240.

### M 260 Data Analysis [4]

An introduction to exploratory and confirmatory data analysis. Classical, portable, and robust statistical methods. Emphasis on model-building, analysis, interpretation, and refinement using statistical software (Minitab, SAS, BMDP, SPSSx).

*Prerequisite:* M 145.

### M 310 History of Mathematics [3]

A historical study of the principal mathematicians of the past 2,500 years and their contributions to the development and growth of the various fields of mathematics. (Offered Fall 2010, 2012, 2014.)

*Prerequisite:* M 222W or permission of instructor.

### M 320 Theory of Numbers [3]

Investigation of the arithmetic properties of the integers. Unique factorization, congruences, quadratic reciprocity, and other topics will be treated. (Offered Spring 2012, 2014, 2016.)

*Prerequisite:* M 222W.

### M 340 Introductory Analysis [3]

A rigorous treatment of differentiation and Riemann integration. Topology of the real line, real-valued sequences and their limits, continuity of real-valued sequences and their limits, continuity of real-valued functions, the Mean Value Theorem, a rigorous definition of the definite (Riemann) integral and proofs of its elementary properties, the Fundamental Theorem of Calculus. Other topics may include sequences of functions, series, or function spaces.

*Prerequisite:* M 222W.

### M 344 Advanced Engineering Mathematics [3]

Series solutions of ordinary differential equations and Bessel functions, Sturm-Liouville systems, and Fourier Series. Partial differential equations in Cartesian and cylindrical coordinates.

*Prerequisites:* M 240 and M 242.

### M 350 Numerical Analysis [3]

Floating point arithmetic; algorithms and error analysis; roots of nonlinear equations; systems of linear equations; direct methods, factorization schemes, and iterative techniques; interpolation: difference schemes, splines; numerical differentiation and integration; solutions of ordinary differential equations; the matrix eigenvalue problem. (Offered Fall 2011, 2013, 2015.)

*Prerequisites:* M 145, M 220, and CS 114.

### M 354 Studies in Mathematical Modeling [3]

The process of developing and simulating mathematical models of real-world phenomena will be studied. The types of models considered will vary from year to year. They may include discrete and continuous dynamical models, stochastic models, neural networks, and optimization models. Applications may be to the natural sciences, management science, engineering, or industry. With departmental permission, the course may be repeated for credit. (Offered Spring 2011, 2013, 2015.)

*Prerequisite:* M 240 or permission of instructor.

### M 360 Probability Theory [3]

Basic combinatorial probability, conditional probability, random variables, expectations, special discrete and continuous random variables and their properties, transformation of variables, Central Limit Theorem. (Offered Fall 2010, 2012, 2014.)

*Prerequisite:* M 240.

### M 362 Elements of Statistics [3]

Sampling distributions; theory of point and interval estimation; hypothesis testing, significance level, power, Neyman-Pearson Lemma, likelihood ratio tests, chi-square test on categorical data; theory and application of linear models; regression and ANOVA; nonparametric techniques based on ranks. (Offered Spring 2011, 2013, 2015.)

*Prerequisite:* M 360.

### M 370 Foundations of Geometry [3]

An axiomatic development of Euclidean geometry; attempts to prove the parallel postulate; the discovery of non-Euclidean geometries and their properties. (Offered Fall 2011, 2013, 2015.)

*Prerequisite:* M 222W.

### M 380 Teaching Secondary School Mathematics—Concepts [3]

A study of mathematics education, including issues related to learning theory, mathematics, curricula, pedagogy, assessment, and the role of research and state and national standards on the teaching and learning of school mathematics.

*Prerequisite:* M 222. Note: This course will not count toward the University mathematics requirement or the upper-level course requirement in either a math minor or the other two math majors.

### M 381W Teaching Secondary School Mathematics—Practice [3]

A course in the methods of designing, teaching, assessing, and revising effective lesson and unit plans across the 7–12 mathematics curriculum, including algebra, geometry, number systems, probability/statistics, and discrete math.

**(Writing-intensive course)** *Prerequisite:* M 380. Note: This course will not count toward the University mathematics requirement or the upper-level course requirement in either a math minor or the other two math majors.

### M 420 Introduction to Modern Algebra [3]

A study of the fundamental algebraic structure of groups, rings, and fields, including substructure, quotient structure, and morphism concepts.

*Prerequisite:* M 222W.

### M 442 Introduction to Complex Analysis [3]

Field of complex numbers, algebraic and geometric representations; analytic functions, the Cauchy-Riemann equations, harmonic functions; integration in the complex plane; power series; Laurent series and singularities of functions; theory of residues and evaluation of integrals. (Offered Spring 2011, 2013, 2015.)

*Prerequisite:* M 240.

### M 470 Introduction to Topology [3]

An introduction to point-set topology. Topics are topological spaces, homeomorphisms, connectedness, compactness, separation axioms, and metric spaces.

*Prerequisites:* M 222W and M 340.

### M 480, 481 Independent Study in Mathematics [1–3, 1–3]

Provides an opportunity for the student to study mathematical topics under the direction of a faculty member.

*Prerequisite:* Approval of the department. The signature of the department chairman is required to register for these courses.

### M 190, 191, 290, 291, 390, 391, 490, 491 Special Topics in Mathematics [1–4]

Investigates mathematical topics not covered in the regular curriculum.

*Prerequisite:* M 221W or permission of department.

# Graduate Courses

### M 515 Methods of Applied Mathematics I [3]

Matrix algebra; simultaneous linear equations and numerical methods for their solution, inverses, and determinants. Linear ordinary differential equations, Laplace transform methods, and Green’s functions. Eigenvalues and eigen-vectors, canonical forms, matrix norms, algebraic variational methods, functions of matrices. Matrix methods for linear systems of ordinary differential equations, including the state-transition matrix. Quadratic forms and positive definite matrices, singular value decomposition. A brief survey of series solutions to ordinary differential equations and special functions. Introduction to nonlinear analysis (if time permits).

*Prerequisites:* Undergraduate calculus and differential equations.

### M 517 Applied Engineering Statistics [3]

Data collection, display, and interpretation. Discrete probability. Special discrete and continuous distributions. Sampling distributions and the Central Limit Theorem. Point and interval estimation, including confidence, prediction, and tolerance intervals. Parametric and non-parametric methods of hypothesis testing. Analysis of variance and the design of experiments, including blocking, factorial designs, and so forth. Simple and multivariate regression analysis, correlation, residual plots, diagnostics and outlier detection. Introduction to statistical process control (if time permits).

*Prerequisite:* Undergraduate calculus.