MATHEMATICS (MTH)

**Professors: **Bange, Barkauskas, Breiter, Host, Riley, B. (Chair), Scheidt, Schelin, Senger, Skala, Sobota, Wine;

**Associate Professors: **Boyle, Erickson, Hoar, Kelly, S., Lewin, Koster, Ma, Matchett, O'Brien, Unbehaun, J.;

**Assistant Professors: **Baggett, Elfessi, Niedfeldt, Reineke, Ross, Wagner.

Major and/or minor requirements differ for students in the College of Business Administration, the College of Liberal Studies, and the College of Science and Allied Health, from those in the School of Education and the College of Health, Physical Education and Recreation. See separate listings below.

**Credit by Examination:
**The mathematics department awards credit by examination in MTH 150, College Algebra; MTH 151, Precalculus; MTH 207, Calculus I; and MTH 208, Calculus II. The exams may be taken by new freshmen and are scheduled for the second week of semester I. Students may not earn credit by examination in both MTH 150 and MTH 151. Credit for MTH 205, Elementary Statistics, will be granted to entering freshmen with a College Board Advanced Placement Statistics Examination score of three or better. Credit for MTH 207 will be granted to entering freshmen with a College Board Advanced Placement AB exam score of three or better. Entering freshmen with a score of three or better on the BC form of this exam will receive credit for MTH 207 and should consult the mathematics department chair about additional credit and placement in mathematics courses.

**Retroactive Credits:
**Students taking MTH 207, 208, or 309, and earning a grade of "B" or better, will be given retroactive credit for MTH 151 provided that the student's transcript shows no record of prior or concurrent enrollment in MTH 151, 207, 208, or 309.

**Mathematics Major
**(Business, Liberal Studies, Science and Allied Health) - 38 credits, including MTH 207, 208, 225, 309, 310, one two-course sequence chosen from MTH 353 and 480, 353 and 461, 407 and 408, 411 and 412, 441 and 442, and 12 additional credits selected from 311, 317, 320, 331, 341, 342, 353, 371, 407, 408, 410, 411, 412, 413, 441, 442, 461, 480, C-S 453, and PHY 470. MTH 151 may be used to fulfill three of the 12 additional credits. In addition, C-S 120 must be taken. Mathematics-computer science double majors may count MTH 317, MTH 371, and C-S 453 for credit in both majors. Mathematics-physics double majors may count MTH 461 and PHY 470 for credit in both majors.

**Mathematics Minor
**(Business, Liberal Studies, Secondary Education, Health, Physical Education and Recreation, Science and Allied Health) - 22 credits, including MTH 207, 208, 309, and nine additional credits selected from MTH 225 and MTH courses numbered 300 and above. Credit for MTH 151 may used to fulfill three of the nine additional credits. Computer science majors may count MTH 317, 371 and C-S 453 for credit in both the computer science major and the mathematics minor. Physics majors may count MTH 461 and PHY 470 for credit in both the physics major and the mathematics minor.

**Mathematics Major with an Emphasis in Statistics
**(Business, Liberal Studies, Science and Allied Health) - 38 credits, including MTH 207, 208, 309, 310, 341, 342, 441, 442, 444 or 447 or 448, 445, and three additional credits selected from MTH 371, 407, 410, 444, 447, and 448. MTH 151 may be used to fulfill the three additional credits. In addition, C-S 120 must be taken.

**Mathematics Major
**(Elementary/Middle/Secondary Education, Health Education, Physical Education, and Recreation) - 37 credits, including MTH 207, 208, 225, 309, 310 or 371, 331, 341, 342, 411 and six additional credits selected from MTH 310, 311, 317, 320, 353, 371, 407, 408, 410, 412, 413, 441, 442, 461, and 480. MTH 151 may be used to fulfill three of the six additional credits. In addition, C-S 120 must be taken.

**Mathematics Minor
**(Elementary/Middle Education) - 22 credits, including MTH 125, 171, 280 and 12 additional credits selected from MTH 151, 205, 175 or 207, 208, and MTH courses numbered 300 and above.

**Statistics Minor
**(Open to students in all schools and colleges within the university) - 20 credits, including MTH 175 or 207, 205, 305, and nine additional credits selected from MTH 444, 445, 447, and 448. With the approval of the mathematics department chair, a research methods course from another department may be substituted for three of the nine additional credits. MTH 341 and 342 may be substituted for MTH 205 and 305. This minor is not available to mathematics majors.

+ above a course number indicates a General Education course.

**MTH 050 Cr. 3 transcript*
Basic Algebra
**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 Cr. 2 transcript*
Topics in Intermediate Algebra
**A course to enhance the student's skills in selected areas of intermediate algebra; areas covered include polynomials, rational expressions, exponents, quations, and inequalities. Prerequisite: MTH 050 or an appropriate placement test score. Letter grade, but only F calculated in GPA.

**MTH 125 Cr. 4
**Mathematics for Elementary Teachers

A study of the mathematical concepts and techniques that are fundamental to, and form the basis for, elementary school mathematics. Topics include: sets, logic, functions, numeration systems, real numbers, number theory, geometry and statistics. Prerequisite: MTH 050 or equivalent placement.

**+
MTH 150 Cr. 4
College Algebra
**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 a satisfactory placement test score.

**+
MTH 151 Cr. 4
Precalculus
**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 a satisfactory 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 Cr. 3
Geometry for Elementary Teachers
**Analysis and description of 2- and 3-dimensiongeometric 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 Sem. I.

**+
MTH 175 Cr. 4
Applied Calculus
**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. Prerequisites: MTH 150 or two years of high school algebra and a satisfactory placement test score. (Successful completion of MTH 175 precludes taking MTH 150 for credit. Successful completion of MTH 207 precludes taking MTH 175 for credit.)

**+
MTH 205 Cr. 4
Elementary Statistics
**An introductory course covering fundamentals of modern statistical methods. Topics include descriptive statistics, 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 equivalent placement.

**MTH 207 Cr. 5
Calculus I
**A rigorous introduction to calculus. Topics include limits, derivatives of algebraic and trigonometric functions, and integration. Applied problems from related rates, extrema, volumes. Prerequisite: MTH 151 or four years of high school mathematics, including trigonometry.

**MTH 208 Cr. 4
Calculus II: Calculus with Linear Algebra and Differential Equations
**A continuation of Calculus I with an introduction to linear algebra and differential equations. Topics include: differentiation and integration of transcendental functions, indeterminate forms, improper integrals, techniques of integration, applications to the physical sciences, first order linear differential equations, and an introduction to vectors, matrices, and systems of linear equations. Prerequisite:MTH 207.

**+
MTH 225 Cr. 3
Mathematical Logic
**An introduction to mathematical reasoning. Mathematical logic, including quantification and the predicate calculus is introduced and used to discuss set theory, relations, functions and the natural number system. Elementary proofs, including proofs by induction are stressed. Prerequisite: MTH 151 or four years of high school mathematics.

**MTH 280 Cr. 3
Problem Solving for Elementary Teachers
**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 Sem. II.

**MTH 305/505 Cr. 3
Statistical Methods
**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 205. Not applicable to a mathematics major. May be applied only to mathematics and statistics minors. Offered Sem. I.

**MTH 309 Cr. 4
Calculus III: Calculus with Linear Algebra and Differential Equations
**A continuation of the study of calculus and linear algebra, with applications to differential equations. Topics include: determinants, vector spaces, subspaces, basis and dimension, linear transformations and their matrix representations, similar matrices and diagonalization, infinite sequences and series, and solutions of second and higher order differential equations. Prerequisite: MTH 208.

**MTH 310 Cr. 4
Calculus IV: Multivariate Calculus
**The final course in the introductory calculus-linear algebra-differential equations sequence. Topics include: parametric equations and polar coordinates, partial derivatives, multiple integrals and an introduction to vector calculus. Applications to differential equations. Prerequisite: MTH 309.

**MTH 311 Cr. 3
Number Theory
**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. Prerequisites: MTH 225 and 309. Offered Sem. I, even-numbered years.

**MTH 317 Cr. 3
Graph Theory
**An introduction to graph theory emphasizing algorithms. Topics include graphs and subgraphs, isomorphism, degree sequences, digraphs, networks, algorithm complexity and NP-completeness, trees, Euler circuits and Hamilton cycles, planarity and graph coloring. Prerequisites: MTH 225, 309 and C-S 120. Offered Sem. I, odd numbered years.

**MTH 320 Cr. 3
History of Mathematics
**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 mathe-matics. Prerequisite: MTH 309. Offered Sem. II, odd-numbered years.

**MTH 331 Cr. 3
Introduction to Modern Geometry
**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. Prerequisites: MTH 225 and 309. Offered Sem. II.

**MTH 341 Cr. 3
Probability and Statistics I
**Chance experiments and sample spaces, sophisticated counting, random variables and their distributions, independence, binomial and other standard discrete distributions and their applications. Continuous random variables with emphasis on the normal, uniform and exponential. Prerequisite: MTH 309.

**MTH 342 Cr. 3
Probability and Statistics II
**An introduction to modern applied statistics. Topics include estimation theory, hypotheses testing, simple and multiple linear regression, experimental design, one-way and two-way ANOVA, Scheffe's test, use of applicable computer programs, nonparametric statistics. Prerequisite: MTH 341. Offered Sem. II.

**MTH 353 Cr. 3
Differential Equations
**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 310. Offered Sem. I.

**MTH 371 Cr. 3
Introduction to Numerical Methods
**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. Offered Sem. II.

**MTH 390 Cr. 1
Calculus and Linear Algebra for Actuarial Students
**Topics include: precalculus review, limits, continuity, derivatives, integrals, partial derivatives, multiple integrals, sequences and series, vectors, matrices, linear transformations and first order linear differential equations. Prerequisite: MTH 310.

**MTH 395 Cr. 1-3
Special Topics in Mathematics
**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 Cr. 3
Analysis I
**A careful examination of the structure of the real number system and of differentiation and integration for real-valued funcitons. Prerequisites: MTH 225 and 310. Offered Sem. I.

**MTH 408 Cr. 3
Analysis II
**Continuation of MTH 407. Sequences and series of functions, followed by an introduction to areas such as Fourier Analysis where the ideas and methods of real analysis are usefully applied. Prerequisite: MTH 407. Offered Sem. II, odd-numbered years.

**MTH 410 Cr. 3
Complex Analysis
**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. Prerequisites: MTH 225 and 310. Offered Sem. II, even-numbered years.

**MTH 411 Cr. 3
Abstract Algebra I
**A rigorous approach to algebraic systems including the study of groups, rings, integral domains and fields with primary emphasis on the study of groups. Prerequisites: MTH 225 and 309. Offered Sem. I.

**MTH 412 Cr. 3
Abstract Algebra II.
**Continuation of MTH 411. Further study of rings, integral domains and fields with application to polynomials. Prerequisite: MTH 411. Offered Sem. II, even-numbered years.

**MTH 413 Cr. 3
Topics in Linear Algebra
**A thorough study of selected topics such as abstract vector spaces, linear transformations and their matrix representations, inner product spaces, canonical forms; selected applications. Prerequisites: MTH 225 and 309. Offered Sem. II, odd-numbered years.

**MTH 441 Cr. 3
Mathematical Statistics I
**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 341. Offered Sem. I.

**MTH 442 Cr. 3
Mathematical Statistics II
**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. Offered Sem. II, even-numbered years.

**MTH 444/544 Cr. 3
Introduction to Sampling
**Methodology of simple random sampling, stratified sampling, systematic sampling, cluster sampling, and multistage sampling is developed and applications related to physical, social, and biological sciences are given. Single and two variable estimation techniques are discussed. Prerequisite: MTH 305 or 342. Offered Sem. I, odd-numbered years.

**MTH 445/545 Cr. 3
General Linear Models with Applications in Regression and Analysis of Variance
**A brief review of simple linear regression, introduction to General Linear Models (GLM), applications of GLM in multiple regression, polynomial regression, single factor and two-factor Analysis of Variance (ANOVA). Inferences, appropriateness of model, auto-correlation and multi-collinearity are discussed. A brief introduction to Analysis of Covariance is given. A computer package is used. Prerequisite: MTH 305 or 342. Offered Sem. II, odd-numbered years.

**MTH 447/547 Cr. 3
Nonparametric Statistics
**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 342. Offered Sem. I, even-numbered years.

**MTH 448 Cr. 3
Operations Research
**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. Prerequisite: MTH 305 or 342. Offered Sem. II, even-numbered years.

**MTH/PHY 461 Cr. 3
Mathematical Physics
**In depth study of topics from vector analysis, Fourier analysis and special functions with emphasis on modeling physical phemomena involving conservative fields, fluid flow, heat conduction, and wave motion. Prerequisite: 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 Sem. II, odd numbered years.

**MTH 480 Cr. 3
Studies in Applied Mathematics
**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. Offered Sem. II.

**MTH 495/595 Cr. 1-3
Special Topics in Mathematics
**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 the instructor. Prerequisite: written consent of the department chair. Repeatable for credit - maximum 6.

**MTH 498 Cr. 1-3
Independent Study
**Directed readings or presentation of material not available in formal departmental courses under the supervision of a faculty member. Prerequisites: written consent of the supervising faculty member and the department chair. Repeatable for credit - maximum 6.

**MTH 499 Cr. 1-3
Research Topics
**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.