Course Descriptions

In addition to reading the course descriptions, students planning to Major or Minor in Mathematics should study The Guide and discuss program planning with their academic advisor.  Keep in mind that some advanced classes are offered infrequently. 

MTH 050    Basic Algebra    Cr. 3   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    Cr. 2   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 125    Mathematics for Elementary Teachers    Cr. 4
A study of the mathematical concepts and techniques that are fundamental to, and form the basis for, elementary school mathematics. Topics include: problem solving, inductive and deductive reasoning, sets, number systems through the real numbers, number theory, measurement, and 2- and 3-dimensional geometry. Prerequisite: MTH 051 or satisfactory placement test score. 

MTH 126 Mathematics for Elementary Teachers II Cr. 4
Continued Study of the mathematical concepts and techniques that are fundamental to, and form the basis for, elementary school mathematics. Topics include: use of probability and statistics to explore real-world problems; representation and analysis of discrete mathematical problems using counting techniques, sequences, graph theory, arrays and networks; use of functions, algebra and the basic concepts underlying the calculus in real-world applications.  Prerequisite: MTH 125 (and MTH 051 or satisfactory placement test score for transfer students).

MTH 145    Elementary Statistics    Cr. 4
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    Cr. 4
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    Cr. 4
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    Cr. 3
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 125 and either MTH 150 or math placement above MTH 150.  Offered Semester I.

MTH 175    Applied Calculus    Cr. 4
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     Cr. 5
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    Cr. 4
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 Cr. 4
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 280    Problem Solving for Elementary Teachers    Cr. 3
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 125 and either MTH 150 or math placement above MTH 150.  Offered Semester II.

MTH 305/505     Statistical Methods      Cr. 3
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 341. Usually offered Semester I.

MTH 309     Linear Algebra with Differential Equations     Cr. 4
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      Cr. 4
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      Cr. 3
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 225and 309. Usually offered Semester I, even numbered years.

MTH 317    Graph Theory       Cr. 3
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      Cr. 3
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 331     Introduction to Modern Geometry     Cr.3
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 341     Probability and Statistics I     Cr. 4
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. Usually offered each semester.

MTH 353     Differential Equations     Cr. 3
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     Cr. 3
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 C-S 120.  Usually offered Semester II.

MTH 395    Special Topics in Mathematics    Cr. 1-3
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 407     Analysis I      Cr. 3
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    Analysis II     Cr. 3
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     Cr. 3
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     Cr. 3
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     Cr. 3
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     Cr. 3
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 440    Statistical Consulting   Cr. 1
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 305 or MTH 341 and written consent of the Statistical Consulting Center director.

MTH 441     Mathematical Statistics I     Cr. 3
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 341. Usually offered Semester I.

MTH 442     Mathematical Statistics II     Cr. 3
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 446/546   Analysis of Variance and Design of Experiments    Cr. 3
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 305 or 341.  Offered Semester II, odd-numbered years.

MTH 447/547     Nonparametric Statistics     Cr. 3
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 305 or MTH 341. Usually offered Semester II, even numbered years.

MTH 448     Operations Research     Cr. 3
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 305 or MTH 341. Usually offered Semester II, odd numbered years.  

MTH 449/549    Applied Multivariate Statistics     Cr. 3
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 305 or 341. Offered Semester II, odd-numbered years.

MTH 461     Mathematical Physics     Cr. 3
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     Cr. 3
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 495/695     Special Topics in Mathematics     Cr. 1-3
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    Cr. 1-3
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    Cr. 1-3
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    Cr. 1-3
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.