Students with credit in MTH 182, or in any mathematics course numbered above 220, may not register for a mathematics course numbered 168 or lower. A student who attempts to do so will be given a grade of W in the ineligible course. This rule takes precedence over the university regulations on repeated courses whenever both are applicable.

Placement Tests: All students must take the Mathematics Placement Examination before they will be permitted to register for mathematics courses numbered 115, 116, 117, 127, 147, 151, 167, 168, and 181, except for students who have passed the appropriate prerequisite course. Mandatory placement for these courses is in effect. Students are not permitted to register for a higher-level course than indicated by their placement exam score.

- Preparatory Courses
- Courses for Humanities, Business, Education, and Social Sciences
- Courses for Mathematics, Science, Engineering, Computer Science and Education Majors

A student who has been unconditionally admitted to the university should have already mastered the material in these courses. Credit earned in MTH 087 or MTH 088 does not count toward graduation.

**MTH 087 Basic Math and Algebra for Liberal Arts Majors (4-0-4).** MTH 087 begins with a review of arithmetic topics such as fractions, decimals, percents, integers, and order of operation. It then proceeds to a review of algebra topics such as solving and graphing linear equations and inequalities, solving and graphing simultaneous equations and inequalities. MTH 087 concludes with an introduction to statistics and probability. Pass/fail system of grading, but students receive modified letter grades: S(A), S(B), S(C), U(D), U(F). The letter grades in parentheses are not computed in the students' GPAs. No credit toward graduation. Return to top

**MTH 088 Basic Math and Algebra for Business and Science Majors (4-0-4).** MTH 088 begins with a pre-algebra review. It then proceeds to basic algebra topics such as linear and quadratic equations and inequalities, rational and radical expressions, linear systems with emphasis on graphing and applications through problem-solving as well as relations and functions. Pass/fail system of grading, but students receive modified letter grades: S(A), S(B), S(C), U(D), U(F). The letter grades in parentheses are not computed in the students' GPAs. No credit toward graduation. Return to top

**MTH 115 Intermediate Algebra (4-0-4).** Prerequisite: MTH 087 or MTH 088 or suitable placement-test score. Extension of basic algebra techniques, linear equations, and linear inequalities, an introduction to functions, roots, radicals, exponents, quadratic equations, solution of second degree equations and applications, and the analysis and solution of word problems. Return to top

#### Courses for Humanities, Business, Education, and Social Sciences

Any course in this section, except MTH 127, is suitable for meeting the requirement of the** GenEd**. Credit earned in these courses does not count toward the mathematics major.

**MTH 116 Foundations of Quantitative Literacy (4-0-4).** Prerequisite: a grade of SC or better in MTH 087 or suitable placement-exam score. Not open to students who have previously earned credit for or are currently taking MTH 147 and/or MTH 119. This course is designed to develop quantitative reasoning skills as applied to personal and social issues. Students will learn mathematics and basic statistics needed for success in other college courses, advancement of one's career, and understanding of major issues in life. This course is for students not planning to major in a field requiring advanced mathematical skills. Return to top

**MTH 117 Mathematical Applications in the Real World (4-0-4).** Prerequisite: a grade of C or better in MTH 116, MTH 119. Not open to students who have previously earned credit for MTH 118. This course continues the development of quantitative reasoning skills as started in MTH 116. Topics in this course include the mathematics in population growth models, architecture, art, music, and voting systems. This course is for students not planning to major in a field requiring advanced mathematical skills. Return to top

**MTH 127 Mathematics for Elementary and Middle School Teachers I (4-0-4).** Prerequisite: A grade of SC or better in MTH 087 or suitable placement-test score. Topics needed to teach elementary and middle school mathematics, including numeration systems and whole number arithmetic, integers and number theory, rational and real numbers, problem solving, and applications. Return to top

**MTH 128 Mathematics for Elementary and Middle School Teachers II (4-0-4).** Prerequisite: MTH 127. Additional topics for the elementary curriculum, including geometry, measurement, and applications. The course will incorporate the use of appropriate computer software for the elementary school classroom such as LOGO and Cabri. Return to top

**MTH 129 Mathematics for Elementary and Middle School Teachers III (2-0-2).** Prerequisite: MTH 127. Additional topics for the elementary curriculum, including probability and statistics. The course will incorporate the use of appropriate technology for the elementary school classroom such as the TI-73 calculator with the CBR and computer software Fathom and Excel. Return to top

**MTH 147 Statistical Concepts with Applications (4-0-4).** Prerequisite: A grade of SC or better in MTH 087 or suitable placement-test score. A first course in statistics that emphasizes statistical methodology as applied in the social and behavioral sciences, education, and business; topics include descriptive statistics, elementary probability, elementary sampling theory, estimation, hypothesis testing, regression and correlation. (Note that students who earn credit for MTH 147 cannot earn subsequent credit for MTH 119.) Return to top

**MTH 151 through MTH 156 Mathematical Concepts**. Each of these is a 1- or 2-credit course. Normally a student must register for MTH 151, 152, and 153, or for MTH 154, 155, and 156. One is taught at the beginning of the semester, one in the middle of the semester, and one at the end of the semester.

A graphing calculator is required for MTH 151 to 156. Consult the Mathematics Department for recommended models.

**MTH 151 Mathematical Concepts 1a (1-0-1).** Prerequisite: A grade of SC or better in MTH 088 or suitable placement-test score. Equations of lines, word problems, linear, polynomial and rational inequalities, graphs of functions, linear and quadratic functions, and their applications. Return to top

**MTH 152 Mathematical Concepts 1b (2-0-2).** Prerequisite: MTH 151. Systems of three or more linear equations, Gauss-Jordan elimination, matrix methods, linear programming. Return to top

**MTH 153 Mathematical Concepts 1c (1-0-1).** Prerequisite: MTH 152. Polynomial, exponential, and logarithmic functions and graphs, math of finance. Return to top

**MTH 154 Mathematical Concepts 2a (1-0-1).** Prerequisite: MTH 153. Intuitive differential calculus, derivatives, applications of derivatives. Return to top

**MTH 155 Mathematical Concepts 2b (2-0-2).** Prerequisite: MTH 154. Intuitive integral calculus, antiderivatives, the definite integral, applications, partial derivatives. Return to top

**MTH 156 Mathematical Concepts 2c (1-0-1).** Prerequisite: MTH 155. Probability, permutations, combinations, Bayes' Theorem. Return to top

Courses for Mathematics, Science, Engineering, Computer Science and Education Majors

##### Precalculus and First-Year Calculus Courses

The precalculus courses (MTH 167 and MTH 168) are designed for students who intend eventually to take calculus (MTH 181) and are not intended as general education courses. Depending on the placement-test score, a student starts with MTH 167 or with MTH 168. Credit earned in precalculus courses does not count toward the mathematics major.

A graphing calculator is required for MTH 167, 168, 181, and 182. Consult the Mathematics Department for recommended models.

**MTH 167 Precalculus Mathematics I (4-0-4).** Prerequisite: A grade of SC or better in MTH 088 or suitable placement-test score. Brief review of intermediate algebra techniques, rectangular coordinates, graphs of equations; and functions, lines, circles, detailed study of functions, graphing techniques. Return to top

**MTH 168 Precalculus Mathematics II (4-0-4).** Prerequisite: A grade of C or better in MTH 167 or suitable placement-test score. Functions, polynomial and rational functions, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Return to top

**MTH 181 Calculus I (4-0-4).** Prerequisite: A grade of C or better in MTH 168 or suitable placement-test score. Topics covered include limits, derivatives, continuity, applications of derivatives, antiderivatives and the definite integral. Return to top

**MTH 181H Honors Calculus I (4-0-4). **Prerequisites: A grade of C or better in MTH 168 or suitable placement test score, Honors standing or permission of university Honors Program. Topics to be covered include limits, derivatives, continuity, applications of the derivative, antiderivatives and the definite integral. Covers the same basic topics as MTH 181, but with greater emphasis on rigorous treatment of the underlying mathematical ideas and real world applications. Return to top

**MTH 182 Calculus II (4-0-4).** Prerequisite: A grade of C or better in MTH 181. Topics to be covered include applications of integration, techniques of integration, improper intergrals, infinite series, power series, polar coordinates, conic sections, and vectors. Return to top

**MTH 182H Honors Calculus II (4-0-4).** Prerequisites: A grade of C or better in MTH 181H or suitable placement score, Honors standing or permission of university Honors Program. Topics to be covered include applications of integration, techniques of integration, improper intergrals, infinite series, power series, polar coordinates, conic sections, and vectors. This course covers the same basic topics as MTH 182, but with greater emphasis on rigorous treatment of the underlying mathematical ideas and real world applications. Return to top

##### Intermediate Courses

**MTH 220 Introduction to Discrete Mathematics (4-0-4).** Prerequisites: A grade of C or better in MTH 156 or a grade of C or better in MTH 182; and CIS 260 or equivalent. Sets, relations, and functions; the concept of algorithm; mathematical induction and recursive definition. Applications of these fundamentals are chosen at the instructor's discretion from graph theory, Boolean algebra, lattice theory, finite-state automata, elementary grammars, and the theory of recurrence relations. Return to top

**MTH 247 Applied Statistics (4-0-4).** Prerequisite: A grade of C or better in MTH 147 or consent of instructor. Topics include design of experiments, analysis of variance, multiple and logistic regression, and time series analysis. This course will emphasize the applied nature of statistical analysis and require using a statistical analysis software package such as SPSS. No credit toward the mathematics major. Return to top

**MTH 281 Multivariable Calculus (4-0-4).** Prerequisite: A grade of C or better in MTH 182. Multivariate and vector calculus, including three-dimensional analytic geometry, partial derivatives, multiple integrals, vector calculus, line integrals, Green's Theorem. Only 2 of the 4 credits may be counted toward graduation by students who have passed MTH 283. Return to top

**MTH 283 Multivariable Calculus for Engineers (2-0-2).** Prerequisite: A grade of C or better in MTH 182. Multivariate calculus including three-dimensional analytic geometry, partial derivatives, multiple integrals. Students who have passed MTH 281 may not register for MTH 283. A student who attempts to do so will be given a grade of W. Return to top

**MTH 284 Matrices for Engineers (2-0-2).** Prerequisite: A grade of C or better in MTH 182. Matrix algebra, including matrices and systems of linear equations, determinants, inverses, eigenvalues and eigenvectors. Students who have passed MTH 288 may not register for MTH 284. A student who attempts to do so will be given a grade of W. Return to top

**MTH 286 Introduction to Differential Equations (4-0-4).** Prerequisite: A grade of C or better in MTH 182. First-order differential equations, linear differential equations, first order systems, Laplace transform techniques, and applications. Return to top

**MTH 288 Linear Algebra (4-0-4).** Prerequisite: A grade of C or better in MTH 182. Systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors. Only two of the four credits may be counted toward graduation by students who have passed MTH 284. Return to top

##### Advanced Courses

**MTH 301 Introduction to Applied Mathematics (4-0-4).** Prerequisite: At least one mathematics course numbered 280 or above. Applications of mathematics to real-world problems, including topics such as Monte-Carlo methods (pricing financial securities, light scattering, volumes of irregular shapes); population growth and other environmental issues; and encryption. Emphasis on formulating and evaluating solution strategies and carrying them out using standard software. Return to top

**MTH 311 Numerical Analysis (4-0-4).** Prerequisites: MTH 284 or MTH 288, MTH 286, and a computer programming language. Numerical methods for solving nonlinear equations, systems of linear equations, interpolation problems, integration problems, and differential equations. Return to top

**MTH 323 Statistical Methods (4-0-4).** Prerequisites: MTH 182 and a 200-level mathematics course. Issues of data collection, graphical and numerical summary techniques, basic probability, discrete random variables, continuous random variables, central limit theorem, confidence intervals, hypothesis testing of a proportion, hypothesis testing of a mean, 2 sample hypothesis testing, chi square testing, regression. Return to top

**MTH 326 Numbers, Patterns and Operations for Middle School Teachers (4-0-4).** Prerequisite: Enrollment is restricted to students seeking middle childhood licensure with mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. An in-depth study of mathematical topics in middle school curricula in the area of numbers, patterns and operations. Topics include numeration concepts, concepts of measurement, study of rational and irrational numbers, proportionality, estimation and operations. No credit toward the mathematics major or minor. Return to top

**MTH 327 Algebra and Functions for Middle School Teachers (4-0-4).** Prerequisite: Enrollment is restricted to students seeking middle childhood licensure with mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. Emphasis on algebra as a powerful symbolic language for studying patterns, relations, and variation; for solving linear and quadratic equations and inequalities; and for modeling real life situations. Emphasis is on variables and functions in symbolic and graphical forms, especially linear, quadratic, exponential, logarithmic, and inverse functions. Goals include developing deep understandings of these topics as appropriate for middle school teachers. No credit toward the mathematics major or minor. Return to top

**MTH 328 Geometry for Middle School Teachers (4-0-4).** Prerequisite: Enrollment is restricted to students seeking middle childhood licensure with mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. This course is designed to increase the conceptual understanding of geometry for middle school teachers. Topics will include dynamic geometry integrating use of computer software; basic geometry theorems and constructions; similarity, proportion, scaling, and geometric growth; tessellations; simple trigonometric relationships; van Hiele levels of geometric graphical representations; transformational geometry and analytic geometry. No credit toward the mathematics major or minor. Return to top

**MTH 329 Data Analysis and Probability for Middle School Teachers (4-0-4).** Prerequisite: Enrollment is restricted to students seeking middle childhood licensure with mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. Ratios, fractions, percentages, data collection, graphical experimentation, basic strategies of data analysis, some statistical methods to analyze data, inference based on data and simulation. No credit toward the mathematics major or minor. Return to top

**MTH 330 Conversational Calculus for Middle School Teachers (4-0-4).** Prerequisite: MTH 327. Enrollment is restricted to students seeking childhood licensure or a specialization in childhood education. An introduction to the concepts of calculus. Pictures and hands-on experiments are used to develop an overview of the big ideas and an appreciation of how calculus helps us understand the real world. Includes differentiation, integration and applications of calculus to the real world. No credit toward the mathematics major or minor. Return to top

**MTH 333 Geometry (4-0-4).** Prerequisite: MTH 284 or MTH 288. The main focus is on two-dimensional Euclidean geometry. Basic topics covered include congruence, parallelism, area, and similarity. These are discussed from the axiomatic point of view. Other topics include transformation geometry, non-Euclidean geometry, vectors in geometry and some three-dimensional Euclidean geometry. Many applications are given, such as analysis of repeating patterns, computer graphics, cartography, and robot arm motion. Return to top

**MTH 358 Abstract Algebra (4-0-4).** Prerequisite: MTH 288 . An introduction to modern abstract algebra, concentrating on the integers and number theory, rings, fields, polynomials, and applications of these concepts. Return to top

**Analysis (4-0-4).** Prerequisites: MTH 284 or MTH 288, and at least one mathematics course numbered 300 or above. Introduction to the real-number system, sequences, continuity properties in a metric space, applications to connectedness, sequences and series of functions, basics of differentiation, and Riemann integration. Return to top

**Differential Equations (4-0-4).** Prerequisites: MTH 281 and MTH 288 or MTH 283 and MTH 284, and MTH 286. Series solutions of second-order linear equations, qualitative behavior of linear and almost linear systems of first-order differential equations, boundary value problems, introduction to partial differential equations. Return to top

**MTH 389 Functions of a Complex Variable (4-0-4).** Prerequisite: MTH 281 or MTH 283. This course deals with the fundamentals of complex analysis, including basic properties of complex numbers, analytic functions, harmonic functions, integration, Taylor and Laurent series, residue calculus and conformal mapping. A main focus of the course is the application of conformal mapping techniques (such as Möbius transformations and symmetry) to solve electrostatics, fluid flow, and heat flow problems. Return to top

**CIS 490/590 Foundations of Computing (3-0-3).** Prerequisites: MTH 181, 182, MTH 220, and CIS 335; Mathematics majors may substitute one mathematics course numbered 280 or above for CIS 335. Sets, relations, regular languages, finite automata, context-free languages, pushdown automata, phrase-structure languages, Turing machines, Church's theory, recursion, computability, decidability, computational complexity. Cross-listed with CIS 490. Return to top

**MTH 396 Junior Seminar (2-0-2).** Prerequisites: MTH 182; three of MTH 220, MTH 220, MTH 281, MTH 286 and MTH 288, all grade "C" or better; or departmental approval. Weekly meetings introduce students to a wide range of mathematical topics and also include workshops on various aspects of writing cogent and well-formulated technical reports in mathematics. A primary goal of this course is to prepare the student for MTH 496 Senior Project. Successful completion of the course requires the student having an approved topic and supervisor for MTH 496. Return to top

**MTH 401 Mathematical Modeling (4-0-4).** Prerequisites: MTH 284 or MTH 288, MTH 286, and at least one mathematics course numbered 300 or above (MTH 301 recommended). Deterministic and probabilistic models chosen from the areas of linear optimization, Markov chains, game theory, graphs and networks, axiom systems, growth processes, and queuing systems. Return to top

**MTH 420 Combinatorial Mathematics (4-0-4).** Prerequisite: At least one mathematics course numbered 300 or above. A survey of combinatorial methods, including binomial coefficients and other special numbers, recurrence relations, calculus of finite differences, and generating functions, emphasizing exact evaluation of combinatorial sums in closed form. Return to top

**MTH 424 Probability Theory and Applications (4-0-4).** Prerequisites: MTH 281 or MTH 283, MTH 284 or MTH 288, and a 300-level mathematics course. General probability (set functions, basic axioms, independence); Bayes' theorem; univariate probability distributions (probabilities, moments, variance, mode, percentiIes, transformations); multivariate probability distributions (central limit theorem, joint conditional and marginal distributions - probabilities, moments, variance, covariance); discrete and continuous time Markov chains; selected applications. Return to top

**MTH 434 Differential Geometry (4-0-4).** Prerequisites: MTH 281 or MTH 283, MTH 286, and at least one mathematics course numbered 300 or above. This course focuses on the calculus, linear algebra, and geometry of curves and surfaces, as well as applications to engineering and science. Material covered will include the curvature and torsion of curves, Gaussian and mean curvatures of surfaces, minimal surfaces, geodesics, holonomy, and the Gauss-Bonnet theorem. Optional material includes applications of the calculus of variations to geometry and of minimal surface theory to soap film formation. Return to top

**MTH 487 Dynamical Systems (4-0-4).** Prerequisites: MTH 284 or MTH 288, MTH 286, and at least one mathematics course numbered 300 or above. Systems of differential equations, local and global behavior of a vector field in the plane, discrete dynamical systems, structural stability, the Poincare-Bendixon theorem, bifurcations, chaos, and strange attractors. Return to top

**MTH 493 Special Topics in Mathematics (4-0-4).** Prerequisite: At least one mathematics course numbered 300 or above, or permission of instructor. Detailed study of a selected topic in advanced mathematics. Topic will vary, depending on instructor. May be taken for credit more than once, but no single topic may be repeated. Consult Mathematics Department for current information. Return to top

**MTH 493H Special Topics in Mathematics Honors (4-0-4).** At least one mathematics course at the 300 level or above, <!-- Honors Standing or approval of the Department Honors Liaison --> plus approval of the Department Honors Liaison Officer. Detailed study of a selected topic in advanced mathematics. Topics will vary, depending on instructor. May be taken for credit more than once, but no single topic may be repeated. This course will demand mathematical rigor to a degree beyond regular mathematics courses. In addition, students will play a more active role in the discovery and exploration of mathematical truth. Consult the Mathematics Department for current information. Return to top

**MTH 495 Senior Seminar (2-0-2).** Prerequisites: At least two mathematics courses numbered 300 or above, or departmental approval. This is the department's main assessment tool. Students will read papers in technical journals, choose a research topic, and write a technical report. Three key assessment areas are mathematical modeling (translating real-world situations into mathematics), mathematical reasoning (manipulation, by hand or by computer, of data and expressions using valid mathematical techniques) and communication (ability to write cogent and well-formulated reports). Offered for the last time in fall 2008. Return to top

**MTH 496 Senior Project (4-0-4).** Prerequisites: MTH 396 (grade of S) and at least two other mathematics courses numbered 300 or above, or departmental approval. Prerequisite or co-requisite: At least one other mathematics course numbered 400 or above, or departmental approval. Working individually with a faculty supervisor, each student will read papers in technical journals, make an oral presentation, and write a technical report. Return to top

**MTH 496H Honors Project (4-0-4).** At least two mathematics courses numbered 300 or above, plus approval of the Department Honors Liaison Officer. Students will work individually with a mathematics faculty investigating a mathematical or statistical topic of mutual interest. Students will be required to read articles assigned by the faculty member. A student's work will consist of a written pre-proposal, and a final paper complete with Abstract, Introduction, Methods, Results, Discussion, and References. In addition, students will give an oral presentation of their work to department faculty and students. Return to top

**MTH 497 Readings in Mathematics (1 to 4 credits).** Prerequisite: Departmental approval. Topics studied under supervision of an adviser.