**Full Course Catalog**

**Mathematics Course Catalog**

**MTH 050** - Basic Algebra (3 cr. transcript) (Does not count toward graduation)

A review of beginning algebra. Topics include an elementary treatment of real numbers, polynomials, linear equations, inequalities, rational expressions, systems of linear equations, radicals, and quadratic equations. Letter grade, but only F calculated in GPA.

**MTH 051** - Topics in Intermediate Algebra (2 cr. transcript) (Does not count toward graduation)

A course to enhance the student's skills in selected areas of intermediate algebra; areas covered include polynomials, rational expressions, exponents, equations, and inequalities. Prerequisite: MTH 050 or an appropriate placement test score. Letter grade, but only F calculated in GPA.

**MTH 135** - Mathematics for Elementary Teachers I (4 cr.)

This course is designed for prospsective elementary teachers. Content strands include number and operations and algebra and functions. Number and operations topics include set theory and pre-number concepts, place-value and numeracy, multiple representations and algorithms for arithmetic, number theory (e.g. divisors, multiples), and proportional reasoning. Algebra and functions topics include the concepts of variable and function, algebraic t hinking, linear, polynomial, rational, and exponential functions, mathematical models, rates of change, and multiple representations of relations. Aligned with state and national standard, this course will emphasize problem solving, communication, reasoning, and representation in mathematics. MTH 050 or satisfactory placement test scores; Only open to EC/MC and MC/EA students.

**MTH 136** - Mathematics for Elementary Teachers II (4 cr.)

This course is designed for prospective elementary teachers. Content strands include geometry and measurement, data analysis and statistics, and probability and discrete math. Topics from these strands include: properties of geometric figures, geometric measurement (length, area, volume), congruence and similarity, and transformations; descriptive statistics, sampling design and statistical comparisons, randomness and variability inferential statistics (including the normal distribution); counting techniques, uniform and non-uniform distributions, and representations and calculations of probabilities for simple and compound events. Aligned with state and national standards, this course will emphasize problem solving, communication, reasoning, and representation in mathematics. Prerequisite: MTH 135.

**MTH 145** - Elementary Statistics (4 cr.)

An introductory course covering fundamentals of modern statistical methods. Topics include descriptive statistic, the binomial and normal distributions, estimation, and hypothesis testing. The z, t, F and chi-square test statistics are introduced. Instruction in computer use is included, and statistics software is used throughout the course for analyzing data files and carrying out statistical procedures. Prerequisite: MTH 050 or an appropriate placement test score.

**MTH 150** - College Algebra (4 cr.)

A college algebra course on the properties, graphs, and applications of elementary functions. Topics include the real and complex numbers, concepts from analytic geometry, solutions to equations and inequalities, the elementary algebraic functions, and the logarithmic and exponential functions. Prerequisite: MTH 051 or two years of high school algebra and an appropriate placement test score. Successful completion of MTH 151, 175 or 207 precludes taking MTH 150 for credit.

**MTH 151** - Precalculus (4 cr.)

A precalculus course on properties, graphs, and applications of elementary transcendental functions. Topics include concepts from analytic geometry; theory of equations; the logarithmic, exponential, trigonometric, and inverse trigonometric functions; and analytic trigonometry. Prerequisite: MTH 150 or two years of high school algebra and an appropriate placement test score. Successful completion of MTH 151 precludes taking MTH 150 for credit. Successful completion of MTH 207 precludes taking MTH 151 for credit.

**MTH 171** - Geometry for Elementary Teachers (3 cr.)

Analysis and description of 2- and 3-dimension geometric concepts. Intuitive, direct, and indirect proofs and applications of geometric principles. Transformations, similarities and symmetry. Some topics from measurement. Prerequisite: MTH 135 and MTH 136. Offered Fall Semester.

**MTH 175** - Applied Calculus (4 cr.)

Basic concepts and methods from differential, integral, and multivariate calculus. Logarithmic and exponential functions are included, but not trigonometric functions. Emphasis of the course is on models and applications in business and the social, life, and physical sciences. Prerequisite: MTH 150 or two years of high school algebra and an appropriate placement test score. (Successful completion of MTH 207 precludes taking MTH 175 for credit.)

**MTH 207** - Calculus and Analytic Geometry I (5 cr.)

A rigorous introduction to calculus. Topics include limits, rules for differentiation, derivatives of trigonometric, logarithmic and exponential functions, the Mean Value Theorem, integration, and the Fundamental Theorem of Calculus. In the areas of applications, the course covers problems on related rates, extrema, areas, volumes, and Newton's Second Law. Prerequisite: MTH 151 or four years of high school mathematics, including trigonometry and appropriate math placement score. (Successful completion of MTH 207 precludes taking MTH 151 or 175 for credit.)

**MTH 208** - Calculus II (4 cr.)

A continuation of Calculus I with a rigorous introduction to sequences and series. Topics include techniques of integration and indeterminate forms, improper integrals, applications of integrals, applications of integrals to the physical sciences, tests for the convergence of a series, absolute convergence, power series, and Taylor's Theorem with Remainder. First order linear differential equations are explored, as well as the geometry of space. Prerequisite: MTH 207.

**MTH 225** - Logic and Discrete Math (4 cr.)

An introduction to mathematical reasoning. Mathematical logic, including quantification and the predicate calculus is introduced and used to discuss set theory, relations, functions, counting, graphs, and algorithms. Elementary proofs, including proofs by induction are stressed. Prerequisite: MTH 175 or MTH 207.

**MTH 245** - Probability and Statistics I (4 cr.)

An initial course in probability and statistics for students strong in mathematics. Probability topics include sample spaces, random variables, independence, and the binomial, Poisson, normal, and exponential distributions and their applications. Calculus-based methods will be used for analyzing continuous distributions. Statistics topics include descriptive statistics, sampling distributions, confidence intervals, hypothesis testing, regression, and ANOVA. Prerequisite: MTH 208 or concurrent enrollment. Usually offered each semester.

**MTH 265** - Mathematical Models in Biology (4 cr.)

An introduction to the use of calculus and stochastic based models to the biological sciences. Mathematical tools such as discrete and continuous differential equations, linear algebra, phase portraits, probability theory and descriptive and inferential statistics that are necessary to analyze and interpret biological models will be covered. Biological topics may include single species and interacting population dynamics, modeling infectious diseases, enzyme kinetics, and quantitative genetics. Prerequisite: MTH 175 or MTH 207.

**MTH 280** - Problem Solving for Elementary Teachers (3 cr.)

A high activity course designed to enhance skills in problem solving. Includes methods of representing problems, general strategies for solving problems, creative problem posing and ways to evaluate progress in problem solving skills. Examples taken from the elementary school curriculum. Prerequisite: MTH 135 and MTH 136. Offered Spring Semester

**MTH 309** - Linear Algebra with Differential Equations (4 cr.)

A systematic study of linear algebra, and its interactions with differential equations. Topics include: vectors, matrices, systems of linear equations, determinants, vector spaces, subspaces, basis and dimension, linear transformations and their matrix representations, similar matrices and diagonalization, systems of first order linear differential equations, and higher order linear differential equations. Prerequisite: MTH 208.

**MTH 310** - Calculus III: Multivariate Calculus (4 cr.)

A course in higher dimensional calculus, partial derivatives, and multiple integrals. Topics include parametric curves, polar (and other) coordinate systems, vector fields, scalar fields, the gradient vector, chain rule, Jacobian, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Prerequisite: MTH 208.

**MTH 311** - Number Theory (3 cr.)

Topics are selected from such areas as: divisibility and factorization, congruence, distribution of prime numbers, Diophantine equations. Problem-solving strategies and unsolved problems are stressed. Applications to areas such as coding theory. Prerequisite: MTH 225 and 309. Usually offered Semester I, even numbered years.

** MTH 317** - Graph Theory (3 cr.)

An introduction to graph theory emphasizing algorithms. Topics include: graphs and subgraphs, isomorphism, degree sequences, digraphs, networks, algorithmic complexity and NP-completeness, trees, Euler circuits and Hamilton cycles, planarity, and graph coloring. Prerequisites: MTH 225 and MTH 309 or concurrent enrollment. Usually offered Semester I, odd numbered years.

**MTH 320** - History of Mathematics (3 cr.)

A study of the evolution of mathematics. Discussion and evaluation of major periods of development including the lives and works of preeminent mathematicians. A sampling of problem solving methods from various historical periods. Emphasis is on Western mathematics from earliest recorded history through the initial developments of calculus and modern mathematics. Prerequisite: MTH 309 or concurrent enrollment. Usually offered Semester II, odd numbered years.

**MTH 321** - Teaching Mathematics with Technology (3 cr.)

This course covers traditional, emerging, and interactive technologies used in the teaching and learning of mathematics. Teacher education candidates will gain an understanding of the use and application of instructional technology. The will explore how software, hardware, and instructional media can be used to enhance mathematics instruction in grades 6-12. Topics include instructional technology for visualizing and exploring mathematics, enhancing and delivering lessons, as well as interactive communication tools. Prerequisite: MTH 175 or MTH 207; CT 100 or CS 120. Admission to teacher education program or consent of instructor. Usually offered Semester I.

**MTH 331** - Introduction to Modern Geometry (3 cr.)

A thorough discussion of transformations and their use in proving congruence of geometric figures; selected theorems concerning the triangle and circle, and constructions possible given different parts of a triangle. Prerequisite: MTH 225 and 309 or concurrent enrollment. Usually offered Semester II.

**MTH 353** - Differential Equations (3 cr.)

Fundamental existence and uniqueness theory, linear independence and the Wronskian, series solutions near regular singular points, Laplace transforms and systems of first order linear equations. Fourier series and the method of separation of variables will be applied to the heat equation, wave equation, and Laplace's equation. Prerequisite: MTH 309 and MTH 310. Usually offered Semester I.

**MTH 371** - Introduction to Numerical Methods (3 cr.)

Techniques devised for use with computing machinery are applied to problems such as: solving non-linear equations and linear systems, curve-fitting and function approximation, numerical integration. Prerequisites: MTH 309 and CS 120. Usually offered Semester II.

**MTH 395** - Special Topics in Mathematics (1-3 cr.)

Special topics in mathematics not covered by regular courses taught in this department. The particular topic is decided mutually by the student and instructor. Prerequisite: written consent of department chair. Repeatable for credit -- maximum 6.

**MTH 405/505** - Statistical Methods (3 cr.)

A survey of statistical methods from the point of view of how these methods are implemented with a standard statistics software package. Topics include descriptive statistics, graphical methods, tests of location, goodness of fit, simple and multiple regression, design of experiments, ANOVA, multiple comparisons, chi-square tests. Both parametric and nonparametric methods are treated. Computer use is an integral part of the course. Prerequisite: MTH 145 or 245. Usually offered Semester I.

**MTH 407** - Real Analysis I (3 cr.)

This course covers the basic theory underlying the differential and integral calculus. Convergence of sequences and series is examined. Theoretical concepts of calculus are examined and particular attention is given to writing proofs. Prerequisite: MTH 225, MTH 309 and MTH 310. Offered Fall Semesters only

**MTH 408** - Real Analysis II (3 cr.)

Further study of real analysis via selected topics such as the theory of convergence, Lebesque-Stieltjes integration, Fourier Analysis, probability theory, approximation theory and metric-spaces. Prerequisite: MTH 407. Offered Spring semester, odd years only.

**MTH 410 **- Complex Analysis (3 cr.)

Introduction to complex numbers and complex functions. Analytical functions are developed via power series and Cauchy's Theorem. Topics include: Cauchy-Riemann conditions, integration theorems, residues, conformal mapping and applications. Prerequisite: MTH 309 and MTH 310. Usually offered Semester II, even numbered years.

**MTH 411** - Abstract Algebra I (3 cr.)

A rigorous approach to algebraic systems including the study of groups, rings, integral domains and fields with application to polynomials. Prerequisite: MTH 225 and 309.

**MTH 412** - Abstract Algebra II (3 cr.)

Continuation of MTH 411. Further study of rings, integral domains and fields. Prerequisite: MTH 411. Offered Semester II, even-numbered years.

**MTH 413 **- Topics in Linear Algebra (3 cr.)

A thorough study of selected topics such as abstract vector spaces, linear transformations and their matrix representations, inner product spaces, canonical forms and selected applications. Prerequisites: MTH 225 and MTH 309. Usually offered Semester II, odd numbered years.

**MTH 421** - Teaching and Learning Mathematics and Computer Science in the Secondary School (4 cr.)

This course will be integrated with a field experience. In the context of a real classroom, teacher candidates will learn how to plan for and assess student learning in mathematics and computer science. With a focus on content knowledge, teacher candidates will plan a variety of meaningful learning experiences, assess student learning, and monitor and modify instruction to best support the individual learners in the classroom. The teacher candidate will design, enact, and assess activities that advance student understanding to more complex levels. Teacher candidates will gain experience in monitoring the obstacles and barriers that some students or groups of students face in school and learn how to design learning experiences to support all learners. Prerequisites: EDS 351; MTH 321 Usually offered Semester I.

**MTH 440** - Statistical Consulting (1 cr.)

Experiences will include interpersonal written and oral communication and interdisciplinary exposure as well as opportunities to apply statistical knowledge in a broad variety of situations. Students will take part in consultations (i.e. extracting information, listening, asking appropriate questions), apply knowledge in experimental design, data modeling, use of statistical software, and/or sampling; diagnose and conduct appropriate statistical procedures and interpret and communicate results. Reading past and present literature on statistical consulting also will be required. Prerequisite: MTH 405 or MTH 245 and written consent of the Statistical Consulting Center director.

**MTH 441** - Mathematical Statistics I (3 cr.)

Review of discrete and continuous random variables. Moment generating functions, multivariate probability distributions, marginal and conditional probability distributions, functions of random variables, order statistics, Central Limit Theorem, point estimation and confidence intervals. Prerequisites: MTH 310 and MTH 245. Usually offered Semester I.

**MTH 442** - Mathematical Statistics II (3 cr.)

Methods of estimating, including method of moments and maximum likelihood. Sufficient statistics, hypothesis testing, power of tests, likelihood ratio tests and introduction to regression and analysis of variance. Prerequisite: MTH 441. Usually offered Semester II, even numbered years.

**MTH 443/543** - Categorical Data Analysis (3 cr.)

An introduction to categorical data analysis covering summaries and inference for categorical response and count data, analysis of contingency tables, generalized linear models for binary and count data, logistic regression, multicategory logit models and loglinear models for contingency tables with an emphasis on applications and implementation using computer software. Prerequisite: MTH 245 of MTH 405. Usually offered Semester I, even numbered years.

**MTH 445/545** - General Linear Models (3 cr.)

An introduction to simple linear regression, multiple regression, polynomial regression. Inferences, appropriateness of model, model diagnostics/adequacy, difficulties in the application of models are discussed. A computer package will be used. Course participants will be involved with hands-on statistical applications and consulting. Prerequisite: MTH 405 or 245. Offered Semester I, even-numbered years.

**MTH 446/546** - Analysis of Variance and Design of Experiments (3 cr.)

An introduction to single factor, multiple factor, and randomized block designs in analysis of variance. Inferences, appropriateness of model, model diagnostics/adequacy, difficulties in the application of models are discussed. Design or structure of an experiment will be discussed. A computer package will be used. Course participants will be involved with hands-on statistical applications and consulting. Prerequisite: MTH 405 or 245. Offered Semester II, odd-numbered years.

**MTH 447/547** - Nonparametric Statistics (3 cr.)

An introductory course presenting the theory and procedures for using distribution-free methods in data analysis. Standard procedures, such as the Wilcoxon tests, Kruskal-Wallis, Kolmogorov-Smirnov, nonparametric confidence intervals, regression analysis, and powers of the tests will be included. Computer programs will be used when appropriate. Prerequisite: MTH 405 or MTH 245. Usually offered Semester II, even numbered years.

**MTH 448 **- Operations Research (3 cr.)

An introductory course which applies mathematics/ statistics to management decision making. Included are methods of optimizing systems, inventory and production control, scheduling, game theory bidding, queuing, quality control, reliability and time series. Various programming, analysis and Monte Carlo techniques are introduced with the computer used as a tool where appropriate. Prerequisites: MTH 405 or MTH 245. Usually offered Semester II, odd numbered years.

**MTH 449/549** - Applied Multivariate Statistics (3 cr.)

An introduction to applied multivariate statistical methods covering multivariate analysis of variance, multivariate analysis of covariance, repeated measures design factor analysis, principle component analysis, cluster analysis, discriminate analysis, and multivariate regression. Course participants will be involved with hands-on statistical aplications. Prerequisite: MTH 405 or 245. Offered Semester II, odd-numbered years.

**MTH 461** - Mathematical Physics (3 cr.)

In depth study of topics from vector analysis, Fourier analysis and special functions with emphasis on modeling physical phenomena involving conservative fields, fluid flow, heat conduction, and wave motion. Prerequisites: MTH 353. (Cross listed with PHY; may only earn credit in MTH or PHY.) MTH 461 may be counted towards both a MTH and PHY major. Offered Semester II, odd numbered years.

**MTH 480** - Studies in Applied Mathematics (3 cr.)

Advanced studies of applications of mathematics and computation to solve problems and understand processes from a variety of fields (for example, industry, medicine and the physical and life sciences). Requirements include an application/modeling project with a written report and class presentation. Prerequisite: MTH 353. Usually offered Semester II.

**MTH 495/595** - Special Topics in Mathematics (1-3 cr.)

Special topics in mathematics not covered by regular courses taught in this department, such as topology, set theory and advanced numerical analysis. The particular topic is decided mutually by the students and instructor. Prerequisite: written consent of the department chair. Repeatable for credit - maximum 6.

**MTH 496/596** - Special Topics in Statistics (1-3 cr.)

Special topics in statistics not covered by regular courses taught in this department. The particular topic is decided by the instructor.

**MTH 498** - Independent Study (1-3 cr.)

Directed readings or presentation of material not available in formal departmental courses under the supervision of a faculty member. Prerequisite: written consent of the supervising faculty member and the department chair. Repeatable for credit -- maximum 6.

**MTH 499** - Research Topics (1-3 cr.)

An opportunity to pursue individual research topics under the direction of a faculty member. Depending on the nature of the research project, study is expected to involve substantial computational or theoretical work in addition to literature review and instruction. In addition to a written report to the supervising faculty member, expected outcomes may include: software, papers and presentations to the department and regional meetings. Prerequisite: written consent of the supervising faculty member and the department chair. Not applicable to a mathematics major or minor. Repeatable for credit -- maximum 6.