2007-2008 Course Listings

112Q. The Language of Mathematics. 4 semester hours.

College-level experience with the logic, language and methods of mathematics through the study of topics from a variety of areas of mathematics. Not intended as or suitable for preparation for other mathematics courses. Prerequisite: Appropriate level on the Math Placement Exam. Every year.

118Q. Mathematics for Elementary and Middle School Teachers. 4 semester hours.

Study of number systems, number theory, patterns, functions, measurements, algebra, logic, probability and statistics with a special emphasis on the processes of mathematics; problem-solving, reasoning, communicating mathematically; and making connections with mathematics and between mathematics and other areas. Open only to students intending to major in education. Prerequisite: Appropriate level on the Math Placement Exam. Every year.

119Q. Geometry with Computer Applications for Elementary and Middle School Teachers. 2 semester hours.

Study of basic concepts of plane and solid geometry, including topics from Euclidean, transformational, and projective geometry and from topology. Includes computer programming experiences using Logo with a special emphasis on geometry and problem-solving. Prerequisite: Mathematics 118. Every year.

120Q. Elementary Functions. 4 semester hours.

Exploration of functions and their graphs and applications of functions in formulating and solving real-world problems. Examination of polynomial, rational, exponential, logarithmic, trigonometric and inverse trig functions. Discussion of limits and continuity. Intended for the student planning to take Mathematics 131 or 201 but whose high school preparation is insufficient for entering calculus directly. Prerequisite: appropriate level on the Math Placement Exam. Every year.

127Q. Introductory Statistics. 4 semester hours.

Study of statistics as the science of using data to glean insight into real-world problems. Includes graphical and numerical methods for describing and summarizing data, sampling procedures and experimental design, inferences about the real-world processes that underlie the data, and student projects for collecting and analyzing data. Open to non-majors only. (Note: A student may not receive credit for more than one of the following: Mathematics 127, Mathematics 227, Psychology 107, or Management 210.) Prerequisite: Appropriate level on the Math Placement Exam. Every year.

131Q. Essentials of Calculus. 4 semester hours.

A one-semester study of the fundamental concepts and techniques of single-variable differential and integral calculus. The majority of applications are drawn from management and the biological and social sciences; in particular, no trigonometric applications are covered. This course is intended to be a terminal course and does not satisfy the prerequisite for Mathematics 202. A student who plans to take more than one calculus course should enroll in Mathematics 201 instead of this course. (Note: A student cannot receive credit for both Mathematics 131 and 201.) Prerequisite: Mathematics 120 or appropriate level on the Math Placement Exam. Every year.

201Q. Calculus I. 4 semester hours.

First course in a detailed two-semester introduction to a graphical, numerical, and symbolic approach to differential and integral calculus of one variable. (Note: A student cannot receive credit for both Mathematics 201 and 131.) Prerequisite: Mathematics 120 or appropriate level on the Math Placement Exam. Every year.

202Q. Calculus II. 4 semester hours.

Continuation of Mathematics 201. Prerequisite: Mathematics 201. Every year.

205Q. Applied Matrix Algebra. 4 semester hours.

Course in matrix algebra and discrete mathematical modeling. Study of the formulation of mathematical models, together with analysis of the models and interpretation of the results. Primary emphasis is on modeling techniques that use matrix methods. Prerequisite: Mathematics 201. Every year.

210Q. Fundamentals of Analysis. 4 semester hours.

Study of functions, set theory, sequences, the real number line, logic and methods of mathematical proof. Prerequisite: Mathematics 202. Writing intensive. Every year.

212Q. Multivariable Calculus. 4 semester hours.

Calculus of functions of several variables and associated analytic geometry. Prerequisite: Mathematics 202. Every year.

215Q. Differential Equations. 4 semester hours.

Study of elementary ordinary differential equations, with particular emphasis on techniques and applications using algebraic, numerical and graphical approaches. Prerequisites: Mathematics 202. Every year.

221Q. Foundations of Geometry. 4 semester hours.

Rigorous study of Euclidean and non-Euclidean geometry from an axiomatic point of view. The mathematics is studied in an historical context. Prerequisite: Mathematics 210. Writing intensive. Usually offered in alternate years.

227Q. Data Analysis. 4 semester hours.

This introductory statistics course is designed not only for students majoring or minoring in math, but for any student who would benefit from a more substantial introduction to the field - especially prospective teachers of mathematics or statistics, as well as students considering careers as statisticians or actuaries.  Students will learn general principles and techniques for summarizing and organizing data effectively, and will explore the connections between how the data were collected and the scope of conclusions that can be drawn from the data.  Also emphasized are the logic and techniques of formal statistical inference, with greater focus on the mathematical underpinnings of these basic statistical procedures than is found in other introductory statistics courses.  Software for probability and data analysis is used daily.  Prerequisites: Mathematics 131 or 201.  (Note: a student may not receive credit for more than one of the following:  Mathematics 127, Mathematics 227, Psychology 107, or Management 210.)

228Q. Univariate Probability. 4 semester hours.

Axiomatic and applied introduction to probability as the mathematical study of random processes and building and assessing stochastic models. Prerequisite: Mathematics 202. Usually offered in alternate years.

271Q. Discrete Mathematical Structures. 4 semester hours.

The mathematics of discrete sets, sets which are finite or at most countably infinite.  Starting on the foundation of logic, set theory, and basic proof techniques, the course will cover various topics dealing with relations and functions, counting arguments, discrete probability, number theory, and graph theory.  Prerequisite: Mathematics 131 or 201..

320Q. Numerical Analysis. 4 semester hours.

Introduction to the numerical solution of mathematical problems. Primary emphasis is on the development of computational techniques that can be implemented on a digital computer and methods for establishing error bonds for approximate solutions. Prerequisites: Mathematics 202 and 205 and Computer Science 150. Usually offered in alternate years.

327Q. Statistical Modeling. 4 semester hours.

In this second course in statistics, regression analysis is the main vehicle for illustrating the principles of statistical modeling in real-world contexts. After a brief review of the modeling unit from the end of the first data analysis course, students learn strategies for selecting and constructing models, criteria for assessing and comparing models, and tools for making formal inferences using these models. Class sessions include discussion of conceptual issues with practice in data analysis, and they put strong emphasis on interpreting the results of analyses. Students are required to collaborate on projects in which they design studies, collect and analyze data, and present their findings orally and in writing. Prerequisite: Mathematics 227. Writing Intensive. Offered alternate years.

328Q. Mathematical Statistics. 4 semester hours.

Theoretical introduction to the concepts and methods of statistical inference and a development of the distribution theory underlying such methods. Prerequisites: Mathematics 228. Usually offered in alternate years.

337Q. Statistical Design. 4 semester hours.

Whereas the introductory statistics sequence focuses primarily on exploratory and formal analysis of data that have already been observed, this course focuses primarily on how to design the comparative observational and experimental studies in which data are collected for formal analysis.  Students will learn:  (1) to choose sound and suitable design structures; (2) to recognize the structure of any balanced design built from crossing and nesting; (3) to assess how well standard analysis assumptions fit the given data and to choose a suitable remedy or alternative when appropriate; (4) to decompose any balanced dataset into components corresponding to the factors of a design; (5) to construct appropriate interval estimates and significance tests from such data; and (6) to interpret patterns and formal inferences in relation to relevant applied context.  Students are required to collaborate on projects in which they design studies, collect and analyze data, and present their findings orally and in writing.  Prerequisite: Mathematics 227.

345Q. Optimization. 4 semester hours.

Optimization is a very successful area of applied mathematics and its applications are very broad and diverse.  This course addresses the problem of doing the "best" thatone can do, possibly subject to resource constraints.  Simulation models allow one to determine how a function behaves as its variables change.  Optimization models are used to determine the "optimal" values of these variables so that the function can be maximized or minimized.  In this course, one learns how to recognize and formulate different types of optimization models, sometimes called "mathematical programming" models (e.g., unconstrained, linear programming, quadratic programming, and general nonlinear programming).  One learns how to identify local and global solutions to these models and how to find these solutions by using various algorithms (e.g., steepest descent, Newton, BFGS, simplex, gradiient projection, evolution).  This course will present theory, methods, and applications equally.  Both analytic and programming assignments will be given, together with exams.  Mathematica will be used.  This course is cross-listed as Computer Science 345. Prerequisites: Mathematics 201 and 205 and Computer Science 150.

360Q. Linear Algebra. 4 semester hours.

Introduction to abstract vector spaces with particular emphasis on the axiomatic method. Topics include Euclidean spaces, matrix spaces, function spaces, linear systems, linear independence and basis, inner product, orthogonality and linear functions. Prerequisites: Mathematics 205 and 210. Writing intensive. Every year.

365Q. Abstract Algebra. 4 semester hours.

Introduction to various algebraic structures with particular attention to groups. The axiomatic method is emphasized throughout the course. Prerequisites: Mathematics 205 and 210. Writing intensive. Every year.

370Q. Real Analysis. 4 semester hours.

Course in the basic theoretical concepts of single variable calculus: continuity, differentiation, integration and infinite series. Prerequisite: Mathematics 210. Writing intensive. Every year.

380Q. Topics in Mathematics. Variable credit.

Study of special topics not included in other departmental offerings. Offered occasionally according to the needs and interests of students and/ or faculty. This course may be repeated for credit.

460Q. Senior Seminar. 2 semester hours.

In this capstone experience for the math major, the student works individually and in groups to synthesize knowledge from and seek interrelationships among areas of mathematics previously encountered. Includes written and oral presentations, bibliographic research, and modeling and problem-solving projects. Prerequisite: Senior math major status or permission of instructor. Every year.

480Q. Topics in Mathematics. Variable credit.

Study of special topics not included in other departmental offerings. Offered occasionally according to the need and interests of students and/or faculty. This course may be repeated for credit.

490. Independent Study. Variable credit.

Individual study by the advanced student of a topic that is beyond the scope of regular courses. Prerequisite: Approval of the instructor directing the study. This course may be repeated for credit.

491. Internship. Variable credit.

Open to the junior or senior mathematics major by departmental permission only.

499. Honors Thesis/Project. Variable credit.

Prerequisite: 3.50 GPA and permission of the department chair.